Curriculum

Unit 1 Counting and Cardinality

Description: The students will understand number sequence, cardinality, one-to-one correspondence, and written number symbols.  Students will connect sorting a group into parts and decomposing numbers.

Louisiana Student Standards for Mathematics (LSSM)

Counting and Cardinality
K.CC.1 Count to 100 by ones and by tens.
K.CC.3 Write numbers from 0-20.  Represent a number of objects with a written numeral 0-20. (with 0 representing a count of no objects).
K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
a. When counting objects in standard order, say the number names as they relate to each object in the group, demonstrating one-to-on correspondence.
b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
c. Understand that each successive number name refers to a quantity that is one larger.
K.CC.5 Count to answer “How many?” questions.
a. Count objects up to 20, arranged in a line, a rectangular array, or a circle.
b. Count objects up to 10 in a scattered configuration.
c. When given a number from 1-20, count out that many objects.
K.MD.3 Classify objects into given categories based on their attributes, count the number of objects in each category and sort the categories by count.

Students will be able to:

• Classify objects into groups by attribute.
• Consider different ways and reasons to count while learning three strategies to help them count accurately.
• Write numerals and count out objects to match a given number, and determine if they have enough of something.
• Explore number relationships, and begin to use number sentences (5 is 2 and 3).
• Consider how to choose an accurate counting strategy.
• Count things or events that happen over time.  
• Analyze the count sequence focusing on that each successive number is 1 more when counting forward and 1 less when counting backward.
   

Unit 2 Two-Dimensional and Three-Dimensional Shapes

Description: The students will analyze and describe two-and three-dimensional shapes by considering their attributes. Students will identify shapes in the world and create examples through building and drawing.

Louisiana Student Standards for Mathematics (LSSM)

Geometry
K.MD.3 Classify objects into given categories based on their attributes, count the number of objects in each category and sort the categories by count..
K.G.1 Describe objects in the environment using names of shapes and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.
K.G.2 Correctly name shapes regardless of their orientation or overall size.
K.G.3 Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”)
K.G.4 Analyze and compare two- and three- dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/”corners” and other attributes (e.g., having sides of equal lengths).
K.G.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

Students will be able to:

• Identify specific qualities that are used to classify shapes (number of sides and corners).
• Discover that some attributes are common to both flat and solid shapes, such as corners.
• Construct and compose shapes to observe how shapes look from multiple perspectives, how parts fit together to make a whole, and how shapes relate to one another.
   

Unit 3 Comparison

Description: The students will describe and compare measurable attributes and compare the length and weight of objects. Students will develop a toolbox of strategies to compare sets and numbers within 10.

Louisiana Student Standards for Mathematics (LSSM)

Counting and Cardinality
K.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g. by using matching and counting strategies.
K.CC.7 Compare two numbers between 1 and 10 presented as written numerals.
Measurement and Data
K.MD.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.
K.MD.2 Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.
K.MD.3 Classify objects into given categories based on their attributes, count the number of objects in each category and sort the categories by count.
K.MD.4 Recognize pennies, nickels, dimes, and quarters by name and value (e.g., This is a nickel and it is worth 5 cents.)

Students will be able to:

• Develop their understanding of size by focusing on height and length as measurable attributes, and accurately compare the length of two objects using the terms taller, longer, and shorter.
• Use a balance scale to compare the weights of two objects or groups of objects.  
• Compare the number of objects in a set and describe the comparison by using the terms more and fewer.   
• Compare numbers using the terms greater, less, and equal to describe the relationship between numbers.
   

Unit 4 Composition and Decomposition

Description: The students will explore part-total relationships by composing and decomposing shapes and numbers in more than one way. Students will represent the quantities and relationships in story problems with objects, fingers, drawings, and number bonds.

Louisiana Student Standards for Mathematics (LSSM)

Operations and Algebraic Thinking
K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g. claps).
K.OA.2 Solve addition and subtraction word problems and add and subtract within 10, e.g. by using objects or drawings to represent the problem.
K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g. by using objects or drawings, and record each decomposition by a drawing or equation (e.g. 5 = 2 + 3 and 5 = 4 + 1).
Geometry
K.G.6 Compose simple shapes to form larger shapes.

Students will be able to:

• Construct a larger composite shape by putting together simple shapes.  
• Compose and decompose shapes and numbers in more than one way.
• Expand part-total thinking to include decomposition and composition story situations. 

Unit 5 Addition and Subtraction

Description: The students will develop a conceptual understanding of addition and subtraction.  Students will represent situations with number sentences and model story problems in many different ways.

Louisiana Student Standards for Mathematics (LSSM)

Counting and Cardinality
K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
Operations and Algebraic Thinking
K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g. claps).
K.OA.2 Solve addition and subtraction word problems and add and subtract within 10, e.g. by using objects or drawings to represent the problem.
K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g. by using objects or drawings, and record each decomposition by a drawing or equation (e.g. 5 = 2 + 3 and 5 = 4 + 1).
K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
K.OA.A.5 Fluently add and subtract within 5.
Geometry
K.G.6 Compose simple shapes to form larger shapes.

Students will be able to:

• Represent addition stories by using number sentences with mathematical symbols, such as 4 + 2 = 6, and read their work by using mathematical symbols.  
• Solve subtraction problems and represent their thinking by using number sentences with mathematical symbols.  
• Make sense and persevere in solving problems.  
• Look for and make use of structure by looking for and making use of patterns. 
   

Unit 6 Place Value Foundations

Description: The students will compose and decompose numbers 11 to 20 as 10 ones and some more ones in different ways. Students will explore patterns in the number sequence and base ten number system.

Louisiana Student Standards for Mathematics (LSSM)

Counting and Cardinality
K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
a. When counting objects in standard order, say the number names as they relate to each object in the group, demonstrating one-to-one correspondence.
b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
c. Understand that each successive number name refers to a quantity that is one larger.
K.CC.5 Count to answer “How many?” questions.
a. Count objects up to 20, arranged in a line, a rectangular array, or a circle.
b. Count objects up to 10 in a scattered configuration.
c. When given a number from 1-20, count out that many objects.
K.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g. by using matching and counting strategies.
Operations and Algebraic Thinking
K.OA.2 Solve addition and subtraction word problems and add and subtract within 10, e.g. by using objects or drawings to represent the problem.
K.NBT.1 Gain understanding of place value; understand that the numbers 11-19 are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones; compose and decompose numbers 11-19 using place value; record each composition or decomposition using a drawing or equation.

Students will be able to:

• Understand place value concepts as they count and write numbers 11-20.  
• Expand their experience with place value and part-total relationships by representing teen numbers with number bonds and number sentences.
• Master the count to 100 by using pattern and structure.  
• Apply comparison strategies to situations involving greater numbers and measureable attributes.

 

Unit 1 Counting, Comparison, and Addition

Description: Students organize data to make counting and comparing easier.  Students will apply counting on as a strategy for addition.  Students compare equivalent ways to make the same total and reason about the meaning of the equal sign.  

Louisiana Student Standards for Mathematics (LSSM)

Number and Operations in Base Ten
1.OA.3 Apply properties of operations as strategies to add and subtract.  Examples:  If 8 + 3 = 11 is known, then 3 + 8 =11 is also known.  (Commutative property of addition.)  To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition.)
1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
Numbers and Operations in Base Ten
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.
1.NBT.3 Compare two two-digit numbers based on meaning of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
Measurement and Data
1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

The Students will be able to:

• Collect data by answering questions, sorting sets, and making observations.
• Create bar graphs, picture graphs, and tally charts to visually represent the data.  
• Count by naming the known part and then keep counting the objects in the second part to find the total.
• Count on to find totals for expressions rather than for sets of countable objects.
• Reason about more complex number sentences to determine whether they are true or false.

Unit 2 Addition and Subtraction Relationships

Description: Students use word problems to notice relationships between addition and subtraction.  Students explore ways of finding an unknown part.

Louisiana Student Standards for Mathematics (LSSM)

Operations and Algebraic Thinking
1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, take from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.OA.4 Understand subtraction as an unknown-addend problem.  For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.
1.OA.5  Relate counting addition and subtraction (e.g., by counting on 2 to add 2).
1.OA.6  Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use mental strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 –1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13.
1.OA.7  Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.  For example, which of the following equations are true and which are false?  6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
1.OA.8  Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.  For example, determine the unknown number that makes the equation true in each of the equations: 8 + ? = 11, 5 = __ - 3, 6 + 6 = __
Measurement and Data
1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

The Students will be able to:

• Reason about take from situations, and subtract by using the unit of five.
• Reason that related addition and subtraction problems have the same parts and total.  
• Solve add to with change unknown and take from with change unknown word problems.  
• Use part-whole relationships and related facts to find the value of various unknowns in equations.
• Represent comparison word problems by making groups equal.  

Unit 3 Properties of Operations to Make Easier Problems

Description: Students use the unit of ten to make easier problems by decomposing addends and grouping them in any order.  Students apply the associative and commutative properties and learn how to use strategies such as counting on, making ten, taking from ten, subtracting to get a ten, and relating operations to break down larger addition and subtraction problems.

Louisiana Student Standards for Mathematics (LSSM)

Operations and Algebraic Thinking
1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.OA.2  Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.OA.3  Apply properties of operations as strategies to add and subtract.  Examples:  If 8 + 3 = 11 is known, then 3 + 8 =11 is also known.  (Commutative property of addition.)  To add 2 + 6 + 4, , the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12 (Associative property of addition.)
1.OA.6  Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use mental strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 –1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13.
Numbers and Operations in Base Ten
1.NBT.1 Count to 120, starting at any number less than 120.  In this range, read and write numerals and represent a number of objects with a written numeral.
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.

The Students will be able to:

• Solve three-addend problems in which two addends are partners to 10.  
• Solve two-addend problems in which the addends do not make ten.  
• Make ten and add and represent their thinking on a number path.  
• Represent and compare two- and three- addend equations on the number path.
• Recognize ten as a unit by building, drawing, and visualizing quantities.  
• Understand that all two-digit numbers are composed of tens and ones.
• Use subtraction strategies (take from ten, counting on by using ten, and counting back by using ten) to solve problems.

Unit 4 Comparison and Composition of Length Measurements

Description: Students explore units within the context of measurement and describe and compare lengths iterating length units such as centimeter cubes and 10-centimeter sticks.  

Louisiana Student Standards for Mathematics (LSSM)

Operations and Algebraic Thinking
1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Numbers and Operations in Base Ten
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.  
1.NBT.3 Compare two two-digit numbers based on meaning of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
Measurement and Data
1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.
1.MD.2  Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-sized length units that span it with no gaps or overlaps.  Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
1.MD.5 Determine the value of a collection of coins up to 50 cents.  (Pennies, nickels, dimes, and quarters in isolation; not to include a combination of coins.)

The Students will be able to:

• Compare the length of objects by direct and indirect methods.
• Measure and compare lengths of objects by using centimeter cubes and recording the measurements in tens and ones.  
• Solve comparison word problems.

Unit 5 Place Value Concepts to Compare, Add, and Subtract

Description: Students develop understanding of the base ten system.  Students use tens and ones to compose and compare numbers.  Students make easier problems to add and subtract within 100. 

Louisiana Student Standards for Mathematics (LSSM)

Operations and Algebraic Thinking
1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.  For example, which of the following equations are true and which are false?  6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
Numbers and Operations in Base Ten
1.NBT.1 Count to 120, starting at any number less than 120.  In this range, read and write numerals and represent a number of objects with a written numeral.
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.  
1.NBT.3 Compare two two-digit numbers based on meaning of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10.
a. Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a number sentence; justify the reasoning used with a written explanation.
b. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
1.NBT.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero difference), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Measurement
1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks. Recognize and identify coins, their names, and their values.

The Students will be able to:

• Group units in Tens and Ones.
• Compare two-digit numbers by using place value structure.
• Add one- and two- digit numbers using place value.
• Add tens to a multiple of ten, add tens to any two-digit number, subtract tens from a multiple of ten.
• Use place value understanding to add two-digit numbers.

Unit 6 Attributes of Shapes- Advancing Place Value, Addition, and Subtraction

Description: Students reason about shapes and their attributes.  Students will compose and decompose shapes building an understanding of part-whole relationships, including fractions.  Students advance place value understanding through 120, and within 100, and solve more complex problems. 

Louisiana Student Standards for Mathematics (LSSM)

Operations and Algebraic Thinking
1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, take from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Numbers and Operations in Base Ten
1.NBT.1 Count to 120, starting at any number less than 120.  In this range, read and write numerals and represent a number of objects with a written numeral.
1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10.
a. Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a number sentence; justify the reasoning used with a written explanation.
b. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
Geometry
1.G.1 Distinguish between defining attributes (e.g, triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) and three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Note: Students do not need to learn the formal names such as right rectangular prisms.)
1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.  Describe the whole as two of or four of the shares.  Understand for these examples that decomposing into more equal shares creates smaller shares.
Measurement
1.MD.3  Tell and write time in hours and half-hours using analog and digital clocks.

The Students will be able to:

• Describe and name two-dimensional flat shapes by using defining attributes.
• Describe and name three-dimensional solid shapes, including cubes, cones, cylinders, rectangle prisms, triangular prisms, and pyramids.
• Decompose and compose flat and solid composite shapes.
• Partition shapes in a variety of ways and determine if the parts are equal shares of the whole, also identifying halves, fourths, and quarters.  
• Count and represent three-digit numbers from 100-120 by counting, reading numerals, writing totals, and representing numbers.
• Make sense of word problems by representing with tape diagrams.  
• Add 2 two-digit numbers that have sums within 100.

 

Unit 1 Place Value Concepts Through Metric Measurement and Data Place Value, Counting, Comparing, within 1,000.

Description: Students will represent and interpret data.  Students will explore place value within the context of metric measurement.  Students will use various models-bundles, bills, and disks to further develop place value understanding. 

Louisiana Student Standards for Mathematics (LSSM)

Measurement and Data
2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
2.MD.3 Estimate lengths using inches, feet, centimeters, and meters.
2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
Operations and Algebraic Thinking
2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Number and Operation in Base Ten
2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
a. 100 can be thought of as a bundle of ten tens – called a   
“hundred.”
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800,    
900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
2.NBT.2  Count within 1000; skip-count by 5s, 10s and 100s.
2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
Measurement and Data
2.MD.10 Draw a picture graph and a bar graph to represent a set of data with up to four categories.  Solve simple put-together, take apart, and compare problems using information presented in a bar graph.

The Students will be able to:

• Represent data to solve problems by counting, matching, or using strategies.  
• Use a ruler to understand metric measurement concepts.
• Estimate, measure, and compare lengths of objects.
• Model adding and subtracting efficiently by getting to a benchmark number when using a number line.
• Expand understanding of ones, tens, and hundreds up to 1,000 using concrete bundles.
• Use the base-ten place value system to represent counts with bundles, then digits.
• Use $1, $10, and $100 bills to make connections between the value of the bill and the connecting place value units.
• Model numbers ones, tens, and hundreds, with place value disks and drawings.
• Compare two three-digit numbers by using place value drawings and comparison statements with symbols (˃, =, ˂)

Unit 2 Addition and Subtraction within 200

Description: Students will use the properties of operations, the relationships between numbers, and place value understanding to add and subtract within 200.  Students will apply these operations to representing and solving various word problems.  

Louisiana Student Standards for Mathematics (LSSM)

Numbers and Operations in Base Ten
2.NBT.6  Add up to four two-digit numbers using strategies based on place value and properties of operations.
2.NBT.7 Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; justify the reasoning used with a written explanation. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Operations and Algebraic Thinking
2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

The Students will be able to:

• Use place value understanding, properties of operations, and relationships between numbers to solve problems in a simplified way.
• Compose a ten and a hundred to add by using their understanding of the place value system.
• Use models and recording methods to simplify subtraction problems.
• Develop a conceptual understanding of subtraction by taking from a unit of ten or a hundred.

Unit 3 Shapes and Time with Fraction Concepts

Description: Students reason about the attributes of geometric shapes.  Students build fractional understanding by working with composite shapes and partitioning circles and rectangles into equal shares and apply fractional understanding to telling time.

Louisiana Student Standards for Mathematics (LSSM)

Number and Operation in Base Ten
2.NBT.2 Count within 1000; skip-count by 5s, 10s and 100s.
Measurement and Data
2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
Geometry
2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.  Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.  
2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc, and describe the whole as two halves, three thirds, four fourths.  Recognize that equal shares of identical wholes need not have the same shape.

The Students will be able to:

• Recognize and characterize two-dimensional shapes by their defining attributes, such as the number of sides or angles.  
• Use part-whole understanding to compose and decompose composite shapes.
• Partition same-size circles and rectangles into fractional parts and describe them as halves, thirds, and fourths or quarters.
• Apply their understanding of halves and fourths to concepts about time.  
• Read and show times on an analog clock to the nearest 5 minutes and write the time.

Unit 4 Addition and Subtraction within 1,000

Description: Students deepen understanding of addition and subtraction working within 1,000.  Students will reason about place value, properties of operations, and the relationship between numbers as they choose efficient strategies to solve problems. 

Louisiana Student Standards for Mathematics (LSSM)

Operations and Algebraic Thinking
2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
2.OA.B.2 Fluently add and subtract within 20 using mental strategies.  By the end of Grade 2, know from memory all sums of two one-digit numbers.
Numbers and Operations in Base Ten
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.
2.NBT.7 Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; justify the reasoning used with a written explanation. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
2.NBT.8 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.

The Students will be able to:

• Use mental place value strategies to add and subtract tens and hundreds.  
• Use strategies to make the next ten or hundred and use compensation to add larger numbers.   
• Continue to relate place value disks to and drawings to vertical form.
• Apply the take from a ten or hundred strategy to subtract within 1,000.
• Use strategies for decomposing tens and hundreds within 1,000.
• Use multiple strategies to add and subtract finding the unknown.  

Unit 5 Money, Data, and Customary Measurement

Description: Students apply place value strategies and properties of operations to work with coins and bills.  Students will review measurement concepts using customary units, and solve problems in the context of money, length, and data. 

Louisiana Student Standards for Mathematics (LSSM)

Measurement and Data
2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
2.MD.3 Estimate lengths using inches, feet, centimeters, and meters.
2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢.
2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object.  Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

The Students will be able to:

• Organize, count, and represent a collection of coins.
• Manipulate different combinations of coins to make the same total value.
• Find the total value of a group of coins or bills in one- and two- step problems, and use models and drawings to represent part-total relationships.  
• Measure and estimate length using customary units.   
• Apply knowledge of the ruler to a number line diagram.  
• Apply place value strategies and the properties of operations to solve measurement problems.  

Unit 6 Multiplication and Division Foundations

Description: Students will count and solve problems with equal groups of objects.  Students will organize equal groups into rows and columns to create rectangular arrays.  Students gain foundations for multiplication by composing and decomposing arrays. 

Louisiana Student Standards for Mathematics (LSSM)

Operations and Algebraic Thinking
2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
Geometry
2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

The Students will be able to:

• Count and create equal groups to solve problems.
• Organize equal groups into rows and columns to compose rectangular arrays.
• Compose and decompose rectangles with rows and columns to model the foundation of multiplication and division.
• Apply understanding of the meaning of even and odd numbers.   

Unit 1 Multiplication and Division with Units of 2, 3, 4, 5, and 10

Description: Students will relate repeated addition, equal groups, and arrays to multiplication and division.  Students will use the commutative and distributive properties as strategies to multiply.  Students will express division as both unknown factor problems and division equations and break apart and distribute the total to divide.

Louisiana Student Standards for Mathematics (LSSM)

Operations and Algebraic Thinking
3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5×7.
3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
3.OA.A.3 Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
3.OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = □ ÷ 3, 6 × 6 = ?
3.OA.B.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3× 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Numbers and Operations in Base Ten
3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

The Students will be able to:

• Understand and connect equal groups and repeated addition to multiplication.
• Use equal group models and arrays to understand division.
• Use properties of multiplication to explore strategies to multiply efficiently.
• Understand division as both unknown factor problems and division equations and connect multiplication to division.
• Apply the distributive property to solve multiplication and division problems.

Unit 2 Place Value Concepts through Metric Measurement

Description: Students will compose and decompose metric measurement units and relate them to place value units up to 1 thousand.  Students will use place value understanding and the vertical number line to round two- and three- digit numbers.  Students also add and subtract two- and three- digit numbers within 1,000 by using a variety of strategies, using the standard algorithm.  Students use the properties of operations, the relationships between numbers, and place value understanding to add and subtract within 200.  Students will apply these operations to representing and solving various word problems.

Louisiana Student Standards for Mathematics (LSSM)

Measurement and Data
3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.  Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.  For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
Operations and Algebraic Thinking
3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Number and Operations in Base Ten
3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.
3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

The Students will be able to:

• Measure weight and liquids using metric measurements while connecting to place value concepts.
• Use a vertical number line to round to the nearest ten and hundred.
• Explore a variety of addition and subtraction strategies based on place value, properties of operations, and the relationship between addition and subtraction.
• Use concrete and drawings to represent and record addition and subtraction work.

Unit 3 Multiplication and Division with Units of 0, 1, 6, 7, 8, and 9

Description: Students will apply conceptual understanding to extend learning of multiplication and division by using the commutative, distributive, and associative properties.  Students will multiply with two-digit multiples of 10 and solve one- and two- step word problems involving the four operations.  

Louisiana Student Standards for Mathematics (LSSM)

Operations and Algebraic Thinking
3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5×7.
3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ∆ ÷ 3, 6 × 6 =?.
3.OA.5 Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
3.OA.6 Understand division as an unknown‐factor problem. For example, find 32  8 by finding the number that makes 32 when multiplied by 8.
3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
Number and Operation in Base Ten
3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

The Students will be able to:

• Apply understanding of multiplication from Module 1 to work with units of 6 and 8.
• Use properties of operations to solve and multiply efficiently with a focus on the unit 7.
• Explore patterns to multiply and divide with 9, 0, and 1.
• Multiply multiples of 10 by one-digit numbers.

Unit 4 Multiplication and Area

Description: Students recognize area as an attribute of two-dimensional regions.  Students will measure the area of a shape by finding the total number of same-sized square units required to cover the shape without gaps or overlaps.  Students will understand that rectangular arrays can be decomposed into identical rows or identical columns.  Students will connect the number of rows and columns to the side lengths and connect area to multiplication.  

Louisiana Student Standards for Mathematics (LSSM)

Geometry
3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).  Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
Measurement and Data
3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement:
a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
3.MD.7 Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

The Students will be able to:

• Use polygons to understand area.
• Use multiplication to determine the area of a rectangle.
• Compose and decompose larger rectangles from smaller rectangles.
• Apply area concepts to a variety of real-world problems.

Unit 5 Fractions as Numbers

Description: Students will develop an understanding of fractions as numbers.  Students will partition a whole into equal parts and recognize 1 of a fractional unit as a unit fraction.  Students will compose non-unit fractions from unit fractions and use visual fraction models and written fractions to represent parts of a whole.  Students will use fractions to represent numbers equal to, less than, and greater than 1 and compare fractions by using visual fraction models and by reasoning about the size of the fractions that have the same numerator/denominator. 

Louisiana Student Standards for Mathematics (LSSM)

Number and Operations – Fractions
3.NF.1 Understand a fraction 1/b, with denominators 2, 3, 4, 6, and 8, as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a part of size 1/b.  
3.NF.2 Understand a fraction with denominators 2, 3, 4, 6, and 8 as a number on a number line diagram.
a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by marking off the length 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
3.NF.3 Explain equivalence of fractions with denominators 2, 3, 4, 6, and 8 in special cases, and compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)
b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form of 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Geometry
3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape.
Measurement and Data
3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.  Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

The Students will be able to:

• Understand fractions as numbers by naming the fractional parts of the whole in unit form and describing the relationship.
• Understand unit fractions and their relationship to the whole.
• Represent fractions from 0 to 1 on a number line.
• Compare fractions using the number line.
• Find equivalent fractions using the number line.

Unit 6 Geometry, Measurement, and Data

Description: Students will tell time to the nearest minute and use linear models to solve and represent elapsed time word problems.  Students will describe, analyze, and compare properties of two-dimensional shapes.  Students will compare and classify shapes by the number of sides and angles and make connections to the attributes of shapes.  Students will recognize perimeter as an attribute of plane figures and solve real-world and mathematical problems involving perimeter.  Students will represent and interpret data by using scaled picture graphs, scaled bar graphs, and line plots.   

Louisiana Student Standards for Mathematics (LSSM)

Geometry
3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).  Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Measurement and Data
3.MD.1 Understand time to the nearest minute.
a. Tell and write time to the nearest minute and measure time intervals in minutes, within 60 minutes, on an analog and digital clock.
b. Calculate elapsed time greater than 60 minutes to the nearest quarter and half hour on a number line diagram.
c. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.  Solve one- and two- step “how many more” and “how many less” problems using information presented in scaled bar graphs.  
3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.  Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.
3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including the finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
3.MD.9 Solve word problems involving pennies, nickels, dimes, quarters, and bills greater than one dollar, suing the dollar and cent symbols appropriately.
 

The Students will be able to:

• Use a number line to represent the scale of a clock.  Solve time interval problems.
• Describe, define, and sort quadrilaterals using attributes such as pairs of parallel sides, sides that have the same length, and right angles.
• Solve problems and find the perimeter of a given shape.  
• Reason about the relationship between area and perimeter.  
• Collect and represent data involving fractional lengths.
• Identify place value patterns to name units up to 1 million.

Unit 1 Place Value Concepts for Addition and Subtraction

Description: Students use multiplicative comparisons to describe place value relationships and the relative sizes of metric units. They build fluency with the standard algorithm for addition and subtraction with numbers of up to 6 digits.

Louisiana Student Standards for Mathematics (LSSM)
Operations and Algebraic Thinking
4.OA.1 Interpret a multiplication equation as a comparison and represent verbal statements of multiplicative comparisons as multiplication equations, e.g., interpret 35 = 5 X 7 as a statement that is 35 times as many as 7 and 7 times as many as 5.
4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and/or equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
4.OA.3 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.  Represent these problems using equations with a letter standing for the unknown quantity.  Assess the reasonableness of answers using mental computation and estimation strategies including rounding.  
Number and Operations in Base Ten
4.NBT.1 Recognize that in a multi-digit whole number less than or equal to 1,000,000, a digit in one place represents ten times what it represents in the place to its right.
4.NBT.2 Read and write multi-digit whole numbers less than or equal to 1,000,000 using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
4.NBT.3 Use place value understanding to round multi-digit whole numbers, less than or equal to 1,000,000, to any place.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
4.NBT.4 Fluently add and subtract multi-digit whole numbers with sums less than or equal to 1,000,000, using the standard algorithm.
Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit to smaller unit.
4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

The student will be able to:

• Identify, represent, and interpret multiplicative comparisons in patterns, tape diagrams, multiplication equations, measurements, and units of money.
• Name the place value units of ten thousand, hundred thousand, and million.
• Recognize the multiplicative relationship between place value units and will write and compare numbers with up to 6 digits in standard, expanded, word, and unit forms.  
• Round four-digit, five-digit, and six-digit numbers to the nearest thousand, ten thousand, and hundred thousand.
• Build fluency with addition and subtraction of numbers of up to 6 digits by using the standard algorithm.
• Add and subtract to solve two-step and multi-step word problems.
• Use multiplicative comparisons to describe the relative sizes of metric units of length (kilometers, meters, centimeters), mass (kilograms, grams), and liquid volume (liters, milliliters).
• Express larger units in terms of smaller units and complete conversion tables. Students add and subtract mixed unit measurements.

Unit 2 Place Value Concepts for Multiplication and Division

Description: Students multiply two-digit numbers by one-digit numbers by using the distributive property. They divide two- and three-digit numbers by one-digit numbers by using the break apart and distribute strategy. Students apply their multiplication skills to convert customary units of length. They also identify factors and multiples of numbers within 100.

Louisiana Student Standards for Mathematics (LSSM)
Number and Operations in Base Ten
4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.  Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
4.NBT.6 Find whole number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.  Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models
Measurement and Data
4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
4.MD.3 Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.  
4.MD.8 Recognize angle measure as additive.  When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts.  Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a letter for the unknown angle measure. 
Operations and Algebraic Thinking
4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison e.g., by using drawings and/or equations with a symbol for the unknown number to represent the problem, distinguish multiplicative comparison from additive comparison.
4.OA.5 Generate a number or shape pattern that follows the given rule.  Identify apparent features of the pattern that were not explicit in the rule itself.   

The student will be able to:

• Use place value understanding help me solve multiplication and division problems.
• Use the four operations related to one another.
• Determine what types of problems can be solved using multiplication and division.
• Determine the important components of a problem in order to solve real-world story problems.
• Use their understanding of patterns to help solve problems.
• Understand the difference between perimeter and area.
• Use distributive property to solve multiplication and division problems.
• Decompose 2-digit numbers to solve multiplication and division problems.
• Use multiplication and division to help them identify factors, multiples, prime numbers, and composite numbers within 100.
   

Unit 3 Multiplication and Division of Multi-Digit Numbers

Description: Students multiply numbers of up to four digits by one-digit numbers and two-digit numbers by two-digit numbers. Students also divide numbers of up to four digits by one-digit numbers, resulting in whole-number quotients and remainders.

Louisiana Student Standards for Mathematics (LSSM)
Number and Operations in Base Ten
4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Measurement and Data
4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit.
4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
Operations and Algebraic Thinking
4.OA.3 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

The student will be able to:

• Use multiplication strategies to both multiply and divide by multiples of 100 and 1000.
• Multiply a two-digit by a two-digit using different strategies.
• Use place value strategies to divide by hundreds, tens, and ones.
• Connect pictorial representations of division to long division using place value understanding.
• Multiply using partial products.
• Multiply a single digit by a four-digit using partial products, distributive property, and vertical method.
• Express and convert units of measure in customary units.
• Solve division word problems using estimation.
• Solve division problems by interpreting a remainder.

Unit 4 Multiplication and Division of Multi-Digit Numbers

Description: Students rename fractions greater than 1 as mixed numbers, generate equivalent fractions, compare fractions with unlike units, and add and subtract fractions and mixed numbers with like units. Students also multiply fractions and mixed numbers by whole numbers.

Louisiana Student Standards for Mathematics (LSSM)
Number and Operations- (Fractions)
4.NF.1 Explain why a fraction 𝑎/𝑏 is equivalent to a fraction (𝑛 × 𝑎)/(𝑛 × 𝑏) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
4.NF.3 Understand a fraction 𝑎/𝑏 with 𝑎 > 1 as a sum of fractions 1/𝑏.
4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
Measurement and Data
4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

The student will be able to:

• Decompose whole numbers into unit fractions.
• Decompose fractions into a sum of unit fractions.
• Represent fractions using various fraction models.
• Rename fractions greater than 1 as mixed numbers.
• Generate equivalent fractions with both unit fractions and non-unit fractions.
• Represent equivalent fractions using tape diagrams, number lines, and multiplication or division.
• Compare fractions with related denominators
• Generate common denominators in order to comparing fractions.
• Add and subtract fractions with like units.
• Subtract a fraction from a whole number.
• Add and subtract a fraction to a mixed number.
• Represent repeated addition of fractions to multiplication.
   

Unit 5 Place Value Concepts for Decimal Fractions

Description: Students’ understanding of tenths and hundredths as fractional units to recognizing tenths and hundredths as place value units. They compare decimal numbers and add mixed numbers and fractions with the unlike, but related, units of tenths and hundredths.
 
Louisiana Student Standards for Mathematics (LSSM)
Number and Operations- (Fractions)

4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.
4.NF.6 Use decimal notation for fractions with denominators 10 or 100.
4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.
Measurement and Data (MS)

The student will be able to:

• Represent tenths and hundredths as place value units.
• Write mixed numbers with tenths and hundredths in decimal form.
• Represent decimal numbers in expanded form.
• Compare measurements expressed in decimal form.
• Compare and order decimals.
• Apply fraction equivalence to add tenths and hundredths.
• Solve word problems with tenths and hundredths.
   

Unit 6 Place Value Concepts for Decimal Fractions

Description: Students identify attributes of polygons including side length and the presence or absence of pairs of parallel sides, pairs of perpendicular sides, and angle types. They use protractors to measure and draw angles accurately. Students also identify and draw lines of symmetry.

Louisiana Student Standards for Mathematics (LSSM)
Geometry
4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
4.G.3  Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
Measurement and Data
4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.
4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.

The student will be able to:

• Identify and draw points, lines, rays, line segments, and angles.
• Identify the 4 types of angles: right, acute, obtuse, and straight.
• Identify and draw parallel and perpendicular lines.
• Use a protractor to measure angles.
• Determine the unknown angle measure within right and straight angles and around a point.
• Recognize, identify, and draw lines of symmetry.
• Sort polygons based on a given rule.
• Classify triangles based on given attributes.

Unit 1 Place Value Concepts for Multiplication and Division with Whole Numbers

Description: Students describe place value relationships, express powers of ten with exponents, convert metric measurements, and multiply and divide by multi-digit numbers. They develop fluency with the standard algorithm for multiplication.

Louisiana Student Standards for Mathematics (LSSM)

Numbers in Base Ten
5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
5.NBT.6 Find quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Operations and Algebraic Thinking
5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
Measurement and Data- MD
5.MD.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

The student will be able to:

• Explain that a digit in one place represents 10 times as much as what it represents in the place to the right.
• Multiply and divide by powers of 10.
• Use exponents to multiply and divide.
• Convert metric measure.
• Multiply two- and three- digits numbers but two-digit numbers using the distributive property.
• Multiply two- and three- digits numbers but two-digit numbers using the standard algorithm.
• Divide up to a four- digit dividend by one and two-digits divisors using division strategies.
• Write, interpret, and compare numerical expressions.
• Create and solve real-world problems for a given numerical expression.
• Solve multi-step problems using all four operations.  

