1. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Multiplication of Fractions Part 2 February 12, 2013 Common Core Leadership in Mathematics2 (CCLM) This material was developed for use by 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.

2. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Agenda Multiplication of Fractions Word Problems Applying the Distributive Property MP 5 – Use appropriate tools strategically.

3. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Understanding Multiplication of Fractions Isn’t this everything I need to know?

4. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 We are learning to …. Understand multiplication of fractions by fractions using meaningful visual models and real-world contexts. We will be successful when we can …. Represent, contextualize, and justify problems involving multiplication of fractions by fractions (5.NF.4, 4.NF.4 and 5.NF.6) using tape diagrams and area models. Learning Intentions and Success Criteria

5. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Where we are headed Multiplication and Division of Fractions: Standards Progression 4.NF.4, 5.NF.3 5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction 5.NF.5, 5.NF.6 5.NF.7, 6.NS.1

6. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 5.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a.Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Study this standard. Then work in small groups to create a visual model and identify a context for (2/3) x 4 and for (2/3) x (4/5). Standard 5.NF.4a

7. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 I have 30 marbles. 2/5 of them are red. How many of the marbles are red? Example for Standard 5.NF.4a Partition 30 into fifths. Each fifth represents 6 marbles. We need 2 of the partitions (2/5). (2/5) X 30 = (30 ÷ 5) X 2 6 marbles

8. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Another Use of the Tape Diagram Draw tape diagrams to solve this problem. Write a series of equations to show your reasoning. Compare your diagrams and reasoning with your shoulder partner. In an 8 th grade class, 2/3 of the girls have braces. How many girls have braces if there are 75 girls in the class?

9. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 TCM Article: Multiplying Fractions All read the introduction (pp. 174-175 stop at “Problem 1.”) Read your assigned problem. On your white board draw a strip diagram that you used to help you solve the problem. Present your solution to your table using your strip diagram and discuss how your problem and strip diagram connects back to 4NF4c and/or 5NF6

10. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Multiplying Mixed Numbers

11. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Using the Distributive Property If each batch of pancakes uses 1 ¼ cups of flour and you make 3 batches, how much flour do you use? Draw a visual model (area model) to show the distributive property.

12. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Using the Distributive Property Make up a realistic story problem for 2 ½ x 3/8 Draw a visual model (area model) to show the distributive property.

13. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Released Item 4.NF.4c

14. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments & critique 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.

15. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 MP5 Use Appropriate Tools Strategically List 3 specific examples for: – Student Disposition: What did you do as students that illustrated this practice? – Teacher Actions: What experiences and opportunities did the teachers provide to foster the desired student dispositions?

16. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Sense Making…. Share with your shoulder partner a few ideas that struck you as critical to developing a sound understanding of multiplication of fractions.

17. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 We are learning to …. Understand multiplication of fractions by fractions using meaningful visual models and real-world contexts. We will be successful when we can …. Represent, contextualize, and justify problems involving multiplication of fractions by fractions (5.NF.4, 4.NF.4 and 5.NF.6) using tape diagrams and area models. Learning Intentions and Success Criteria