Unit 2

Arithmetic Operations Including Division by a Fraction

Math

Unit Length and Description:

25 days

In Unit 2, students extend their knowledge of dividing whole numbers by unit fractions using visual models and equations to divide whole numbers by fractions and fractions by fractions to solve word problems. During this unit, students develop procedural fluency. Students become fluent in the use of the standard division algorithm.  Students also become fluent in the use of the standard algorithm as they add, subtract, multiply, and divide multi-digit decimals. The focus of instruction is on operations and number sense. The use of estimation strategies supports student understanding of decimal operations.

Students extend their understanding of greatest common factor and least common multiple that began in Unit 1. Students find the greatest common factor of two whole numbers less than or equal to 100, they understand that the greatest common factor of two prime numbers will be 1, they use the greatest common factor and the distributive property to find the sum of two whole numbers, and students use the least common multiple of two whole numbers less than or equal to twelve.

Standards:

 RP – Ratios and Proportional Relationships Apply and extend previous understandings 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. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc). How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 3/4- cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? NS- The Number System 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. 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. For example, express 36 + 8 as 4 (9 + 2). 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   ·         6.NS.A.1: o   I can compute quotients of fractions divided by fractions (including mixed numbers.) o   I can interpret quotients of fractions. o   I can figure out how to solve division problems with fractions in a real-world situation. o   I can solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. ·         6.NS.B.2: o   I can divide multi-digit numbers using the standard algorithm with speed and accuracy, without any math tools. ·         6.NS.B.3 o   I can fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation with speed and accuracy, without math tools. ·         6.NS.B.4 o   I can identify the factors of two whole numbers less than or equal to 100 and determine the Greatest Common Multiple. o   I can identify the multiples of two whole numbers less than or equal to 12 and determine the Least Common Multiple. o   I can apply the Distributive Property to rewrite addition problems by factoring out the Greatest Common Factor.

Enduring Understandings:

·         The relationship of the location of the digits and the value of the digits is part of understanding multi-digit operations.

·         Operations on decimals and whole numbers are based upon place value relationships.

·         When we divide one number by another, we may get a quotient that is bigger than the original number, smaller than the original number, or equal to the original number.

·         Least common multiple and greatest common factor are helpful when solving real-world problems.

·         Multiplication and division are inverse operations.

Essential Questions:

·         What role does place value play in multi-digit operations?

·         How can the distributive property help me with computation?

·         When I divide one number by another number, do I always get a quotient smaller than my original number?

·         Which strategies are helpful when performing operations on multi-digit decimals?

·         What kind of models can I use to show solutions to word problems involving fractions?

·         How can I check a division problem?