Unit 2 Place Value Concepts for Multiplication and Division with Whole Numbers

Description: Enhances students’ prior work with fractions to add and subtract fractions and mixed numbers with unlike denominators. Students also interpret a fraction as the result of dividing the numerator by the denominator and interpret data in line plots.

Louisiana Student Standards for Mathematics (LSSM)

Number and Operations-Fractions
5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
5.NF.3 Interpret a fraction as division of the numerator by the denominator (𝑎/𝑏 = 𝑎 ÷ 𝑏). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Measurement and Data- MD
5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.

The student will be able to:

• Interpret a fraction as division.
• Add and subtract fractions with related units using pictorial models, area models, and numerically.
• Add and subtract fractions with unrelated units using pictorial models, area models, and numerically.
• Add and subtract whole numbers and mixed numbers with related and unrelated units using number lines, arrow way, and number bonds.
• Represent data on a line plot.
• Solve problems by using data on a line plot.

Unit 3 Multiplication and Division of Fractions 

Description: Students use various strategies to multiply and divide with fractions. They multiply fractions by whole numbers and by fractions, divide whole numbers by unit fractions and unit fractions by whole numbers, and convert customary measurements.

Louisiana Student Standards for Mathematics (LSSM)

Number and Operations-Fractions
5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.5 Interpret multiplication as scaling (resizing) by comparing the size of a product to the size of one factor on the basis of the size of the other factor and explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number
5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
5.NF.7 Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
Interpret division of a whole number by a unit fraction, and compute such quotients.
Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions

The student will be able to:

• Find fractions of a set with arrays, tape diagrams, and number lines.
• Multiply a whole number by a fraction less than 1.
• Multiply a whole number by a fraction.
• Convert customary units.
• Multiply fractions pictorially.
• Divide a nonzero whole number by a unit fraction.
• Divide a unit fractions by a nonzero whole number.
• Solve word problems involving fractions with multiplication and division.
• Evaluate expressions with grouping symbols.
• Solve multi-step word problems involving fractions.

Unit 4 Place value concepts for Decimal Operations

Description: Students relate their understanding of whole numbers and fractions to decimals. Decimal concepts include: describing place value relationships, rounding, comparing, adding, subtracting, multiplying, dividing, and converting measurements.

Louisiana Student Standards for Mathematics (LSSM)

Number and Base Ten
5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
5.NBT.3 Read, write, and compare decimals to thousandths.
5.NBT.4 Use place value understanding to round decimals to any place.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Operations and Algebraic Thinking
5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
Measurement and Data
5.MD.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

The student will be able to:

• Model decimal place value units to the thousandths.
• Represent decimal numbers to the thousandths in different forms.
• Multiply and divide decimal numbers by powers of 10.
• Compare decimals to the thousandths.
• Round decimals to the nearest thousandths.
• Add and subtract decimals using place value understanding.
• Solve word problems with addition and subtraction of decimals.
• Multiply decimals numbers by one- and two-digit whole numbers.
• Multiply a decimals number by a decimal number.
• Divide decimals using place value understanding.
• Apply decimal understanding to solve metric measurement problems.

Unit 5 Addition and Multiplication with Area and Volume

Description: Students connect operations to geometric concepts. They find area of rectangles with fraction side lengths, multiply mixed numbers, and find the volume of right rectangular prisms. Students also categorize two-dimensional figures in a hierarchy.

Louisiana Student Standards for Mathematics (LSSM)

Number and Operations- Fractions
5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
b.Construct a model to develop understanding of the concept of multiplying two fractions and create a story context for the equation. [in general, (m/n) × (c/d) = (mc) / (nd).]
5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Measurement and Data
5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Geometry B. Classify two-dimensional figures into categories based on their properties.
5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
5.G.4 Classify quadrilaterals in a hierarchy based on properties.

The student will be able to:

• Classify quadrilaterals based on their properties.
• Identify quadrilaterals when given properties.
• Classify quadrilaterals in a hierarchy based on properties.
• Determine the area of rectangular figures with fractional side lengths.
• Solve problems involving area of composite figures with mixed numbers.  
• Multiply mixed numbers.
• Solve multi-step word problems involving mixed numbers.
• Identify attributes of rectangular prisms related to volume.
• Find the volume using unit cubes and layers.
• Relate volume of a solid and liquid volume.
• Find the volume by multiplying by the area of the base times the height
• Find the volume by multiplying the edge lengths.
• Solve word problems involving perimeter, area, and volume.

Unit 6 Foundations to Geometry in the Coordinate Plane

Description: Students are introduced to the coordinate plane Students construct a coordinate plane, identify the location of points in the plane, and identify patterns in ordered pairs that create lines. They draw quadrilaterals in the plane and use the plane to represent data.

Louisiana Student Standards for Mathematics (LSSM)

Number and Operations- Fractions
5.NF.4 Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Geometry
5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number in the ordered pair indicates how far to travel from the origin in the direction of one axis, and the second number in the ordered pair indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x‐axis and x‐coordinate, y‐axis and y‐coordinate).
5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
5.G.4 Classify two-dimensional figures in a hierarchy based on properties.
Operations and Algebraic Thinking
5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

The student will be able to:

• Identify and plot points on a coordinate plane.
• Describe the distance and directions between points.
• Use the properties of horizontal and vertical lines to solve problems.
• Identify relationships between corresponding terms in number patterns.
• Draw lines and identify points on the line in the coordinate plane.
• Solve problems with rectangles in the coordinate plane.
• Use the coordinate plane to reason about perimeters and areas of rectangles.
• Interpret graphs, plot data, interpret lines graphs, and reason about patterns in real-world situations.

Unit 1 Expressions and Equations

Description: During this unit, students will find area of a variety of two-dimensional figures and surface area of three-dimensional figures which will lead students into the beginning work with algebraic expressions, including those with whole-number exponents.

Major Themes of the Unit:

• Relate prior knowledge of a rectangle to find the area of other two-dimensional figures along with determining surface area of three-dimensional figures.
• Relate prior knowledge about writing, interpreting and evaluating numerical expressions to understanding work with algebraic expressions.
• Apply prior understanding of multiplication to evaluate expressions that include exponents to determine the GCF (Greatest Common Factor) and LCM (Least Common Multiple) of two whole numbers.

Louisiana Student Standards for Mathematics (LSSM)

G. Geometry
A. Solve real-world and mathematical problems involving area and surface area.
6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
6.G.A.4 Represent three - dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real -world and mathematical problems.
EE. Expressions and Equations
A. Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents.
6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers.
a. Write expressions that record operations with numbers and with letters standing for numbers.
b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, and coefficient); view one or more parts of an expression as a single entity.
c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
NS. Number Systems
B.Compute fluently with multi - digit numbers and find common factors and multiples.
6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1 –100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

The student will be able to….

• Find the area of parallelograms.
• Find the area of triangles and other polygons.
• Identify and draw a net for a three-dimensional figure.
• Find the surface area of a three-dimensional figure.
• Write and evaluate algebraic expressions.
• Write and evaluate numerical expressions, including those with whole-number exponents.
• Find the greatest common factor and least common multiple of two whole numbers to solve real-world problems.
• Actively participate in discussions by asking questions and rephrasing or building on classmates’ ideas.

Unit 2 Decimals and Fractions

Description: During this unit, students will divide fractions, using the standard algorithms to add, subtract, multiply, and divide decimals, and using standard algorithms to divide whole numbers.

Major Themes of the Unit:

• Relate prior knowledge about place value and operations with whole numbers to better understand how to perform all four operations with decimals.
• Relate prior knowledge of area models and partial quotients to make sense of an algorithm for dividing whole numbers and decimals.
• Apply the understanding of division of fractions and mixed numbers to be thought of as forming equal groups to determine the number or size of groups knowing the relationship between multiplication and division will help divide fractions.

Louisiana Student Standards for Mathematics (LSSM)

NS. Number Systems
A. Apply and extend previous understanding of multiplication and division to divide fractions by fractions.
6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
B. Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.
6.NS.B.3 Fluently add, subtract, multiply, and divide multi -digit decimals using the standard algorithm for each operation.
G. Geometry
A. Solve real-world and mathematical problems involving volume.
6.G.A.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Appl y the formulas 𝑉 = 𝑙𝑤ℎ and 𝑉 = 𝑏ℎ to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

The student will be able to….

• Add, subtract, and multiply multi-digit decimals using standard algorithms.
• Divide multi-digit whole numbers and multi-digit decimals using standard algorithms.
• Divide fractions.
• Solve real-world problems that involve dividing fractions.
• Find the volume of a right rectangular prism with fractional edge lengths.
• Use math vocabulary and precise language to describe a strategy and how that strategy is used to solve a problem.  

Unit 3 Ratio Reasoning: Ratio Concepts and Equivalent Ratios

Description: During this unit, students will be introduced to representing ratios using ratio language and finding equivalent ratios. 
 
Major Themes of the Unit:

• Relate prior knowledge about place value and operations with whole numbers to better understand how to perform all four operations with decimals.
• Relate prior knowledge of area models and partial quotients to make sense of an algorithm for dividing whole numbers and decimals.
• Apply the understanding of division of fractions and mixed numbers to be thought of as forming equal groups to determine the number or size of groups knowing the relationship between multiplication and division will help divide fractions.

Louisiana Student Standards for Mathematics (LSSM)

RP. Ratios and Proportional Relationships
A.Understand ratio concepts and use ratio reasoning to solve problems.  
6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratios relating quantities with whole - number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

The student will be able to….

• Use ratio language to describe a ratio relationship between two quantities.
• Use ratio reasoning to solve real-world problems.   
• Identify and write equivalent ratios.
• Represent equivalent ratios as points in the coordinate plane.
• Use tables to compare ratios.
• Justify solutions to ratio problems by using ratio language and models, such as double number lines, tables, tape diagrams, and coordinates.

Unit 4 Ratio Reasoning: Unit Rates and Percent

Description: During this unit, students will be introduced to rates and percent.

Major Themes of the Unit:

• Make the connection that a rate is a ratio telling how many units of one quantity which will help students solve problems involving equivalent ratios.
• Use unit rate to find the amount of one quantity in a ratio relationship when given the amount of the other quantity.
• Use what they know about ratios and rates to solve problems about percent.

Louisiana Student Standards for Mathematics (LSSM)

RP. Ratios and Proportional Relationships
A. Understand ratio concepts and use ratio reasoning to solve problems.  
6.RP.A.2 Understand the concept of a unit rate a / b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.
6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
b. Solve unit rate problems including those involving unit pricing and constant speed.
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30 / 100 times the quantity); solve problems involving finding the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
NS. Number Systems
6.NS.B.3 Fluently add, subtract, multiply, and divide multi -digit decimals using the standard algorithm for each operation.

The student will be able to….

• Compare rates to solve real-world problems.
• Use unit rates to find equivalent ratios.
• Convert measurement units using rates.
• Express percent as a decimal or a fraction.
• Find a given percent of a number.
• Find what percent one number is of another number.
• Find the whole when given a part and a percent.
• Use math vocabulary and precise language to explain ratios, rates, and percent.  

Unit 5 Algebraic Thinking: Equivalent Expressions and Equations with Variables

Description: During this unit, students will be introduced to generating equivalent expressions, solving one-variable equations, and analyzing two-variable relationships.

Major Themes of the Unit:

• Writing expressions in different, but equivalent, forms in order to help make sense of problems.
• Discovering that one can perform the same operation on both sides of an equation (inverse operation) and the two sides will remain equal.
• Understand that solving an equation means determining the value of the variable or unknown that makes the equation true.
• Knowing how patterns can help describe two quantities differ from each other.

Louisiana Student Standards for Mathematics (LSSM)

EE. Expressions and Equations
A. Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers.
b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, and coefficient); view one or more parts of an expression as a single entity.
c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order
6.EE.A.3 Apply the properties of operations to generate equivalent expressions.
6.EE.A.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).
B. Reason about and solve one-variable equations and inequalities
6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.B.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations and inequalities of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers. Inequalities will include >, <, ≤, and ≥.
C. Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.C.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

The student will be able to….

• Identify when two expressions are equivalent.
• Write equivalent expressions.
• Determine whether a number is a solution of an equation and write equations with variables to represent real-world problems.
• Solve equations that represent real-world problems.
• Identify the independent and dependent variable in a relationship between two quantities.
• Write an equation to represent the relationship between an independent and dependent variable.
• Analyze the relationship between independent and dependent variable.
• Use math vocabulary and precise language to describe writing equivalent expressions and solving equations.

Unit 6 Positive and Negative Numbers: Absolute Value, Inequalities, and the Coordinate Plane

Description: During this unit, students will be introduced to positive and negative rational numbers and their absolute values, graphing inequalities with variables on a number line, and plotting points on a four-quadrant coordinate plane.

Major Themes of the Unit:

• Use positive and negative numbers to describe quantities with opposite values.
• Discover that every positive and negative number has both a distance and direction from 0 on a number line.
• Extend a number line to show both positive and negative rational numbers to explain absolute value.
• Learn that an inequality with a variable can have infinite many solutions on a number line.
• Extend their knowledge of the coordinate plane from one quadrant to all four quadrants.
• Knowing about absolute value can help find the distance between points.

Louisiana Student Standards for Mathematics (LSSM)

NS. Number Systems
C. Apply and extend previous understandings of the system of rational numbers.
6.NS.C.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/ below zero, elevation above/ below sea level, credits/ debits, positive/ negative electric charge); use positive and negative numbers to represent quantities in real -world contexts, explaining the meaning of 0 in each situation.
6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -( -3) = 3, and that 0 is its own opposite.
b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
6.NS.C.7 Understand ordering and absolute value of rational numbers.
a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.
b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 o C > –7 o C to express the fact that –3 o C is warmer than –7 o C.
c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real- world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than – 30 dollars represents a debt greater than 30 dollars.
6.NS.C.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
B. Reason about and solve one-variable equations and inequalities
6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.B.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real- world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
G. Geometry
A. Solve real- world and mathematical problems involving area, surface area, and volume.
6.G.A.3  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

The student will be able to….

• Plot integers and rational numbers on number lines to represent real-world contexts.
• Compare and order positive and negative numbers.
• Determine whether a number is a solution of an inequality.
• Write and graph inequalities to represent real-world contexts.
• Plot ordered pairs in all four quadrants of the coordinate plane.
• Use absolute value to find the distance between points on a horizontal or vertical line.
• Solve problems about polygons in the coordinate plane.
• Listen carefully during discussion in order to understand and explain another persons’ ideas.  

Unit 7 Statistical Thinking:  Data Distributions and Measures of Center of Variability

Description: During this unit, students will represent and describe data in dot plots, histograms, and box plots.  Students will learn to choose the appropriate measures of center and variability to summarize data sets.

Major Themes of the Unit:

• Become familiar with data distributions and how they help answer statistical questions.
• Relate knowledge of number lines to organize a set of data to help make sense of the data.
• Summarize data sets using a single number to describe a typical value and a single number to describe data spread out.
• Describe a data set based on the statistical question being answered and on the characteristics of the data set.

Louisiana Student Standards for Mathematics (LSSM)

SP. Statistics and Probability
A. Develop understanding of statistical variability
6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
6.SP.A.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
B. Summarize and describe distributions
6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.B.5 Summarize numerical data sets in relation to their context.

The student will be able to….

• Represent data in a frequency table, dot plot, and histograms.
• Describe a set of data by its center, spread, and overall shape.
• Summarize data by describing how the data were measured and their units of measurement.
• Represent data in a box plot.
• Calculate median and IQR of a data set, then interpret them in different contexts.
• Compare measures of center and variability, then choose measures of center and variability to summarize a data set.
• Use math vocabulary and precise language to describe sets of data.

Unit 1 Geometric Figures: Rigid Transformations and Congruence

Description: During this unit, students will be introduced to rigid transformations, including those in the coordinate plane.

Major Themes of the Unit:
Discover rigid transformations are slides, flips, or turns that change the location and orientation of a figure but not its size or shape. Also using the coordinate plane to explore how transformations affect the placement of a figures’ vertices.
Use rigid transformations to make sense of congruence and understand why corresponding side and angles of a congruent figure are the same.

Louisiana Student Standards for Mathematics (LSSM)

G- Geometry
A. Understand congruence and similarity using physical models, transparencies, or geometry software.
8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations:
a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
8.G.A.2    Explain that a two - dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between the m. (Rotations are only about the origin and reflections are only over the y- axis and x -axis.)
8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two -dimensional figures using coordinates. (Rotations are only about the origin, dilations only use the origin as the center of dilation, and reflections are only over the y -axis and x -axis.

The student will be able to….

• Recognize translations, reflections, and rotations, as rigid transformations.
• Understand that rigid transformations do not change the size and shape of a figure.
• Perform translations, reflections, and rotations in the coordinate plane.
• Describe a rigid transformation that maps a figure onto an image.
• Understand that two figures are congruent if one can be mapped exactly onto he other by a sequence of one or more rigid transformations.  
• Perform sequences of translations, rotations, and reflections that maps a figure onto an image.
• Use math vocabulary and precise language to describe that effects of rigid transformations on a figure.

 
Unit 2 Geometric Figures: Transformations, Similarity, and Angle Relationships

Description: During this unit, students are extending their knowledge of transformations to dilations, angle relationships formed by parallel lines but by a transversal, and angle relationships in triangles.  Students also explore angle relationships in triangles.

Major Themes of the Unit:

• Use prior knowledge of scale drawings to understand that a dilation is a transformation that can enlarge or reduce the figure creating similar figures.   
• Build upon the knowledge of transformations to discover angle relationships between angles formed by a pair of parallel lines and a line that intersects them.
• Extend upon the knowledge of angle pairs to help when exploring angle relationships in triangles proving triangles similar.

Louisiana Student Standards for Mathematics (LSSM)

G- Geometry
A. Understand congruence and similarity using physical models, transparencies, or geometry software.
8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two -dimensional figures using coordinates. (Rotations are only about the origin, dilations only use the origin as the center of dilation, and reflections are only over the y -axis and x -axis.
8.G.A.4  Explain that a two - dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two -dimensional figures, describe a sequence that exhibits the similarity between them. (Rotations are only about the origin, dilations only use the origin as the center of dilation, and reflections are only over the y -axis and x -axis.
8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle -angl e criterion for similarity of triangles.

The student will be able to….

• Understand that a dilation is a transformation in which the shape of a figure stays the same, but its size can change.  
• Understand that if a figure can be obtained by transforming a different figure, they are similar.
• Perform and describe a sequence of transformations that shows two figures are similar.
• Identify pairs of angles that are formed when two lines are cut by a transversal.
• Use angle relationships to find unknown angle measurements given a pair of parallel lines cut by a transversal.
• Find unknown angle measurements by using the interior and exterior angle relationships of a triangle.
• Show that it two triangles have two pairs of corresponding angles that are congruent, then the triangles are similar.
• Agree or disagree with ideas in discussions about geometric figures and explain why.

Unit 3 Linear Relationships

Description: During this unit, students are introduced to the concept of slope, and solving linear equations and systems of equations.

Major Themes of the Unit:

• Understand that linear equations with two variables has a graph that is a straight line. Using prior knowledge of ratios and unit rates will help make sense of the slope and y-intercept.    
• Learn that a linear equation in one variable can have one solution, no solution, or infinitely many solutions.
• Understand that a system of equations is a group of related linear equations where a solution makes all the equations true at the same time.

Louisiana Student Standards for Mathematics (LSSM)

EE- Expressions and Equations
B. Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.EE.B.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non -vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
C. Analyze and solve linear equations and pairs of simultaneous linear equations.
8.EE.C.7 Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
8.EE.C.8  Analyze and solve pairs of simultaneous linear equations.
a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

The student will be able to….

• Define slope and show that the slope of a line is the same between any two points on the line.
• Find the slope of a line and graph linear equations given in any form.
• Derive the linear equations y=mx and y=mx +b.
• Represent and solve one-variable linear equations with the variable on both sides of the equation.
• Determine whether one-variable linear equations have one solution, infinitely many solutions, or no solutions, and give examples.
• Solve systems of linear equations graphically and algebraically.
• Represent and solve systems of linear equations to solve real-world and mathematical problems.
• Justify solutions to problems about linear equations by telling what I noticed and what I decided to do as a result.

Unit 4 Functions

Description: During this unit, students are introduced to comparing and interpreting functions, describing qualitatively, and writing equations for linear functions.

Major Themes of the Unit:

• Learn that a function is a rule that assigns exactly one output to each input.   
• Use tables, graphs, equations and verbal descriptions to model, evaluate, and compare characteristics of linear functions.
• Describe functions qualitatively based on its graph.   

Louisiana Student Standards for Mathematics (LSSM)

F- Functions
A. Define, evaluate, and compare functions.
8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
8.F.A.2 Compare proper ties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
8.F.A.3  Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; categorize functions as linear or nonlinear when given equations, graphs, or tables.
B. Use functions to model relationships between quantities.
8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

The student will be able to….

• Understand that a function is a type of rule where each input results in exactly one output.
• Identify relationships that are functions from different representations, such as descriptions, tables, graphs, or equations.
• Determine whether a function is linear or nonlinear.
• Identify and interpret the rate of change and initial value for a linear function.
• Write an equation to model a linear function.
• Compare two functions represented in different way, such as in words, with tables, as equations, and as graphs.
• Use a graph to describe a function qualitatively.
• Sketch a graph of a function from a qualitative description.
• Make connections between different representations of functions by explaining how they are similar and different.  

 
Unit 5 Integer Exponents

Description: During this unit, students are introduced to operations with powers, comparing integer powers of ten, and expressing and operating with numbers in scientific notation.

Major Themes of the Unit:

• Explore operations with powers and discover patterns that help to understand and apply properties of exponents.
• Use knowledge of properties of exponents to operate numbers that are very large and very small.

Louisiana Student Standards for Mathematics (LSSM)

EE- Expressions and Equations
A. Work with radicals and integer exponents.
8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
8.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.

The student will be able to….

• Simplify expressions with two or more powers using exponent properties.
• Apply exponent properties to rewrite or simplify expressions with zero and negative integer exponents.
• Express, estimate, and compare quantities using integer powers of 10.
• Perform operations with numbers in scientific notation.
• Work with scientific notation to solve problems.
• Listen carefully during discussion in order to understand and explain another person’s ideas.
   

Unit 6 Real Numbers

Description: During this unit, students are introduced to irrational numbers, Pythagorean Theorem, and its converse, and finding the volume of cylinders, cones, and spheres.

Major Themes of the Unit:

• Use knowledge about working with rational numbers to solve problems with both rational and irrational numbers in both algebra and geometry topics understanding that an irrational number cannot be written as a terminating or repeating decimal.
• Discover the side lengths of a right triangle have a special relationship and this relationship can you used to find an unknown side length.
• Use prior knowledge of pi and the area of circles to solve real-world problems about volume of cylinders, cones, and spheres.

Louisiana Student Standards for Mathematics (LSSM)

EE- Expressions and Equations
A. Work with radicals and integer exponents.
8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
NS- Number Systems
A. Know that there are numbers that are not rational, and       approximate them by rational numbers.
8.NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually. Convert a decimal expansion which repeats eventually into a rational number by analyzing repeating patterns.
8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.
G-Geometry
B. Understand and apply the Pythagorean Theorem.
8.G.B.6  Explain a proof of the Pythagorean Theorem and its converse using the areas of squares.
8.G.B.7  Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
8.G.B.8  Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
C. Solve real-world and mathematical problems involving volume of    cylinders, cones, and spheres.
8.G.C.9  Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real - world and mathematical problems.

The student will be able to….

• Recognize numbers as perfect squares and perfect cubes.
• Take the square root or cube root of a number to solve problems.
• Know every rational number can be written as a repeating or a terminating decimal.
• Write repeating decimals as fractions.
• Find rational approximations of irrational numbers and locate them on the number line.
• Explain the Pythagorean Theorem and its converse.
• Apply the Pythagorean Theorem to find an unknown length in a figure or distance between two points in the coordinate plane.
• Know the volume formulas for cones, cylinders, and spheres and use them to solve problems.
• Actively participate in discussions by asking questions and rephrasing or building on a classmates’ ideas.
   

Unit 7 Statistics: Two-Variable Data

Description: During this unit, students are introduced to bivariate data, including quantitative data displayed in scatter plots and analyzed with lines of fit.  Students will also experience categorical data displayed in two-way tables and analyzed with relative frequencies.  

Major Themes of the Unit:

• Build upon one-variable data displays by constructing and analyzing two-variable data displays.
• Use prior knowledge of linear equations to help model a linear pattern in a two-variable data set to make predictions.
• Organize and interpret two-variable categorical data and describe possible associations.

Louisiana Student Standards for Mathematics (LSSM)

SP- Statistics and Probability
A. Investigate patterns of association in bivariate data.
8.SP.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
8.SP.A.4 Understand that pat terns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two -way table. Construct and interpret a two -way table summarizing data on two categorical variables collected from the same subject s. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.
8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.

The student will be able to….

• Make and use scatter plots to recognize and describe patterns and associations in two-variable data.
• Assess linear models for good fit to a set of data.
• Write and interpret equations for linear models that are good lines of fit for data.
• Understand and identify associations in two-variable categorical data by displaying frequencies in two-way tables.
• Construct and interpret two-way tables with relative frequency.
• Explain ideas about two-variable data clearly by using models to show why the ideas make sense for the problem.

FIRST SEMESTER

Unit 1 Proportional Relationships

Description: During this unit, students are introduced to scale factors, will build upon their knowledge of unit rates now involving ratios of fractions, represent proportional relationships with equations and graphs, and compute the circumference and area of circles.

Major Themes of the Unit:

• Use prior knowledge of unit rate and dividing fractions to explore ratios that compare fractions.
• Relate knowledge of ratios to explore the meaning of a proportional relationship in which one quantity is a constant multiple of another. Y= kx, where k is the constant multiple or constant of proportionality.
• Discover the distance around a circle, circumference, divided by the distance across, diameter, is always the same, a number called pi.

Louisiana Student Standards for Mathematics (LSSM)

RP- Ratios and Proportional Relationships
A. Analyze proportional relationships and use them to solve real - world and mathematical problems.
7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
7.RP.A.2 Recognize and represent proportional relationships between quantities.
a. Decide whether two quantities are in a proportional relationship
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
c. Represent proportional relationships by equations.
d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
G.Geometry
A. Draw, construct, and describe geometrical figures and describe the relationship between them.
7.G.A.1  Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
B. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
7.G.B.4  Know the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

The student will be able to….

• Find actual distance given a scale drawing.
• Find actual area given a scale drawing.
• Draw a scale drawing in a different scale.
• Find unit rates with complex fractions.
• Identify proportional relationships and the constant of proportionality.
• Write an equation to represent a proportional relationship.
• Interpret graphs of proportional relationships.
• Find the circumference and area of circles.
• Make connections between representations of proportional relationships by explaining how they are similar and different.

 
Unit 2 Numbers and Operations: Add and Subtract Rational Numbers

Description: During this unit, students are extending their knowledge of positive and negative numbers to now combining by adding and subtracting negative numbers.

Major Themes of the Unit:

• Use prior knowledge about positive and negative numbers and about addition on the number line to help add with positive and negative numbers.
• Use prior knowledge of how addition and subtraction are related to gain an understanding of subtracting positive and negative numbers.

Louisiana Student Standards for Mathematics (LSSM)

NS-Number System
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers .
7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
b. Understand p + q as the number located a distance |q | from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (– q). Show that the distance between two rational numbers on the number line is the absolute value of their difference and apply this principle in real world contexts.
d. Apply properties of operations as strategies to add and subtract rational numbers.

The student will be able to….

• Add positive and negative integers.
• Add positive and negative fractions and decimals.
• Subtract positive and negative integers.
• Justify solutions to problems about adding and subtracting rational numbers by telling what I noticed and what I decided at a result.

Unit 3 Numbers and Operations: Multiply and Divide Rational Numbers

Description: During this unit, students are working with rational numbers in decimals forms that either terminate or repeat along with continuing work with rational numbers by multiplying and dividing negative numbers.

Major Themes of the Unit:

• Extending the properties of operations to include operations with negative numbers to help understand how to multiply and divide with signed numbers.
• Divide an integer by any integer except 0, and the quotient is a rational number.  Rational numbers have decimals forms that either terminate or repeat.
• Write any division problem as a fraction, including problems with negative numbers.

Louisiana Student Standards for Mathematics (LSSM)

NS-Number System
A.Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers .
7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1) (–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non - zero divisor) is a rational number. If p and q are integers, then – (p / q) = (–p) / q = p / (–q). Interpret quotients of rational numbers by describing real - world contexts.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
EE- Expressions and Exponents
B. Solve real- life and mathematical problems using numerical and algebraic expressions and equations.
7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form.

The student will be able to….

• Multiply positive and negative integers.
• Divide positive and negative integers.
• Multiply positive and negative fractions and decimals.  
• Divide positive and negative fractions and decimals.
• Express rational numbers as terminating or repeating decimals.
• Solve word problems with rational numbers.
• Use math vocabulary and precise language to explain problems with rational numbers.

 
Unit 4 Algebraic Thinking: Expressions, Equations, and Inequalities

Description: During this unit, students are generating equivalent expressions and solving multi-step equations and inequalities.  

Major Themes of the Unit:

• Apply properties of operations to generate equivalent expressions.
• Apply knowledge of solving one-step equations to solve multi-step equations and inequalities.
• Discover/Reason about the effect of multiplying by a negative number can help to understand why the inequality symbol sometimes changes when solving inequalities.  

Louisiana Student Standards for Mathematics (LSSM)

EE-Expressions and Exponents
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers .
7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients to include multiple grouping symbols (e.g., parentheses, brackets, and braces).
7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
EE- Expressions and Exponents
B. Solve real- life and mathematical problems using numerical and algebraic expressions and equations.
7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

The student will be able to….

• Find equivalent expressions.
• Rewrite expressions in different forms.
• Solve multi-step equations.
• Solve problems using equations.
• Solve inequalities.
• Graph the solution to an inequality on a number line.
• Actively participate in discussions by asking questions and rephrasing or building on classmates’ ideas.

Unit 5 Proportional Reasoning

Description: During this unit, students are introduced to proportional reasoning with percents and statistical samples.  Random sampling will be explored by students as well in this unit.   

Major Themes of the Unit:

• Apply knowledge of proportional reasoning to understand applications of percents, for example simple interest, percent change, and percent error.
• Apply knowledge of proportional reasoning in order to draw conclusions about populations based on random sampling.
• Use prior knowledge of data distribution and measures of center and variability to compare two populations.

Louisiana Student Standards for Mathematics (LSSM)

RP- Ratios and Proportional Relationships
A. Analyze proportional relationships and use them to solve real - world and mathematical problems.
7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems of simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.
SP- Statistics and Probability
A. Use random sampling to draw inferences about a population.
7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that rand om sampling tends to produce representative samples and support valid inferences.
7.SP.A.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
7.SP.A.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities using quantitative measures of center (median and/ or mean) and variability (interquartile range and/ or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
7.SP.A.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

The student will be able to….

• Calculate simple interest.
• Solve percent problems involving markups, markdowns, tips, tax, and commission.
• Solve percent problems involving percent change or percent error.
• Identify random samples.
• Make statistical inferences from random samples.
• Compare data using measures of center and variability.
• Agree or disagree with ideas in discussions about random samples and explain why?

Unit 6 Geometry

Description: During this unit, students will take part in writing and solving equations for problems involving area, surface area, volume, and angle relationships, describing plane sections of three-dimensional figures, and drawing shapes with given attributes.

Major Themes of the Unit:

• Apply knowledge of writing and solving equations to geometry concepts such as area, surface area, volume, and angle relationships.
• Apply knowledge of surface area and volume of rectangular prisms to compute surface area and volume of any prism.
• Apply knowledge of two-dimensional figures to help identify shapes forms when a plane is sliced.
• Apply knowledge of angles, triangles, and quadrilaterals to draw shapes with given parameters.

Louisiana Student Standards for Mathematics (LSSM)

G-Geometry
A. Draw, construct, and describe geometrical figures and describe the relationships between them.
7.G.A.3    Draw (freehand, with ruler and protractor, or with technology) geometric shapes with given conditions.
B. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (Pyramids limited to surface area only.)

The student will be able to….

• Solve problems involving area and surface area.
• Solve problems involving volume.
• Describe plane sections of prisms, pyramids, and cylinders.
• Solve problems with angles.
• Draw triangles and quadrilaterals to meet given conditions.
• Listen carefully during discussion in order to understand and explain another person’s ideas.

Unit 7 Probability

Description: During this unit, students will be introduced to the concept of probability. Students will learn how to find the probability of single and compound events along with comparing experimental and theoretical probability.  

Major Themes of the Unit:

• Use proportional reasoning to understand probabilities and to make predictions about future events.
• Apply knowledge of collecting and analyzing data to help estimate the probability of a chance event.
• Analyze possible outcomes and use knowledge of fractions, decimals, and percent to help find probabilities.

Louisiana Student Standards for Mathematics (LSSM)

A. Draw, construct, and describe geometrical figures and describe the relationships between them.
7.G.A.3    Draw (freehand, with ruler and protractor, or with technology) geometric shapes with given conditions.
B. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (Pyramids limited to surface area only.)

The student will be able to….

• Describe the probability of an event using words and numbers.
• Find probabilities of single events.
• Use the results of an experiment to find the experimental probability of an event.
• Find the theoretical probability of an event.
• Compare theoretical and experimental probabilities.
• Find probabilities of compound events.
• Use simulations to find probabilities of events.
• Explain ideas about probability clearly by using models to show why the ideas make sense for the problem.

