1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Grade 4 – Module 7 Exploring Measurement with Multiplication

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Session Objectives – Examination and overview of the development of mathematical understanding across the module with a focus on the standards within the lessons. – Introduction to mathematical models and instructional strategies to support implementation of A Story of Units. – C onsideration of scaffolding to provide multiple entry points for students at all levels.

3. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Story of Units Scaffolding Mathematics Instruction Key Points – Amplify Language – Move from Concrete to Representation to Abstract – Give Specific Guidelines for Speaking, Reading, Writing, or Listening

4. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Curriculum Overview of A Story of Units

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Module Overview Narrative Focus and foundational standards Mathematical practices Overview of Topics and Lesson Objectives Terminology

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units New Terminology Metric system of measurement Customary system of measurement cup pint quart gallon ounce pound

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Suggested Tools and Representation Centimeter ruler, Meter stick 12 inch ruler, Yard stick Digital scale (metric and customary units) Balance scale with mass weights Gallon, quart, pint, and cup containers Beaker marked with liters and milliliters Analog clock with second hand

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda

10. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Core Fluency Differentiated Practice Sets Opportunity for review and mastery of the addition and subtraction algorithm. 4 Practice Sets – A: Multi-digit addition – B: Multi-digit subtraction – C: Multi-digit subtraction with zeros in the minuend – D: Multi-digit addition and subtraction Differentiated Practice – Part 1 – Part 2: fewer regroupings – Both parts have same solutions.

11. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Core Fluency Differentiated Practice Sets 120 seconds to complete. – Correct Sets move on. – Incorrect Sets used as remedial practice. Repeat until mastery. Keep record of progress. – Share with caring adults. – Celebrate improvement and advancement. Found in G4-M7-L2. Used throughout Module 7.

12. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic A: Measurement Conversion Tables 5 lessons to discover conversion from larger to smaller measurement units – focus on customary units of length, weight, and capacity New terms – customary units – metric units – customary system of measurement – metric system of measurement 4.OA.1, 4.OA.2, 4.MD.1 – balance scale – 1 lb and 1 oz weights – yardstick, inch ruler – capacity containers – water – analog clock, stopwatch – pound – ounce – cup – pint – quart – gallon Tools/Representations – multiplicative comparison – 2-column table – number line – tape diagrams

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Convert Pounds to Ounces Use a balance scale to: – discover 1 pound is heavier than 1 ounce. – determine how many ounces equal 1 pound. Use multiplication to: – convert pounds to ounces. – apply the distributive property to convert number of pounds not found in 2-column table to ounces. Lesson 1

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Convert Pounds to Ounces Lesson 1 PoundsOunces 116 2 3 4 5 6 7 8 9 10 Rule for converting pounds to ounces: Multiply the number of pounds by 16 ounces. 15 pounds = ____ ounces 10 lb + 5 lb = (10 × 16 oz) + (5 × 16 oz) = 160 oz + 80 oz = 240 oz 32 48 64 80 96 112 128 144 160 12 lb 10 oz = ___ oz = (12 × 16 oz) + 10 oz = 192 oz + 10 oz = 202 oz

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Convert Yards to Feet & Feet to Inches Lesson 1

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Turn and Talk How does this task align with the Universal Design for Learning (UDL) in providing multiple options for: Representation: the “what of learning” Action/Expression: the “how” of learning Engagement: the “why” of learning G4–M7–Lesson 1

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Convert Gallons to Quarts In groups, students discover the rule for converting gallons to quarts. – Multiply the number of gallons by 4 quarts. How many quarts are in 13 gallons? – 13 × 4 qt = 52 qt – (10 × 4 qt) + (3 × 4qt) = 40 qt + 12 qt = 52 qt How many quarts are in 18 gallons 3 quarts? – 18 × 4 qt = 72 qt – 72 qt + 3 qt = 75 qt Lesson 2

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Convert Quarts to Pints & Pints to Cups Continue interactive experiment of determining conversion rules for quarts to pints and pints to cups. Relate pints to gallons. Relate cups to quarts and gallons. Discuss relationships and record on Practice Sheet. Lesson 2

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Conversion of Days, Hours, Minutes, and Seconds Lesson 3

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Complete Problems #1-4. Use RDW process to solve. Be prepared to share your strategies with peers. Lesson 4

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Problem 1: Beth is allowed 2 hours of TV time each week. Her sister is allowed 2 times as much TV as her. How many minutes of TV can Beth’s sister watch? Lesson 4

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Problem 2: Clay weighs 9 times as much as his baby sister. Clay weighs 63 pounds. How much does his baby sister weigh in ounces? Lesson 4

23. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Problem 3: Helen has 4 yards of rope. Daniel has 4 times as much rope as Helen. How many more feet of rope does Daniel have than Helen? Lesson 4

24. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Problem 4: A dishwasher uses 11 liters of water for each cycle. A washing machine uses 5 times as much water as a dishwasher uses for each load. Combined, how many milliliters of water are used for 1 cycle of each machine? Lesson 4

25. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Share and Critique Peer Strategies Mathematical Practice 3 Construct viable arguments and critique the reasoning of others. Lesson 5 x x

26. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic B: Problem Solving with Measurement 6 lessons to develop strategies for adding and subtracting mixed units of measurement and solve word problems including multiplicative comparison problems. Tools/Representations: – Number bonds – Arrow way – Tape diagrams 4.OA.2, 4.OA.3, 4.MD.1, 4.MD.2

27. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Teaching Sequence for Addition and Subtraction for Mixed Units of Measurement  Lesson 6: Capacity  Lesson 7: Length  Lesson 8: Weight  Lesson 9: Time Topic B Addition single unit + single unit mixed unit + single unit mixed unit + mixed unit Subtraction single unit – single unit mixed unit – single unit mixed unit – mixed unit

28. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Composing Units 2 fourths + 3 fourths = 5 fourths Topic Opener B 2 quarts + 3 quarts = 5 quarts = 1 one 1 fourth 4 fourths 1 fourth = 1 gallon 1 quart 4 quarts 1 quart 1 1

29. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Adding Mixed Units Lesson 6 2 quarts + 3 quarts 3 pints + 4 pints

30. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Adding Mixed Units 5 gallons 2 quarts + 3 quarts Lesson 6 5 quarts 3 cups + 3 cups

31. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Adding Mixed Units 5 gallons 2 quarts + 4 gallons 3 quarts Lesson 6 7 quarts 3 cups + 2 quarts 3 cups

32. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Decomposing Units 1 − 3 fourths = 4 fourths − 3 fourths Topic Opener B 1 quart − 3 cups = 4 cups − 3 cups = 1 fourth = 1 cup 7 quarts 4 cups 1 8 quarts − 3 cups = 7 quarts 1 cup 4 fourths − 3 fourths = 1 fourth

33. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Subtracting Mixed Units 1 gallon – 1 pint Lesson 6 8 gallons – 1 pint 1 quart – 2 cups 6 quarts – 2 cups

34. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Subtracting Mixed Units 8 quarts 1 cup – 3 cups Lesson 6 8 quarts 1 cup – 6 quarts 3 cups 9 gallons 2 quarts – 3 quarts 9 gallons 2 quarts – 4 gallons 3 quarts

35. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Turn and Talk How does this task align with the Universal Design for Learning (UDL) in providing multiple options for: Representation: the “what of learning” Action/Expression: the “how” of learning Engagement: the “why” of learning G4–M7–Lessons 6 and 7

36. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Try Problems #6-11. Practice different addition and subtraction strategies for length, weight and time. Lessons 7-9

37. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Solving Multi-Step Measurement Word Problems Patti went swimming for 1 hour 15 minutes on Monday. On Tuesday, she swam twice as long as she swam on Monday. On Wednesday, she swam 50 minutes less than the time she swam on Tuesday. How much time did she spend swimming during these three days? Lesson 10 – Problem Set #12

38. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic C: Investigation of Measurements Expressed as Mixed Numbers 3 lessons to convert mixed number measurement units to smaller units and solve word problems. Tools/Representations: – Tape diagrams – Number line – Number bond – Yardstick – 12 inch ruler – 1 qt container – 1 gal container 4.OA.3, 4.MD.1, 4.MD.2

39. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Convert Mixed Number Measurements to Smaller Units length capacity Lesson 12

40. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Convert Mixed Number Measurements to Smaller Units weight time Lesson 13

41. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Try Problems #13-16. Sample questions from the Exit Tickets for Lessons 12 and 13. Consider how a student may solve pictorially or abstractly. Lessons 12-14 Try Problems #19-20. Sample questions from the Problem Set of Lesson 14. Use RDW to solve.

42. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Turn and Talk What difficulties would you anticipate with student understanding of the mathematics in this section? What scaffolds would be effective for addressing those difficulties? G4–M7–Lesson 14

43. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda

44. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Review the End-of-Module Assessment Complete #6 of the assessment. Compare your responses to the sample student work. Discuss your results with a peer. – What may students struggle with? – What may teachers struggle with? Complete the remaining problems.

45. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda

46. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Year in Review Lessons 15-16: Create and determine the area of composite figures Lesson 17: Practice and solidify Grade 4 fluency Lesson 18: Practice and solidify Grade 4 vocabulary

47. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Determine the Area for Composite Figures Emma’s rectangular bedroom is 11 feet long and 12 feet wide with an attached closet that is 4 feet by 5 feet. How many square feet of carpet does Emma need to cover both the bedroom and closet? Lesson 15

48. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Mini-Personal Boards Materials: plastic page protector, manila folder, tape Steps: 1.Cut page protector in half horizontally. 2.Tape to top half of folder with the opening at the top. 3.Slip Problem Set into page protector. Fold back top half of Problem Set. 4.Complete. Check answers by unfolding top half of Problem Set. Special Note: Do NOT copy Homework back-to-back in Topic D.

49. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Practice and Solidify Grade 4 Fluency Lesson 17

50. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Practice and Solidify Grade 4 Vocabulary Lesson 18

51. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Module 7 Key Points Students develop an understanding of the two measurement systems. Students convert from larger to smaller units of measurements. Students apply knowledge of the four operations to solve real world problems. Students connect the practice of solving with mixed units to mixed measurement units.