1. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011- 2012 School Year Unpacking Multiplication of Fractions Part 1 ½ Connie Laughlin and Melissa Hedges Tuesday October 11, 2011 Common Core Leadership in Mathematics (CCLM)

2. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011- 2012 School Year Learning Intentions & Success Criteria  We are learning to…  Understand how to solve fraction word problems and use tape (number line) diagrams to illustrate the solutions.  We will be successful when….  We can solve fraction word problems and use tape (number line) diagrams to illustrate the solutions.

3. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011- 2012 School Year Sense Making….  Share with your shoulder partner a few ideas that struck you as critical to developing a sound understanding of multiplication of fractions.

4. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011- 2012 School Year Examine Multiplication Homework  Reread your reflection on your ‘necessity of precision’. Have a table discussion bout this topic.  Pass your homework problems two people down. Study the multiplicative comparison problems and provide feedback on a post-it.

5. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011- 2012 School Year Money, money, money  David spent 2/5 of his money on a storybook. The storybook cost $20. How much money did he have at first?  On your slate, draw a model to help you solve this problem. Solve the problem. Record your thinking

6. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011- 2012 School Year Let’s Look at Some Student Problems Solve the problems on pages 20 and 21(from Singapore Mathematics 4A) with your partner. Record your thinking. How did the tape diagram help you solve complicated fraction word problems?

7. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011- 2012 School Year Comparing Performance on TIMMS Items (8 th grade)  Laura had $240. She spent 5/8 of it. How much money did she have left? Singapore 78%, United States 25%  Penny had a bag of marbles. She gave one-third of them to Rebecca and then one-fourth of the remaining marbles to John. Penny then had 24 marbles left in the bag. How many marbles were there to start with? Singapore 81%, United States 14%

8. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011- 2012 School Year The power of strip diagrams With the aid of simple strip diagrams, children can use straightforward reasoning to solve many challenging story problems conceptually. Beckmann 2004

9. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011- 2012 School Year Big Ideas A Focus on 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 in a range of situations and build procedural fluency with understanding.

10. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011- 2012 School Year The School Problem  There are 3 ½ times as many fifth graders at School A as School B. There are 115 more students at School A than at School B. How many students are there at each school?  Draw a tape diagram to help you solve this problem.

11. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011- 2012 School Year Reflecting on the Practices

12. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011- 2012 School Year Learning Intentions & Success Criteria  We are learning to…  Understand how to solve fraction word problems and use tape (number line) diagrams to illustrate the solutions.  We will be successful when….  We can solve fraction word problems and use tape (number line) diagrams to illustrate the solutions.