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Multiplication of Fractions Part 2

Multiplication of Fractions Part 2. February 12, 2013 Common Core Leadership in Mathematics2 (CCLM).

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Multiplication of Fractions Part 2

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  1. Multiplication of FractionsPart 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. Agenda • Multiplication of Fractions Word Problems • Applying the Distributive Property • MP 5 – Use appropriate tools strategically.

  3. Understanding Multiplication of Fractions Isn’t this everything I need to know?

  4. Learning Intentions and Success Criteria • 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.

  5. 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. Standard 5.NF.4a 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). 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) × qas 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.)

  7. Example for Standard 5.NF.4a I have 30 marbles. 2/5 of them are red. How many of the marbles are red? 6 marbles 6 marbles 6 marbles 6 marbles 6 marbles 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

  8. 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 8th grade class, 2/3 of the girls have braces. How many girls have braces if there are 75 girls in the class?

  9. 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. Multiplying Mixed Numbers

  11. 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. 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. Released Item 4.NF.4c

  14. Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Constructviablearguments&critiquereasoningofothers. 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. 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. 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. Learning Intentions and Success Criteria • 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.

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