SECOND SEMESTER

Unit 1 Geometric Figures: Rigid Transformations and Congruence

Description: During this unit, students will be introduced to rigid transformations, including those in the coordinate plane.

Major Themes of the Unit:
Discover rigid transformations are slides, flips, or turns that change the location and orientation of a figure but not its size or shape. Also using the coordinate plane to explore how transformations affect the placement of a figures’ vertices.
Use rigid transformations to make sense of congruence and understand why corresponding side and angles of a congruent figure are the same.

Louisiana Student Standards for Mathematics (LSSM)

G- Geometry
A. Understand congruence and similarity using physical models, transparencies, or geometry software.
8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations:
a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
8.G.A.2    Explain that a two - dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between the m. (Rotations are only about the origin and reflections are only over the y- axis and x -axis.)
8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two -dimensional figures using coordinates. (Rotations are only about the origin, dilations only use the origin as the center of dilation, and reflections are only over the y -axis and x -axis.

The student will be able to….

• Recognize translations, reflections, and rotations, as rigid transformations.
• Understand that rigid transformations do not change the size and shape of a figure.
• Perform translations, reflections, and rotations in the coordinate plane.
• Describe a rigid transformation that maps a figure onto an image.
• Understand that two figures are congruent if one can be mapped exactly onto he other by a sequence of one or more rigid transformations.  
• Perform sequences of translations, rotations, and reflections that maps a figure onto an image.
• Use math vocabulary and precise language to describe that effects of rigid transformations on a figure.

 
Unit 2 Geometric Figures: Transformations, Similarity, and Angle Relationships

Description: During this unit, students are extending their knowledge of transformations to dilations, angle relationships formed by parallel lines but by a transversal, and angle relationships in triangles.  Students also explore angle relationships in triangles.

Major Themes of the Unit:

• Use prior knowledge of scale drawings to understand that a dilation is a transformation that can enlarge or reduce the figure creating similar figures.   
• Build upon the knowledge of transformations to discover angle relationships between angles formed by a pair of parallel lines and a line that intersects them.
• Extend upon the knowledge of angle pairs to help when exploring angle relationships in triangles proving triangles similar.

Louisiana Student Standards for Mathematics (LSSM)

G- Geometry
A. Understand congruence and similarity using physical models, transparencies, or geometry software.
8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two -dimensional figures using coordinates. (Rotations are only about the origin, dilations only use the origin as the center of dilation, and reflections are only over the y -axis and x -axis.
8.G.A.4  Explain that a two - dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two -dimensional figures, describe a sequence that exhibits the similarity between them. (Rotations are only about the origin, dilations only use the origin as the center of dilation, and reflections are only over the y -axis and x -axis.
8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle -angl e criterion for similarity of triangles.

The student will be able to….

• Understand that a dilation is a transformation in which the shape of a figure stays the same, but its size can change.  
• Understand that if a figure can be obtained by transforming a different figure, they are similar.
• Perform and describe a sequence of transformations that shows two figures are similar.
• Identify pairs of angles that are formed when two lines are cut by a transversal.
• Use angle relationships to find unknown angle measurements given a pair of parallel lines cut by a transversal.
• Find unknown angle measurements by using the interior and exterior angle relationships of a triangle.
• Show that it two triangles have two pairs of corresponding angles that are congruent, then the triangles are similar.
• Agree or disagree with ideas in discussions about geometric figures and explain why.

Unit 3 Linear Relationships

Description: During this unit, students are introduced to the concept of slope, and solving linear equations and systems of equations.

Major Themes of the Unit:

• Understand that linear equations with two variables has a graph that is a straight line. Using prior knowledge of ratios and unit rates will help make sense of the slope and y-intercept.    
• Learn that a linear equation in one variable can have one solution, no solution, or infinitely many solutions.
• Understand that a system of equations is a group of related linear equations where a solution makes all the equations true at the same time.

Louisiana Student Standards for Mathematics (LSSM)

EE- Expressions and Equations
B. Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.EE.B.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non -vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
C. Analyze and solve linear equations and pairs of simultaneous linear equations.
8.EE.C.7 Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
8.EE.C.8  Analyze and solve pairs of simultaneous linear equations.
a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

The student will be able to….

• Define slope and show that the slope of a line is the same between any two points on the line.
• Find the slope of a line and graph linear equations given in any form.
• Derive the linear equations y=mx and y=mx +b.
• Represent and solve one-variable linear equations with the variable on both sides of the equation.
• Determine whether one-variable linear equations have one solution, infinitely many solutions, or no solutions, and give examples.
• Solve systems of linear equations graphically and algebraically.
• Represent and solve systems of linear equations to solve real-world and mathematical problems.
• Justify solutions to problems about linear equations by telling what I noticed and what I decided to do as a result.

Unit 4 Functions

Description: During this unit, students are introduced to comparing and interpreting functions, describing qualitatively, and writing equations for linear functions.

Major Themes of the Unit:

• Learn that a function is a rule that assigns exactly one output to each input.   
• Use tables, graphs, equations and verbal descriptions to model, evaluate, and compare characteristics of linear functions.
• Describe functions qualitatively based on its graph.   

Louisiana Student Standards for Mathematics (LSSM)

F- Functions
A. Define, evaluate, and compare functions.
8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
8.F.A.2 Compare proper ties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
8.F.A.3  Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; categorize functions as linear or nonlinear when given equations, graphs, or tables.
B. Use functions to model relationships between quantities.
8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

The student will be able to….

• Understand that a function is a type of rule where each input results in exactly one output.
• Identify relationships that are functions from different representations, such as descriptions, tables, graphs, or equations.
• Determine whether a function is linear or nonlinear.
• Identify and interpret the rate of change and initial value for a linear function.
• Write an equation to model a linear function.
• Compare two functions represented in different way, such as in words, with tables, as equations, and as graphs.
• Use a graph to describe a function qualitatively.
• Sketch a graph of a function from a qualitative description.
• Make connections between different representations of functions by explaining how they are similar and different.  

 
Unit 5 Integer Exponents

Description: During this unit, students are introduced to operations with powers, comparing integer powers of ten, and expressing and operating with numbers in scientific notation.

Major Themes of the Unit:

• Explore operations with powers and discover patterns that help to understand and apply properties of exponents.
• Use knowledge of properties of exponents to operate numbers that are very large and very small.

Louisiana Student Standards for Mathematics (LSSM)

EE- Expressions and Equations
A. Work with radicals and integer exponents.
8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
8.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.

The student will be able to….

• Simplify expressions with two or more powers using exponent properties.
• Apply exponent properties to rewrite or simplify expressions with zero and negative integer exponents.
• Express, estimate, and compare quantities using integer powers of 10.
• Perform operations with numbers in scientific notation.
• Work with scientific notation to solve problems.
• Listen carefully during discussion in order to understand and explain another person’s ideas.
   

Unit 6 Real Numbers

Description: During this unit, students are introduced to irrational numbers, Pythagorean Theorem, and its converse, and finding the volume of cylinders, cones, and spheres.

Major Themes of the Unit:

• Use knowledge about working with rational numbers to solve problems with both rational and irrational numbers in both algebra and geometry topics understanding that an irrational number cannot be written as a terminating or repeating decimal.
• Discover the side lengths of a right triangle have a special relationship and this relationship can you used to find an unknown side length.
• Use prior knowledge of pi and the area of circles to solve real-world problems about volume of cylinders, cones, and spheres.

Louisiana Student Standards for Mathematics (LSSM)

EE- Expressions and Equations
A. Work with radicals and integer exponents.
8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
NS- Number Systems
A. Know that there are numbers that are not rational, and       approximate them by rational numbers.
8.NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually. Convert a decimal expansion which repeats eventually into a rational number by analyzing repeating patterns.
8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.
G-Geometry
B. Understand and apply the Pythagorean Theorem.
8.G.B.6  Explain a proof of the Pythagorean Theorem and its converse using the areas of squares.
8.G.B.7  Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
8.G.B.8  Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
C. Solve real-world and mathematical problems involving volume of    cylinders, cones, and spheres.
8.G.C.9  Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real - world and mathematical problems.

The student will be able to….

• Recognize numbers as perfect squares and perfect cubes.
• Take the square root or cube root of a number to solve problems.
• Know every rational number can be written as a repeating or a terminating decimal.
• Write repeating decimals as fractions.
• Find rational approximations of irrational numbers and locate them on the number line.
• Explain the Pythagorean Theorem and its converse.
• Apply the Pythagorean Theorem to find an unknown length in a figure or distance between two points in the coordinate plane.
• Know the volume formulas for cones, cylinders, and spheres and use them to solve problems.
• Actively participate in discussions by asking questions and rephrasing or building on a classmates’ ideas.
   

Unit 7 Statistics: Two-Variable Data

Description: During this unit, students are introduced to bivariate data, including quantitative data displayed in scatter plots and analyzed with lines of fit.  Students will also experience categorical data displayed in two-way tables and analyzed with relative frequencies.  

Major Themes of the Unit:

• Build upon one-variable data displays by constructing and analyzing two-variable data displays.
• Use prior knowledge of linear equations to help model a linear pattern in a two-variable data set to make predictions.
• Organize and interpret two-variable categorical data and describe possible associations.

Louisiana Student Standards for Mathematics (LSSM)

SP- Statistics and Probability
A. Investigate patterns of association in bivariate data.
8.SP.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
8.SP.A.4 Understand that pat terns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two -way table. Construct and interpret a two -way table summarizing data on two categorical variables collected from the same subject s. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.
8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.

The student will be able to….

• Make and use scatter plots to recognize and describe patterns and associations in two-variable data.
• Assess linear models for good fit to a set of data.
• Write and interpret equations for linear models that are good lines of fit for data.
• Understand and identify associations in two-variable categorical data by displaying frequencies in two-way tables.
• Construct and interpret two-way tables with relative frequency.
• Explain ideas about two-variable data clearly by using models to show why the ideas make sense for the problem.

Topic 1
Solving Equations and Inequalities

Topic 1 focuses on extending students’ understanding of writing and solving equations and inequalities to include equations and inequalities that require multiple steps to solve, as well as those that have variables on both sides of the equation or inequality.

The Student Will Be Able To

• Reason about operations on real numbers.
• Create and solve linear equations with one variable.
• Write and solve equations with a variable on both sides to solve problems.
• Rewrite and use literal equations to solve problems.
• Solve and graph inequalities.
• Write and solve compound inequalities.
• Write and solve absolute value equations and inequalities.

Academic Vocabulary

• element of a set
• set
• subset
• identity
• formula
• literal equation
• compound inequality

 
Louisiana Student Standards for Mathematics (LSSM)

N-RN.B.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a non-zero rational number and an irrational number is irrational.

A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.

A-REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling.

N-Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

A-CED.A.4 ­ Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.  

A-CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

F-BF.A.1 Write a linear, quadratic, or exponential function that describes a relationship between two quantities.  

Topic 2
Linear Equations

Topic 2 focuses on extending students’ understanding of linear equa-tions. Students analyze descriptions of lines and write their equations in different forms.

The Student Will Be Able To

• Solve absolute value equations and inequalities.
• Use absolute value equations and inequalities to solve problems.
• Write linear equations in two variables using slope-intercept form to represent the relationship between two quantities.
• Interpret the slope and the intercept of a linear model.•Write and graph linear equations in standard form.
• Use linear equations in standard form to interpret the x- and y-intercepts in the context of given data.

Academic Vocabulary

• point-slope form
• slope-intercept form
• standard form of a linear equation
• y-intercept

Louisiana Student Standards for Mathematics (LSSM)

A-CED.A.2 ­ Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

S-ID.C.7 ­ Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

F-LE.A.2 ­ Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

A-CED.A.3 ­ Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling  context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

A-CED.A.1 ­ Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.

A-CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.

A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling.  

F-BF.A.1 Write a linear, quadratic, or exponential function that describes a relation-ship between two quantities.

Topic 3
Linear Functions

Topic 3 focuses on extending students’ understanding of linear equa-tions to linear functions. Students learn methods to write, graph, and transform linear functions. They also apply analytic methods to tabular and graphic data sets that have linear relationships.

The Student Will Be Able To

• Understand that a relation is a function if each element of the domain is assigned to exactly one element in the range.
• Determine a reasonable domain and identify constraints on the domain based on the context of a real-world problem.
• Write and evaluate linear functions using function notation.
• Graph a linear function and relate the domain of a function to its graph.
• Interpret functions represented by graphs, tables, verbal descriptions, and function notation in terms of a context.
• Write and evaluate linear functions using function notation.
• Graph a linear function and relate the domain of a function to its graph.
• Interpret functions represented by graphs, tables, verbal descriptions, and function notation in terms of a context.
• Identify the common difference in a sequence.
• Write arithmetic sequences both recursively and with an explicit formula.
• Construct arithmetic sequences, given a graph, a description of a relationship, or two input-output pairs.
• Fit a function to linear data shown in a scatter plot and use fitted functions to solve problems in the context of the data.
• Interpret the slope of a trend line within the context of data.

Academic Vocabulary

• Continuous
• Discrete
• Domain
• Function
• One-to-one
• Range
• Relation
• Function notation
• Linear function
• Transformation
• Translation
• Arithmetic sequence
• Common difference
• Explicit formula
• Recursive formula
• Sequence
• Term of the sequence
• Negative association
• Negative correlation
• No association
• Positive association
• Positive correlation
• Trend line

Louisiana Student Standards for Mathematics (LSSM)

F-IF.A.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the out-put of f corresponding to the input x. The graph off is the graph of the equation y = f(x).

F-IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

F-IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

F-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs include reading these from a table).

F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-BF.A.1 ­ Write a function that describes a relationship between two quantities.

F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). Without technology, find the value of k given the graphs of linear and quadratic functions. With technology, experiment with cases and illustrate an explanation of the effects on the graph that include cases where f(x) is a linear, quadratic, piecewise linear (to include absolute value) or exponential function.

F-BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation from a context.

F-LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

F-LE.A.1b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

S-ID.B.6 ­ Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

S-ID.B.6.a  Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context Emphasize linear and quadratic models.

S-ID.B.6b Informally assess the fit of a function by plotting and analyzing residual.

S-ID.B.6.c ­ Fit a linear function for a scatter plot that suggests a linear association.

S-ID.C.7 ­ Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

S-ID.C.8 ­ Compute (using technology) and interpret the correlation coefficient of a linear fit.

S-ID.C.9 ­ Distinguish between correlation and causation.

F-BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation from a context.

Topic 4
Systems of Linear Equations and Inequalities

Topic 4 focuses on students extending their understanding of linear equations and inequalities to systems of linear equations and inequalities. Students learn methods to solve systems of linear equations and inequalities. Students identify when each solution method is most useful.

The Student Will Be Able To

• Graph systems of linear equations in two variables to find an approximate solution.
• Write a system of linear equations in two variables to represent real-world problems.
• Use the substitution method to solve systems of equations.
• Represent situations as a system of equations and interpret solutions as viable/nonviable options for the situation.
• Solve systems of linear equations by elimination and prove that the sum of one equation and a multiple of the other produces a system with the same solutions as the original system.
• Represent constraints with a system of equations in a modeling context.
• Graph solutions to linear inequalities in two variables.
• Represent constraints with inequalities and interpret solutions as viable or nonviable options in a modeling context.
• Graph the solution set of a system of linear inequalities in two variables.
• Interpret solutions of linear inequalities in a modeling context.

Academic Vocabulary

• Linear Inequality in Two Variables
• Solution of an Inequality in Two Variables
• Solution of a System of Linear Inequalities
• System of Linear Inequalities

Louisiana Student Standards for Mathematics (LSSM)

A-REI.C.6 ­ Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

A-CED.A.3 ­ Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

A-REI.C.5 ­ Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

A-REI.D.12 ­ Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

A-CED.A.2 ­ Create equations in two or more variables to represent relationships between    quantities; graph equations on coordinate axes with labels and scales.

Topic 5
Piecewise Functions  

Topic 5 focuses on extending the concept of functions to include absolute value functions and other piecewise-defined functions. Students identify the characteristics of each of these types of functions and understand that transformations can be applied to these functions.

The Student Will Be Able To

• Graph an absolute value function and identify the key features of the graph.
• Calculate and interpret the rate of change of an absolute value function over a specified interval.
• Graph step functions including ceiling functions and floor functions.
• Calculate and interpret the average rate of change of step functions.

Academic Vocabulary

• Absolute value function
• Axis of symmetry
• Vertex
• Piecewise-defined function
• Ceiling function
• Floor function
• Step function

Louisiana Student Standards for Mathematics (LSSM)

F-IF.B.4 ­ For linear, piecewise linear (to include absolute value), quadratic, and exponen-tial functions that model a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.

F-IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F-IF.C.7b ­ Graph piecewise linear (to include absolute value) and exponential func-tions.  

F-IF.C.9 ­ Compare properties of two functions (linear, quadratic, piecewise linear [to include absolute value] or exponential) each represented in a different way (algebrai-cally, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, determine which has the larger maximum.

F-BF.B.3 ­ Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). Without technology, find the value of k given the graphs of linear and quadratic functions. With technology, experi-ment with cases and illustrate an explanation of the effects on the graph that include cas-es where f(x) is a linear, quadratic, piecewise linear (to include absolute value) or expo-nential function.

F-IF.A.2 Use function notation, evaluate functions for inputs in their domains, and inter-pret statements that use function notation in terms of a context.

F-IF.A.3 Recognize that sequences are functions whose domain is a subset of the inte-gers. Relate arithmetic sequences to linear functions and geometric sequences to expo-nential functions.

A-SSE.A.1 Interpret expressions that represent a quantity in terms of its context.

Topic 6
Exponents and Exponential Functions

Topic 6 focuses on extending knowledge of functions to include the exponential function. Students learn to identify, write, graph, and trans-form exponential functions. Students use exponential functions to model real-world situations and make predictions.

The Student Will Be Able To

• Extend the properties of integer exponents to rational exponents to rewrite radical expressions using rational exponents.
• Use the properties of exponents to generate equivalent algebraic expressions.
• Write equivalent radical expressions to solve problems with rational exponents.
• Sketch graphs showing key features of exponential functions.
• Write exponential functions using tables and graphs.
• Compare linear and exponential functions.
• Sketch graphs showing key features of exponential functions.
• Write exponential functions using tables and graphs.
• Compare linear and exponential functions.
• Construct a geometric sequence given a graph, table, or description of a relation-ship.
• Translate between geometric sequences written in recursive and explicit forms.
• Use the formula for the sum of a finite geometric series to solve problems.
• Translate the graph of an exponential function vertically and horizontally, identifying the effect different values of h and k have on the graph of the function.
• Compare characteristics of two exponential functions represented in different ways, such as tables and graphs.

Academic Vocabulary

• Rational exponent
• Asymptote
• Constant ratio
• Exponential function
• Compound interest
• Decay factor
• Exponential decay
• Exponential growth
• Growth factor
• Geometric Sequence

Louisiana Student Standards for Mathematics (LSSM)

F-IF.B.4  For linear, piecewise linear (to include absolute value), quadratic, and exponen-tial functions that model a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.

F-IF.B.5 ­ Relate the domain of a function to its graph and, where applicable, to the quan-titative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

F-IF.B.6 Calculate and interpret the average rate of change of a linear, quadratic, piece-wise linear (to include absolute value), and exponential function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F-BF.A.1 ­ Write a function that describes a relationship between two quantities.

F-LE.A.1 ­ Distinguish between situations that can be modeled with linear functions and with   exponential functions.

F-LE.A.1a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

N-Q.A.3 ­ Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

A-SSE.A.1.b ­ Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.

A-SSE.B.3.c ­ Use the properties of exponents to transform expressions for exponential functions emphasizing integer exponents.

A-CED.A.2 ­ Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

F-LE.A.1c Recognize situations in which a quantity grows or decays by a constant per-cent rate per unit interval relative to another.

F-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

F-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a con-text.

F-IF.C.9 Compare properties of two functions (linear, quadratic, piecewise linear [to include absolute value] or exponential) each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, determine which has the larger maximum.

F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). Without technology, find the value of k given the graphs of linear and quadratic functions. With technology, experiment with cases and illustrate an explanation of the effects on the graph that include cases where f(x) is a linear, quadratic, piecewise linear (to include absolute value) or exponential function.

Topic 7
Polynomials and Factoring

Topic 7 focuses on extending polynomials. Students identify the parts and factors of polynomials. Students understand how to factor trinomials using the greatest common factor, binomial factors, and special patterns. Students learn methods to add, subtract, and multiply polynomials.

The Student Will Be Able To

• Identify the parts of a polynomial, such as coefficients, variables, and constants.
• Classify polynomials by number of terms and by degree.
• Write a polynomial in standard form.
• Add or subtract two polynomials and recognize that polynomials are closed under addition and subtraction like the system of integers.
• Use the Distributive Property with polynomials, recognizing that polynomials are closed under multiplication.
• Multiply polynomials using a table and an area model.
• Apply the product of polynomials to solve real-world problems.
• Determine the square of a binomial.
• Find the product of a sum and difference of two squares.
• Solve real-world problems involving the square of a binomial.
• Divide a polynomial by a monomial.
• Find the greatest common factor of the terms of a polynomial.
• Write polynomials in factored form.
• Factor a trinomial in the form x²+ bx + c by finding two binomial factors whose product is equal to the trinomial.
• Identify patterns in the signs of the coefficients of the terms of a trinomial expression and use those patterns to determine the signs of the second terms in the binomial factors.
• Factor trinomials in the context of solving real-world problems.

Academic Vocabulary

• Closure Property
• Degree of a monomial
• Degree of a polynomial
• Monomial
• Polynomial
• Standard form of a polynomial
• Difference of two squares
• Perfect-Square trinomial

Louisiana Student Standards for Mathematics (LSSM)

A-APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, sub-tract, and multiply polynomials.

A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it.

A-SSE.A.1 Interpret expressions that represent a quantity in terms of its context.

A-SSE.A.1a Interpret parts of an expression, such as terms, factors, and coefficients.

A-SSE.A.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.

A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Topic 8
Quadratic Functions

Topic 8 focuses on extending students’ previous understanding of functions to include quadratic functions: graphing them, using them to model real-world situations, and comparing them to linear and exponential functions.

The Student Will Be Able To

• Identify key features of the graph of a quadratic function using graphs, tables, and equations.
• Explain the effect of the value of a on the quadratic parent function.
• Identify key features of the graph of quadratic functions written in vertex form
• Graph quadratic functions in vertex form.
• Graph quadratic functions in standard form and show intercepts, maxima, and minima
• Determine how the values of a, b, and c affect the graph of f(x) = ax² + bx + c.
• Identify key features of parabolas.
• Compare properties of quadratic functions, presented in different forms (algebraically, in a table, graphically).
• Use quadratic functions fitted to data to model real-world situations.
• Use the vertical motion model to write an equation.
• Determine which model—linear, exponential, or quadratic best fits a set of data.
• Use fitted functions to solve problems in the context of data.

Academic Vocabulary

• Parabola
• Quadratic parent function
• Vertex of a parabola
• Vertex form of a quadratic function
• Standard form of a quadratic function
• Quadratic regression
• Vertical motion model

Louisiana Student Standards for Mathematics (LSSM)

A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

F-IF.B.6 Calculate and interpret the average rate of change of a linear, quadratic, piece-wise linear (to include absolute value), and exponential function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). Without technology, find the value of k given the graphs of linear and quadratic functions. With technology, experiment with cases and illustrate an explanation of the effects on the graph that include cases where f(x) is a linear, quadratic, piecewise linear (to include absolute value) or exponential function.

F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-IF.B.4 For linear, piecewise linear (to include absolute value), quadratic, and exponential functions that model a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.

F-IF.C.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.

F-IF.C.8 Write a function defined by an expression in different but equivalent forms to re-veal and explain different properties of the function.

F-IF.C.9 Compare properties of two functions (linear, quadratic, piecewise linear [to include absolute value] or exponential) each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, determine which has the larger maximum.

F-IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

F-BF.A.1 Write a linear, quadratic, or exponential function that describes a relationship be-tween two quantities.

S-ID.B.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and quadratic models.

S-ID.B.6b Informally assess the fit of a function by plotting and analyzing residuals.

A-REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

F-LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

A-APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, sub-tract, and multiply polynomials.

A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Topic 9
Solving Quadratic Equations  

Topic 9 focuses on extending knowledge of quadratic functions. Stu-dents learn to solve quadratic equations using tables, graphs, and factoring. Students also solve equations using square roots, completing the square and the quadratic formula. Students learn different methods, such as graphing, elimination, and substitution, for solving linear-quadratic systems.

The Student Will Be Able To

• Use a graph to identify the x-intercepts as solutions of a quadratic equation.
• Use a graphing calculator to make a table of values to approximate or solve a quadratic equation.
• Use the Zero-Product Property and factoring to find the solutions of a quadratic equation.
• Apply factoring to solve real-world problems.
• Use the zeros of a quadratic equation to sketch a graph.
• Write the factored form of a quadratic function from a graph.
• Use properties of exponents to rewrite radical expressions.
• Multiply radical expressions.
• Write a radical expression to model or represent a real-world problem.
• Solve quadratic equations by finding square roots.
• Determine reasonable solutions for real-world problems.
• Solve a quadratic trinomial by completing the square to transform a quadratic equation into a perfect square trinomial.
• Use completing the square to write a quadratic equation in vertex form.
• Derive the quadratic formula by completing the square.
• Solve quadratic equations in one variable by using the quadratic formula.
• Use the discriminant to determine the number and type of solutions to a quadratic equation.
• Describe a linear-quadratic system of equations.
• Solve a linear-quadratic system of equations by graphing, elimination, or substitution.

Academic Vocabulary

• Quadratic equation
• Zeros of a function
• Standard form of a quadratic equation
• Zero-Product Property
• Product Property of Square Roots
• Completing the square
• Discriminant
• Quadratic formula
• Root
• Linear-quadratic system

Louisiana Student Standards for Mathematics (LSSM)

A-SSE.B.3a Factor a quadratic expression to reveal the zeros of the function it defines.

A-APR.B.3 Identify zeros of quadratic functions, and use the zeros to sketch a graph of the function defined by the polynomial.

A-REI.B.4b Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as “no real solution”.

F-IF.C.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.

A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it.

A-REI.B.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions. Derive the quadratic formula from this form.

A-SSE.B.3b Complete the square in a quadratic expression to reveal the maximum or mini-mum value of the function it defines.

N-Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A-REI.B.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions. Derive the quadratic formula from this form.

A-CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.

A-REI.B.4 Solve quadratic equations in one variable.

A-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, piecewise linear (to include absolute value), and exponential functions.

A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A-SSE.A.1 Interpret expressions that represent a quantity in terms of its context.

Topic 10
Working With Functions

Topic 10 extends students’ knowledge of functions to include radical functions. Students identify the key features of the graphs of radical functions. They also learn to transform functions.

The Student Will Be Able To

• Graph translations of the square root function
• Calculate and interpret the average rate of change for a square root function over a specified interval.
• Solve real-world problems by evaluating and comparing two square root functions.
• Identify key features of the graph of cube root functions and graph translations of them
• Model real-world situations using the cube root function.
• Calculate and interpret the average rate of change of a cube root function over a specified interval.
• Relate the domain and range of a function to its graph.
• Analyze the key features of the graph of a function including the domain, range, maximum and minimum values, axis of symmetry, and end behavior to identify the type of function it represents.
• Graph translations of absolute value, exponential, quadratic, and radical functions
• Determine how combining translations affects the key features of the graph of a function.
• Identify the effect on the graph of a function of multiplying the output by −1
• Identify the effect on the graph of a function of replacing f(x) by kf(x) or by f(kx) for specific values of k.
• Combine functions by addition, subtraction, multiplication, or division and iden-tify the domain of the result.
• Demonstrate that, while the resulting domains of new functions from other operations is the intersection of the domains of the original functions, division results in a domain that is the set of all real numbers for which both original functions and the new function are defined.
• Write an equation for the inverse of a linear function.
• Write the inverse of a quadratic function after restricting the domain so the original function is one-to-one.

Academic Vocabulary

• Square root function
• Cube root function

Louisiana Student Standards for Mathematics (LSSM)

F-IF.B.4 For linear, piecewise linear (to include absolute value), quadratic, and exponential functions that model a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features giv-en a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.

F-IF.B.6 Calculate and interpret the average rate of change of a linear, quadratic, piece-wise linear (to include absolute value), and exponential function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F-IF.C.7b Graph piecewise linear (to include absolute value) and exponential functions.

F-IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of per-son-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). Without technology, find the value of k given the graphs of linear and quadratic functions. With technology, experiment with cases and illustrate an explanation of the effects on the graph that include cases where f(x) is a linear, quadratic, piecewise linear (to include absolute value) or exponential function.

F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-IF.A.3 Recognize that sequences are functions whose domain is a subset of the integers.     Relate arithmetic sequences to linear functions and geometric sequences to exponential functions.

F-BF.A.1 Write a linear, quadratic, or exponential function that describes a relationship be-tween two quantities.

N-RN.B.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a non-zero rational number and an irrational number is irrational.

Topic 11
Statistics

Topic 11 focuses on extending students’ knowledge of dot plots, box plots, and histograms. Students identify that standard deviation is used to compare a specific value to other values. Students understand how to find joint, marginal, and relative frequencies. Students learn methods to interpret data displays and create inferences based on the data.

The Student Will Be Able To

• Represent data using dot plots, box plots, and histograms.
• Interpret the data displayed in dot plots, box plots, and histograms within the con-text it represents.
• Use measures of center to interpret and compare data sets displayed in dot plots, box plots, and histograms.
• Use measures of variability, such as the MAD and IQR, to interpret and compare data sets.
• Interpret and compare differences in the shape, center, and spread of different data sets.
• Determine the relationship between the mean and median of a data set when the shape of the data display is evenly spread, skewed right, or skewed left.
• Interpret differences in the variability or spread in the context of a data set.
• Calculate the standard deviation of a data set and use it to compare and interpret data sets.

Academic Vocabulary

• Normal distribution
• Standard deviation
• Variance
• Conditional relative frequency
• Joint frequency
• Joint relative frequency
• Marginal frequency

Louisiana Student Standards for Mathematics (LSSM)

S-ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

S-ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

S-ID.B.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

Topic 1
Foundations of Geometry

Topic 1 begins by focusing on the measurements and properties of line segments and angles. The rest of the topic introduces proofs. Students examine the nature of basic reasoning in both inductive and deductive forms, explore if-then statements, and then write their first proofs.

The Student Will Be Able To

• Communicate precise definitions of angle and segment using the undefined terms: point, line, and plane.
• Use absolute value and the Segment Addition Postulates.
• Use the Protractor Postulate and the Angle Addition Postulate.
• Identify congruent segments and congruent angles.
• Construct copies of segments and angles.
• Construct segments, perpendicular bisectors of segments, and bisectors of angles.
• Apply construction to solve problems.
• Determine the weighted average of two points and use it to partition segments.
• Use the Midpoint Formula to find the midpoint of a segment drawn on a coordinate plane.
• Use the Distance Formula to find the length of a segment drawn on the coordinate plane.
• Use deductive reasoning to prove geometric theorems about lines and angles.

Academic Vocabulary

• angle bisector
• biconditional
• conditional
• conjecture
• construction
• contrapositive
• converse
• counterexample
• deductive reasoning
• inductive reasoning
• inverse
• Law of Detachment
• Law of Syllogism
• negation
• proof
• perpendicular bisector
• postulate
• theorem
• truth table
• truth value

Louisiana Student Standards for Mathematics (LSSM)

G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

G-CO.D.12 Make formal geometric constructions with a variety of tools and methods, e.g., compass and straightedge, string, reflective devices, paper folding, or dynamic geometric software. Examples: Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

G-GPE.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

G-CO.C.9 Prove and apply theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

Topic 2
Parallel and Perpendicular Lines

Topic 2 begins by focusing on the properties of parallel lines and the angle relationships formed when parallel lines are cut by a transversal. The rest of the topic examines how these angle relationships can help prove whether or not lines are parallel, the relationships between parallel lines and triangle angles, and the relationships between the slopes of parallel and perpendicular lines.

The Student Will Be Able To

• Define parallel lines using the undefined terms point and line.
• Prove relationships and theorems about lines and angles.
• Use the Same-Side Interior Angles Postulate and the Alternate Interior Angles, Corresponding Angles, and Alternate Exterior Angles Theorems to find the measures of angles formed by parallel lines and a transversal.
• Prove that two lines cut by a transversal are parallel using the converses of parallel line angle relationship theorems.
• Use properties of parallel lines and transversals to solve real-world and mathematical problems.
• Write and use flow proofs.
• Use lines constructed parallel to another line to solve problems and prove theorems.
• Use the sum of the angle measures in a triangle to solve problems.
• Use coordinate geometry to show that two lines in the coordinate plane are parallel by comparing their slopes, and solve problems.
• Use coordinate geometry to show that two lines in the coordinate plane are perpendicular by comparing their slopes, and use that information to solve problems.

Academic Vocabulary

• flow proof

Louisiana Student Standards for Mathematics (LSSM)

G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

G-CO.C.9 Prove and apply theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

G-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

G-MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

G-CO.C.10 Prove and apply theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

G-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Topic 3
Transformations

Topic 3 begins by focusing on transformations, moving from the definition of rigid motion to the rigid transformations: reflections, translations, and rotations. The rest of the topic examines how transformations can be combined to create new images and complete proofs, such as the proof for demonstrating that a composition of two or more rigid motions is also a rigid motion.

