Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Division Common Core Leadership in Mathematics (CCLM) Monday July 9, 2012 This material was developed for use by the project staff and participants in the Common Core Leadership in Mathematics (CCLM^2) project through the University of Wisconsin-Milwaukee. Use by school district personnel to support learning of its teachers and staff is permitted provided appropriate acknowledgement of its source. Use by others is prohibited except by prior written permission.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Learning Intentions We are learning to… Understand two types of division situations. Learn division strategies that develop fluency in basic division facts. We will be successful when we can … Articulate the meaning of third grade standards that focus on division.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Are These Contexts the Same?

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Two Contexts for Division Context 1: Connor has 24 Skittles. He puts them into bags containing 6 Skittles each. How many bags did Connor use? Context 2: Connor has 24 Skittles. He shares them equally among 6 cousins. How many Skittles will each cousin get?

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Two Interpretations for Division Context 1 – unknown number of shares Connor has 24 Skittles. He puts them into bags containing 6 Skittles each. How many bags did Connor use? Known: Size of the share (number of Skittles in each bag) Unknown: Number of shares (bags) Context 2 – unknown number of objects in each share Connor has 24 Skittles. He shares them equally among 6 cousins. How many Skittles will each cousin get? Known: Number of shares (cousins) Unknown: Size of the share (Skittles)

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 What Have We Done? 3.OA.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 a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. Turn to your shoulder partner and explain this standard in relationship to what we just explored.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 How do the Standards Support Division? Division is finding an unknown factor in problems involving equal sized groups, arrays, and area models. For equal size group situations, division can require finding the unknown number of groups or the unknown group size. p. 21 CCSSM 3 rd grade critical area #1

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Identifying Division Situations Read a problem on a card. Use the division mat to act out each problem. Follow the action of the story. Is the problem asking you to find the unknown number of equal shares or the unknown number of objects in each share? Draw a sketch. Write an equation. Label each accordingly.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 What Have We Done? 3.OA.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 a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. Turn to your shoulder partner and explain this standard in relationship to what we just explored.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Division Strategies

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Division Strategies How do you teach the relationship between Multiplication and Division?

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Standards 3OA2 two types of division 3OA4 relationship between three numbers 3OA5 properties 3OA6 division as unknown factor problem 3OA7 fluency and basic facts Decide on connections between the standards.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 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 = ?.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Standard 3.OA.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.) 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.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = = 56. (Distributive property.) What is the relationship between these two standards? Compare and contrast them.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Standard 3.0A.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Standard 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.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Learning Intentions We are learning to… Understand two types of division situations. Learn division strategies that develop fluency in basic division facts. We will be successful when we can … Articulate the meaning of third grade standards that focus on division