1. Muliplication of Fractions Class 9 June 30, 2011 Common Core Leadership in Mathematics Project

2. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Learning Intentions We are learning to  Develop strategies related to multiplying fractions.  Understand how estimation should be an integral part of fraction computation development.  Read and interpret the cluster of CCSS standards related to multiplication of fractions. We will know we are successful when we can  Justify our thinking when multiplying fractions using concrete models and estimation strategies.  Clearly explain and provide examples for specific CCSS standards

3. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Big Ideas for Multiplication and Division of Fractions Multiplication and division of fractions are among the most complicated fraction concepts that elementary students encounter. Instructional opportunities that students encounter should include the meaning of multiplication and division on a range of situations and build procedural fluency with understanding.

4. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Launch: Building on What We Know What do you know about multiplication / division of whole numbers? As a table group, make a list of what students have learned as they interact with multiplication and division problems. Are they all true for fractions?

5. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 The Importance of Models Researchers indicate that teachers need knowledge of concrete models to help students transition from multiplication of whole numbers to multiplication of fractions. (Fendel, 2000)

6. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Thinking in Whole Numbers 3 X 4 = 12 Write a word problem for this equation What does each number mean?

7. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Some Stories Solve these problems individually. Use a visual model to record and then discuss your thinking with the group. Then write an equation. There are 15 cars in Derek’s toy car collection. Two-thirds of the cars are red. How many red cars does Derek have? Frelesha has 11 cookies. She wants to share them with her three friends. How many cookies will Frelesha and each of her friends get, if they share them equally? Jason filled 5 glasses with 2/3 liter of soda in each glass. How much soda did Jason use?

8. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 More Stories Solve these problems individually. Use a model to record and then discuss your thinking with your group. Write an equation for each problem. You have of a pizza left. If you give of the left-over pizza to your brother, how much of a whole pizza will your brother get? Someone ate of a cake, leaving only. If your brother eats 2/3 of the cake that is left, how much of a whole cake will your brother eat?

9. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 And Still More Stories Draw pictures to solve these problems. Do not use a computational algorithm. Write an equation. Joe had 2/3 of the lawn left to cut. After lunch, he cut 3/ 4 of the lawn he had left. How much of the whole lawn did Joe cut after lunch? The zookeeper had a huge bottle of the animals’ Zoo Cola. The monkey drank 1/5 of the bottle. The zebra drank 2/3 of what was left. How much of the bottle of Zoo Cola did the zebra drink?

10. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Multiplying with Mixed Numbers Determine the solution to these problems. Do not use a computational algorithm. 6 ½ x 4 2 ½ x 5 ¾

11. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Revisiting Word Problems Examine the five problems on the handout. Which are story problems for 2/3 x 1/ 4 and which are not? Why?

12. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Multiplication of Fraction Standards 4NF4a, 4NF4b, 5NF3, 5NF4, 5NF5 On your Standards Interpretation Sheet rephrase these standards and provide an example. Share with your partner.

13. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Standards for Mathematical Practice