The Student Will Be Able To

• Find a reflected image and write a rule for a reflection algebraically using coordinates.
• Define a reflection as a transformation across a line of reflection with given properties and perform reflections on and off a coordinate grid.
• Translate a figure and represent the transformation algebraically using coordinates.
• Find the image of a figure after a sequence of rigid motions.
• Prove that a translation is a composition of two reflections.
• Rotate a figure and represent the transformation algebraically using coordinates.
• Prove that a rotation can be written as a sequence of transformations.
• Specify a sequence of transformations that will carry a given figure onto another.
• Use geometric descriptions of rigid motions to transform figures.
• Identify a sequence of translations, rotations, and/or reflections that map a given figure onto itself.
• Predict the effect of a given rigid motion on a figure.
• Determine symmetries of reflection, symmetries of rotation and symmetries of translation of a geometric figure.

Academic Vocabulary

• composition of rigid motions
• glide reflection
• point symmetry
• reflectional symmetry
• rigid motion
• rotational symmetry

Louisiana Student Standards for Mathematics (LSSM)

G-CO.A.2 Represent transformations in the plane using, e.g., transparencies, tracing paper, or geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

G-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G-CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

G-CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

G-CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Topic 4
Triangle Congruence

Topic 4 focuses on congruence and transformations resulting in congruent figures. The lesson includes the definitions of congruence and congruence transformations and provides examples to help students determine if figures are congruent. The topic then explores various triangles and defines congruence theorems that prove triangles are congruent given congruent angles and sides of the triangles.

The Student Will Be Able To

• Identify a sequence of rigid motions to justify the congruence of two figures.
• Demonstrate that two figures are congruent by using one or more rigid motions to map one onto the other.
• Students will be able to:
• Use properties of and theorems about isosceles and equilateral triangles to solve problems.
• Identify congruent triangles using properties of isosceles and equilateral triangles.
• Prove triangle congruence by SAS and SSS criteria and use triangle congruence to solve problems.
• Understand that corresponding parts of congruent triangles are congruent and use CPCTC to prove theorems and solve problems.
• Prove that two triangles are congruent using ASA and AAS criteria and apply ASA to solve problems.
• Prove that when all corresponding sides and angles of two polygons are congruent, the polygons are congruent.
• Prove the Hypotenuse-Leg Theorem.
• Use congruence criteria for triangles to solve problems and to prove relationships in geometric figures.
• Apply congruence criteria to increasingly intricate problems involving overlapping triangles and multiple triangles.
• Prove triangles are congruent by identifying corresponding parts and applying the correct theorems.

Academic Vocabulary

• congruence transformation
• congruent

Louisiana Student Standards for Mathematics (LSSM)

G-CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

G-CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

G-CO.C.10 Prove and apply theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

G-CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

G-CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Topic 5
Relationships in Triangles

Topic 5 begins by focusing on the concurrent points found in a triangle using perpendicular bisectors, angle bisectors, medians, and altitudes. The rest of the topic examines the relationships of the angle measures and
side lengths within a triangle, as well as the angle measures and side lengths of two triangles.

The Student Will Be Able To

• Prove the Perpendicular Bisector Theorem, the Angle Bisector Theorem, and their converses.
• Use the Perpendicular Bisector Theorem to solve problems.
• Use the Angle Bisector Theorem to solve problems.
• Prove that the point of concurrency of the perpendicular bisectors of a triangle, called the circumcenter, is equidistant from the vertices.
• Prove that the point of concurrency of the angle bisectors of a triangle, called the incenter, is equidistant from the sides.
• Identify special segments in triangles and understand theorems about them.
• Find and use the point of concurrency of the medians of a triangle to solve problems and prove relationships in triangles.
• Find the point of concurrency of the altitudes of a triangle.
• Prove that the side lengths of a triangle are related to the angle measures of the triangle.
• Use the angle measures of a triangle to compare the side lengths of the triangle.
• Use the Triangle Inequality Theorem to determine if three given side lengths will form a triangle and to find a range of possible side lengths for a third side given two side lengths.
• Prove the Hinge Theorem and use the Hinge Theorem to compare side lengths.
• Prove the Converse of the Hinge Theorem and use the Converse of the Hinge Theorem to compare angle measures.

Academic Vocabulary

• altitude
• centroid
• circumcenter
• circumscribed
• concurrent
• equidistant
• incenter
• inscribed
• median
• orthocenter
• point of concurrency

Louisiana Student Standards for Mathematics (LSSM)

G-CO.C.9 Prove and apply theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoint.

G-CO.C.10 Prove and apply theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

G-C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Topic 6
Quadrilaterals and Other Polygons

Topic 6 begins by focusing on the interior and exterior angles of polygons. The rest of the topic focuses on quadrilaterals, examining properties of kites and trapezoids, and then the properties and conditions of parallelograms and special parallelograms.

The Student Will Be Able To

• Use properties of the diagonals of a kite to solve problems.
• Use properties of isosceles trapezoids to solve problems.
• Use the relationship between the lengths of the bases and midsegment of a trapezoid to solve problems.
• Show that the consecutive angles of a parallelogram are supplementary and opposite angles are congruent.
• Show that opposite sides of a parallelogram are congruent.
• Show that diagonals of a parallelogram bisect each other.
• Demonstrate that a quadrilateral is a parallelogram based on its sides and diagonals.
• Demonstrate that a quadrilateral is a parallelogram based on its angles.
• Prove that the diagonals of rhombuses are perpendicular bisectors of each other and angle bisectors of the angles of the rhombus.
• Prove that the diagonals of a rectangle are congruent.
• Use properties of rhombuses, rectangles, and squares to solve problems.
• Identify rhombuses, rectangles, and squares by the characteristics of diagonals of parallelograms.

Academic Vocabulary

• midsegment of a trapezoid

 

Louisiana Student Standards for Mathematics (LSSM)

G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

G-C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle

G-CO.C.11 Prove and apply theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonal.

Topic 7
Similarity

Topic 7 begins with an examination of dilations and similarity transformations. These concepts are then applied to triangles; students examine the criteria for proving two triangles similar and analyze similarity in right triangles, including applications of the geometric mean. Finally, students consider proportions in triangles.

The Student Will Be Able To

• Dilate figures on and off the coordinate plane.
• Understand how distances and lengths in a dilation are related to the scale factor and center of dilation.
• Understand that two figures are similar if there is a similarity transformation that maps one figure to the other.
• Identify a combination of rigid motions and dilation that maps one figure to a similar figure.
• Identify the coordinates of an image under a similarity transformation.
• Use dilations and rigid motions to prove triangles are similar.
• Prove and use the AA~, SSS~, and SAS~ theorems to prove triangles are similar.
• Use similarity of right triangles to solve problems.
• Use length relationships of the sides of right triangles and an altitude drawn to the hypotenuse to solve problems.
• Use the Side-Splitter Theorem and the Triangle Midsegment Theorem to find lengths of sides and segments of triangles.
• Use the Triangle Angle-Bisector Theorem to find lengths of sides and segments of triangles.

Academic Vocabulary

• center of dilation
• geometric mean
• similarity transformation

Louisiana Student Standards for Mathematics (LSSM)

G-CO.A.2 Represent transformations in the plane using, e.g., transparencies, tracing paper, or geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

G-CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

G-SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor.

G-SRT.A.1a A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

G-SRT.A.1b The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

G-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

G-C.A.1 Prove that all circles are similar.

G-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

G-SRT.B.4 Prove and apply theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity; SAS similarity criteria, SSS similarity criteria, AA similarity criteria.

G-CO.C.10 Prove and apply theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Topic 8
Right Triangles and Trigonometry

Topic 8 begins by applying properties of similar right triangles to understand the Pythagorean Theorem, relationships in special right triangles, and trigonometric ratios. Students then extend their understanding of trigonometric ratios to include the Law of Sines and Law of Cosines. Finally, students apply what they have learned to various contextual problems.

The Student Will Be Able To

• Prove the Pythagorean Theorem using similar right triangles.
• Understand and apply the relationships between side lengths in 45°-45°-90° and 30°-60°-90° triangles.
• Define and calculate sine, cosine, and tangent ratios.
• Use trigonometric ratios to solve problems.
• Distinguish between angles of elevation and depression.
• Use trigonometric ratios and the Pythagorean Theorem to solve problems including finding the area of a triangle.

Academic Vocabulary

• angle of depression
• angle of elevation
• cosine
• Law of Cosines
• Law of Sines
• Pythagorean triple
• sine
• tangent
• trigonometric ratios

Louisiana Student Standards for Mathematics (LSSM)

G-SRT.B.4 Prove and apply theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity; SAS similarity criteria, SSS similarity criteria, AA similarity criteria.

G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

G-SRT.C.6 Understand that by similarity, side ratios in right triangles, including special right triangles (30-60- 90 and 45-45-90), are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

G-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.

Topic 9
Coordinate Geometry

Topic 9 examines several aspects of coordinate geometry. It begins by analyzing figures on the coordinate plane using slope, midpoint, and distance. Next, students examine coordinate proofs, using coordinate geometry to prove properties of figures. Finally, circles and parabolas on the coordinate plane are considered. Students develop equations of circles and parabolas and use them to solve problems.

The Student Will Be Able To

• Use coordinate geometry to classify triangles and quadrilaterals on the coordinate plane.
• Solve problems involving triangles and polygons on the coordinate plane.
• Plan and use coordinate proofs to solve geometric problems.
• Justify theorems using algebra and the coordinate plane.
• Write the equation for a circle given the graph of the circle or given the center and radius of the circle.

Academic Vocabulary
no new academic vocabulary

Louisiana Student Standards for Mathematics (LSSM)

G-GPE.B.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

G-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

G-GPE.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

G-CO.C.10 Prove and apply theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

G-GPE.A.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Topic 10
Circles

Topic 10 begins with an examination of arc length, sector area, and segment area, and an introduction to radians as a unit of angle measure. Students then examine properties of tangents, chords, and inscribed angles. Finally, students learn about the properties of angles, arcs, and segments lengths that are formed when two lines intersect inside or outside a circle.

The Student Will Be Able To

• Calculate the length of an arc when the central angle is given in degrees or radians.
• Calculate the area of sectors and segments of circles.
• Identify lines that are tangent to a circle using angle measures and segment lengths.
• Solve problems involving tangent lines.
• Prove and apply relationships between chords, arcs, and central angles.
• Find lengths of chords given the distance from the center of the circle and use this information to solve problems.
• Identify and apply relationships between the measures of inscribed angles, arcs, and central angles.
• Identify and apply the relationships between an angle formed by a chord and a tangent to its intercepted arc.
• Recognize and apply angle relationships formed by secants and tangents intersecting inside and outside a circle.
• Recognize and apply segment length relationships formed by secants and tangents intersecting inside and outside a circle.

Academic Vocabulary

• arc length
• central angle
• chord
• inscribed angle
• intercepted arc
• major arc
• minor arc
• point of tangency
• radian
• secant
• sector of a circle
• segment of a circle
• tangent to a circle

Louisiana Student Standards for Mathematics (LSSM)

G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

G-C.B.5 Use similarity to determine that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

G-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords, including the following: the relationship that exists between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; and a radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Topic 11
Two- and Three-Dimensional Models

Topic 11 opens by considering the relationship between the numbers of faces, vertices, and edges in polyhedrons, examining cross sections, and determining the three-dimensional figure formed by rotating a two-dimensional figure. Students then consider the volume of oblique solids by comparing the cross sections of oblique solids to corresponding right solids. Throughout the topic, students apply the volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.

The Student Will Be Able To

• Understand how the volume formulas for prisms and cylinders apply to oblique prisms and cylinders.
• Model three-dimensional figures as cylinders and prisms to solve problems.
• Understand how the volume formulas for pyramids and cones apply to oblique pyramids and cones.
• Model three-dimensional figures as pyramids and cones to solve problems.
• Use Cavalieri’s Principle to show how the volume of a hemisphere is related to the volume of a cone and a cylinder.
• Calculate volumes and surface areas of spheres and composite figures.

Academic Vocabulary

• Cavalieri’s Principle
• hemisphere
• oblique cylinder
• oblique prism

Louisiana Student Standards for Mathematics (LSSM)

G-GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

G-GMD.A.1 Give an informal argument, e.g., dissection arguments, Cavalieri’s principle, and informal limit arguments, for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

G-GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

G-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

G-MG.A.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

G-GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Topic 12
Probability

Topic 12 focuses on extending students’ previous knowledge of ratios and basic probability to the probability of multiple events, combinatorics, probability distributions, and expected value. Students understand and graph probability distributions. Students learn methods for using probability models and expected value to make decisions.

The Student Will Be Able To

• Explain independence of events in everyday language and everyday situations.
• Determine the probability of the union of two events (A or B) and the intersection of two independent events (A and B).
• Calculate the conditional probability of A given B as the fraction of outcomes in B that also belong to A.
• Interpret independence of events in terms of conditional probability.
• Use a two-way frequency table to decide of events are independent and to approximate conditional probabilities.
• Calculate the number of permutations and combinations in mathematical and real-world contexts.
• Use permutations and combinations to compute probabilities of compound events and solve problems.
• Develop a probability distribution based on theoretical probabilities or empirical data.
• Graph probability distributions.
• Calculate probability in binomial experiments.
• Calculate the expected value in situations involving chance.
• Weigh the possible outcomes of a decision by comparing expected values and finding expected payoffs.
• Analyze decisions and evaluate fairness using probability concepts.

Academic Vocabulary

• binomial distribution
• binomial experiment
• binomial probability
• combination
• complement
• conditional probability
• dependent events
• expected value
• factorial
• Fundamental Counting Principle
• independent events
• mutually exclusive
• permutation
• probability distribution
• uniform probability distribution

Louisiana Student Standards for Mathematics (LSSM)

S-CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

S-CP.A.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

S-CP.A.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

S-CP.A.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

S-CP.A.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

S-CP.B.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

Topic 1
Linear Functions and Systems

Topic 1 focuses on extending students’ previous knowledge of functions. Students identify the key features of functions and understand how to interpret graphs of functions. Students learn methods for solving equations and inequalities and systems of linear equations and inequalities by using graphing, tables, and matrices.

The Student Will Be Able To

• Identify key features of a graph of a function, including the intercepts, positive and negative intervals, and areas where the function is increasing or decreasing.
• Solve real-world problems and interpret them in terms of their context.
• Write the domain and range of functions using set-builder and interval notations.
• Graph a transformed function by identifying the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f (x + k) for specific values of k.
• Write an equation of a transformed function.
• Relate the domain of a function to its graph and the real-world situation it describes.
• Identify the common difference in an arithmetic sequence.
• Write arithmetic sequences both recursively and with an explicit formula.
• Construct arithmetic sequences, given a graph, a description of a relationship, or two input-output pairs.
• Use graphs, tables, and graphing technology to find or approximate solutions to equations and inequalities.
• Find approximate solutions to equations and inequalities by setting each expression equal to y and graphing.
• Solve linear and nonlinear systems graphically and algebraically.
• Identify regions that satisfy systems of inequalities.
• Represent a system of linear equations as a matrix and solve using row operations.
• Rewrite a matrix in reduced row echelon form.
• Represent constraints as a system of linear equations, use row operations on matrices to solve the system, and interpret the solution in terms of the original constraints.

Academic Vocabulary

• arithmetic
• sequence
• arithmetic series
• augmented matrix
• average rate of
• change
• coefficient matrix
• common difference
• compression
• dimensions
• explicit definition
• inconsistent system
• interval notation
• matrix
• maximum
• minimum
• piecewise-defined
• function
• recursive definition
• reduced row
• echelon form
• reflection
• sequence
• series
• set-builder notation
• sigma notation
• solution of a system
• of linear equations
• step function
• stretch
• system of linear
• equations
• system of linear
• inequalities
• transformation
• translation
• zero of a function

Louisiana Student Standards for Mathematics (LSSM)

F-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F-IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

F-IF.C.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F-BF.A.1 Write a function that describes a relationship between two quantities.

F-BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation from a context.

F-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

A-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

A-REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), limited to systems of at most three equations and three variables. With graphic solutions, systems are limited to two variables.

Topic 2
Quadratic Functions and Equations

Topic 2 focuses on extending previous understanding of quadratic functions. Students identify different forms of quadratic functions and their key features. Students explore complex numbers and solve problems with complex numbers. Students learn different methods for solving quadratic equations.

The Student Will Be Able To

• Write quadratic functions in vertex form to represent relationships between variables as shown in their graphs.
• Graph functions on coordinate axes using their key features.
• Interpret key features of the graph of a quadratic function.
• Write quadratic functions written in standard form.
• Identify key features of quadratic functions and graph a quadratic function written in standard form.
• Write a quadratic equation in factored form and use it to identify the zeros of the function it defines.
• Determine the intervals over which a quadratic function is positive or negative.
• Add, subtract, and multiply complex numbers using the properties of operations and the relation i²= −1.
• Extend understanding of the real number system to use complex numbers to represent numbers that are not on the real number line.
• Solve a quadratic trinomial by completing the square to transform a quadratic equation into a perfect square trinomial.
• Use completing the square to write a quadratic equation in vertex form.
• Use the Quadratic Formula to solve quadratic equations that have complex solutions.

Academic Vocabulary

• completing the square
• complex conjugates
• complex number
• discriminant
• imaginary number
• imaginary unit i
• parabola
• Quadratic Formula
• quadratic function
• standard form of a quadratic function
• vertex form of a quadratic function
• Zero Product Property

Louisiana Student Standards for Mathematics (LSSM)

F-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

S-ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

S-ID.B.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize exponential models.

A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²).

A-APR.B.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

N-CN.A.1 Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real.

N-CN.A.2 Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

N-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.

F-BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation from a context.

A-REI.B.4 Solve quadratic equations in one variable.

A-REI.B.4b Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

A-REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = - 3x and the circle x2 + y2 = 3.

A-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Topic 3
Polynomial Functions

Topic 3 focuses on extending students’ previous knowledge of polynomials. Students identify the key features of polynomial functions and interpret graphs of polynomial functions. They learn methods to add, subtract, multiply, and divide polynomial expressions. They use polynomial identities to multiply and factor polynomial expressions, use multiple theorems as tools to understand the roots of polynomial functions, and transform graphs from cubic or quartic parent functions.

The Student Will Be Able To

• Sketch a graph of polynomial functions and show the key features of the graph.
• Predict the end behavior of polynomial functions by interpreting the leading coefficients and degrees.
• Sketch graphs showing key features, given a verbal description.
• Add, subtract, and multiply polynomials and understand that polynomials are closed under these operations.
• Compare a polynomial function represented algebraically.
• Prove polynomial identities and use them to multiply and factor polynomials.
• Expand binomials using the Binomial Theorem and coefficients determined by Pascal’s Triangle.
• Divide polynomial expressions using long division.
• Use synthetic division to rewrite rational expressions.
• Solve for the zeros of a function by factoring or using synthetic division.
• Sketch a graph of a polynomial function using its zeros.
• Extend polynomial theorems and identities to find the real and complex solutions of a polynomial equation.
• Write polynomial functions using conjugates.
• Determine whether functions are even or odd from their graphs and algebraic equations.
• Identify the effect on the graphs of cubic and quartic functions of replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k).
• Given a graph, determine the equation as it is related to its parent cubic function or quartic function.

Academic Vocabulary

• Binomial Theorem
• degree of a polynomial
• end behavior
• even function
• identity
• leading coefficient
• multiplicity of a zero
• odd function
• Pascal’s triangle
• polynomial function
• relative maximum
• relative minimum
• Rational Root Theorem
• Remainder Theorem
• standard form of a polynomial
• synthetic division
• turning point

 
Louisiana Student Standards for Mathematics (LSSM)

F-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F-IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F-IF.C.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F-IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, determine which has the larger maximum.

F-BF.A.1b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²).

A-APR.B.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

A-APR.B.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Topic 4
Rational Functions

Topic 4 focuses on extending students’ previous knowledge of polynomial functions to rational functions. Students identify the key features of the graphs of rational functions. Students learn methods of solving rational equations.

The Student Will Be Able To

• Use inverse variation to write and graph the reciprocal function.
• Identify the effect of transformations on the graph of the reciprocal function and define the effects of h and k on the function f(x) = f(x-h)+k.
• Graph rational functions by identifying asymptotes and end behavior.
• Rewrite simple rational expressions in different forms using long division.
• Use the structure of rational expressions to rewrite simple rational expressions in different forms.
• Apply previous understanding that rational expressions form a system analogous to the system of rational numbers and use that understanding to multiply and divide rational expressions.
• Apply previous understanding that rational expressions form a system analogous to the system of rational numbers and use that understanding to add and subtract rational expressions.
• Solve one-variable rational equations.
• Identify extraneous solutions to rational equations and give examples of how they arise.

Academic Vocabulary

• asymptote
• compound fraction
• constant of variation
• extraneous solution
• inverse variation
• rational equation
• rational expression
• rational function
• reciprocal function

Louisiana Student Standards for Mathematics (LSSM)

F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

A-APR.D.6 Rewrite simple rational expressions in different forms; write a(x) /b(x) in the form q(x) +r(x) /b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

A-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²).

A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

A-REI.A.1 Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Topic 5
Rational Exponents and Radical Functions

Topic 5 extends knowledge of radical functions. Students understand properties of rational exponents and radicals. They learn methods to graph radical functions, solve radical equations, and combine functions. Students identify inverses of functions and learn to write the equations of inverse functions.

The Student Will Be Able To

• Use properties of exponents to rewrite expressions involving radicals in terms of rational exponents.
• Find all real nth roots of a number.
• Evaluate expressions with rational exponents.
• Use nth roots to solve equations by rewriting expressions using the properties of exponents.
• Use the properties of exponents and radicals to identify ways to generate radical expressions.
• Interpret radical expressions that represent a quantity in terms of its context.
• Graph radical functions, including square root and cube root functions.
• Identify the effect of transformations on the key features of the graphs of radical functions.
• Solve radical equations in one variable.
• Explain how extraneous solutions may arise when solving radical equations.
• Solve radical inequalities and apply the solution within a real-world context.
• Combine functions by addition, subtraction, multiplication, or division, and identify the domain of the result.
• Represent the composition of two or more functions algebraically, specifying the order in which the functions are applied and describing the domain of the composite function.
• Represent the inverse of a function algebraically, graphically or in a table.
• Write an equation for the inverse of a function and determine if the inverse is also a function.
• Use composition of functions to verify that one function is the inverse of another.

Academic Vocabulary

• composite function
• composition of functions
• extraneous solution
• index
• inverse function
• inverse relation
• like radicals
• nth root
• radical function
• radical symbol
• radicand
• reduced radical form

Louisiana Student Standards for Mathematics (LSSM)

N-RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.

N-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

A-REI.A.1 Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²).

F-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F-IF.C.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

A-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

F-BF.A.1b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

F-BF.B.4 Find inverse functions.

F-BF.B.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x-1) for x ≠1.

Topic 6
Exponential and Logarithmic Functions

Topic 6 focuses on extending previous understanding of exponential functions. Students identify the key features of exponential functions. Students understand logarithms and their properties. Students learn how to solve exponential and logarithmic equations.

The Student Will Be Able To

• Represent the inverse of a function algebraically, graphically or in a table.
• Write an equation for the inverse of a function and determine if the inverse is also a function.
• Use composition of functions to verify that one function is the inverse of another.
• Rewrite exponential functions to identify rates.
• Interpret the parameters of an exponential function within the context of compound interest problems.
• Construct exponential models given two points or by using regression.
• Understand the inverse relationship between exponents and logarithms.
• Use logarithms to solve exponential models.
• Evaluate logarithms using technology.
• Graph logarithmic functions and interpret their key features.
• Write and interpret the inverses of exponential and logarithmic functions.
• Use Properties of Logarithms to rewrite logarithmic expressions.
• Use the Change of Base Formula to evaluate logarithmic expressions and solve equations.
• Use logarithms to express the solutions to exponential models.
• Solve exponential and logarithmic equations.
• Construct a geometric sequence given a graph, table, or description of a relationship.
• Translate between geometric sequences written in recursive and explicit forms.
• Use the formula for the sum of a finite geometric series to solve problems.

Academic Vocabulary

• Change of Base Formula
• common logarithm
• compound interest
• continuously compounded interest
• decay factor
• exponential equation
• exponential function
• exponential decay function
• exponential growth function
• growth factor
• logarithm
• logarithmic equation
• logarithmic function
• natural base e
• natural logarithm

Louisiana Student Standards for Mathematics (LSSM)

F-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F-IF.C.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F-IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, determine which has the larger maximum.

F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

F-LE.A.2 Given a graph, a description of a relationship, or two input-output pairs (include reading these from a table), construct linear and exponential functions, including arithmetic and geometric sequences to solve multistep problems.

F-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context.

A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²).

A-SSE.B.3c Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

F-IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F-IF.C.8b Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)ᵗ, y = (0.97)ᵗ, y = (1.01)12ᵗ, y = (1.2)^(t/10), and classify them as representing exponential growth or decay.

S-ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

S-ID.B.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize exponential models.

F-BF.B.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x-1) for x ≠ 1.

F-LE.A.4 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

F-IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A-REI.A.1 Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

A-SSE.B.4 Apply the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.

F-BF.A.1 Write a function that describes a relationship between two quantities.

F-BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation from a context.

F-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Topic 7
Trigonometric Functions

Topic 7 focuses on extending knowledge of functions to trigonometric functions. Students learn the trigonometric ratios and use them to find missing side lengths of triangles. They learn to graph trigonometric functions and identify the key features of the graphs. Students learn methods to solve problems using trigonometric functions.

The Student Will Be Able To

• Use special triangles to determine trigonometric ratios geometrically.
• Use trigonometric functions and the Pythagorean Theorem to find missing side lengths.
• Identify and explain trigonometric identities.
• Find the measures of an angle in standard position and its reference angle.
• Use radian measure on the unit circle to find arc length.
• Convert between degrees and radians.
• Use reference angles and triangles to evaluate trigonometric functions and their reciprocal functions.
• Use the Pythagorean Identity to find the sine, cosine, and quadrant of an angle.
• Graph and identify the key features of sine and cosine functions.
• Find and interpret the average rate of change of a periodic function over a specified interval.
• Compare key features of different periodic functions.
• Describe and compare key features of the graphs of trigonometric functions.
• Graph functions of the form f(x)= atan bx and relate the graph of a function to the graph of the parent function.
• Identify how changing the parameters of the sine or cosine function affects the graph of the function.
• Use trigonometric functions to model situations with specified amplitude, frequency, and midline.

Academic Vocabulary

• amplitude
• cofunction
• cofunction identities
• cosecant
• cosine
• cotangent
• coterminal angles
• frequency
• initial side
• midline
• period
• periodic function
• phase shift
• radian
• radian measure
• reciprocal trigonometric functions
• reference angle
• reference triangle
• secant
• sine
• standard position
• tangent
• terminal side
• unit circle

Louisiana Student Standards for Mathematics (LSSM)

F-TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

F-TF.C.8 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

F-TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

F-IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F-IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, determine which has the larger maximum.

F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

F-IF.C.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F-TF.B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Topic 8
Trigonometric Equations and Identities

Topic 8 focuses on extending previous knowledge of trigonometric functions to trigonometric equations and identities. Students learn to use trigonometric identities to rewrite and solve trigonometric equations. They learn about the complex plane and how to write the polar form of complex numbers.

The Student Will Be Able To

• Define and evaluate inverse trigonometric functions.
• Solve trigonometric equations using inverse functions, and interpret the solutions within a modeling context.
• Derive the Law of Sines and the Law of Cosines.
• Use the Law of Cosines and the Law of Sines to find unknown angles and sides of non-right triangles.
• Verify trigonometric identities using the unit circle.
• Use trigonometric identities to rewrite expressions.
• Prove sum and difference formulas for sine, cosine, and tangent, and use them to solve real-world problems.
• Represent complex numbers and their relationships on the complex plane.
• Find the midpoint of a segment on the complex plane.
• Calculate the distance between numbers in the complex plane using the modulus of the difference.
• Use the complex plane to represent addition and subtraction of complex numbers geometrically.
• Represent a complex number in polar form and convert between rectangular and polar forms.
• Verify and use the sum and difference formulas.
• Use polar form to calculate products and powers.

Academic Vocabulary

• argument
• complex plane
• imaginary axis
• Law of Cosines
• Law of Sines
• modulus of a complex number
• polar form of a complex number
• real axis
• trigonometric identity

Louisiana Student Standards for Mathematics (LSSM)

All standards in this Topic are not included in the LSSM, meaning they are extension or enrichment standards.

Topic 9
Conic Sections

Topic 9 focuses on extending students’ previous knowledge of second-degree equations and their graphs. Students learn methods for deriving the equations of conic sections. Students understand the key features of the graphs of conic sections. Students learn methods to classify second-degree equations.

The Student Will Be Able To

• Derive the equation of a parabola.
• Relate a parabola’s focal length to its equation.
• Rewrite an expression by completing the square and then use it to find the focus and directrix of a parabola.
• Use the center, the radius, and the Pythagorean Theorem to derive the equation of a circle.
• Write and graph the equation of a circle and use it to model a real-world situation.
• Find the center and radius of a circle by completing the square.
• Solve a linear-quadratic system algebraically and verify by graphing.
• Derive the equation of an ellipse.
• Write and graph the equation of an ellipse and use an ellipse to model a real-world situation.
• Graph a transformed ellipse by completing the square to rewrite the equation in an equivalent form.
• Use the foci and the Distance Formula to derive an equation of a hyperbola.
• Write and graph the equation of a hyperbola and use it to model a real-world situation.
• Determine which conic section is represented by a second-degree equation.

Academic Vocabulary

• center of an ellipse
• center of a hyperbola
• conic section
• conjugate axis
• co-vertices
• directrix
• ellipse
• focal length
• foci of an ellipse
• foci of a hyperbola
• focus of a parabola
• general form of a
• second-degree equation
• hyperbola
• major axis
• minor axis
• parabola
• standard form of the
• equation of a circle
• standard form of the
• equation of an ellipse
• standard form of the
• equation of a hyperbola
• transverse axis
• vertices of an ellipse

Louisiana Student Standards for Mathematics (LSSM)

A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²).

A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A-REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = - 3x and the circle x² + y² = 3.

Topic 10
Matrices

Topic 10 focuses on extending matrices. Students understand that matrices use rows and columns to organize and represent data. Students learn methods to add, subtract, and multiply matrices and to solve systems of linear equations with matrices. Students understand that vectors can be used to determine the position of one point in space relative to another and to find the area of triangles and parallelograms.

The Student Will Be Able To

• Use a matrix to represent data.
• Apply scalar multiplication to produce a new matrix.
• Add and subtract matrices by adding and subtracting the corresponding elements.
• Translate and dilate figures using matrices.
• Multiply two matrices when the number of columns in the first matrix is equal to the number of rows in the second matrix.
• Understand the identity matrix and recognize that it is similar to the role of 1 in multiplication of real numbers.
• Use vectors to represent quantities with both magnitude and direction.
• Add and subtract vectors graphically, algebraically, and by the Parallelogram Rule.
• Apply scalar multiplication to produce a new vector.
• Transform a vector using matrix multiplication.
• Determine if a matrix has an inverse, and if it does, find it.
• Use the absolute value of the determinant of a matrix to find the areas of triangles and parallelograms.
• Represent a system of equations, in two or three variables, as a single matrix equation.
• Find the inverse of a matrix and use it to solve a system of linear equations.

Academic Vocabulary

• component form
• constant matrix
• determinant of a 2×2matrix
• direction
• equal matrices
• identity matrix
• initial point
• inverse matrix
• magnitude
• scalar
• scalar multiplication
• square matrix
• terminal point
• variable matrix
• vector
• zero matrix

Louisiana Student Standards for Mathematics (LSSM)

All standards in this Topic are not included in the LSSM, meaning they are extension or enrichment standards.

Topic 11
Data Analysis and Statistics

Topic 11 focuses on the comparison of statistical data. Students identify statistical questions and types of statistical studies. They understand that data distributions can be normal and skewed and sample statistics can be used to estimate population parameters. Students learn methods to explain where data values fall within a population and use statistical data to compare groups and formulate and test a hypothesis.

The Student Will Be Able To

• Define and recognize a statistical question.
• Define and identify the type of statistical variable that is represented by a question or the data represented on a graph.
• Distinguish between quantities such as population/sample and parameter/statistic for the purpose of descriptive modeling.
• Identify different types of statistical studies.
• Understand principles of selecting subjects for a valid study.
• Find measures of center and spread, such as median, mean, interquartile range, and standard deviation.
• Compare data sets using statistical measures that are appropriate for the distribution of the data.
• Fit a normal distribution to data.
• Compare and evaluate data values using z-scores.
• Use technology to calculate the area under the standard normal distribution curve.
• Evaluate reports by estimating population parameters.
• Use multiple samples to make an inference about a population.
• Calculate the margin of error for quantitative or categorical data.
• Formulate two hypotheses for a statistical question and test using statistics to draw a conclusion.
• Use graphs and simulation to determine whether differences between parameters are significant.
• Use data from a randomized experiment to evaluate a report.

Academic Vocabulary

• alternative hypothesis
• bias
• control group
• experiment
• experimental group
• margin of error
• normal distribution
• null hypothesis
• observational study
• parameter
• random sample
• sample survey
• sampling distribution
• standard deviation
• statistic
• z-score

Louisiana Student Standards for Mathematics (LSSM)

N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling.

S-IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

S-IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

S-IC.B.6 Evaluate reports based on data.

