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A Story of Units

A Story of Units. Grade 4 – Module 7 Exploring Measurement with Multiplication. Session Objectives. E xamination and overview of the development of mathematical understanding across the module with a focus on the standards within the lessons.

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A Story of Units

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  1. A Story of Units Grade 4 – Module 7 Exploring Measurement with Multiplication

  2. 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. • Consideration of scaffolding to provide multiple entry points for students at all levels.

  3. A Story of UnitsScaffolding Mathematics Instruction Key Points • Amplify Language • Move from Concrete to Representation to Abstract • Give Specific Guidelines for Speaking, Reading, Writing, or Listening

  4. Agenda Introduction to the Module Concept Development Module Review Year in Review

  5. Curriculum Overview of A Story of Units

  6. Module Overview • Narrative • Focus and foundational standards • Mathematical practices • Overview of Topics and Lesson Objectives • Terminology

  7. New Terminology • Metric system of measurement • Customary system of measurement • cup • pint • quart • gallon • ounce • pound

  8. 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. Agenda Introduction to the Module Concept Development Module Review Year in Review

  10. 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. 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. Topic A: Measurement Conversion Tables • pound • ounce • cup • pint • quart • gallon • balance scale • 1 lb and 1 oz weights • yardstick, inch ruler • capacity containers • water • analog clock, stopwatch • Tools/Representations • multiplicative comparison • 2-column table • number line • tape diagrams 4.OA.1, 4.OA.2, 4.MD.1 • 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

  13. Convert Pounds to Ounces 1 lb. 1 oz Lesson 1 • 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.

  14. Convert Pounds to Ounces Rule for converting pounds to ounces: Multiply the number of pounds by 16 ounces. 32 48 64 80 96 112 128 144 160 15 pounds = ____ ounces 10 lb + 5 lb = (10×16 oz) + (5×16 oz) = 160 oz + 80 oz = 240 oz 12 lb 10 oz = ___ oz = (12×16 oz) + 10 oz = 192 oz + 10 oz = 202 oz Lesson 1

  15. Convert Yards to Feet & Feet to Inches Lesson 1

  16. Turn and Talk G4–M7–Lesson 1 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

  17. Convert Gallons to Quarts Lesson 2 • 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

  18. Convert Quarts to Pints & Pints to Cups Lesson 2 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.

  19. Conversion of Days, Hours, Minutes, and Seconds Lesson 3

  20. Complete Problems #1-4. Lesson 4 Use RDW process to solve. Be prepared to share your strategies with peers.

  21. Problem 1: Lesson 4 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?

  22. Problem 2: Lesson 4 Clay weighs 9 times as much as his baby sister. Clay weighs 63 pounds. How much does his baby sister weigh in ounces?

  23. Problem 3: Lesson 4 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?

  24. Problem 4: Lesson 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?

  25. Share and Critique Peer Strategies x x Lesson 5 Mathematical Practice 3 Construct viable arguments and critique the reasoning of others.

  26. Topic B: Problem Solving with Measurement 4.OA.2, 4.OA.3, 4.MD.1, 4.MD.2 • 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

  27. Teaching Sequence for Addition and Subtraction for Mixed Units of Measurement 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 Topic B • Lesson 6: Capacity • Lesson 7: Length • Lesson 8: Weight • Lesson 9: Time

  28. Composing Units = 1 one 1 fourth 4 fourths 1 fourth 2 quarts + 3 quarts = 5 quarts = 1 gallon 1 quart 1 1 4 quarts 1 quart Topic Opener B 2 fourths + 3 fourths = 5 fourths

  29. Adding Mixed Units 2 quarts + 3 quarts 3 pints + 4 pints Lesson 6

  30. Adding Mixed Units 5 quarts 3 cups + 3 cups Lesson 6 5 gallons 2 quarts + 3 quarts

  31. Adding Mixed Units 7 quarts 3 cups + 2 quarts 3 cups Lesson 6 5 gallons 2 quarts + 4 gallons 3 quarts

  32. Decomposing Units 4 fourths − 3 fourths = 1 fourth = 1 fourth 1 quart − 3 cups = 4 cups − 3 cups = 1 cup 8 quarts − 3 cups = 7 quarts 1 cup 1 7 quarts 4 cups Topic Opener B 1− 3 fourths = 4 fourths − 3 fourths

  33. Subtracting Mixed Units 1 quart – 2 cups 8 gallons – 1 pint 6 quarts – 2 cups Lesson 6 1 gallon – 1 pint

  34. Subtracting Mixed Units 9 gallons 2 quarts – 3 quarts 9 gallons 2 quarts – 4 gallons 3 quarts 8 quarts 1 cup – 6 quarts 3 cups Lesson 6 8 quarts 1 cup – 3 cups

  35. Turn and Talk G4–M7–Lessons 6 and 7 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

  36. Try Problems #6-11. Lessons 7-9 Practice different addition and subtraction strategies for length, weight and time.

  37. Solving Multi-Step Measurement Word Problems Lesson 10 – Problem Set #12 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?

  38. Topic C: Investigation of Measurements Expressed as Mixed Numbers 4.OA.3, 4.MD.1, 4.MD.2 • 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

  39. Convert Mixed Number Measurements to Smaller Units Lesson 12 length capacity

  40. Convert Mixed Number Measurements to Smaller Units Lesson 13 weight time

  41. Try Problems #13-16. Try Problems #19-20. • Sample questions from the Problem Set of Lesson 14. • Use RDW to solve. Lessons 12-14 Sample questions from the Exit Tickets for Lessons 12 and 13. Consider how a student may solve pictorially or abstractly.

  42. Turn and Talk G4–M7–Lesson 14 • What difficulties would you anticipate with student understanding of the mathematics in this section? • What scaffolds would be effective for addressing those difficulties?

  43. Agenda Introduction to the Module Concept Development Module Review Year in Review

  44. 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. Agenda Introduction to the Module Concept Development Module Review Year in Review

  46. 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. Determine the Area for Composite Figures Lesson 15 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?

  48. Mini-Personal Boards Materials: plastic page protector, manila folder, tape Steps: Cut page protector in half horizontally. Tape to top half of folder with the opening at the top. Slip Problem Set into page protector. Fold back top half of Problem Set. Complete. Check answers by unfolding top half of Problem Set. Special Note: Do NOT copy Homework back-to-back in Topic D.

  49. Practice and Solidify Grade 4 Fluency Lesson 17

  50. Practice and Solidify Grade 4 Vocabulary Lesson 18

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