Unit 1

Place Value, Rounding, and Algorithms for Addition and Subtraction

Math

Unit Length and Description:

25 days

Students extend their work with whole numbers.  They begin with hundreds and thousands and develop their understanding of millions by building knowledge of the pattern of times ten in base ten system on the place value chart. Students use their place-value knowledge to read, write, compare and round multi-digit whole numbers.  Students become fluent with the standard algorithms for addition and subtraction.  They apply their algorithmic knowledge to solve multi-step word problems accessing the reasonableness of an answer using mental math and estimation strategies.

Standards:

 Number and Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. 4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. 4.NBT.2 Read and write multi-digit whole numbers 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 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 using the standard algorithm. Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. 4.OA.3 Solve multistep 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. Operations and Algebraic Thinking Generate and analyze patterns. 4.OA.5 Generate a number or shape pattern that follows a given rule.  Identify apparent features of the pattern that were not explicit in the rule itself.  For example, given the rule, “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers.  Explain informally why the numbers will continue to alternate in this way. Standards for Mathematical Practices 1.   Make sense of problems and persevere in solving them. 2.   Reason abstractly and quantitatively. 3.   Construct viable arguments and critique the reasoning of others. 4.   Model with mathematics. 5.   Use appropriate tools strategically. 6.   Attend to precision. 7.   Look for and make use of structure. 8.   Look for and express regularity in repeated reasoning. Instructional Outcomes:   4.NBT.1 ·         I can explain that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. 4.NBT.2 ·         I can read and write numbers in standard form up to one million. ·         I can read and write numbers in word form up to one million. ·         I can read and write numbers in expanded form up to one million. ·         I can compare two numbers with digits up to one million and identify whether they are less than, greater than, or equal to another number. 4.NBT.3 ·         I can round numbers, up to one million, to any given place value. 4.NBT.4 ·         I can add and subtract numbers up to one million. 4.OA.3 ·         I can divide whole numbers including division with remainders. ·         I can solve a word problem that includes letters representing numbers. ·         I can choose the correct operation to solve a word problem. ·         I can use mental math and estimation to determine whether my answer is reasonable. 4.OA.5 ·         I can continue a given number or shape pattern. ·         I can make a number or shape pattern that follows a given rule. ·         I can explain how different patterns are built. ·         I can analyze a pattern to determine parts not stated in the rule.

Enduring Understandings:

Place value is crucial when operating with numbers.

Estimation helps me see whether or not my answer is reasonable.

Using rounding is an appropriate estimation strategy for solving problems and estimating.

Knowing the meaning of the digits helps me compare numbers.

It is important to understand that a digit represents 10 times the value of what it represents in the place to its right.

Using place value understanding helps me to compose and decompose numbers.

Composing and decomposing numbers helps me to add and subtract using a standard algorithm.

Addition and subtraction are inverse operations; one undoes the other.

Knowing when to add and subtract helps me solve one and multi-step problems.

Essential Questions:

·         Does rounding a number change its value relative to other numbers?

·         How are addition and subtraction alike and how are they different?

·         How can I show what I know about addition and subtraction, problem solving, and estimation?

·         How can I use what I know about addition and subtraction to help me solve real world problem?

·         How do I compose and decompose numbers when using a standard algorithm.

·         What type of situations do we add and subtract?

·         How do we round numbers up to the hundred thousand place?

·         How is rounding used in everyday life?