S-ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

S-IC.A.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

S-IC.B.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

S-IC.B.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Topic 12
Probability

Topic 12 focuses on extending students’ previous knowledge of ratios and basic probability to the probability of multiple events, combinatorics, probability distributions, and expected value. Students understand and graph probability distributions. Students learn methods for using probability models and expected value to make decisions

The Student Will Be Able To

• Explain independence of events in everyday language and everyday situations.
• Determine the probability of the union of two events (A or B) and the intersection of two independent events (A and B).
• Calculate the conditional probability of A given B as the fraction of outcomes in B that also belong to A.
• Interpret independence of events in terms of conditional probability.
• Use a two-way frequency table to decide of events are independent and to approximate conditional probabilities.
• Calculate the number of permutations and combinations in mathematical and real-world contexts.
• Use permutations and combinations to compute probabilities of compound events and solve problems.
• Develop a probability distribution based on theoretical probabilities or empirical data.
• Graph probability distributions.
• Calculate probability in binomial experiments.
• Calculate the expected value in situations involving chance.
• Weigh the possible outcomes of a decision by comparing expected values and finding expected payoffs.
• Analyze decisions and evaluate fairness using probability concepts.

Academic Vocabulary

•  binomial distribution
• binomial experiment
• binomial probability
• combination
• complement
• conditional probability
• dependent events
• expected value
• factorial
• Fundamental Counting Principle
• independent events
• mutually exclusive
• permutation
• probability distribution
• uniform probability distribution

Louisiana Student Standards for Mathematics (LSSM)

All standards in this Topic are not included in the LSSM, meaning they are extension or enrichment standards.

 

Skills Unit 1

Unit Length: 13 instructional days
Description: This unit lays the groundwork for reading and writing. Students build awareness of environmental noises, of words within sentences, and of sounds within words. They also learn several writing strokes used to create letters.
ELA Standards:
RF.K.1.a: Follow words from left to right, top to bottom, and page by page.
RF.K.2: Demonstrate understanding of spoken words, syllables, and sounds.
Big Ideas:

• Environmental noises and words in sentences make different sounds.
• Speech is made up of words.
• Position words describe a relative location.
• Handwriting strokes are made by holding a writing utensil and moving it across paper.

Skills Unit 2

Unit Length: 13 instructional days
Description: Students learn how to blend syllables together to form multi-syllabic words. They also learn how to orally produce two- and three-sound words by blending sounds.
ELA Standards:
RF.K.1.a: Follow words from left to right, top to bottom, and page by page.
RF.K.2.b: Count, recognize, blend, and segment syllables in spoken words.
Big Ideas:

• Words are made of sound parts (syllables, phonemes).
• Phonemes (sounds) are blended to form words.
• Position words describe a relative location.
• Handwriting strokes are made by holding a writing utensil and moving it across paper.

Skills Unit 3

Unit Length: 16 instructional days
Description: Students are introduced to eight sounds and they practice blending these sounds into words. They also learn how to form the letters that make these sounds.  
ELA Standards:
L.K.1.a: Print many upper- and lowercase letters.
L.K.2.c: Write a letter or letters for most consonant and short vowel sounds.
Big Ideas:

• Students are introduced to high-frequency words in the Picture Reader.
• Sounds in words are represented with symbols.
• Sounds pictures can be blended to read words.
• Sound pictures are used to spell words.
   

Skills Unit 4

Unit Length: 19 instructional days
Description: This unit introduces students to eight new sounds. Through oral language games, chaining exercise, and shared reading, students practice blending these sounds into words. Students also practice previously learned letter-sound correspondences.
ELA Standards:
RF.K.2.d: Isolate and pronounce the initial, medial vowel, and final sounds in three-phoneme words.
RF.K.3.a: Demonstrate basic knowledge of one-to-one letter-sound correspondences by producing the primary or many of the most frequent sounds for each consonant.
L.K.1.a: Print many upper- and lowercase letters.
L.K.2.c: Write a letter or letters for most consonant and short vowel sounds.
Big Ideas:

• Students are introduced to the decodable Big Book, Pet Fun.
• Print concepts and fluency are reinforced using the Big Book.
• Sounds/symbols can be blended to read words.
• Symbols are used to spell words.
• Words make up phrases and sentences.
• Words are read from left to right.
• Words in a book tell a story.

Skills Unit 5

Unit Length: 19 instructional days
Description: This unit introduces students to eight new sounds, including a spelling alternative for /k/. Through oral language games, chaining exercises, and shared reading, students practice blending these sounds into words. Students also practice previously learned letter-sound correspondences.
ELA Standards:
RF.K.3.a: Demonstrate basic knowledge of one-to-one letter-sound correspondences by producing the primary or many of the most frequent sounds for each consonant.
RF.K.3.b: Associate the long and short sounds with common spellings for the five major vowels.
RF.K.3.c: Read common high frequency words by sight.

RF.K.3.d: Distinguish between similarly spelled words by identifying the sounds of the letters that differ.
L.K.1.a: Print many upper- and lowercase letters.
L.K.2.d: Spell simple words phonetically, drawing on knowledge of sound-letter relationships.
Big Ideas:

• The decodable Big Book Ox and Man is used to reinforce print concepts, model fluency, and provides practice reading complete sentences.
• Words are spelled with sound pictures (letters).
• There are uppercase and lowercase sound pictures.
• Words make up phrases and sentences.
• Sentences begin with a capital letter (sound picture) and end with a period.

Skills Unit 6

Unit Length: 20 instructional days
Description: Students automatize the letter-sound correspondences and blending procedures they learned so far. They are introduced to consonant clusters, letter names, rhyming words, and reading text independently.
ELA Standards:
RL.K.1: With prompting and support, ask and answer questions about key details in a text.
RF.K.2.a: Recognize and produce rhyming words.
RF.K.2.c: Blend and segment onsets and rimes of single-syllable spoken words.
RF.K.3.c: Read common high-frequency words by sight.
RF.K.4: Read emergent-reader texts with purpose and understanding.
Big Ideas:

• Students use their own decodable Reader to practice reading previously learned sound
• spellings, punctuation, and to reinforce print concepts.
• Sound pictures are called letters, and each one has a name.
• Letters make up the alphabet and are arranged in alphabetical order
• Sentences begin with a capital letter (sound picture) and end with a period.

Skills Unit 7

Unit Length: 20 instructional days
Description: This unit introduced students to digraphs. Students develop automaticity in blending and segmenting these sounds through phonemic awareness activities, chaining exercises, practice activities, and partner and independent reading.
ELA Standards:
RL.K.1: With prompting and support, ask and answer questions about key details in a text.
RL.K.7: With prompting and support, make connections between the illustrations in the story and the text.
RF.K.2.b: Count, pronounce, blend, and segment syllables in spoken words.
RF.K.3.c: Read common high-frequency words by sight.
RF.K.4: Read emergent-reader texts with purpose and understanding.
Big Ideas:

• Students use the decodable Reader Seth to practice fluency and print concepts.
• Digraphs are two letters that make a single sound.
• Consonant clusters are blended so two individual sounds are heard.

Skills Unit 8

Unit Length: 22 instructional days
Description: This unit introduces students to double-letter spellings for consonant sounds, as well as four high-frequency Tricky Words. Results from this unit’s student performance task assessment inform which students are ready for the next unit and those who need targeted support with previously taught skills.
ELA Standards:
RL.K.3: With prompting and support, identify characters, settings, and major events in a story.
RF.K.1.d: Recognize and name all upper- and lowercase letters of the alphabet.
RF.K.3.b: Associate the long and short sounds with common spellings for the five major vowels.
RF.K.3.c: Read common high-frequency words by sight.
RF.K.4: Read emergent-reader texts with purpose and understanding.
Big Ideas:

• The decodable Reader, Sam, is about a boy and a series of events including fishing, swimming, and going on a class trip to the seaside.
• Double-letter spellings most frequently follow a short vowel sound.
• Sentences have different ending marks, depending on the type of sentence.
• Apostrophes show possession or are used in contractions.

Skills Unit 9

Unit Length: 28 instructional days
Description: In Unit 9, students practice writing uppercase letters and learn fifteen new Tricky Words. This unit also introduces activity pages with comprehension questions related to the Student Reader. Students will be assessed on uppercase letter identification and formation, punctuation and sentence reading.
ELA Standards:
RL.K.7: With prompting and support, make connections between the illustrations in the story and the text.
W.K.3: Use a combination of drawing, dictating, and writing to narrate a single event or several loosely linked events, tell about the events in the order in which they occurred, and provide a reaction to what happened.
L.K.1.a: Print many upper- and lowercase letters.
L.K.2.c: Write a letter or letters for most consonant and short-vowel sounds.
RF.K.4: Read emergent-reader texts with purpose and understanding.
Big Ideas:

• The chapters in the decodable Reader focus on a brother and sister and their adventures.
• Letter names and the sounds they make
• Uppercase letter formation
• Sentences have different ending marks, depending on the type of sentence.
• Answering questions about the story through discussions and in writing

 

Knowledge Domain 1: Nursery Rhymes and Fables

Unit Length: 18 instructional days
Description: This unit is an introduction to nursery rhymes and fables, including Mother Goose poems and Aesop’s fables. By listening to nursery rhymes and repeating or reciting them, students learn vocabulary and build phonemic awareness. Well-known fables introduce students to new vocabulary and prompt discussion of character, virtues, and behavior.
ELA Standards:
RL.K.2: With prompting and support, retell familiar stories, including key details.
RL.K.3: With prompting and support, identify characters, settings, and major events in a story.
RL.K.9: With prompting and support, compare and contrast the adventures and experiences of characters in familiar stories.
RF.K.2.a: Recognize and produce rhyming words.

Big Ideas:

• Nursery rhymes and fables have been favorites with children for generations.
• Traditional rhymes help students learn vocabulary and build phonemic awareness.
• Listening to and learning to recite nursery rhymes help students develop language awareness, leading to better readers and writers.

Knowledge Domain 2: The Five Senses

Unit Length: 12 instructional days
Description: Students explore how they learn about the world using their five senses. Students also hear inspirational stories about individuals who overcame significant challenges posed by disabilities related to sight and hearing. 
ELA Standards:
RI.K.2: With prompting and support, identify the main topic and retell key details of a text.
RI.K.3: With prompting and support, describe the connection between two individuals, events, ideas, or pieces of information in a text.
W.K.2: Use a combination of drawing, dictating, and writing to compose informative/explanatory texts in which they name what they are writing about and supply some information about the topic.

Big Ideas:

• Everything we know about the world comes through our five senses.
• Each sense uses a unique body part to take in information.
• Conducting observations and using language to describe those observations are key skills in the scientific process.

Knowledge Domain 3: Stories

Unit Length: 14 instructional days
Description: Students are introduced to classic stories as well as trickster tales and fiction from other cultures. Students develop an awareness of language and recurring themes in children’s literature.
ELA Standards:
RL.K.2: With prompting and support, retell familiar stories, including key details.
RL.K.3: With prompting and support, identify characters, settings, and major events in a story.
RL.K.9: With prompting and support, compare and contrast the adventures and experiences of characters in familiar stories.
W.K.1: Use a combination of drawing, dictating, and writing to compose opinion pieces in which they tell a reader the topic or name of the book they are writing about and state an opinion or preference about the topic or book.
W.K.3: Use a combination of drawing, dictating, and writing to narrate a single event or several loosely linked events, tell about the events in the order in which they occurred, and provide a reaction to what happened.
Big Ideas:

• Memorable characters in classic stories and trickster tales have delighted children for
• generations.
• Students gain an appreciation for fiction from other cultures.
• Students acquire and understanding of the elements of story including characters, plot, and setting.
• Recurring themes appear in classic and popular children’s literature.

Knowledge Domain 4: Plants

Unit Length: 17 instructional days
Description: Read-aloud texts introduce students to the parts of plants and how they grow. Students gain a basic knowledge of ecology and the interdependence of all living things.
ELA Standards:
RI.K.3: With prompting and support, describe the connection between two individuals, events, ideas, or pieces of information in a text.
RL.K.2: With prompting and support, retell familiar stories, including key details.
W.K.2: Use a combination of drawing, dictating, and writing to compose informative/explanatory texts in which they name what they are writing about and supply some information about the topic.
Big Ideas:

• Plants make up one kingdom in the scientific system that classifies different living things.
• There are over 350,000 species of plants on earth.
• Plants need basic things to stay alive and grow.
• Plants have life cycles, like other living things.
• All living things are interconnected.

Knowledge Domain 5: Farms

Unit Length: 15 instructional days
Description: Students learn about the importance of farms as a source of food and other products. They identify several farm animals and crops, and contrast how plants make their own food with how animals get their food by eating plants and other living things.
ELA Standards:
RI.K.2: With prompting and support, identify the main topic and retell key details of a text.
RL.K.2: With prompting and support, retell familiar stories, including key details.
W.K.2: Use a combination of drawing, dictating, and writing to compose informative/explanatory texts in which they name what they are writing about and supply some information about the topic.
Big Ideas:

• Students draw on information gained in the Plants domain to understand what plants and animals need to grow.
• Farms are an important source of food and other products people use.
• The classic story “The Little Red Hen” describes the seasonal rhythm of planting, growing, and harvesting.

Knowledge Domain 6: Native Americans

Unit Length: 15 instructional days
Description: Students are introduced to the broad concept that indigenous people lived on the continents of North and South America long before European explorers arrived. Students explore the distinctive cultures of three Native American groups, as well as how conditions in different geographical regions influence their ways of life.
ELA Standards:
RI.K.9: With prompting and support, identify similarities and differences between two texts on the same topic.
W.K.2: Use a combination of drawing, dictating, and writing to compose informative/explanatory texts in which they name what they are writing about and supply some information about the topic.

Big Ideas:

• Indigenous people lived on the North and South American continents long before European explorers visited and settled this area.
• There were many different tribes and each had their own way of life.
• Geographical locations influenced lifestyles and individual cultures of different tribes.
• The three tribes are the focus of the unit are Lakota Sioux, Wampanoag, and Lenape.

Knowledge Domain 7: Kings and Queens

Unit Length: 14 instructional days
Description: Students listen to read-aloud texts, both fiction and nonfiction, about kings, queens, and royal families. The selections build students’ understanding of responsibilities and customs associated with royalty throughout history.
ELA Standards:
RL.K.2: With prompting and support, retell familiar stories, including key details.
RL.K.3: With prompting and support, identify characters, settings, and major events in a story.
RL.K.7: With prompting and support, make connections between the illustrations in the story and the text.
RI.K.3: With prompting and support, describe the connection between two individuals, events, ideas, or pieces of information in a text.
W.K.3: Use a combination of drawing, dictating, and writing to narrate a single event or several loosely linked events, tell about the events in the order in which they occurred, and provide a reaction to what happened.

Big Ideas:

• Throughout history, royalty has played a major role in the governance of countries in the world.
• The responsibilities, lifestyles, and customs associated with royalty provide context for many classic and well-loved stories and rhymes.
• This unit provides background knowledge for later domains and builds knowledge for understanding different forms of government.

Knowledge Domain 8: Seasons and Weather

Unit Length: 15 instructional days
Description: An introduction to weather and the seasons. Students learn that regions of Earth experience different characteristic weather patterns throughout the year.  
ELA Standards:
RI.K.2: With prompting and support, identify the main topic and retell key details of a text.
RI.K.3: With prompting and support, describe the connection between two individuals, events, ideas, or pieces of information in a text.
W.K.2: Use a combination of drawing, dictating, and writing to compose informative/explanatory texts in which they name what they are writing about and supply some information about the topic.
Big Ideas:

• Different regions of the Earth experience different weather patterns throughout the year.
• Weather patterns in the year are called seasons: winter, spring, summer, and fall.
• Knowing about the weather is important to our daily lives and activities.

Knowledge Domain 9: Columbus and the Pilgrims

Unit Length: 15 instructional days
Description: Students are introduced to key figures, events, and ideas associated with two episodes in the founding of the United States of America-the first voyage of Columbus in 1492 and the arrival of the Pilgrims in 1620.
ELA Standards:
RI.K.2: With prompting and support, identify the main topic and retell key details of a text.
RI.K.3: With prompting and support, describe the connection between two individuals, events, ideas, or pieces of information in a text.
Big Ideas:

• The arrival of Columbus and, more than 100 years later, the Pilgrims in North America, are important events in the history of the United States.
• There are similarities and differences between the two voyages of Columbus and the Pilgrims, their motivations, and their interactions with Native Americans.

Knowledge Domain 10: Colonial Towns and Townspeople

Unit Length: 16 instructional days
Description: Students are introduced to the early history of the United States as they explore what daily life was like for people in colonial times.
ELA Standards:
RI.K.2: With prompting and support, identify the main topic and retell key details of a text.
RI.K.3: With prompting and support, describe the connection between two individuals, events, ideas, or pieces of information in a text.
W.K.2: Use a combination of drawing, dictating, and writing to compose informative/explanatory texts in which they name what they are writing about and supply some information about the topic.
W.K.3: Use a combination of drawing, dictating, and writing to narrate a single event or several loosely linked events, tell about the events in the order in which they occurred, and provide a reaction to what happened.
Big Ideas:

• Students draw on knowledge from Columbus and the Pilgrims as they learn more about America’s history during colonial times.
• The daily life of people during the colonial era are contrasted with students’ present-day experiences.
• The differences between living in a town versus living in the country are explored.

Knowledge Domain 11: Taking Care of the Earth

Unit Length: 18 instructional days
Description: Students are introduced to the importance of environmental awareness and conservation as they become familiar with the earth’s natural resources and how people’s actions affect the environment.
ELA Standards:
RI.K.2: With prompting and support, identify the main topic and retell key details of a text.
W.K.2: Use a combination of drawing, dictating, and writing to compose informative/explanatory texts in which they name what they are writing about and supply some information about the topic.
W.K.3: Use a combination of drawing, dictating, and writing to narrate a single event or several loosely linked events, tell about the events in the order in which they occurred, and provide a reaction to what happened.
Big Ideas:

• People’s actions affect the environment in which we live.
• Earth’s natural resources include land, water, and air.
• The best way to conserve Earth’s resources is to practice the three Rs of conservation—reduce, reuse, and recycle.

Skills Unit 1

Unit Length: 30 instructional days
Description: Unit 1 provides a review of the sounds and spellings from kindergarten. Students are introduced to Tricky Spellings (spellings that can be sounded out more than one way) and Tricky Words (words that cannot be sounded out using the letter-sound correspondences taught so far).
ELA Standards:
RL.1.1: Ask and answer questions about key details in a text.
RF.1.2: Demonstrate understanding of spoken words, syllables, and sounds.
RF.1.3.a: Know the spelling-sound correspondences for common consonant digraphs.
RF.1.3.b: Decode regularly spelled one-syllable words.
RF.1.4.a: Read on-level text with purpose and understanding.
L.1.2.d: Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words.  
Big Ideas:

• Students read the decodable reader Snap Shots to practice fluency.
• The stories (chapters) in the reader are told from Beth’s point of view. Beth is a young girl who travels to the United Kingdom to visit friends.
• Students answer comprehension questions orally and/or in writing after reading each story.

Skills Unit 2

Unit Length: 21 instructional days
Description: This unit introduces five vowel sounds and the most common spelling for each sound. Students learn to read and write words with separated digraphs. This unit also includes grammar lessons on nouns as well as practice with new Tricky Words.
ELA Standards:
RF.1.3.b: Decode regularly spelled one-syllable words.
RF.1.3.c: Know final –e and common vowel team conventions for representing long vowel sounds.
RF.1.4.a: Read on-level text with purpose and understanding.
RF.1.4.b: Read on-level text orally with accuracy, appropriate rate, and expression on successive readings.
L.1.1.b: Use common, proper, and possessive nouns.
L.1.2.d: Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words.  
Big Ideas:

• Students read the decodable Reader Gran to practice fluency.
• The stories follow the character Gran, a well-traveled grandmother, who visits her
• grandchildren, Josh and Jen.
• Students answer comprehension questions orally and/or in writing after reading each story.

Skills Unit 3

Unit Length: 21 instructional days
Description: Unit 3 introduces students to five vowel sounds and the most common spelling for each sound, five new Tricky Words, and the Tricky Spelling “oo”. Grammar exercises focus on identifying verbs and verb tense (regular present, past, and future). Students begin formal instruction in the writing process with a focus on narrative writing.
ELA Standards:
RF.1.3.b: Decode regularly spelled one-syllable words.
RF.1.4: Read with sufficient accuracy and fluency to support comprehension.
W.1.3: Write narratives in which they recount two or more appropriately sequenced events, include some details regarding what happened, use temporal words to signal event order, and provide some sense of closure.
L.1.1.j: Produce and expand complete simple and compound declarative, interrogative, imperative, and exclamatory sentences in response to prompts.
L.1.2.d: Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words.  
L.1.2.e: Spell untaught words phonetically, drawing on phonemic awareness and spelling conventions.
Big Ideas:

• Students read the decodable Reader Fables to practice fluency.
• The Reader has versions of famous fables, most of
• which are attributable to the ancient Greek storyteller Aesop.
• Fables are special types of stories that teach important lessons or morals.
• Fables often feature talking animals as main characters.
• Students answer comprehension questions orally and/or in writing after reading each story.

Skills Unit 4

Unit Length: 30 instructional days
Description: This unit introduces the most common spellings for r-controlled vowel sounds. Students learn the concept of a syllable and practice two-syllable words. Students are introduced to past-tense verb forms ending with –ed as they continue to work with nouns and verbs in phrases. They are introduced to adjectives and they practice descriptive writing.
ELA Standards:
RF.1.3.d: Use knowledge that every syllable must have a vowel sound to determine the number of syllables in a printed word.
RF.1.3.e: Decode two-syllable words following basic patterns by breaking the words into syllables.
RF.1.3.g: Recognize and read grade-appropriate spelled words.
W.1.2: Write informative/explanatory texts in which they name a topic, supply some facts about the topic, and provide some sense of closure.
L.1.1.e: Use verbs to convey a sense of past, present, and future.
L.1.2.d: Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words.  
Big Ideas:

• Students read the decodable Reader The Green Fern Zoo to practice fluency.
• The main character is fictional, but the information in the book is factual.
• Informational text features such as headings and a picture glossary are introduced.
• Students answer comprehension questions orally and/or in writing after reading each story.

Skills Unit 5

Unit Length: 23 instructional days
Description: Students begin learning spelling alternatives that make up the advanced code. They practice making nouns plural and changing spelling when adding suffixes. In grammar, students identify sentence types (statements, questions, and exclamations) and practice creating longer sentences. They plan, draft, and edit a letter in which they express their opinions to the main character of the Student Reader.
ELA Standards:
RF.1.3.f: Read words with inflectional endings.
W.1.1: Write opinion pieces in which they introduce the topic or name the book they are writing about, state an opinion, supply a reason for the opinion for the opinion, and provide some sense of closure.
L.1.1.c: Use singular and plural nouns with matching verbs in basic sentences.
L.1.1.j: Produce and expand complete simple and compound declarative, interrogative, imperative, and exclamatory sentences in response to prompts.
L.1.2.d: Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words.  
Big Ideas:

• Students read the decodable Reader Kate’s Book to practice fluency.
• The Reader tells the story of a girl named Kate who writes a book about her summer vacation. The premise is that students are reading the book that Kate wrote, which her grandmother also illustrated.
• Students answer comprehension questions orally and/or in writing after reading each story.

Skills Unit 6

Unit Length: 27 instructional days
Description: Students continue to work with several spelling alternatives for consonant sounds. Students review nouns and learn to match pronouns to the nouns to which they refer. They plan, draft, and edit a personal narrative.
ELA Standards:
RF.1.3.b: Decode regularly spelled one-syllable words.
RF.1.4: Read with sufficient accuracy and fluency to support comprehension.
W.1.3: Write narratives in which they recount two or more appropriately sequenced events, include some details regarding what happened, use temporal words to signal event order, and provide some sense of closure.
L.1.1.d: Use personal and possessive pronouns.
L.1.2.d: Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words.  
Big Ideas:

• Students read the decodable Reader Grace to practice fluency.
• The Reader is about a girl named Grace who lives on a farm in the Midwest. The stories take us through her daily life on a farm and in the country.
• Students answer comprehension questions orally and/or in writing after reading each story.

Skills Unit 7

Unit Length: 21 instructional days
Description: Students continue to learn the advanced code, focusing on spelling alternatives for vowel sounds. In addition, students learn about the use of conjunctions and commas as well as noun-verb agreement in sentences. Students practice the writing process by planning, drafting, and editing an informative/explanatory text.
ELA Standards:
RF.1.3.b: Decode regularly spelled one-syllable words.
RF.1.3.e: Decode two-syllable words following basic patterns by breaking the words into syllables.
RF.1.3.g: Recognize and read grade-appropriate irregularly spelled words.
W.1.2: Write informative/explanatory texts in which they name a topic, supply some facts about the topic, and provide some sense of closure.
L.1.1.c: Use singular and plural nouns with matching verbs in basic sentences.
L.1.1.g: Use frequently occurring conjunctions.
L.1.2.d: Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words.  
Big Ideas:

• The Reader focuses on a young girl, Kay, and her friend Martez, a Mexican-American boy. Kay, Martez, and Kay’s family go on a trip to Mexico.
• The text incorporates Grade 1 history and geography topics from the CKLA Knowledge strand.
• Students answer comprehension questions orally and/or in writing after reading each story.

 

 

Knowledge Domain 1: Fables and Stories

Unit Length: 19 instructional days
Description: In this unit, students are introduced to fables and stories that have delighted people for generations, including Aesop’s fables, a folktale of Anansi the Spider, and Beatrix Potter’s, The Tale of Peter Rabbit. Students increase their vocabulary and reading comprehension skills, learn valuable lessons about virtues and behavior, and become familiar with the key elements of a story.
ELA Standards:
RL.1.2a: Retell stories, including key details.
W.1.3: Write narratives in which they recount two or more appropriately sequenced events, include some details regarding what happened, use temporal words to signal event order, and provide some sense of closure.
Big Ideas:

• Fables and stories have delighted generations of people around the world and are essential for cultural literacy.
• They contain valuable lessons about ethics and behavior, and students will develop an understanding of different types of fiction.
• This domain helps students develop a strong foundation for the understanding and enjoyment of fiction.

Knowledge Domain 2: The Human Body

Unit Length: 16 instructional days
Description: Students are introduced to the systems of the human body and the function of major organs. They learn about care of the body, germs and diseases, vaccines, and keys to good health.
ELA Standards:
RI.1.2: Identify main topic and retell key details of a text.
W.1.2: Write informative/explanatory texts in which they name a topic, supply some facts about the topic, and provide some sense of closure.
Big Ideas:

• The body is a network of systems comprised of organs that work together to perform vital jobs.
• There are many parts and functions related to the skeletal, muscular, digestive, circulatory, and nervous systems.
• Germs can cause disease; some activities will help stop the spread of germs.
• The five keys of good health are: eat well, exercise, sleep, keep clean, and have regular checkups.

Knowledge Domain 3: Different Lands, Different Stories

Unit Length: 15 instructional days
Description: Students encounter different cultures from around the world as they explore the ways in which folktales from different lands treat similar themes or characters, including variations of the Cinderella story, the adventures of supernaturally small characters, and the exploits of cunning tricksters.
ELA Standards:
RL.1.3: Describe characters, settings, and major events in a story, using key details.
RL.1.9: Compare and contrast the adventures and experiences of characters in stories.
Big Ideas:

• The fairy tales and folktales we’ve grown up with are known throughout the world; each culture has its own unique retelling.
• There are many common themes in these tales, such as people who are treated unfairly and ultimately find happiness, supernaturally small characters, and cunning animals who try and trick children.

Knowledge Domain 4: Early World Civilizations

Unit Length: 17 instructional days
Description: What is needed to build a civilization? Going back to the ancient Middle East, students explore Mesopotamia and Egypt and learn about the importance of rivers, farming, writing, laws, art, and beliefs.
ELA Standards:
RI.1.2: Identify main topic and retell key details of a text.
RI.1.3: Describe the connection between two individuals, events, ideas, or pieces of information in a text.
W.1.3: Write narratives in which they recount two or more appropriately sequenced events, include some details regarding what happened, use temporal words to signal event order, and provide some sense of closure.
Big Ideas:

• Civilizations have fundamental features, including cities and government, forms of communication, and religion.
• The Tigris and Euphrates rivers were vital to the establishment of Mesopotamia, from which we received the earliest form of writing and first codification of laws.
• Egypt was founded on the Nile river, and its contributions include hieroglyphics, pharaohs, pyramids, and the significance of mummification.

Knowledge Domain 5: Early American Civilizations

Unit Length: 19 instructional days
Description: Students compare and contrast key features of the early civilizations of the Maya, Aztec, and Inca, and explore the development of cities such as Tenochtitlan and Machu Picchu. They are also introduced to the work of archaeologists who unearth ancient civilizations.
ELA Standards:
RI.1.2: Identify main topic and retell key details of a text.
W.1.2: Write informative/explanatory texts in which they name a topic, supply some facts about the topic, and provide some sense of closure.
Big Ideas:

• The Maya, Aztec, and Inca civilizations had shared features, including farming, the establishment of cities and government, and religion.
• Despite having common features, these civilizations were all unique in their own ways.
• Much of what we learn about people from the past is discovered by archeologists, who study artifacts from the past and use that information to make informed hypotheses

Knowledge Domain 6: Astronomy

Unit Length: 14 instructional days
Description: In this introduction to the solar system, students learn about Earth in relation to the moon, the other planets, the sun, and the stars. They learn about the sun as a source of light, heat and energy. They are introduced to space exploration, including the Apollo missions to the moon.
ELA Standards:
RL.1.5: Explain major differences between books that tell stories and books that give information, drawing on a wide reading of a range of text types.
RI.1.2: Identify main topic and retell key details of a text.
RI.1.9: Identify basic similarities in and differences between two texts on the same topic.
Big Ideas:

• The Earth is one of many different celestial bodies within our solar system.
• The sun, stars, moon, and other planets relate to the earth’s position in space in definite ways.
• The sun is a star and the source of light, heat, and energy for the earth.
• NASA, the Space Race, the Apollo missions and astronauts have all contributed to what we know about space.

Knowledge Domain 7: The History of the Earth

Unit Length: 14 instructional days
Description: Students learn about the geographical features of the earth’s surface, the layers of the earth, rocks and minerals, volcanoes, geysers, fossils, and dinosaurs.
ELA Standards:
RI.1.2: Identify main topic and retell key details of a text.
RI.1.3: Describe the connection between two individuals, events, ideas, or pieces of information in a text.
RI.1.5: Know and use various text features to locate key facts or information in a text.
W.1.2: Write informative/explanatory texts in which they name a topic, supply some facts about the topic, and provide some sense of closure.
Big Ideas:

• The earth is comprised of various layers, each with its own characteristics.
• Geographical features, such as volcanoes and geysers give us information about these layers.
• Rocks and minerals are important in our daily lives. They are taken from the crust and used in many ways.
• There are three types of rock, each with their own characteristics. Fossils are found in rock and give us knowledge about the history of living things on Earth.

Knowledge Domain 8: Animals and Habitats

Unit Length: 16 instructional days
Description: Students focus on the interconnectedness of living things with their physical environment as they learn what a habitat is and explore plants and animals in specific types of habitats.
ELA Standards:
RI.1.2: Identify main topic and retell key details of a text.
W.1.2: Write informative/explanatory texts in which they name a topic, supply some facts about the topic, and provide some sense of closure.
Big Ideas:

• All living things are interconnected to both their environments and other living things.
• Different plants and animals are indigenous to specific habitats, often suited to them through unique characteristics that enable them to adapt to that habitat.
• Animals can be classified by the types of foods they eat, and one example of interconnectedness is the food chain to which all living things belong.

Knowledge Domain 9: Fairy Tales

Unit Length: 15 instructional days
Description: Students are introduced to fairy tales that have been favorites for generations, including Sleeping Beauty, Rumpelstiltskin, The Frog Prince, Hansel and Gretel, and Jack and the Beanstalk. Students learn about the Brothers Grimm, identify common elements of fairy tales, consider problems and solutions, make interpretations, and compare and contrast different tales.
ELA Standards:
RL.1.2a: Retell stories, including key details.
RL.1.3: Describe characters, settings, and major events in a story, using key details.
RL.1.9: Compare and contrast the adventures and experiences of characters in stories.
W.1.3: Write narratives in which they recount two or more appropriately sequenced events, include some details regarding what happened, use temporal words to signal event order, and provide some sense of closure.
Big Ideas:

• Fairy tales are a unique type of fiction, with distinct elements, that still maintain traditional story grammar.
• Students will explore concepts such as bravery and heroism, good and evil, and valuable life lessons.
• The Brothers Grimm shared these tales with others because of their ability to make people feel happy, sad, and sometimes afraid.

Knowledge Domain 10: A New Nation: American Independence

Unit Length: 22 instructional days
Description: Students learn about the birth of the United States of America. They are introduced to important historical figures and events in the story of how the thirteen colonies became an independent nation. They also learn the significance of patriotic symbols, including the U.S. flag, the Liberty Bell, and the bald eagle.
ELA Standards:
RI.1.2: Identify main topic and retell key details of a text.
RI.1.6: Distinguish between information provided by pictures or other illustrations and information provided by the words in a text.
W.1.2: Write informative/explanatory texts in which they name a topic, supply some facts about the topic, and provide some sense of closure.
Big Ideas:

• Several important historical figures and events led to how the thirteen colonies determined and gained their independence from Britain to become the United States of America.
• The British imposed taxes on the thirteen colonies, which led to the Boston Tea Party, the Revolutionary War, and the Declaration of Independence.
• The roles of women, Native Americans, and African Americans during this time period are highlighted.

Skills Unit 1

Unit Length: 23 instructional days
Description: This unit focuses on reviewing various spellings with an emphasis on consonant sounds, one- and two-syllable words, and high frequency Tricky Words.
ELA Standards:
RF.2.3.a: Distinguish long and short vowels when reading regularly spelled one-syllable words.
RF.2.3.c: Decode regularly spelled two-syllable words with long vowels.
RF.2.3.f: Recognize and read appropriate irregularly spelled words.
RF.2.4: Read with sufficient accuracy and fluency to support comprehension.
L.2.1.d: Form and use past tense of frequently occurring irregular verbs.
L.2.2.d: Generalize learned spelling patterns when writing words.
Big Ideas:

• The stories in the Reader The Cat Bandit, tell of the adventures of a hungry cat and the increasingly clever ways he gets food items seemingly out of his reach.
• Students answer comprehension questions orally and/or in writing after reading each story.

