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A Story of Units

A Story of Units. Grade 5 – Module 4. Session Objectives. Examine the development of mathematical understanding across Grade 5 Module 4: Multiplication and Division of Fractions and Decimal Fractions. Explore specific lessons to support planning .

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A Story of Units

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  1. A Story of Units Grade 5 – Module 4

  2. Session Objectives • Examine the development of mathematical understanding across Grade 5 Module 4: Multiplication and Division of Fractions and Decimal Fractions. • Explore specific lessons to support planning. • Review key mathematical models and instructional strategies to support student understanding.

  3. Curriculum Overview of A Story of Units

  4. Agenda • Module 4 Overview • Lesson Study by topics – Demonstration and Practice • Topic B • Topic C • Topic E • Topic G • Module Review

  5. Module Overview Students extend their understanding of Multiplication and Division of Fractions and Decimal Fractions.

  6. Topic B Demo: Fractions as Division Lesson 3, CD, Problem 1. Lesson 3 Objective: Interpret a fraction as division. A baker poured 4 kilograms of oats equally into 3 bags. What is the weight of each bag of oats?

  7. Topic B Practice Lesson 3, CD, Problem 2. If the baker doubles the number of kilograms of oats to be poured equally into 3 bags, what is the weight Of each bag of oats?

  8. Topic B Demo: Fractions as Division Lesson 4, CD, Problem 2. Lesson 4 Objective: Use tape diagrams to model fractions as division. 5 tons of gravel is equally divided between 4 dump trucks. How much gravel is in one dump truck?

  9. Topic B Practice Lesson 4, CD, Problem 3. A 3m ribbon is cut into 4 equal pieces to make flowers. What is the length of each piece?

  10. Topic B Practice Lesson 5, CD and Problem Set. • Lesson 5 Objective: Solve word problems involving the division of whole numbers with answers in the form of fractions or whole numbers. • Browse the CD & Problem Set. • Study the Problem 7 in the Problem Set.

  11. Topic B Practice Lesson 5, CD, Problem 7. • The Calef family likes to paddle along the Susquehanna River. • a). They paddled the same distance each day over the course of 3 days, traveling a total of 14 miles. How many miles did they travel each day? Show your • thinking in a tape diagram. • b). If the Calef’s went half their daily distance • each day, but extended their trip to twice as • many days, how far would they travel?

  12. Topic B Practice Lesson 5, CD, Problem 7.

  13. Topic B Debrief • What’s the main focus of Topic B? • Students learn to think of a division problem as a fraction, and that a fraction represents a division problem. • They use visual models such as the tape diagram, and the standard division algorithm.

  14. Topic C Demo: Multiplication of a Whole Number by a Fraction Lesson 6, CD, Problem 1. Lesson 6 Objective: Relate fractions as division to fraction of a set.

  15. Topic C Practice Lesson 6, CD, Problem 4. of the students in a class of 24 are boys. How many boys are in the class?

  16. Topic C Demo: Multiplication of a Whole Number by a Fraction Lesson 7, CD, Problem 1. Lesson 7 Objective: Multiply any whole number by a fraction using tape diagrams. What is of 35?

  17. Topic C Practice Lesson 7, CD, Problem 4. of a number is 8. What’s the number?

  18. Topic C Demo: Multiplication of a Whole Number by a Fraction Lesson 8, CD, Problem 1. Lesson 8 Objective: Relate fraction of a set to the repeated addition interpretation of fraction multiplication.

  19. Topic C Practice Lesson 8, CD, Problem 3.

  20. Topic C Practice Lesson 9, CD, Problem 1. • Lesson 9Objective: Find a fraction of a measurement and solve word problems. • Browse the CD. • Study Problem 1.

  21. Topic C Debrief • What is the main focus of Topic C? • Students interpret finding a fraction of a set as multiplication of a whole number by a fraction.

  22. Topic E Demo: Multiplication of a Fraction by a Fraction Lesson 13, CD, Problem 2. Lesson 13 Objective: Multiply unit fractions by unit fractions. Jan has pan of crispy rice treats. She sends of the pan to school with her children. How many pans of crispy rice treats does Jan send to school?

  23. Topic E Practice Lesson 13, CD, Problem 3. Jan has a pan of crispy rice treats. She sends of the pan to school with her children. How many pans of crispy rice treats does Jan send to school?

  24. Topic E Demo: Multiplication of a Fraction by a Fraction Lesson 14, CD, Problem 1. Lesson 14 Objective: Multiply unit fractions by non-unit fractions. Jan had pan of crispy rice treats. She sent of the treats to school. What fraction of the whole pan did she send to school?

  25. Topic E Practice Lesson 14, CD, Problem 3.

  26. Topic E Demo: Demo: Multiplication of a Fraction by a Fraction Lesson 15, CD, Problem 1 and 3a. • Lesson 15 Objective: Multiply non-unit fractions by • non-unit fractions.

  27. Topic E Practice Lesson 15, CD, Problem 3c.

  28. Topic E Demo: Multiplication of a Fraction by a Fraction Lesson 16, CD, Problem 2. • Lesson 16 Objective: Solve word problems using • tape diagrams and fraction by fraction multiplication. • Joakim is icing 30 cupcakes. He spreads • mint icing on of the cupcakes and chocolate • on of the remaining cupcakes. The rest will • get vanilla icing. How many cupcakes have • vanilla icing?

  29. Topic E Practice Lesson 16, CD, Problem 1. • Mrs. Onusko made 60 cookies for a bake sale. She • sold of them and gave of the remaining cookies • to the students working at the sale. How • many cookies did she have left?

  30. Topic E Debrief What is the main focus in Topic E? Students learn to multiply a fraction by a fraction, using visual models to enhance conceptual understanding.

  31. Topic G Demo: Division of Fractions and Decimal Fractions Lesson 25, CD, Problem 1. Jenny buys 2 pounds of pecans. If she puts pound in each bag, how many bags can she make?

  32. Topic G Practice Lesson 25, CD, Problem 2. Tien wants to cut foot lengths from a board that is 5 feet long. How many boards can he cut?

  33. Topic G Demo: Division of Fractions and Decimal Fractions Lesson 26, CD, Problem 1. Lesson 26 Objective: Divide a unit fraction by a whole number. Nolan has pan of brownies. He givesthem to his 3 friends to share equally. How many pans of brownies will each friend get?

  34. Topic G Practice Lesson 26, CD, Problem 2.

  35. Topic G Practice Lesson 31, CD • Lesson 31 Objective: Divide decimal dividends by non‐unit decimal divisors. • Browse the CD. • Study the Problem Set.

  36. Topic G Debrief • What is the mainfocus for Topic G? • Students learn to divide whole numbers by fractions and fractions by whole numbers.

  37. Summary of Module 4 Topic A: Line Plots of Fraction Measurements Topic B: Fractions as Division Topic C: Multiplication of a Whole Number by a Fraction Topic D: Fraction Expressions and Word Problems Topic E: Multiplication of a Fraction by a Fraction Topic F: Multiplication with Fractions and Decimals as Scaling and Word Problems Topic G: Division of Fractions and Decimal Fractions Topic H: Interpretation of Numerical Expressions

  38. Biggest Takeaway • Turn and Talk: • What questions were answered for you? • What new questions have surfaced?

  39. Key Ideas of Module 4. Operations of fractions can be supported by a variety of visual models: tape diagrams, arrays, folding paper. Conceptual understanding is essential.

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