Skills Unit 2

Unit Length: 19 instructional days
Description: Focus is on various spellings with an emphasis on vowel sounds. Students one- and two-syllable words, as well as contractions. They practice with a number of high frequency Tricky Words. They learn about the use of quotation marks and begin instruction in the writing process, writing narratives and opinions.
ELA Standards:
RF.2.3.a: Distinguish long and short vowels when reading regularly spelled one-syllable words.
RF.2.3.c: Decode regularly spelled two-syllable words with long vowels.
RF.2.4: Read with sufficient accuracy and fluency to support comprehension.
L.2.1.f: Produce, expand, and rearrange complete simple and compound sentences.
L.2.2.c: Use an apostrophe to form contractions and frequently occurring possessives.
L.2.2.d: Generalize learned spelling patterns when writing words.
Big Ideas:

• The Reader for this unit is Bedtime Tales. In it, a father shares bedtime stories with his son and daughter. This Reader explores two fiction genres: fables and trickster stories.
• Close reading lessons are introduced in this unit using chapters from the Reader.
• Students answer comprehension questions orally and/or in writing after reading each story.

Skills Unit 3

Unit Length: 29 instructional days
Description:  This unit introduces spelling alternatives for vowel sounds, as well as various tricky spellings (spellings that can stand for more than one sound). Students practice writing a personal narrative. Grammar instruction focuses on capitalization, quotation marks, ending punctuation, and common and proper nouns. Students are also introduced to antonyms and synonyms.
ELA Standards:
RF.2.3.a: Distinguish long and short vowels when reading regularly spelled one-syllable words.
RF.2.3.b: Know spelling-sound correspondences for additional common vowel teams.
RF.2.3.c: Decode regularly spelled two-syllable words with long vowels.
RF.2.3.e: Identify words with inconsistent but common spelling-sound correspondences.
RF.2.3.f: Recognize and read appropriate irregularly spelled words.
L.2.2.d: Generalize learned spelling patterns when writing words.
Big Ideas:

• The Reader for this unit is Kids Excel. This fictional Reader consists of profiles of kids who excel at various activities—spelling, swimming, soccer, jumping rope, splashing, math, rock skipping. Each profile progresses across several selections.
• Close reading lessons in this unit use chapters from the Reader.
• Students answer comprehension questions orally and/or in writing after reading each story.

Skills Unit 4

Unit Length: 30 instructional days
Description: Students are introduced to more spelling alternatives for vowel sounds, as well as three tricky spellings. Students practice persuasive writing as part of a friendly letter. In grammar, students review singular and regular plural nouns. They are introduced to the formation of irregular plural nouns, as well as action verbs and to be verbs.
ELA Standards:
RF.2.3.e: Identify words with inconsistent but common spelling-sound correspondences.
W.2.1: Write opinion pieces in which they introduce the topic or book they are writing about, state an opinion, supply reasons that support the opinion, use linking words to connect opinion and reasons, and provide a concluding statement or section.
L.2.1.b: Form and use frequently occurring irregular plural nouns.
L.2.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
Big Ideas:

• The Job Hunt is a fictional Reader that describes a nineteen-year-old girl’s search for a job in New York City with the help of her younger brother. The introduction contains information about New York City, including a map.
• Close reading lessons in this unit use chapters from the Reader.
• Students answer comprehension questions orally and/or in writing after reading each story.

Skills Unit 5

Unit Length: 35 instructional days
Description: This unit introduces spelling alternatives for vowel sounds and the schwa sound. Students practice chunking phonemes as a means of reading multi-syllable words. They review grammar skills and learn about adjectives, as well as how to identify the subject and predicate in a complete sentence. Additionally, students continue to practice narrative writing by rewriting an ending to a story from their Student Reader.
ELA Standards:
RF.2.3.e: Identify words with inconsistent but common spelling-sound correspondences.
RF.2.3.f: Recognize and read appropriate irregularly spelled words.
RF.2.4.a: Read on-level text with purpose and understanding.
W.2.3: Write narratives in which they recount a well-elaborated event or short sequence of events, include details to describe actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of closure.
L.2.1.e: Use adjectives and adverbs, and choose between them depending on what is to be modified.
L.2.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
Big Ideas:

• Sir Gus is a fictional Reader detailing the serendipitous undertakings of Sir Gus, one of King Alfred’s knights. Despite his title as “Sir Gus the Fearless,” Sir Gus actually has many different fears. Sir Gus has to face a thief, a troll, pirates, an evil wizard, and an enemy king.
• Close reading lessons in this unit use chapters from the Reader.
• Students answer comprehension questions orally and/or in writing after reading each story.

Skills Unit 6

Unit Length: 35 instructional days
Description: This unit introduces spelling alternatives for vowel sounds and the schwa sound. Students practice chunking phonemes as a means of reading multi-syllable words. They review grammar skills and learn about adjectives, as well as how to identify  
ELA Standards:
RF.2.3: Know and apply grade-level phonics and word analysis skills in decoding words.
RF.2.4: Read with sufficient accuracy and fluency to support comprehension.
L.2.1.f: Produce, expand, and rearrange complete simple and compound sentences.
L.2.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
L.2.3: Use knowledge of language and its conventions when writing, speaking, reading or listening.
W.2.2: Write informative/explanatory texts in which they introduce a topic, use facts and definitions to develop points, and provide a concluding statement or section.
Big Ideas:

• The letter-sound correspondences taught in CKLA up to this point represent most of the important letter-sound correspondences needed to read English writing.
• The Reader for this unit is The War of 1812 and covers topics included in G2 Domain 5 of the Knowledge Strand.
• Students answer comprehension questions orally and/or in writing after reading each story.

 

Knowledge Domain 1: Fairy Tales and Tall Tales

Unit Length: 15 instructional days
Description: Students are introduced to three classic fairy tales: The Fisherman and His Wife, The Emperor’s New Clothes, and Beauty and the Beast. They consider characteristic elements of fairy tales and consider problems faced by the characters as well as lessons each story conveys. Students then turn to the American frontier and tall tales about Paul Bunyan, Pecos Bill, John Henry, and Casey Jones. They learn about the characteristics of tall tales, such as exaggeration and larger than life characters.
ELA Standards:
RL.2.2: Recount stories, including fables and folktales from diverse cultures, and determine their central message, lesson, or moral.
RL.2.3: Describe how characters in a story respond to major events and challenges.
RL2.9: Compare and contrast two or more versions of the same story by different authors or from different cultures.
W.2.3: Write narratives in which they recount a well-elaborated event or short sequence of events, include details to describe actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of closure.
Big Ideas:

• Fairy Tales and Tall Tales lay the foundation of understanding stories in future grades.
• Fairy Tales is a continuation and deepening of prior knowledge about the genre and will allow for a greater understanding of story grammar.
• Tall Tales introduces students to the setting of the American frontier and some of the occupations there.

Knowledge Domain 2: Early Asian Civilizations

Unit Length: 18 instructional days
Description: In this unit, students are introduced to the continent of Asia and its two most populous countries, India and China. Students learn about early India, the importance of the Indus and Ganges Rivers, and the basics of their culture. Students then explore early Chinese civilization and its lasting contributions, including paper, silk, and the Great Wall of China. In addition, students are introduced to related folktales and poetry.
ELA Standards:
RI.2.1: Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.
RI.2.2: Identify the main topic of a multi-paragraph text as well as the focus of specific paragraphs within the text.
W.2.2: Write informative/explanatory texts in which they introduce a topic, use facts and definitions to develop points, and provide a concluding statement or section.
Big Ideas:

• India and China, the two most populous countries in Asia, were able to form because of mighty rivers.
• The early Chinese civilization provided many contributions to the world, including paper, silk, and the Great Wall of China.

Knowledge Domain 3: The Ancient Greek Civilization

Unit Length: 17 instructional days
Description: Students explore the civilization of ancient Greece, which lives on in many ways- in our language, government, art, architecture and the Olympics. Student learn about the city-states of Sparta and Athens, Greek democracy, the gods and goddesses of the ancient Greeks, and the philosophers Socrates, Plato and Aristotle.  
ELA Standards:
RL.2.1: Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.
W.2.3: Write narratives in which they recount a well-elaborated event or short sequence of events, include details to describe actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of closure.
Big Ideas:

• Ancient Greek civilization contributed to many areas of our lives today.
• Ancient Greece was the birthplace of democracy, the ideals of which are used today in our own and other governments.
• Great philosophers, gods and goddesses, the Olympic games, significant battles, and the conquests of Alexander the Great all added to the importance of the ancient Greeks.

Knowledge Domain 4: Greek Myths

Unit Length: 17 instructional days
Description: Building on the Ancient Greek Civilization domain, students explore several well-known Greek myths and mythical characters, including Prometheus and Pandora, Demeter and Persephone, Arachne the Weaver, Oedipus and the Sphinx, Theseus and the Minotaur, and others. Students learn about common characteristics of myths and examine story elements in the myths.
ELA Standards:
RL.2.2: Recount stories, including fables and folktales from diverse cultures, and determine their central message, lesson, or moral.
RL.2.3: Describe how characters in a story respond to major events and challenges.
RL.2.6: Acknowledge differences in the points of view of characters, including by speaking in a different voice for each character when reading dialogue aloud.
W.2.3: Write narratives in which they recount a well-elaborated event or short sequence of events, include details to describe actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of closure.
Big Ideas:

• Ancient Greeks worshipped many gods and goddesses.
• A myth is a fictional story, once thought to be true, that tried to explain mysteries of nature and humankind.
• References to Greek mythology are still culturally relevant today, and give students a frame of reference with which to understand literary allusions and the meanings of common words and phrases.

Knowledge Domain 5: The War of 1812

Unit Length: 13 instructional days
Description: Students are introduced to major figures and events in the War of 1812, sometimes called America’s second war for independence. Students learn about James and Dolley Madison, “Old Ironsides”, “The Star-Spangled Banner”, the Battle of New Orleans, and more, all of which build a foundation for more in-depth study in later grades.
ELA Standards:
RI.2.1: Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.
RI.2.3: Describe the connection between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text.
W.2.1: Write opinion pieces in which they introduce the topic or book they are writing about, state an opinion, supply reasons that support the opinion, use linking words to connect opinion and reasons, and provide a concluding statement or section.
Big Ideas:

• The War of 1812 is best remembered as the war that gave birth to “The Star-Spangled Banner.”
• It is often called America’s second war for independence.
• The United States was greatly affected by the Napoleonic Wars between France and Great Britain.
• This domain builds the foundation for learning about westward expansion and the U.S. Civil War later this year.

Knowledge Domain 6: Cycles in Nature

Unit Length: 13 instructional days
Description: Students are introduced to natural cycles that make life on Earth possible. Students will learn about seasonal cycles, plant and animal life cycles, and the water cycle. Students will enjoy poems by Emily Dickinson and Robert Louis Stevenson
ELA Standards:
RI.2.3: Describe the connection between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text.
RI.2.6: Identify the main purpose of a text, including what the author wants to answer, explain or describe.
W.2.2: Write informative/explanatory texts in which they introduce a topic, use facts and definitions to develop points, and provide a concluding statement or section.
W.2.7: Participate in shared research and writing projects.
Big Ideas:

• Nature has many natural cycles that make life on Earth possible.
• Seasonal cycles, flowering plants and trees, animal life cycles, and the water cycle are a few examples of natural cycles.
• Natural cycles are interconnected, and a change in one cycle often affects the cycles of many.

Knowledge Domain 7: Westward Expansion

Unit Length: 13 instructional days
Description: In this unit, students are introduced to an important period in the history of the United States—the time of westward expansion during the 1800s. Students explore why pioneers were willing to endure the hardships to move westward, and learn about innovations in transportation and communication, including the steamboat, the Transcontinental Railroad, and the Pony Express. Students will come to understand the hardships and tragedies that Native Americans endured because of westward expansion.
ELA Standards:
RI.2.3: Describe the connection between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text.
RI.2.6: Identify the main purpose of a text, including what the author wants to answer, explain or describe.
W.2.2: Write informative/explanatory texts in which they introduce a topic, use facts and definitions to develop points, and provide a concluding statement or section.

Big Ideas:

• Pioneers were willing and eager to endure hardships to move westward during the 1800s.
• Many important innovations in both transportation and communication occurred during that time period.
• Native Americans endured both intended and unintended hardships and tragedies as a result of westward expansion.

Knowledge Domain 8: Insects

Unit Length: 14 instructional days
Description: Students learn about the characteristics of insects, the largest group of animals on Earth. Students explore insect life cycles and social insects such as bees and ants. They consider helpful and harmful aspects of insects.
ELA Standards:
W.2.2: Write informative/explanatory texts in which they introduce a topic, use facts and definitions to develop points, and provide a concluding statement or section.
W.2.7: Participate in shared research and writing projects.
Big Ideas:

• Insects are the largest group of animals on Earth.
• Insects have identifiable characteristics and life cycles, are categorized as either solitary of social, and can be viewed as both helpful and harmful.
• Insects are important to the process of pollination and also to the production of honey, some cosmetics, and even medicines.

Knowledge Domain 9: The U.S. Civil War

Unit Length: 15 instructional days
Description: This domain lays the foundation for more in-depth study in later grade of a critical period in American history. Students learn about the controversy between the North and the South over slavery. Students also become familiar with the achievements of key historical figures during the time, including Harriet Tubman, Clara Barton, Abraham Lincoln, Ulysses S. Grant, and Robert E. Lee.
ELA Standards:
RI.2.8: Describe how reasons or evidence support specific points the author makes in a text.
RI.2.9: Compare and contrast the most important points presented by two texts on the same topic.
Big Ideas:

• Controversy over slavery between the North and the South eventually led to the U.S. Civil War.
• Africans were taken from Africa against their will and forced into slavery in the U.S. until the end of the Civil War.
• Significant women and men from the time period include Harriet Tubman, Abraham Lincoln, Clara Barton, Robert E. Lee, and Ulysses S. Grant.

Knowledge Domain 10: The Human Body: Building Blocks and Nutrition

Unit Length: 15 instructional days
Description: Students learn about Anton van Leeuwenhoek and his pioneering work with the microscope. They then proceed to explore a number of topics regarding the human body, including cells, tissues, organs, and body systems, with a focus on the digestive and excretory systems. In addition, students learn about good nutrition and other keys to good health.
ELA Standards:
RI.2.3: Describe the connection between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text.
W.2.2: Write informative/explanatory texts in which they introduce a topic, use facts and definitions to develop points, and provide a concluding statement or section.
Big Ideas:

• Cells form the building blocks of life on Earth.
• Collections of cells form tissues, tissues form organs, and organs form systems within the body.
• Anton van Leeuwenhoek was important in science for his work with microscopes and the discovery of one-celled bacteria.
• The five keys to good health are: eat well, exercise, sleep, keep clean, and have regular checkups.

Knowledge Domain 11: Immigration

Unit Length: 21 instructional days
Description: This domain introduces students to the concept of immigration in the United States. Students will learn about the biggest wave of immigration to the United States, which occurred between 1880 and 1920. They will discover why people immigrated, what factors pushed them from homelands and pulled them to the United States, and why many immigrants settled in particular cities or regions upon their arrival. These basic facts about immigration will help students further their awareness of U.S. history. Learning about immigration in the United States is also an opportunity for students to find out more about their family history and what brought them and/or ancestors to the United States.

ELA Standards:
RI.2.2: Identify the main topic of a multi-paragraph text as well as the focus of specific paragraphs within the text.
W.2.3: Write narratives in which they recount a well-elaborated event or short sequence of events, include details to describe actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of closure.
Big Ideas:

• The United States is often referred to as a country of immigrants, with the biggest wave of immigration taking place from 1880 to 1920.
• Immigrants had many different reasons for immigrating to the United States, and settled in particular cities or regions upon their arrival.
• The Constitution and the Bill of Rights are two important documents that detail the privileges and rights of American citizens.

Unit 1 The Stories Julian Tells

Unit Length: 50.5 instructional days
Description: Students read literary and informational texts to learn that stories and books are important for learning about themselves and others. Students understand that storytelling can be a way to connect them to others and pass on family history and traditions. Students express their understanding by explaining how characters learn lessons through their experiences with one another and by writing their own story based on illustrations.

Standards:

RL.3.2: Recount stories, including fables, folktales, and myths from diverse cultures; determine the central message, lesson, or moral and explain how it is conveyed through the key details in the text.

RL.3.3: Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events.

RL.3.6: Distinguish the student’s point of view from that of the narrator or those of the characters.

RI.3.2: Determine the main idea of a text; recount the key details and explain how they support the main idea.

RI.3.5: Use text features and search tools (e.g., key words, sidebars, hyperlinks) to locate information relevant to a given topic efficiently.

RI.3.7: Use information gained from illustrations (e.g., maps, photographs) and the words in a text to demonstrate understanding of the text (e.g., where, when, why, and how key events occur).

Reading Foundational Skills:

RF.3.3:  Know and apply grade-level phonics and word analysis skills in decoding words.

a.  Identify and know the meaning of the most common prefixes and suffixes and derivational suffixes.

b.  Decode words with common Latin suffixes.

c.    Decode multisyllable words.

d.   Read grade-appropriate irregularly spelled words.

Writing Standards

W.3.1: Write opinion pieces on topics or texts, supporting a point of view with reasons.

W.3.3: Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.

W.3.5: With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.

W.3.8: Recall information from experiences or gather information from print and digital sources; take brief notes on sources and sort evidence into provided categories.

Speaking and Listening:

SL.3.2: Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.

SL.3.3: Ask and answer questions about information from a speaker, offering appropriate elaboration and detail.

SL.3.4: Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking clearly at an understandable pace.

SL.3.5: Create engaging audio recordings of stories or poems that demonstrate fluid reading at an understandable pace; add visual displays when appropriate to emphasize or enhance certain facts or details.

Language:

L.3.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

L.3.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

L.3.4: Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies.

L.3.5: Demonstrate understanding of word relationships and nuances in word meanings.

These standards are embedded in every unit:

RL. /RI.3.1: Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.

RL.3.10: By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 2–3 text complexity band independently and proficiently.

RI.3.10: By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 2–3 text complexity band independently and proficiently.

RF.3.4: Read with sufficient accuracy and fluency to support comprehension.

a. Read on-level text with purpose and understanding.

b. Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.

c. Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

W.3.4: With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose.

W.3.6: With guidance and support from adults, produce and publish grade-appropriate writing, using technology, either independently or in collaboration with others.

W.3.10: Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

SL.3.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others’ ideas and expressing their own clearly.

L.3.3: Use knowledge of language and its conventions when writing, speaking, reading, or listening.

L.3.6: Acquire and use accurately grade-appropriate conversational, general academic and domain-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them).

 

Enduring Understandings:

• Stories and books are important for learning about yourself and others.
• Storytelling can be a way to connect to others and pass on family history and traditions.
• Readers notice when characters change and think about the lessons that the character has learned.

Essential Questions:

• How can a reader determine the central message in a story?
• How can a reader understand a character’s motivations, feelings, and actions when they are put in different situations?

 

Unit 2 Because of Winn Dixie

Unit Length: 45.5 instructional days
Description: Students read literary and informational texts to understand the value of companionship, the joy of finding friends in unexpected places, and the significance of building a community of different perspectives. Students express their understanding by explaining how characters change throughout Because of Winn-Dixie based on the relationships formed during the book. Students also engage in independent reading of texts based on similar themes to further develop their understanding.

Standards:

RL.3.2: Recount stories, including fables, folktales, and myths from diverse cultures; determine the central message, lesson, or moral and explain how it is conveyed through the key details in the text.

RL.3.3: Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events.

RL.3.4: Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliteral language.

RL.3.5: Refer to parts of stories, dramas, and poems when writing or speaking about a text, using terms such as chapter, scene and stanza; describe how each successive part builds on earlier sections.

RL.3.6: Distinguish the student’s point of view from that of the narrator or those of the characters.

RL.3.9: Compare and contrast the themes, settings, and plots of stories written by the same author about the same or similar characters (e.g., in books from a series).

RI.3.2: Determine the main idea of a text; recount the key details and explain how they support the main idea.

RI.3.3: Describe the relationship between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text, using language that pertains to time, sequence, and cause/effect.

RI.3.4: Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject.

RI.3.7: Use information gained from illustrations (e.g., maps, photographs) and the words in a text to demonstrate understanding of the text (e.g., where, when, why, and how key events occur).

RI.3.8: Describe the logical connection between particular sentences and paragraphs in a text (e.g., comparison, cause/effect, first/second/third in a sequence).

RI.3.9:   Compare and contrast the most important points and key details presented in two texts on the same topic.

Reading Foundational Skills

RF.3.3:  Know and apply grade-level phonics and word analysis skills in decoding words.

                a.  Identify and know the meaning of the most common prefixes and suffixes and derivational suffixes.

                b.  Decode words with common Latin suffixes.

                c.   Decode multisyllable words.

                d.   Read grade-appropriate irregularly spelled words.

Writing Standards

W.3.1: Write opinion pieces on topics or texts, supporting a point of view with reasons.

W.3.2: Write informative/explanatory texts to examine a topic and convey ideas and information clearly.

W.3.8: Recall information from experiences or gather information from print and digital sources; take brief notes on sources and sort evidence into provided categories.

Speaking and Listening:

SL.3.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others’ ideas and expressing their own clearly.

SL.3.2: Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.

SL.3.3: Ask and answer questions about information from a speaker, offering appropriate elaboration and detail.

SL.3.4: Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking clearly at an understandable pace.

SL.3.6: Speak in complete sentences when appropriate to task, audience, and situation in order to provide requested detail or clarification.

Language Standards:

L.3.1 Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

L.3.2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

L.3.5 Demonstrate understanding of word relationships and nuances in word meanings.

These standards are embedded in every unit:

RL. /RI.3.1 Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.

RL.3.10 By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 2–3 text complexity band independently and proficiently.

RI.3.10 By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 2–3 text complexity band independently and proficiently.

RF.3.4 Read with sufficient accuracy and fluency to support comprehension.

a. Read on-level text with purpose and understanding.

b. Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.

c. Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

SL.3.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others’ ideas and expressing their own clearly.

W.3.4 With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose.

W.3.5 With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.

W.3.6 With guidance and support from adults, produce and publish grade-appropriate writing, using technology, either independently or in collaboration with others.

W.3.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

L.3.4 Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies.

L.3.6 Acquire and use accurately grade-appropriate conversational, general academic and domain-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them).

 

Enduring Understandings:

• Friendship can be found in unexpected places.
• Readers think about the struggles characters go through, the lessons characters learn, and think about how this may change the way they themselves act.

Essential Questions:

• What is the central message or theme that the author wants us to learn by reading this novel?
• How can I look closely at a character to help me think about what kind of person they are?

 

Unit 3 Louisiana Purchase

Unit Length: 52.5 instructional days
Description: Students read literary and informational texts to learn about the Louisiana Purchase and the characteristics of pioneers during this time period. While exploring these texts, including quotes from primary source documents, students develop their understanding of narrative writing and make connections between sentences and paragraphs in a text. Students express their understanding of the Louisiana Purchase by explaining the events leading up to the acquisition of the territory and the results of those events.

Standards:

RL.3.2: Recount stories, including fables, folktales, and myths from diverse cultures; determine the central message, lesson, or moral and explain how it is conveyed through the key details in the text.

RL.3.3: Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events.

RL.3.4: Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliteral language.

RL.3.5: Refer to parts of stories, dramas, and poems when writing or speaking about a text, using terms such as chapter, scene and stanza; describe how each successive part builds on earlier sections.

RL.3.6: Distinguish the student’s point of view from that of the narrator or those of the characters.

Reading Informational Text:

RI.3.2: Determine the main idea of a text; recount the key details and explain how they support the main idea.

RI.3.3: Describe the relationship between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text, using language that pertains to time, sequence, and cause/effect.

RI.3.4: Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject.

RI.3.5: Use text features and search tools (e.g., key words, sidebars, hyperlinks) to locate information relevant to a given topic efficiently.

RI.3.6: Distinguish the student’s point of view from that of the author of a text.

RI.3.7: Use information gained from illustrations (e.g., maps, photographs) and the words in a text to demonstrate understanding of the text (e.g., where, when, why, and how key events occur).

RI.3.8: Describe the logical connection between particular sentences and paragraphs in a text (e.g., comparison, cause/effect, first/second/third in a sequence).

RI.3.9: Compare and contrast the most important points and key details presented in two texts on the same topic.

Reading Foundational Skills:

RF.3.3:  Know and apply grade-level phonics and word analysis skills in decoding words.

• Identify and know the meaning of the most common prefixes and suffixes and derivational suffixes.
• Decode words with common Latin suffixes.
• Decode multisyllable words.
• Read grade-appropriate irregularly spelled words.

Writing:

W.3.1: Write opinion pieces on topics or texts, supporting a point of view with reasons.

W.3.2: Write informative/explanatory texts to examine a topic and convey ideas and information clearly.

W.3.3: Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.

W.3.8: Recall information from experiences or gather information from print and digital sources; take brief notes on sources and sort evidence into provided categories.

Speaking and Listening:

SL.3.2: Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.

SL.3.3: Ask and answer questions about information from a speaker, offering appropriate elaboration and detail.

SL.3.4: Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking clearly at an understandable pace.

SL.3.6: Speak in complete sentences when appropriate to task, audience, and situation in order to provide requested detail or clarification.

Language:

L.3.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

L.3.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

L.3.5: Demonstrate understanding of word relationships and nuances in word meanings.

These standards are embedded in every unit:

RL. /RI.3.1: Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.

RL.3.10: By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 2–3 text complexity band independently and proficiently.

RI.3.10: By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 2–3 text complexity band independently and proficiently.

RF.3.4: Read with sufficient accuracy and fluency to support comprehension.

a. Read on-level text with purpose and understanding.

b. Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.

c. Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

SL.3.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others’ ideas and expressing their own clearly.

W.3.4: With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose.

W.3.5: With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.

W.3.6: With guidance and support from adults, produce and publish grade-appropriate writing, using technology, either independently or in collaboration with others.

W.3.10: Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

L.3.4: Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies.

L.3.6: Acquire and use accurately grade-appropriate conversational, general academic and domain-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them).

 

Enduring Understandings:

• The spirit of exploration and the values of American pioneers were evident during the early 1800s.
• Narrative writing and primary source documents can help a reader understand a person or character’s point of view.

Essential Questions:

• What events led to the United States acquiring the Louisiana Territory?
• What are the causes and effects of the Louisiana Purchase?

 

Unit 4 Cajun Folktales

 

Unit Length: 22.5 instructional days

Description: Students read folktales to learn how storytelling can be entertaining as well as educational. Students develop an understanding of Louisiana history and culture as well as character and theme development. Students express their understanding by writing their opinion about the main character’s actions. This mini Guidebook unit will build student capacity for future Guidebook coursework.

 

Standards:

RL.3.2: Recount stories, including fables, folktales, and myths from diverse cultures; determine the central message, lesson, or moral and explain how it is conveyed through the key details in the text.

RL.3.3: Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events.

RL.3.4: Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliteral language.

RL.3.5: Refer to parts of stories, dramas, and poems when writing or speaking about a text, using terms such as chapter, scene and stanza; describe how each successive part builds on earlier sections.

RL.3.7: Explain how specific aspects of a text’s illustration contribute to what is conveyed by the words in a story (e.g., create mood, emphasize aspects of a character or setting).

Reading Foundational Skills:

RF.3.3:  Know and apply grade-level phonics and word analysis skills in decoding words.

a. Identify and know the meaning of the most common prefixes and suffixes and derivational suffixes.

b. Decode words with common Latin suffixes.

c.  Decode multisyllable words.

d. Read grade-appropriate irregularly spelled words.

Writing Standards

W.3.1: Write opinion pieces on topics or texts, supporting a point of view with reasons.

Speaking and Listening:

SL.3.2: Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.

SL.3.3: Ask and answer questions about information from a speaker, offering appropriate elaboration and detail.

SL.3.4: Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking clearly at an understandable pace.

Language:

L.3.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

L.3.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

L.3.5: Demonstrate understanding of word relationships and nuances in word meanings.

rs’ ideas and expressing their own clearly.

These standards are embedded in every unit:

RL. /RI.3.1 Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.

RL.3.10 By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 2–3 text complexity band independently and proficiently.

RI.3.10 By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 2–3 text complexity band independently and proficiently.

RF.3.4 Read with sufficient accuracy and fluency to support comprehension.

a. Read on-level text with purpose and understanding.

b. Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.

c. Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

SL.3.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others’ ideas and expressing their own clearly.

W.3.4 With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose.

W.3.5 With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.

W.3.6 With guidance and support from adults, produce and publish grade-appropriate writing, using technology, either independently or in collaboration with others.

W.3.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

L.3.4 Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies.

L.3.6 Acquire and use accurately grade-appropriate conversational, general academic and domain-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them).

 

Enduring Understandings:

• Storytelling can be entertaining as well as educational.
• Cajun culture and traditions are part of Louisiana history.

Essential Questions:

• What are elements of a folktale?
• Why is storytelling important?
• How does understanding a character’s thoughts, feelings, and actions help me as a reader?
• How do I form an opinion, write about it and provide reasons?

Unit 1 Hurricanes

Unit Length: 54.5 days
Description: Students read literary and informational texts to learn about hurricanes and their impact on Louisiana. Students understand how history involves the sharing of memories and the differences between firsthand and secondhand accounts. Students express their understanding of the impact of hurricanes on Louisiana by writing a first person narrative about an experience in a hurricane based on texts they have read.

Standards:

Reading Literature:
RL.4.2 Determine a theme of a story, drama, or poem from details in the text; summarize the text.
RL.4.3 Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text (e.g., a character’s thoughts, words, or actions).
Reading Informational Text:
RI.4.2 Determine the main idea of a text and explain how it is supported by key details; summarize the text.
RI.4.3 Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text.
RI.4.7 Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears.
RI.4.8 Explain how an author uses reasons and evidence to support particular points in a text.
RI.4.9 Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably.

Writing:
W.4.1a-d Write opinion pieces on topics or texts, supporting a point of view with reasons and information.
a. Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer’s purpose.
b. Provide reasons that are supported by facts and details.
c. Link opinion and reasons using words and phrases (e.g., for instance, in order to, in addition).
d. Provide a concluding statement or section related to the opinion presented.
W.4.2a-e Write informative/explanatory texts to examine a topic and convey ideas and information clearly.
a. Introduce a topic clearly and group related information in paragraphs and sections; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.
b. Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.
c. Link ideas within categories of information using words and phrases (e.g., another, for example, also, because).
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
e. Provide a concluding statement or section related to the information or explanation presented.
W.4.3a-e Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.
a. Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally.
b. Use dialogue and description to develop experiences and events or show the responses of characters to situations.
c. Use a variety of transitional words and phrases to manage the sequence of events.
d. Use concrete words and phrases and sensory details to convey experiences and events precisely.
e. Provide a conclusion that follows from the narrated experiences or events.
W.4.7 Conduct short research projects that build knowledge through investigation of different aspects of a topic.
W.4.8 Recall relevant information from experiences or gather relevant information from print and digital sources; take notes and categorize information, and provide a list of sources.
W.4.9 Draw relevant evidence from grade-appropriate literary or informational texts to support analysis, reflection, and research.

Language:
L.4.1a-g Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
a. Use relative pronouns (who, whose, whom, which, that) and relative adverbs (where, when, why).
b. Form and use the progressive (e.g., I was walking; I am walking; I will be walking) verb tenses.
c. Use modal auxiliaries (e.g., can, may, must) to convey various conditions.
d. Order adjectives within sentences according to conventional patterns (e.g., a small red bag rather than a red small bag).
e. Form and use prepositional phrases.
f. Produce complete sentences, recognizing and correcting inappropriate fragments and run-ons.
g. Correctly use frequently confused words (e.g., to, too, two; there, their).
L.4.2a-d Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use correct capitalization.
b. Use commas and quotation marks to mark direct speech and quotations from a text.
c. Use a comma before a coordinating conjunction in a compound sentence.
d. Spell grade-appropriate words correctly, consulting references as needed.
L.4.3a-b Use knowledge of language and its conventions when writing, speaking, reading, or listening.
a. Choose words and phrases to convey ideas precisely.
b. Choose punctuation for effect.

Speaking and Listening:
SL.4.4 Report on a topic or text, tell a story, or recount an experience in an organized manner, using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace.  
SL.4.5 Add audio recordings and visual displays to presentations when appropriate to enhance the development of main ideas or themes.
SL.4.6 Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion); use formal English when appropriate to task, audience, and situation.

The following standards are embedded in all units:
RL. /RI.4.1 Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.
RL.4.10 By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.
RI.4.10 By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.
RF.4.4 Read with sufficient accuracy and fluency to support comprehension.
W.4.4 Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience.
W.4.5 With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.
W.4.6 With some guidance and support from adults, produce and publish grade-appropriate writing using technology, either independently or in collaboration with others.
W.4.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
L.4.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 4 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., definitions, examples, or restatements in text) as a clue to the meaning of a word or phrase.
b. Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word
(e.g., telegraph, photograph, autograph).
c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.
L.4.6 Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation).

Enduring Understandings:

• Hurricanes are powerful storms that impact individuals and the environment.
• First-hand and second-hand accounts provide valuable information about how storms have impacted our environment and our lives.

Essential Questions:

• How do hurricanes impact the environment?
• How can people prepare for a hurricane?
   

Unit 2 American Revolution

Unit Length: 49.5 days
Description: Students read texts about the American Revolution to understand the decisions and choices colonists had to make leading up to and during the Revolutionary War. Students express their understanding of the concept of "taking sides" and how, despite having different points of view about an issue or a situation, those engaged in conflict can still share common ground.

Standards:

Reading Literature:
RL.4.2 Determine a theme of a story, drama, or poem from details in the text; summarize the text.
RL.4.4 Determine the meaning of words and phrases as they are used in a text, including figurative language such as metaphors and similes.
Reading Informational Text:
RI.4.2 Determine the main idea of a text and explain how it is supported by key details; summarize the text.
RI.4.3 Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text.
RI.4.4 Determine the meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic or subject area.
RI.4.7 Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears.
RI.4.8 Explain how an author uses reasons and evidence to support particular points in a text.
RI.4.9 Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably.
Writing:
W.4.1a-d Write opinion pieces on topics or texts, supporting a point of view with reasons and information.
a. Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer’s purpose.
b. Provide reasons that are supported by facts and details.
c. Link opinion and reasons using words and phrases (e.g., for instance, in order to, in addition).
d. Provide a concluding statement or section related to the opinion presented.
W.4.2a-e Write informative/explanatory texts to examine a topic and convey ideas and information clearly.
a. Introduce a topic clearly and group related information in paragraphs and sections; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.
b. Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.
c. Link ideas within categories of information using words and phrases (e.g., another, for example, also, because).
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
e. Provide a concluding statement or section related to the information or explanation presented.
W.4.7 Conduct short research projects that build knowledge through investigation of different aspects of a topic.
W.4.8 Recall relevant information from experiences or gather relevant information from print and digital sources; take notes and categorize information, and provide a list of sources.
W.4.9 Draw relevant evidence from grade-appropriate literary or informational texts to support analysis, reflection, and research.
Language:
L.4.1a-g Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
a. Use relative pronouns (who, whose, whom, which, that) and relative adverbs (where, when, why).
b. Form and use the progressive (e.g., I was walking; I am walking; I will be walking) verb tenses.
c. Use modal auxiliaries (e.g., can, may, must) to convey various conditions.
d. Order adjectives within sentences according to conventional patterns (e.g., a small red bag rather than a red small bag).
e. Form and use prepositional phrases.
f. Produce complete sentences, recognizing and correcting inappropriate fragments and run-ons.
g. Correctly use frequently confused words (e.g., to, too, two; there, their).
L.4.2a-d Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use correct capitalization.
b. Use commas and quotation marks to mark direct speech and quotations from a text.
c. Use a comma before a coordinating conjunction in a compound sentence.
d. Spell grade-appropriate words correctly, consulting references as needed.
L.4.3a-b Use knowledge of language and its conventions when writing, speaking, reading, or listening.
a. Choose words and phrases to convey ideas precisely.
b. Choose punctuation for effect.
c. Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion).
L.4.5 Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
a. Explain the meaning of simple similes and metaphors (e.g., as pretty as a picture) in context.
b. Recognize and explain the meaning of common idioms, adages, and proverbs.
c. Demonstrate understanding of words by relating them to their opposites (antonyms) and to words with similar but not identical meanings (synonyms).
L.4.6 Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation).
Speaking and Listening:
SL.4.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 topics and texts, building on others’ ideas and expressing their own clearly.
a. Come to discussions prepared, having read or studied required material; explicitly draw on that
preparation and other information known about the topic to explore ideas under discussion.
b. Follow agreed-upon rules for discussions and carry out assigned roles.
c. Pose and respond to specific questions to clarify or follow up on information, and make comments that contribute to the discussion and link to the remarks of others.
d. Review the key ideas expressed and explain their own ideas and understanding in light of the discussion.
SL.4.2 Paraphrase portions of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.
SL.4.4 Report on a topic or text, tell a story, or recount an experience in an organized manner, using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace.  
SL.4.6 Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion); use formal English when appropriate to task, audience, and situation.

The following standards are embedded in all units:
RL. /RI.4.1 Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.
RL.4.10 By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.
RI.4.10 By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.
RF.4.4 Read with sufficient accuracy and fluency to support comprehension.
W.4.4 Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience.
W.4.5 With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.
W.4.6 With some guidance and support from adults, produce and publish grade-appropriate writing using technology, either independently or in collaboration with others.
W.4.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
L.4.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 4 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., definitions, examples, or restatements in text) as a clue to the meaning of a word or phrase.
b. Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., telegraph, photograph, autograph).
c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.
L.4.6 Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation).

Enduring Understandings:

• People with different points of view can find common ground.
• The Revolutionary War impacted America in a variety of ways.

Essential Questions:

• How do choices and experiences help a person determine their point of view on a topic or issue?
• Were the colonists justified in declaring their independence and fighting the Revolutionary War?

Unit 3 The Lightning Thief

Unit Length: 67 days
Description: Students read literary and informational texts to understand traditional stories that focus on common patterns in literature, specifically the quest. Students express their understanding of how literature helps us make sense of the world, and how literature from the past influences our current lives and contemporary stories.

Standards:

Reading Literature:
RL.4.2 Determine a theme of a story, drama, or poem from details in the text; summarize the text.
RL.4.3 Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text (e.g.,
a character’s thoughts, words, or actions).
RL.4.7 Make connections between the text of a story or drama and a visual or oral presentation of the text.
RL.4.9 Compare and contrast the treatment of similar themes and topics (e.g., opposition of good and evil) and patterns of events (e.g., the quest) in stories, myths, and traditional literature from different cultures.
RI.4.2 Determine the main idea of a text and explain how it is supported by key details; summarize the text.
RI.4.3 Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text.
RI.4.4 Determine the meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic or subject area.

Writing:
W.4.1a-d Write opinion pieces on topics or texts, supporting a point of view with reasons and information.
a. Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer’s purpose.
b. Provide reasons that are supported by facts and details.
c. Link opinion and reasons using words and phrases (e.g., for instance, in order to, in addition).
d. Provide a concluding statement or section related to the opinion presented.
W.4.2a-e Write informative/explanatory texts to examine a topic and convey ideas and information clearly.
a. Introduce a topic clearly and group related information in paragraphs and sections; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.
b. Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.
c. Link ideas within categories of information using words and phrases (e.g., another, for example, also, because).
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
e. Provide a concluding statement or section related to the information or explanation presented.
W.4.7 Conduct short research projects that build knowledge through investigation of different aspects of a topic.
W.4.8 Recall relevant information from experiences or gather relevant information from print and digital sources; take notes and categorize information, and provide a list of sources.
W.4.9 Draw relevant evidence from grade-appropriate literary or informational texts to support analysis, reflection, and research.
a. Apply grade 4 Reading standards to literature (e.g. “Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text [e.g. a characters’ thoughts, words, or actions].”).
b. Apply grade 4 Reading standards to informational texts (e.g. “Explain how an author uses reasons and evidence to support particular points in a text”).

Language:
L.4.1e-f Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
e. Form and use prepositional phrases.
f. Produce complete sentences, recognizing and correcting inappropriate fragments and run-ons.
g. Correctly use frequently confused words (e.g., to, too, two; there, their).
L.4.2b Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
b. Use commas and quotation marks to mark direct speech and quotations from a text.
L.4.3a Use knowledge of language and its conventions when writing, speaking, reading, or listening.
a. Choose words and phrases to convey ideas precisely.
L.4.5 Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
a. Explain the meaning of simple similes and metaphors (e.g., as pretty as a picture) in context.

Speaking and Listening:
SL.4.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 topics and texts, building on others’ ideas and expressing their own clearly.
a. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.
b. Follow agreed-upon rules for discussions and carry out assigned roles.
c. Pose and respond to specific questions to clarify or follow up on information, and make comments that contribute to the discussion and link to the remarks of others.
d. Review the key ideas expressed and explain their own ideas and understanding in light of the discussion.
SL.4.2 Paraphrase portions of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.
SL.4.4 Report on a topic or text, tell a story, or recount an experience in an organized manner, using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace.  
SL.4.6 Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion); use formal English when appropriate to task, audience, and situation.

The following standards are embedded in all units:
RL. /RI.4.1 Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.
RL.4.10 By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.
RI.4.10 By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.
RF.4.4 Read with sufficient accuracy and fluency to support comprehension.
W.4.4 Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience.
W.4.5 With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.
W.4.6 With some guidance and support from adults, produce and publish grade-appropriate writing using technology, either independently or in collaboration with others.
W.4.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
L.4.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 4 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., definitions, examples, or restatements in text) as a clue to the meaning of a word or phrase.
b. Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., telegraph, photograph, autograph).
c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.
L.4.6 Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation).

Enduring Understandings:

• The quest motif is the pursuit of an important item or knowledge that often leads to a character becoming a hero.
• An author can use a theme in a story to teach a life lesson.

Essential Questions:

• How do lessons learned from literature impact us and our modern culture?
• What is a myth and what can we learn from them?

Unit 1 The Making of a Scientist

Unit Length: 50.5 days
Description: Students read informational and literary texts to understand how different scientific theories have changed over time. They express their understanding about these theories and the process of scientific inquiry by gathering evidence and comparing and contrasting different theories.

Standards:

Reading Literature:
RL.5.2 Determine a theme of a story, drama, or poem from details in the text, including how characters in a story or drama respond to challenges or how the speaker in a poem reflects upon a topic; summarize the text.
RL.5.3 Compare and contrast two or more characters, settings, or events in a story or drama, drawing on specific details in the text (e.g., how characters interact).
RL.5.4 Determine the meaning of words and phrases as they are used in a text, including figurative language and connotative meanings.
RL.5.5 Explain how a series of chapters, scenes, or stanzas fits together to provide overall structure of a particular story, drama, or poem.
Reading Informational Text:
RI.5.2 Determine two or more main ideas of a text and explain how they are supported by key details; summarize the text.
RI.5.3 Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text.
RI.5.4 Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5 topic or subject area.
RI.5.6 Analyze multiple accounts of the same event or topic, noting important similarities and differences in the point of view they represent.
RI.5.7 Utilize information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently.
RI.5.8 Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point(s).
RI.5.9 Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably.

Reading Foundational Skills:
RF.5.3a Know and apply grade-level phonics and word analysis skills in decoding words.
a. Use combined knowledge of letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context.
Writing:
W.5.2 Write informative/explanatory texts to examine a topic and convey ideas and information clearly.
a. Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.
b. Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.
c. Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially).
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
e. Provide a concluding statement or section related to the information or explanation presented.
W.5.5 With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a different approach.
W.5.9 Draw relevant evidence from grade-appropriate literary or informational texts to support analysis, reflection, and research.
Language:
L.5.1 Demonstrate command of the conventions of Standard English grammar and usage when writing or speaking.
a. Explain the function of conjunctions, prepositions, and interjections in general and their function in particular sentences.
b. Form and use the perfect (e.g., I had walked; I have walked; I will have walked) verb tenses.
c. Use verb tense to convey various times, sequences, states, and conditions.
d. Recognize and correct inappropriate shifts in verb tense.
e. Use correlative conjunctions (e.g., either/or, neither/nor).
L.5.2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use punctuation to separate items in a series.
b. Use a comma to separate an introductory element from the rest of the sentence.
c. Use a comma to set off the words yes and no (e.g., Yes, thank you), to set off a tag question from the rest of the sentence (e.g., It’s true, isn’t it?), and to indicate direct address (e.g., Is that you, Steve?).
d. Use underlining, quotation marks, or italics to indicate titles of works.
e. Spell grade-appropriate words correctly, consulting references as needed.
Speaking and Listening:
SL.5.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly.
a. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.
b. Follow agreed-upon rules for discussions and carry out assigned roles.
c. Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others.
d. Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions.
SL.5.2 Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.
SL.5.4 Report on a topic or text or present an opinion, sequencing ideas logically and using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace.

The following standards are embedded in all units:
RL. /RI.5.1 Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.
RL.5.10 By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 4–5 text complexity band independently and proficiently.
RI.5.10 By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 4–5 text complexity band independently and proficiently.
RF.5.4 Read with sufficient accuracy and fluency to support comprehension.
W.5.4 Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience.
W.5.5 With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a different approach.
W.5.6 With some guidance and support from adults, produce and publish grade-appropriate writing using technology, either independently or in collaboration with others.
W.5.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
L.5.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 5 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., cause/effect relationships and comparisons in text) as a clue to the meaning of a word or phrase.
b. Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., photograph, photosynthesis).
c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.
L.5.6 Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships (e.g., however, although, nevertheless, similarly, moreover, in addition).

Enduring Understandings:

• The process of scientific inquiry allows for gathering evidence and comparing and contrasting different theories.
• Authors can use short stories or memoirs to teach a lesson.

Essential Questions:

• How is a scientific theory formed and how does it change over time?
• What is the importance of thinking like a scientist?

Unit 2 The Birchbark House

Unit Length: 57.5 days
Description: Students read literary and informational texts about how Native Americans and global explorers laid the foundation for the United States. Students understand and express their understanding of how we learn about our past and how that impacts who we are today by writing about character and theme development and discussing how point of view is important for constructing meaning.

Standards:

Reading Literature:
RL.5.2 Determine a theme of a story, drama, or poem from details in the text, including how characters in a story or drama respond to challenges or how the speaker in a poem reflects upon a topic; summarize the text.
RL.5.3 Compare and contrast two or more characters, settings, or events in a story or drama, drawing on specific details in the text (e.g., how characters interact).
RL.5.4 Determine the meaning of words and phrases as they are used in a text, including figurative language and connotative meanings
RL.5.5 Explain how a series of chapters, scenes, or stanzas fits together to provide overall structure of a particular story, drama, or poem.
RL.5.6 Describe how a narrator’s or speaker’s point of view influences how events are described.
Reading Informational Text:
RI.5.3 Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text.
RI.5.4 Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5 topic or subject area.
RI.5.6 Analyze multiple accounts of the same event or topic, noting important similarities and differences in the point of view they represent.
RI.5.7 Utilize information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently.
RI.5.8 Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point(s).
RI.5.9 Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably.
Reading Foundational Skills:
RF.5.3a Know and apply grade-level phonics and word analysis skills in decoding words.
a. Use combined knowledge of letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context.
Writing:
W.5.1a-d Write opinion pieces on topics or texts, supporting a point of view with reasons and information.
a. Introduce a topic or text clearly, state an opinion, and create an organizational structure in which ideas are logically grouped to support the writer’s purpose.
b. Provide logically ordered reasons that are supported by facts and details.
c. Link opinion and reasons using words, phrases, and clauses (e.g., consequently, specifically).
d. Provide a concluding statement or section related to the opinion presented.
W.5.2 Write informative/explanatory texts to examine a topic and convey ideas and information clearly.
a. Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.
b. Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.
c. Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially).
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
e. Provide a concluding statement or section related to the information or explanation presented.
W.5.8 Recall relevant information from experiences or gather relevant information from print and digital sources; summarize or paraphrase information in notes and finished work, and provide a list of sources.
Language:
L.5.5 Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
a. Interpret figurative language, including similes and metaphors, in context.
b. Recognize and explain the meaning of common idioms, adages, and proverbs.
c. Use the relationship between particular words (e.g., synonyms, antonyms, homographs) to better understand each of the words.
Speaking and Listening:
SL.5.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly.
a. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.
b. Follow agreed-upon rules for discussions and carry out assigned roles.
c. Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others.
d. Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions.
SL.5.2 Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.
SL.5.3 Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence.
SL.5.6 Adapt speech to a variety of contexts and tasks, using formal English when appropriate to task, audience, and situation.

The following standards are embedded in all units:
RL. /RI.5.1 Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.
RL.5.10 By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 4–5 text complexity band independently and proficiently.
RI.5.10 By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 4–5 text complexity band independently and proficiently.
RF.5.4 Read with sufficient accuracy and fluency to support comprehension.
W.5.4 Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience.
W.5.5 With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a different approach.
W.5.6 With some guidance and support from adults, produce and publish grade-appropriate writing using technology, either independently or in collaboration with others.
W.5.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
L.5.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 5 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., cause/effect relationships and comparisons in text) as a clue to the meaning of a word or phrase.
b. Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., photograph, photosynthesis).
c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.
L.5.6 Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships (e.g., however, although, nevertheless, similarly, moreover, in addition).

Enduring Understandings:

• Authors teach us life lessons through characters and their development.
• The foundation of the United States is based on Native Americans and early explorers.

Essential Questions:

• How does an author of fiction use real events to teach us about the past?
• What was the impact of Christopher Columbus’s arrival in the New World?

Unit 3 The Lion, the Witch, and the Wardrobe

Unit Length: 63 days
Description: Students read literary texts to understand that even in the most fantastical settings, literature can teach us real lessons about life. Students explore the opposition of good vs. evil, the value in courage, adventure, forgiveness, and honesty. They begin to consider how authors convince readers to believe the impossible and discuss the history and use of special effects in movies to begin to see how imagination and creativity can inspire story-telling. Students express their understanding of narrative point of view and the features of the fantasy genre by considering the stories from another perspective.

Standards:

Reading Literature:
RL.5.2 Determine a theme of a story, drama, or poem from details in the text, including how characters in a story or drama respond to challenges or how the speaker in a poem reflects upon a topic; summarize the text.
RL.5.3 Compare and contrast two or more characters, settings, or events in a story or drama, drawing on specific details in the text (e.g., how characters interact).
RL.5.4 Determine the meaning of words and phrases as they are used in a text, including figurative language and connotative meanings.
RL.5.6 Describe how a narrator’s or speaker’s point of view influences how events are described.

Reading Informational Text:
RI.5.2 Determine two or more main ideas of a text and explain how they are supported by key details; summarize the text.
RI.5.3 Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text.
RI.5.9 Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably.
Reading Foundational Skills:
RF.5.3a Know and apply grade-level phonics and word analysis skills in decoding words.
a. Use combined knowledge of letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context.

Writing:
W.5.1 Write opinion pieces on topics or texts, supporting a point of view with reasons and information.
a. Introduce a topic or text clearly, state an opinion, and create an organizational structure in which ideas are logically grouped to support the writer’s purpose.
b. Provide logically ordered reasons that are supported by facts and details.
c. Link opinion and reasons using words, phrases, and clauses (e.g., consequently, specifically).
d. Provide a concluding statement or section related to the opinion presented.
W.5.2 Write informative/explanatory texts to examine a topic and convey ideas and information clearly.
a. Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.
b. Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.
c. Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially).
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
e. Provide a concluding statement or section related to the information or explanation presented.
W.5.3 Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.
a. Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally.
b. Use narrative techniques, such as dialogue, description, and pacing, to develop experiences and events or show the responses of characters to situations.
c. Use a variety of transitional words, phrases, and clauses to manage the sequence of events.
d. Use concrete words and phrases and sensory details to convey experiences and events precisely.
e. Provide a conclusion that follows from the narrated experiences or events.
W.5.8 Recall relevant information from experiences or gather relevant information from print and digital sources; summarize or paraphrase information in notes and finished work, and provide a list of sources.
W.5.9 Draw relevant evidence from grade-appropriate literary or informational texts to support analysis, reflection, and research.
Language:
L.5.1 Demonstrate command of the conventions of Standard English grammar and usage when writing or speaking.
a. Explain the function of conjunctions, prepositions, and interjections in general and their function in particular sentences.
b. Form and use the perfect (e.g., I had walked; I have walked; I will have walked) verb tenses.
c. Use verb tense to convey various times, sequences, states, and conditions.
d. Recognize and correct inappropriate shifts in verb tense.
e. Use correlative conjunctions (e.g., either/or, neither/nor).
L.5.3 Use knowledge of language and its conventions when writing, speaking, reading, or listening.
a. Expand, combine, and reduce sentences for meaning, reader/listener interest, and style.
b. Compare and contrast the varieties of English (e.g., dialects, registers) used in stories, dramas, or poems.

Speaking and Listening:
SL.5.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly.
a. Come to discussions prepared, having read or studied required material; explicitly draw on that
preparation and other information known about the topic to explore ideas under discussion.
b. Follow agreed-upon rules for discussions and carry out assigned roles.
c. Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others.
d. Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions.
SL.5.2 Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.
SL.5.4 Report on a topic or text or present an opinion, sequencing ideas logically and using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace.

The following standards are embedded in all units:
RL. /RI.5.1 Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.
RL.5.10 By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 4–5 text complexity band independently and proficiently.
RI.5.10 By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 4–5 text complexity band independently and proficiently.
RF.5.4 Read with sufficient accuracy and fluency to support comprehension.
W.5.4 Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience.
W.5.5 With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a different approach.
W.5.6 With some guidance and support from adults, produce and publish grade-appropriate writing using technology, either independently or in collaboration with others.
W.5.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
L.5.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 5 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., cause/effect relationships and comparisons in text) as a clue to the meaning of a word or phrase.
b. Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., photograph, photosynthesis).
c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.
L.5.6 Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships (e.g., however, although, nevertheless, similarly, moreover, in addition).

Enduring Understandings:

• Reading fantastical stories can teach us lessons about life.
• Visual representations such as graphs and illustrations, can support and enhance a reader’s understanding of the text.

Essential Questions:

• How does the point of view or perspective help a reader have a deeper understanding of the text?
• How does an author convince readers to believe the impossible?

 

Unit 1 Hatchet

Unit Length: 56.5 days
Description: Students read literary and informational texts to understand how positive thinking, slowing down to think clearly, problem solving, and constant vigilance support survival in the face of grave danger and overwhelming odds. Students express their understanding of characters in literature by analyzing the struggle of man versus nature and the life lessons we can learn from others’ survival situations.

Standards:

Reading Literature:
RL.6.2: Determine a theme or central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments.
RL.6.3: Describe how a particular story’s or drama’s plot unfolds in a series of episodes as well as how the characters respond or change as the plot moves towards a resolution.
RL.6.4: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of a specific word choice on meaning and tone.
RL.6.5: Analyze how a particular sentence, chapter, scene, or stanza fits into the overall structure of a text and contributes to the development of the theme, setting, or plot.
RL.6.6: Explain how an author develops the point of view of the narrator or speaker in a text.

Reading Informational Texts:
RI.6.2: Determine a central ideal of a text and how it is conveyed through particular detail; provide a summary of the text distinct from personal opinions or judgments.
RI.6.6: Determine an author’s point of view or purpose in a text and explain how it is conveyed in the text.
Writing:
W.6.1: Write arguments to support claims with clear reasons and relevant evidence.
a. Introduce claim(s) and organize the reasons and evidence clearly.
b. Support claim(s) with clear reasons and relevant evidence, using credible sources and demonstrating an understanding of the topic or text.
c. Use words, phrases, and clauses to clarify the relationships among claim(s) and reasons.
d. Establish and maintain a formal style.
e. Provide a concluding statement or section that follows from the argument presented.
W.6.2: Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.
W.6.3: Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.
W.6.9: Draw relevant evidence from grade-appropriate literary or informational texts to support analysis, reflection, and research.

Speaking and Listening:
SL.6.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led) with diverse partners on grade 6 topics, texts, issues, building on others’ ideas and expressing their own clearly.
a. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.
b. Follow rules for collegial discussion, set specific goals and deadlines, and define individual roles as needed.
c. Pose and respond to specific questions with elaboration and detail by making comments that contribute to the topic, text, or issue under discussion.
d. Review the key ideas expressed and demonstrate understanding of multiple perspectives through reflection and paraphrasing.
SL.6.4: Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details to accentuate main ideas or themes; use appropriate eye contact, adequate volume, and clear pronunciation.

Language:
L.6.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
a. Ensure that pronouns are in the proper case (subjunctive, objective, possessive)
b. Use intensive pronouns (e.g., myself, ourselves).
c. Recognize and correct inappropriate shifts in pronoun number and person.
d. Recognize and correct vague pronouns (i.e., ones with unclear or ambiguous antecedents).
e. Recognize variation from standard English in their own and others’ writing and speaking, and identify and use strategies to improve expression in conventional language.
L.6.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use punctuation (commas, parentheses, dashes) to set off nonrestrictive/parenthetical elements.
b. Spell correctly.

The following standards are embedded in all units:
RL./RI.6.1 Cite relevant textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
RL.6.10 By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range.
RI.6.10 By the end of the year, read and comprehend literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range.
W.6.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
W.6.5 With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a different approach.
W.6.6 Produce and publish grade-appropriate writing using technology, either independently or in collaboration with others.
W.6.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
L.6.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 6 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase.
b. Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., audience, auditory, audible).
c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech.
d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).
L.6.6 Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Enduring Understandings:

• A person’s character is revealed during difficult times, as well as good times.
• Bravery is the ability to do something you fear even though you are afraid at the time.

Essential Questions:

• Does Hatchet have instructional value as a survival guide?
• What life lessons can we learn by reading other people’s stories of survival?

Unit 2 If Stones Could Speak

Unit Length: 52.5 days
Description: Students read literary and informational texts to understand that archaeologists, like detectives, work to piece together the past through investigation. Students express their understanding by analyzing evidence and drawing meaningful conclusions about history, texts, and their environment.

Standards:

Reading Literature:
RL.6.2: Determine a theme or central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments.
RL.6.4: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of a specific word choice on meaning and tone.

Reading Informational Texts:
RI.6.2: Determine a central ideal of a text and how is it conveyed through particular detail; provide a summary of the text distinct from personal opinions or judgments.
RI.6.3: Analyze in detail how a key individual, event, or idea is introduced, illustrated, and elaborated in a text (e.g., through examples or anecdotes).
RI.6.4: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.
RI.6.5: Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of a text and contributes to the development of the ideas.
RI.6.6: Determine an author’s point of view or purpose in a text and explain how it is conveyed in the text.
RI.6.8: Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not.
RI.6.9: Compare and contrast one author’s presentation of events with that of another (e.g., a memoir written by and a biography on the same person).

Writing:
W.6.1: Write arguments to support claims with clear reasons and relevant evidence.
W.6.2: Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.
a. Introduce a topic; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.
b. Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples.
c. Use appropriate transitions to clarify the relationships among ideas and concepts.
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
e. Establish and maintain a formal style.
f. Provide a concluding statement or section that follows from the information or explanation presented.
W.6.3: Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.
W.6.7: Conduct short research projects to answer a question, drawing on several sources and refocusing the inquiry when appropriate.
W.6.8: Gather relevant information from multiple print and digital sources; assess the credibility of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and providing basic bibliographic information for sources.
W.6.9: Draw relevant evidence from grade-appropriate literary or informational texts to support analysis, reflection, and research.

Speaking and Listening:
SL.6.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led) with diverse partners on grade 6 topics, texts, issues, building on others’ ideas and expressing their own clearly.
a. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.
b. Follow rules for collegial discussion, set specific goals and deadlines, and define individual roles as needed.
c. Pose and respond to specific questions with elaboration and detail by making comments that contribute to the topic, text, or issue under discussion.
d. Review the key ideas expressed and demonstrate understanding of multiple perspectives through reflection and paraphrasing.
SL.6.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use punctuation (commas, parentheses, dashes) to set off nonrestrictive/parenthetical elements.
b. Spell correctly.

Language:
L.6.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
a. Ensure that pronouns are in the proper case (subjunctive, objective, possessive)
b. Use intensive pronouns (e.g., myself, ourselves).
c. Recognize and correct inappropriate shifts in pronoun number and person.
d. Recognize and correct vague pronouns (i.e., ones with unclear or ambiguous antecedents).
L.6.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use punctuation (commas, parentheses, dashes) to set off nonrestrictive/parenthetical elements.
b. Spell correctly.
L.6.3: Delineate a speaker’s argument and specific claims, distinguishing claims that are supported by reasons and evidence from claims that are not.
L.6.5: Include multimedia components (e.g., graphics, images, music, sound) and visual displays in presentations to clarify information.

The following standards are embedded in all units:
RL./RI.6.1 Cite relevant textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
RL.6.10 By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range.
RI.6.10 By the end of the year, read and comprehend literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range.
W.6.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
W.6.5 With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a different approach.
W.6.6 Produce and publish grade-appropriate writing using technology, either independently or in collaboration with others.
W.6.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
L.6.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 6 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase.
b. Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., audience, auditory, audible).
c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech.
d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).
L.6.6 Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Enduring Understandings:

• Archaeology allows us to understand what life was like in the past.
• Thinking about something in a new or fresh way can help us discover new secrets about our world.

Essential Questions:

• What is meant by the saying, “If stones could speak…?”
• How does an author support his/her ideas throughout the text?

Unit 3 The Witch of Blackbird Pond

Unit Length: 62 days
Description: Students read literary and informational texts to understand the influence of family expectations and values on the development of one’s personal identity. Students express their understanding of how informational texts in coordination with literary texts enhance their comprehension of time periods and the theme and setting of the novel.

Standards:

Reading Literature:
RL.6.2: Determine a theme or central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments.
RL.6.3: Describe how a particular story’s or drama’s plot unfolds in a series of episodes as well as how the characters respond or change as the plot moves towards a resolution.
RL.6.4: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of a specific word choice on meaning and tone.
RL.6.5: Analyze how a particular sentence, chapter, scene, or stanza fits into the overall structure of a text and contributes to the development of the theme, setting, or plot.
RL.6.6: Explain how an author develops the point of view of the narrator or speaker in a text.

Reading Informational Texts:
RI.6.2: Determine a central ideal of a text and how it is conveyed through particular detail; provide a summary of the text distinct from personal opinions or judgments.
RI.6.4: Determine the meaning of words and phrases as they are used in a text, including figurative language, connotative, and technical meanings.

Writing:
W.6.1: Write arguments to support claims with clear reasons and relevant evidence.
W.6.2: Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.
W.6.6: Use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of three pages in a single setting.
W.6.7: Conduct short research projects to answer a question, drawing on several sources and refocusing the inquiry when appropriate.

Speaking and Listening:
SL.6.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led) with diverse partners on grade 6 topics, texts, issues, building on others’ ideas and expressing their own clearly.
SL.6.3: Delineate a speaker’s argument and specific claims, distinguishing claims that are supported by reasons and evidence from claims that are not.

Language
L.6.3: Use knowledge of language and its conventions when writing, speaking, reading, or listening.

The following standards are embedded in all units:
RL. /RI.6.1 Cite relevant textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
RL.6.10 By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range.
RI.6.10 By the end of the year, read and comprehend literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range.
W.6.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
W.6.5 With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a different approach.
W.6.6 Produce and publish grade-appropriate writing using technology, either independently or in collaboration with others.
W.6.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
L.6.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 6 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase.
b. Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., audience, auditory, audible).
c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech.
d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).
L.6.6 Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Enduring Understandings:

• A person’s identity is influenced by family values and expectations.
• Various literary texts can present a theme from different points of view.

Essential Questions:

• How can an author use history to influence the setting and plot of literary texts?
• What is loyalty and how do we show our loyalty to what we believe in?

Unit 1 Memoir: Guidebook 2018

Unit Length: 11 Weeks
Description: Students read various memoirs and texts about a writer’s craft to understand the importance of memoirs and “coming of age” literature. Students express their understanding by exploring their own voice and style as a writer, observing the firsthand connection between reading and writing, as they write their own memoir.

Standards
Reading Literature
RL.7.2: Determine a theme or central idea of a text and analyze its development over the course of the text; provide an objective summary of the text.
RL.7.3: Analyze how particular elements of a story or drama interact (e.g., how setting shapes the characters or plot).
RL.7.6: Analyze how an author develops and contrasts the points of view of different characters or narrators in a text.

Reading Informational Text
RI.7.2: Determine two or more central ideas in a text and analyze their development over the course of the text; provide an objective summary of the text.
RI.7.4: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of a specific word choice on meaning and tone.
RI.7.5: Analyze the structure an author uses to organize a text, including how the major sections contribute to the whole and to the development of the ideas.
RI.7.8: Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims.

Writing
W.7.1: Write arguments to support claims with clear reasons and relevant evidence.
a. Introduce claim(s), acknowledge alternate or opposing claims, and organize the reasons and evidence logically.
b. Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text.
c. Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), reasons, and evidence.
d. Establish and maintain a formal style.
e. Provide a concluding statement or section that follows from and supports the argument presented.
W.7.3: Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.
a. Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically.
b. Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters.
c. Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another.
d. Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events.
e. Provide a conclusion that follows from and reflects on the narrated experiences or events.

Speaking and Listening
SL.7.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led) with diverse partners on grade 7 topics, texts, and issues, building on others’ ideas and expressing their own clearly.
a. Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.
b. Follow rules for collegial discussions, track progress toward specific goals and deadlines, and define individual roles as needed.
c. Pose questions that elicit elaboration and respond to others’ questions and comments with relevant observations and ideas that bring the discussion back on topic as needed.
d. Acknowledge new information expressed by others and, when warranted, modify their own views.

Language
L.7.5: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
b. Use the relationship between particular words (e.g., synonym/antonym, analogy) to better understand each of the words.
c. Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., refined, respectful, polite, diplomatic, condescending).

Enduring Understandings:

• Students understand the importance of memoirs and “coming of age” literature.
• Students understand by exploring their own voice and style as a writer.

Essential Questions:

• Does the memoir you read support and/or contradict Zinsser’s advice for writing a memoir in “How to Write a Memoir”?
• How have you learned about your own voice and style in writing?

Unit 2 A Christmas Carol: Guidebook 2018

Unit Length: 13 Weeks
Description: Students read literary and informational texts about the meaning and redemption found through selflessness and valuing people over material possessions. Students understand how writers use stories to teach us these lessons and how characters’ choices affect the plot and build the theme of a story. Students express their understanding by exploring how literature resonates with readers and has “staying power,” becoming a part of our language, culture, and moral code.

Standards
Reading Literature
RL.7.2: Determine a theme or central idea of a text and analyze its development over the course of the text; provide an objective summary of the text.
RL.7.3: Analyze how particular elements of a story or drama interact (e.g., how setting shapes the characters or plot).
RL.7.6: Analyze how an author develops and contrasts the points of view of different characters or narrators in a text.

Reading Informational Text
RI.7.2: Determine two or more central ideas in a text and analyze their development over the course of the text; provide an objective summary of the text.
RI.7.3: Analyze the interactions between individuals, events, and ideas in a text (e.g., how ideas influence individuals or events, or how individuals influence ideas or events).
RI.7.8: Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims.
RI.7.9: Analyze how two or more authors writing about the same topic shape their presentations of key information by emphasizing different evidence or advancing different interpretations of facts.

Writing
W.7.1: Write arguments to support claims with clear reasons and relevant evidence.
a. Introduce claim(s), acknowledge alternate or opposing claims, and organize the reasons and evidence logically.
b. Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text.
c. Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), reasons, and evidence.
d. Establish and maintain a formal style.
e. Provide a concluding statement or section that follows from and supports the argument presented.
W.7.2: Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.
a. Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.
b. Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples.
c. Use appropriate transitions to create cohesion and clarify the relationships among ideas and concepts.
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
e. Establish and maintain a formal style.
f. Provide a concluding statement or section that follows from and supports the information or explanation presented.
W.7.7: Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation.
W.7.9: Draw relevant evidence from grade-appropriate literary or informational texts to support analysis, reflection, and research.
a. Apply grade 7 Reading standards to literature (e.g., “Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history”).
b. Apply grade 7 Reading standards to literary nonfiction (e.g. “Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims”).

Speaking and Listening
SL.7.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led) with diverse partners on grade 7 topics, texts, and issues, building on others’ ideas and expressing their own clearly.
a. Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.
b. Follow rules for collegial discussions, track progress toward specific goals and deadlines, and define individual roles as needed.
c. Pose questions that elicit elaboration and respond to others’ questions and comments with relevant observations and ideas that bring the discussion back on topic as needed.
d. Acknowledge new information expressed by others and, when warranted, modify their own views.

Language
SL.7.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
a. Explain the function of phrases and clauses in general and their function in specific sentences.
b. Choose among simple, compound, complex, and compound-complex sentences to signal differing relationships among ideas.
c. Place phrases and clauses within a sentence, recognizing and correcting misplaced and dangling modifiers.

Enduring Understandings:

• Students understand the meaning and redemption found through selflessness and valuing people over material possessions. Students understand how writers use stories to teach us these lessons and how characters’ choices affect the plot and build the theme of a story.
• Students understand how writers use stories to teach us these lessons and how characters’ choices affect the plot and build the theme of a story.

Essential Questions:

• What does Dickens want us to understand about the “business” of being human?
• How has Charles Dickens influenced modern society?

Unit 3 The Giver: Guidebook 2018

Unit Length: 12 Weeks
Description: Students read dystopian literature and related informational texts to understand how individual perspectives are shaped by knowledge and memory and to determine whether perfection is worth the sacrifice. Students express their understanding by analyzing how a theme is developed through characters and their contrasting points of view and also comparing and contrasting the themes of similar texts.

Standards
Reading Literature
RL.7.2: Determine a theme or central idea of a text and analyze its development over the course of the text; provide an objective summary of the text.
RL.7.3: Analyze how particular elements of a story or drama interact (e.g., how setting shapes the characters or plot).
RL.7.4: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of rhymes and other repetitions of sounds (e.g., alliteration) on a specific verse or stanza of a poem or section of a story or drama.
RL.7.6: Analyze how an author develops and contrasts the points of view of different characters or narrators in a text.

Reading Informational Text
RI.7.2: Determine two or more central ideas in a text and analyze their development over the course of the text; provide an objective summary of the text.
RI.7.4: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of a specific word choice on meaning and tone.

Writing
W.7.1: Write arguments to support claims with clear reasons and relevant evidence.
a. Introduce claim(s), acknowledge alternate or opposing claims, and organize the reasons and evidence logically.
b. Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text.
c. Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), reasons, and evidence.
d. Establish and maintain a formal style.
e. Provide a concluding statement or section that follows from and supports the argument presented.
W.7.2: Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.
a. Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.
b. Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples.
c. Use appropriate transitions to create cohesion and clarify the relationships among ideas and concepts.
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
e. Establish and maintain a formal style.
f. Provide a concluding statement or section that follows from and supports the information or explanation presented.
W.7.7: Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation.
W.7.8: Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.

Speaking and Listening
SL.7.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led) with diverse partners on grade 7 topics, texts, and issues, building on others’ ideas and expressing their own clearly.
a. Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.
b. Follow rules for collegial discussions, track progress toward specific goals and deadlines, and define individual roles as needed.
c. Pose questions that elicit elaboration and respond to others’ questions and comments with relevant observations and ideas that bring the discussion back on topic as needed.
d. Acknowledge new information expressed by others and, when warranted, modify their own views.

Language
L.7.3: Use knowledge of language and its conventions when writing, speaking, reading, or listening.
a. Choose language that expresses ideas precisely and concisely, recognizing and eliminating wordiness and redundancy.
4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 7 reading and content, choosing flexibly from a range of strategies.
L.7.5: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
b. Use the relationship between particular words (e.g., synonym/antonym, analogy) to better understand each of the words.
c. Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., refined, respectful, polite, diplomatic, condescending).

Enduring Understandings:

• Students understand how individual perspectives are shaped by knowledge and memory and determine whether perfection is worth the sacrifice.
• Students understand how a theme is developed through characters and their contrasting points of view and also how to compare and contrast the themes of similar texts.

Essential Questions:

• How does Jonas’ unique point of view reveal a theme of The Giver?
• How does the theme of another dystopian text compare with the theme of The Giver?

Unit 1 Flowers for Algernon: Guidebook 2018

Unit Length: 11 weeks
Description: Students read literary and informational texts about knowledge and intelligence to understand what happens when humans try to manipulate the minds of others and how our understanding of intelligence has evolved over time. Students express their understanding of these ideas by exploring how authors draw on traditional stories and develop characters and themes to teach us about ourselves and others.

Standards
Reading Literature
RL.8.2: Determine a theme or central idea of a text and analyze its development over the course of the text, including its relationship to the characters, setting, and plot; provide an objective summary of the text.
RL.8.3: Analyze how particular lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision.
RL.8.4: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts.
RL.8.5: Compare and contrast the structure of two or more texts and analyze how the differing structure of each text contributes to its meaning and style.
RL.8.6: Analyze how differences in the points of view of the characters and the audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor.

Reading Informational Text
RI.8.4: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts.
RI.8.8: Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced.

Writing
W.8.1: Write arguments to support claims with clear reasons and relevant evidence.
a. Introduce claim(s), acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically.
b. Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text.
c. Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence.
d. Establish and maintain a formal style.
e. Provide a concluding statement or section that follows from and supports the argument presented.
W.8.2: Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.
a. Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.
b. Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples.
c. Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts.
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
e. Establish and maintain a formal style.
f. Provide a concluding statement or section that follows from and supports the information or explanation presented.
W.8.7: Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.

Speaking and Listening
SL.8.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 8 topics, texts, and issues, building on others’ ideas and expressing their own clearly.
a. Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.
b. Follow rules for collegial discussions and decision-making, track progress toward specific goals and deadlines, and define individual roles as needed.
c. Pose questions that connect the ideas of several speakers and respond to others’ questions and comments with relevant evidence, observations, and ideas.
d. Acknowledge new information expressed by others, and, when warranted, qualify or justify their own views in light of the evidence presented.
SL.8.3: Delineate a speaker’s argument and specific claims, evaluating the soundness of the reasoning and relevance and sufficiency of the evidence and identifying when irrelevant evidence is introduced.

Language
L.8.1: Demonstrate command of the conventions of Standard English grammar and usage when writing or speaking.
a. Explain the function of verbals (gerunds, participles, infinitives) in general and their function in particular sentences.
b. Form and use verbs in the active and passive voice.
c. Form and use verbs in the indicative, imperative, interrogative, conditional, and subjunctive mood.
d. Recognize and correct inappropriate shifts in verb voice and mood.
2. Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use punctuation (comma, ellipsis, dash) to indicate a pause or break.
b. Use an ellipsis to indicate an omission.
c. Spell correctly.
3. Use knowledge of language and its conventions when writing, speaking, reading, or listening.
a. Use verbs in the active and passive voice and in the conditional and subjunctive mood to achieve particular effects (e.g., emphasizing the actor or the action; expressing uncertainty or describing a state contrary to fact).

Enduring Understandings:

• Students understand what happens when humans try to manipulate the minds of others and how our understanding of intelligence has evolved over time.
• Students understand how authors draw on traditional stories and develop characters and themes to teach us about ourselves and others.

Essential Questions:

• Consider how Charlie has changed from the beginning of “Flowers for Algernon.” How does the surgery improve or worsen his quality of life?
• What are 2 different theories of intelligence?
• Why or why not are these theories accepted today?

 

Unit 2 The Tell-Tale Heart: Guidebook 2018

Unit Length:13 Weeks
Description: Students read literary and informational texts to understand the role of the narrator and point of view. Students also understand how the narrative voice of a text can blur the line between fact and fiction. Students express their understanding through writing in different points of view and examining motives and bias in various media.
Standards:

Reading Literature:
RL.8.2: Determine a theme or central idea of a text and analyze its development over the course of the text, including its relationship to the characters, setting, and plot; provide an objective summary of the text.
RL.8.3: Analyze how particular lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision.
RL.8.4: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts.
RL.8.5: Compare and contrast the structure of two or more texts and analyze how the differing structure of each text contributes to its meaning and style.
RL.8.6: Analyze how differences in the points of view of the characters and the audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor.

Reading Informational Text:
RI8.4: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts.
RI8.8: Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced.

Writing:
W.8.1: Write arguments to support claims with clear reasons and relevant evidence.
a. Introduce claim(s), acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically.
b. Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text.
c. Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence.
d. Establish and maintain a formal style.
e. Provide a concluding statement or section that follows from and supports the argument presented.
W.8.2: Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.
a. Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.
b. Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples.
c. Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts.
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
e. Establish and maintain a formal style.
f.  Provide a concluding statement or section that follows from and supports the information or explanation presented.
W.8.7: Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.

Speaking and Listening
SL.8.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 8 topics, texts, and issues, building on others’ ideas and expressing their own clearly.
a. Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.
b. Follow rules for collegial discussions and decision-making, track progress toward specific goals and deadlines, and define individual roles as needed.
c.  Pose questions that connect the ideas of several speakers and respond to others’ questions and comments with relevant evidence, observations, and ideas.
d. Acknowledge new information expressed by others, and, when warranted, qualify or justify their own views in light of the evidence presented.
SL.8.3: Delineate a speaker’s argument and specific claims, evaluating the soundness of the reasoning and relevance and sufficiency of the evidence and identifying when irrelevant evidence is introduced.

Language
L.8.1: Demonstrate command of the conventions of Standard English grammar and usage when writing or speaking.
a. Explain the function of verbals (gerunds, participles, infinitives) in general and their function in particular sentences.
b. Form and use verbs in the active and passive voice.
c. Form and use verbs in the indicative, imperative, interrogative, conditional, and subjunctive mood.
d. Recognize and correct inappropriate shifts in verb voice and mood.
L.8.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use punctuation (comma, ellipsis, dash) to indicate a pause or break.
b. Use an ellipsis to indicate an omission.
c.  Spell correctly.
L.8.3: Use knowledge of language and its conventions when writing, speaking, reading, or listening.
a. Use verbs in the active and passive voice and in the conditional and subjunctive mood to achieve particular effects (e.g., emphasizing the actor or the action; expressing uncertainty or describing a state contrary to fact).

Enduring Understandings:

• Students will understand how authors use narrator and point of view to influence our perspective and understanding, write using different points of view to impact meaning, and examine bias in media sources.
• Students will examine the concepts of truth, perception, and reality and understand how authors use text structure to develop these concepts.

Essential Questions:

• What is the relationship between truth, perception, and reality?
• How does each text develop the concept differently?

Unit 3 Call of the Wild: Guidebook 2018

Unit Length: 12 weeks
Description: Students read literary and informational texts about human interaction with animals and nature. They understand how authors portray animals to serve a purpose and make a comment about human interaction with animals. Students then explore scientific and personal accounts of animal cognition to express their understanding of Jack London’s portrayal of Buck and his interaction with humans in The Call of the Wild.

Standards:
Reading Literature
RL.8.2: Determine a theme or central idea of a text and analyze its development over the course of the text, including its relationship to the characters, setting, and plot; provide an objective summary of the text.
RL.8.3: Analyze how particular lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision.
RL.8.4: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts.
RL.8.6: Analyze how differences in the points of view of the characters and the audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor.

Reading Informational Text
RI.8.2: Determine a central idea of a text and analyze its development over the course of the text, including its relationship to supporting ideas; provide an objective summary of the text.
RI.8.6: Determine an author’s point of view or purpose in a text and analyze how the author acknowledges and responds to conflicting evidence or viewpoints.
RI.8.8: Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced.

Writing
W.7.1: Write arguments to support claims with clear reasons and relevant evidence.
a. Introduce claim(s), acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically.
b. Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text.
c. Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence.
d. Establish and maintain a formal style.
e. Provide a concluding statement or section that follows from and supports the argument presented.
W.8.2: Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.
a. Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.
b. Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples.
c. Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts.
d. Use precise language and domain-specific vocabulary to inform about or explain the topic.
e. Establish and maintain a formal style.
f. Provide a concluding statement or section that follows from and supports the information or explanation presented.

Speaking and Listening
SL.8.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 8 topics, texts, and issues, building on others’ ideas and expressing their own clearly.
a. Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.
b. Follow rules for collegial discussions and decision-making, track progress toward specific goals and deadlines, and define individual roles as needed.
c. Pose questions that connect the ideas of several speakers and respond to others’ questions and comments with relevant evidence, observations, and ideas.
d. Acknowledge new information expressed by others, and, when warranted, qualify or justify their own views in light of the evidence presented.
SL.8.4: Present claims and findings, emphasizing salient points in a focused, coherent manner with relevant evidence, sound valid reasoning, and well-chosen details; use appropriate eye contact, adequate volume, and clear pronunciation.

Language
L.8.4: Determine or clarify the meaning of unknown and multiple-meaning words or phrases based on grade 8 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase.
b. Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., precede, recede, secede).

Enduring Understandings:

• Students understand how authors portray animals to serve a purpose and make a comment about human interaction with animals.
• Students understand Jack London’s portrayal of Buck and his interaction with humans in The Call of the Wild.

Essential Questions:

• What central idea or theme about humans’ treatment of animals does The Call of the Wild convey?
• Given Jack London's characterization of Buck in the novel and your understanding of animal cognition, should he be considered a "nature faker"? Why or why not?

Unit 1 A Lesson Before Dying: Guidebook 2020

Unit Length: 12 weeks
Description: We will read A Lesson Before Dying by Ernest Gaines and a series of related literary and informational texts to explore the question: What makes us human?  We will express our understanding through an essay that examines the lessons learned about humanity in the novel, as well as how this lesson is presented in a secondary text.

Standards:
Reading Literature:
Key Ideas and Details
1. Cite relevant and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
2. Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.
3. Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme.
Craft and Structure
4. Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone).
5. Analyze how an author’s choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise.
6. Analyze a particular point of view or cultural experience reflected in works of literature drawing on a wide reading of world literature.

Reading Informational Texts:
Key Ideas and Details
1. Cite relevant and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
2. Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.
3. Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them.
Craft and Structure
4. Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language of a court opinion differs from that of a newspaper).
5. Analyze in detail how an author’s ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter).
6. Determine an author’s point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose.

Writing:
2. Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content.
a. Introduce a topic; organize complex ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.
b. Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic.
c. Use appropriate and varied transitions to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.
d. Use precise language and domain-specific vocabulary to manage the complexity of the topic.
e. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.
f. Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic).

Speaking and Listening:
1. Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher- led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively.
a. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas.
b. Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed.
c. Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions.
d. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented.

Language:
1. Demonstrate command of the conventions of Standard English grammar and usage when writing or speaking. a. Use parallel structure.
b. Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations.
2. Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent
clauses.
b. Use a colon to introduce a list or quotation.
c. Spell correctly.

Knowledge of Language
3. Apply knowledge of language to understand how language functions in different contexts, to make effective
choices for meaning or style, and to comprehend more fully when reading or listening.
a. Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Publication Manual of the American Psychological Association (APA), Turabian’s Manual for Writers) appropriate for the discipline and writing type.

Vocabulary Acquisition and Use
4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 9–10 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase.
b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech
(e.g., analyze, analysis, analytical; advocate, advocacy).
c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology.
d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).
5. Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
a. Interpret figures of speech (e.g., euphemism, oxymoron) in context and analyze their role in the text.
b. Analyze nuances in the meaning of words with similar denotations.
6. Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading,
writing, speaking, and listening at the college and career readiness level; demonstrate independence in
gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Enduring Understandings:

• Determine multiple lessons that Grant and Jefferson learn about what it means to be human.
• Use textual evidence from Lesson Before Dying to support the lessons learned.
• Determine how other texts from the unit support the lessons about being human.

Essential Questions:

• What makes us human?
• Though one is in jail and one is not, what similarities exist between Jefferson’s and Grant’s situations? Where would each character fall on Maslow’s hierarchy of needs?
• What theme about isolation is being developed in Lesson Before Dying and one other text in this section? How is the theme developed in Lesson Before Dying and the secondary text?
• How do the connections that both Grant and Jefferson have with other characters teach them lessons about humanity?
• What change in Grant’s and Jefferson’s views of their role in the world can be seen at the end of the novel? How do changes reflect lessons they have learned about being human?

Unit 2 Romeo and Juliet: Guidebook 2.0 Unit

Unit Length: 14 Weeks
Description: Students read The Tragedy of Romeo and Juliet and various literary and informational texts about choices and consequences. Students understand and express their understanding of how the motivations, decisions, and actions of complex characters propel the action of a story and how patterns and contrasts in language develop various motifs that reveal central ideas. Students will also apply their understanding of the teenage brain to Romeo and Juliet.

Standards:
Reading Literature:
Key Ideas and Details
1. Cite relevant and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
2. Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.
3. Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme.

Craft and Structure
4. Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone).
5. Analyze how an author’s choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise.
6. Analyze a particular point of view or cultural experience reflected in works of literature drawing on a wide reading of world literature.

Reading Informational Texts:
Key Ideas and Details
1. Cite relevant and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
2. Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.
3. Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them.

Craft and Structure
4. Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language of a court opinion differs from that of a newspaper).
5. Analyze in detail how an author’s ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter).
6. Determine an author’s point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose.

Writing:
1. Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.
a. Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among claim(s), counterclaims, reasons, and evidence.
b. Develop claim(s) and counterclaims fairly, supplying evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level and concerns.
c. Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.
d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.
e. Provide a concluding statement or section that follows from and supports the argument presented.
2. Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content.
a. Introduce a topic; organize complex ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.
b. Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic.
c. Use appropriate and varied transitions to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.
d. Use precise language and domain-specific vocabulary to manage the complexity of the topic.
e. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.
f. Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic).

Speaking and Listening:
Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher- led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively.
a. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas.
b. Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed.
c. Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions.
d. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented.
 

Language:
1. Demonstrate command of the conventions of Standard English grammar and usage when writing or speaking. a. Use parallel structure.
b. Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations.
2. Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent
clauses.
b. Use a colon to introduce a list or quotation.
c. Spell correctly.
Knowledge of Language
3. Apply knowledge of language to understand how language functions in different contexts, to make effective
choices for meaning or style, and to comprehend more fully when reading or listening.
a. Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Publication Manual of the American Psychological Association (APA), Turabian’s Manual for Writers) appropriate for the discipline and writing type.
Vocabulary Acquisition and Use
4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 9–10 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase.
b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech
(e.g., analyze, analysis, analytical; advocate, advocacy).
c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology.
d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).
5. Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
a. Interpret figures of speech (e.g., euphemism, oxymoron) in context and analyze their role in the text.
b. Analyze nuances in the meaning of words with similar denotations.
6. Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading,
writing, speaking, and listening at the college and career readiness level; demonstrate independence in
gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Enduring Understandings:

• Students understand and express their understanding of how the motivations, decisions, and actions of complex characters propel the action of a story and how patterns and contrasts in language develop various motifs that reveal central ideas.
• Students understand how research about the teenage brain applies to Romeo and Juliet.

Essential Questions:

• How do patterns or contrasts in language reveal a central idea of The Tragedy of Romeo and Juliet?
• What are the possible scientific causes of Romeo and Juliet’s behavior?
• Could different actions and decisions have prevented the end results?

Unit 3 The Joy Luck Club: Guidebook 2020

Unit Length: 9 Weeks
Description: We will read The Joy Luck Club by Amy Tan and a series of related literary and informational texts to explore the question:  How does a greater understanding of a person’s life experiences change our perception of them?  We will express our understanding through a narrative essay that explores how characters’ perceptions of each other in The Joy Luck Club influence their identity.  

Standards:
Reading Literature:
Key Ideas and Details
1. Cite relevant and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
2. Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.
3. Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme.

Craft and Structure
4. Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone).
5. Analyze how an author’s choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise.
6. Analyze a particular point of view or cultural experience reflected in works of literature drawing on a wide reading of world literature.

Reading Informational Texts:
Key Ideas and Details
1. Cite relevant and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
2. Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.
3. Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them.

Craft and Structure
4. Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language of a court opinion differs from that of a newspaper).
5. Analyze in detail how an author’s ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter).
6. Determine an author’s point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose.

Writing:
Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences.
a. Engage and orient the reader by setting out a problem, situation, or observation, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events.
b. Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, mood, tone, events, and/or characters.
c. Use a variety of techniques to sequence events so that they build on one another to create a coherent whole.
d. Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters.
e. Provide a conclusion (when appropriate to the genre) that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative.

Speaking and Listening:
Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher- led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively.
a. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas.
b. Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed.
c. Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions.
d. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented.

Language:
1. Demonstrate command of the conventions of Standard English grammar and usage when writing or speaking. a. Use parallel structure.
b. Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations.
2. Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent
clauses.
b. Use a colon to introduce a list or quotation.
c. Spell correctly.

Knowledge of Language
3. Apply knowledge of language to understand how language functions in different contexts, to make effective
choices for meaning or style, and to comprehend more fully when reading or listening.
a. Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Publication Manual of the American Psychological Association (APA), Turabian’s Manual for Writers) appropriate for the discipline and writing type.
Vocabulary Acquisition and Use
4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 9–10 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase.
b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech
(e.g., analyze, analysis, analytical; advocate, advocacy).
c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology.
d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).
5. Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
a. Interpret figures of speech (e.g., euphemism, oxymoron) in context and analyze their role in the text.
b. Analyze nuances in the meaning of words with similar denotations.
6. Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading,
writing, speaking, and listening at the college and career readiness level; demonstrate independence in
gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Enduring Understandings:

• Analyze how the narrator's perspective influenced the development of ideas in and understanding of your chosen chapter's themes.
• Establish a context specific to your new chosen character’s perspective and a narrative point of view.
• Analyze relationships among the details of a text and how they develop ideas.
• Group and sequence sentences and paragraphs to create a coherent narrative.
• Use descriptions, devices, and techniques to develop your narrative.
• Develop and maintain an appropriate style.

Essential Questions:

• How does gaining a deeper awareness of others’ experiences allow characters in The Joy Luck Club to change their perceptions?
• How does Tan use words and phrases to create a unique style for each narrator? How do Tan’s experiences shape her writing? How did the experiences of the mother in “I Stand Here Ironing” shape her daughter’s life? How do the experiences of the mothers in The Joy Luck Club shape their daughter’s lives (i.e. An-Mei’s mother)?
• Do the main characters in The Joy Luck Club accurately reflect Chua’s beliefs about “generational decline” in the children of immigrants?
• How does learning about the past in The Joy Luck Club allow the mothers and daughters to alter their perceptions of one another?

Unit 1 Life of Pi: Guidebook 2020

Unit Length: 12 Weeks
Description: We will read Life of Pi by Yann Martel and a series of related literary and informational texts to explore the question: How do our stories reveal our realities? We will examine narrative techniques and their effects in order to understand how a story conveys one person’s perspective of events or experiences. We will express our understanding through a narrative essay that retells a key episode from Life of Pi from another point of view in order to reveal a different perspective on the events or experiences.

Standards:
Reading Literature:
Key Ideas and Details
1. Cite relevant and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
2. Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.
3. Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme.

Craft and Structure
4. Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone).
5. Analyze how an author’s choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise.
6. Analyze a particular point of view or cultural experience reflected in works of literature drawing on a wide reading of world literature.

Reading Informational Texts:
Key Ideas and Details
1. Cite relevant and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
2. Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.
3. Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them.

Craft and Structure
4. Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language of a court opinion differs from that of a newspaper).
5. Analyze in detail how an author’s ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter).
6. Determine an author’s point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose.

Writing:
Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences.
a. Engage and orient the reader by setting out a problem, situation, or observation, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events.
b. Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, mood, tone, events, and/or characters.
c. Use a variety of techniques to sequence events so that they build on one another to create a coherent whole.
d. Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters.
e. Provide a conclusion (when appropriate to the genre) that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative.

Speaking and Listening:
Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher- led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively.
a. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas.
b. Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed.
c. Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions.
d. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented.

Language:
1. Demonstrate command of the conventions of Standard English grammar and usage when writing or speaking. a. Use parallel structure.
b. Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations.
2. Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent
clauses.
b. Use a colon to introduce a list or quotation.
c. Spell correctly.

Knowledge of Language
3. Apply knowledge of language to understand how language functions in different contexts, to make effective
choices for meaning or style, and to comprehend more fully when reading or listening.
a. Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Publication Manual of the American Psychological Association (APA), Turabian’s Manual for Writers) appropriate for the discipline and writing type.

Vocabulary Acquisition and Use
4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 9–10 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase.
b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech
(e.g., analyze, analysis, analytical; advocate, advocacy).
c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology.
d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).
5. Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
a. Interpret figures of speech (e.g., euphemism, oxymoron) in context and analyze their role in the text.
b. Analyze nuances in the meaning of words with similar denotations.
6. Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading,
writing, speaking, and listening at the college and career readiness level; demonstrate independence in
gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Enduring Understandings:

• Orient the reader to the narrative context by establishing the problem or situation. Introduce the narrator and other characters.
• Sequence ideas and events so that they build on each other to create a coherent narrative.
• Provide sufficient details about the events or experiences from the novel to convey an alternate perspective or reality.

Essential Questions:

• How does Yann Martel introduce and develop a convincing narrative in Part One of Life of Pi?
• How does the author use narrative techniques in a key episode from Part Two of Life of Pi to reveal Pi’s perceptions and his reality.
• How do the two versions of the story told in Part Three of Life of Pi contribute to the overall meaning of the novel? What do the differences in the stories reveal about Pi’s perspective and his reality? How might the story change if it were told from a different perspective?

Unit 2 Macbeth: Guidebook 2.0

Unit Length: 14 Weeks
Description: Students read literary and informational texts about ambition and failure. Students understand that conflicts serve as the basis of a text’s meaning and that identifying the internal and external conflicts of a story reveals the motivations of complex characters. They express their understanding of how characters advance a plot and develop a theme and how literature reflects real-life situations in which conflicting motivations propel humans to act in different ways.

Standards:
Reading Literature:
Key Ideas and Details
1. Cite relevant and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
2. Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.
3. Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme.

Craft and Structure
4. Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone).
5. Analyze how an author’s choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise.
6. Analyze a particular point of view or cultural experience reflected in works of literature drawing on a wide reading of world literature.
7. Analyze the representation of a subject or a key scene in two different artistic mediums, including what is emphasized or absent in each treatment (e.g., Auden’s “Musée des Beaux Arts” and Breughel’s Landscape with the Fall of Icarus).

Reading Informational Texts:
Key Ideas and Details
1. Cite relevant and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
2. Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.
3. Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them.

Craft and Structure
4. Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language of a court opinion differs from that of a newspaper).
5. Analyze in detail how an author’s ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter).
6. Determine an author’s point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose.
8. Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and
the evidence is relevant and sufficient; identify false statements and fallacious reasoning.

Writing:
Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.
a. Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among claim(s), counterclaims, reasons, and evidence.
b. Develop claim(s) and counterclaims fairly, supplying evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level and concerns.
c. Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.
d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.
e. Provide a concluding statement or section that follows from and supports the argument presented.

Speaking and Listening:
1. Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher- led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively.
a. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas.
b. Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed.
c. Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions.
d. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented.

Language:
1. Demonstrate command of the conventions of Standard English grammar and usage when writing or speaking. a. Use parallel structure.
b. Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations.
2. Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent
clauses.
b. Use a colon to introduce a list or quotation.
c. Spell correctly.

Knowledge of Language
3. Apply knowledge of language to understand how language functions in different contexts, to make effective
choices for meaning or style, and to comprehend more fully when reading or listening.
a. Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Publication Manual of the American Psychological Association (APA), Turabian’s Manual for Writers) appropriate for the discipline and writing type.

Vocabulary Acquisition and Use
4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 9–10 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase.
b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech
(e.g., analyze, analysis, analytical; advocate, advocacy).
c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology.
d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).
5. Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
a. Interpret figures of speech (e.g., euphemism, oxymoron) in context and analyze their role in the text.
b. Analyze nuances in the meaning of words with similar denotations.
6. Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading,
writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Enduring Understandings:

• Students understand that conflicts serve as the basis of a text’s meaning and that identifying the internal and external conflicts of a story reveals the motivations of complex characters.
• Students understand how characters advance a plot and develop a theme and how literature reflects real-life situations in which conflicting motivations propel humans to act in different ways.

Essential Questions:

• How does the development and interaction of characters in the Macbeth build a central idea and reveal a theme?
• How does society present the ideas of ambition and failure?

Unit 3 Hamilton: Guidebook 2020

Unit Length: 9 Weeks
Description: We will listen to and read Hamilton: An American Musical by Lin-Manuel Miranda, read a series of related texts (literary, informational, primary source documents), and view multimedia to explore the essential question: How does Lin-Manuel Miranda tell Hamilton’s story?  We will express our understanding by writing an essay that analyzes the choices that Lin-Manuel Miranda makes in portraying history and discusses the effect of these choices on our understanding of either the character, time period, or musical.

Standards:
Reading Literature:
Key Ideas and Details
1. Cite relevant and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
2. Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.
3. Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme.

Craft and Structure
4. Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone).
5. Analyze how an author’s choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise.
6. Analyze a particular point of view or cultural experience reflected in works of literature drawing on a wide reading of world literature.
7. Analyze the representation of a subject or a key scene in two different artistic mediums, including what is emphasized or absent in each treatment (e.g., Auden’s “Musée des Beaux Arts” and Breughel’s Landscape with the Fall of Icarus).
9. Analyze how an author draws on and transforms source material in a specific work (e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare).

Reading Informational Texts:
Key Ideas and Details
1. Cite relevant and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
2. Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.
3. Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them.

Craft and Structure
4. Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language of a court opinion differs from that of a newspaper).
5. Analyze in detail how an author’s ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter).
6. Determine an author’s point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose.
7. Analyze various accounts of a subject told in different mediums (e.g., a person’s life story in both print and multimedia), determining which details are emphasized in each account.
8. Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and
the evidence is relevant and sufficient; identify false statements and fallacious reasoning.
9. Analyze seminal U.S. documents of historical and literary significance (e.g., Washington’s Farewell Address, the Gettysburg Address, Roosevelt’s Four Freedoms speech, King’s “Letter from Birmingham Jail”), including how they address related themes and concepts.

Writing:
Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.
a. Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among claim(s), counterclaims, reasons, and evidence.
b. Develop claim(s) and counterclaims fairly, supplying evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level and concerns.
c. Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.
d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.
e. Provide a concluding statement or section that follows from and supports the argument presented.

Speaking and Listening:
Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher- led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively.
a. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas.
b. Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed.
c. Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions.
d. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented.

Language:
1. Demonstrate command of the conventions of Standard English grammar and usage when writing or speaking. a. Use parallel structure.
b. Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations.
2. Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent
clauses.
b. Use a colon to introduce a list or quotation.
c. Spell correctly.

Knowledge of Language
3. Apply knowledge of language to understand how language functions in different contexts, to make effective
choices for meaning or style, and to comprehend more fully when reading or listening.
a. Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Publication Manual of the American Psychological Association (APA), Turabian’s Manual for Writers) appropriate for the discipline and writing type.

Vocabulary Acquisition and Use
4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 9–10 reading and content, choosing flexibly from a range of strategies.
a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase.
b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech
(e.g., analyze, analysis, analytical; advocate, advocacy).
c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology.
d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).
5. Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
a. Interpret figures of speech (e.g., euphemism, oxymoron) in context and analyze their role in the text.
b. Analyze nuances in the meaning of words with similar denotations.
6. Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading,
writing, speaking, and listening at the college and career readiness level; demonstrate independence in
gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Enduring Understandings:

• Discuss how Miranda accurately and inaccurately portrays history within the musical.
• Explain how Miranda’s choices impact the reader’s or listener’s understanding of either the character, time period, or musical.
• Use textual evidence from both primary and secondary sources to support your claims.

Essential Questions:

• How does Lin-Manuel Miranda tell Hamilton’s story?
• How does Hamilton’s letter to John Jay (March 14, 1779) both confirm and complicate our understanding of Hamilton as he’s portrayed in the musical?
• In Hamilton, Lin-Manuel Miranda includes two different songs (“Helpless” and “Satisfied”) to show two different points of view of the same incident. Why does he make this choice in the musical? In other words, what does this show/reveal about Hamilton and his relationships?
• What choices did Lin-Manuel Miranda make in his portrayal of George Washington in Hamilton? What impact do his choices have on your understanding of George Washington?
• How is the duel as portrayed in Hamilton similar and different to the duel as portrayed in Chernow’s biography? What is the impact of this on our understanding of Hamilton and Burr?