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# Day 1, Session 2 - The Progression of Multiplication and Division

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Sudbury Catholic District School Board (SCDSB) Mathematics Professional Learning: The Progression of Multiplication and Division. August 23rd, 2017.

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### Day 1, Session 2 - The Progression of Multiplication and Division

1. 1. Progression of Multiplication and Division @MathletePearcewww.tapintoteenminds.com tapintoteenminds.com/sudbury
2. 2. From: foreverence.com/legends/
3. 3. From: foreverence.com/legends/ VisualConcrete
4. 4. @MathletePearcewww.tapintoteenminds.com 2 Iconic Visual 1 3Enactive Concrete Symbolic Abstract “BE MORE PRINCE”
5. 5. What Do You… Notice? Wonder?
6. 6. How many doughnuts are there? Make a Prediction
7. 7. Update Your Prediction 32 doughnuts 25doughnuts
8. 8. Update Your Prediction 32 doughnuts 25doughnuts 800
9. 9. Update Your Prediction 32 doughnuts 25doughnuts 800
10. 10. DOUBLE DOZEN
11. 11. DOUBLE DOZEN 2 x 100 x 12
12. 12. DOUBLE DOZEN 2 x 100 x 12 = 2,400
13. 13. 2 x 100 x 12 = 2,400
14. 14. Side View 2,400
15. 15. 800 800 800 2,400 800- 1,600 800- 800 800- 0
16. 16. 2,400
17. 17. If your school bought this box of doughnuts to split between 8 classes, how many would each class get? 2,400 8 2,400
18. 18. @MathletePearcewww.tapintoteenminds.com If your school bought this box of doughnuts to split between 8 classes, how many would each class get? 2,400 2,392 2,384 8 88 8- 2,384 2,392 8- 2,400 1 group of 8 1 group of 8
19. 19. @MathletePearcewww.tapintoteenminds.com If your school bought this box of doughnuts to split between 8 classes, how many would each class get? 2,400 2,32080 80 2,240 80- 2,320 2,400 10 groups of 8 80- 2,240 10 groups of 8
20. 20. @MathletePearcewww.tapintoteenminds.com If your school bought this box of doughnuts to split between 8 classes, how many would each class get? 2,400 800- 800 100 groups of 8 1,600 800- 100 groups of 8 800 800800 800 800- 100 groups of 8 0 300 groups of 8300 8 8 8 8
21. 21. @MathletePearcewww.tapintoteenminds.com If your school bought this box of doughnuts to split between 8 classes, how many would each class get? 2,400 800- 800 100 groups of 8 1,600 800- 100 groups of 8800 800800 800 800- 100 groups of 8 0 300 groups of 8 300 88888
22. 22. @MathletePearcewww.tapintoteenminds.com APPLY: Distributive Property = ?÷195 15 19515 ?
23. 23. @MathletePearcewww.tapintoteenminds.com APPLY: Distributive Property = ?÷195 15 19515 ? 15
24. 24. @MathletePearcewww.tapintoteenminds.com APPLY: Distributive Property = ?÷195 15 19515 ? 15 195 - 15 180
25. 25. @MathletePearcewww.tapintoteenminds.com APPLY: Distributive Property = ?÷195 15 195 15 ? 15 195 - 15 180 180
26. 26. @MathletePearcewww.tapintoteenminds.com APPLY: Distributive Property = ?÷195 15 195 15 ? 15 195 - 15 180 18015
27. 27. @MathletePearcewww.tapintoteenminds.com APPLY: Distributive Property = ?÷195 15 195 15 ? 15 195 - 15 180 18015 - 15 165 165
28. 28. @MathletePearcewww.tapintoteenminds.com APPLY: Distributive Property = ?÷195 15 195 15 15 195 - 15 180 180 15 - 15 165 165 15 - 15 150 150 ? 15 15 15 15 15 15 15 15 15 15 1 1 1 1 1 1 1 1 1 1 1 1 1 - 15 . . .
29. 29. @MathletePearcewww.tapintoteenminds.com APPLY: Distributive Property = 13÷195 15 195 15 15 195 - 15 180 180 15 - 15 165 165 15 - 15 150 150 15 15 15 15 15 15 15 15 15 15 - 15 . . . 13
30. 30. @MathletePearcewww.tapintoteenminds.com APPLY: Distributive Property = ?÷195 15 195 15 15 195 - 15 180 180 15 - 15 165 165 15 - 15 150 150 ?
31. 31. @MathletePearcewww.tapintoteenminds.com APPLY: Distributive Property = ?÷195 15 195 15 15 195 - 15 180 180 15 - 15 165 165 15 - 15 150 150 ? - 15(10) 150 - 150 0
32. 32. @MathletePearcewww.tapintoteenminds.com ? APPLY: Distributive Property = 13÷195 15 195 15 1 15 195 - 15 180 180 15 - 15 165 165 15 - 15 150 150 1 1 10 - 15(10) 150 - 150 0
33. 33. @MathletePearcewww.tapintoteenminds.com ? = 13÷195 15 195 15 1 15 195 - 15 180 180 15 - 15 165 165 15 - 15 150 150 1 1 10 - 15(10) 150 - 150 0 O PEN ARRAY 45 3
34. 34. @MathletePearcewww.tapintoteenminds.com ? = 13÷195 15 15 1 15 195 - 15 180 15 - 15 165 15 - 15 150 150 1 1 10 - 15(10) 150 - 150 0 O PEN ARRAY 45 3
35. 35. @MathletePearcewww.tapintoteenminds.com
36. 36. @MathletePearcewww.tapintoteenminds.com
37. 37. @MathletePearcewww.tapintoteenminds.com RECALL
38. 38. @MathletePearcewww.tapintoteenminds.com YO UR TURN A pool has a width of 14 m and an area of 700 m2. What is the length?
39. 39. @MathletePearcewww.tapintoteenminds.com YO UR TURN A pool has a width of 14 m and an area of 700 m2. What is the length? 14 m 700 m2
40. 40. @MathletePearcewww.tapintoteenminds.com YO UR TURN A pool has a width of 14 m and an area of 700 m2. What is the length? 14 m 700 m2 10 m 140 m2
41. 41. @MathletePearcewww.tapintoteenminds.com YO UR TURN A pool has a width of 14 m and an area of 700 m2. What is the length? 14 m 560 m2 10 m 140 m2 700 - 140 560
42. 42. @MathletePearcewww.tapintoteenminds.com YO UR TURN A pool has a width of 14 m and an area of 700 m2. What is the length? 14 m 420 m2 10 m 140 m2 700 - 140 560 10 m 140 m2 - 140 420
43. 43. @MathletePearcewww.tapintoteenminds.com YO UR TURN A pool has a width of 14 m and an area of 700 m2. What is the length? 14 m 280 m2 10 m 140 m2 700 - 140 560 10 m 140 m2 - 140 420 10 m 140 m2 - 140 280
44. 44. @MathletePearcewww.tapintoteenminds.com YO UR TURN A pool has a width of 14 m and an area of 700 m2. What is the length? 14 m 140 m2 10 m 140 m2 700 - 140 560 10 m 140 m2 - 140 420 10 m 140 m2 - 140 280 10 m 140 m2 - 140 140
45. 45. @MathletePearcewww.tapintoteenminds.com YO UR TURN A pool has a width of 14 m and an area of 700 m2. What is the length? 14 m 140 m2 10 m 140 m2 700 - 140 56010 m 140 m2 - 140 420 10 m 140 m2 - 140 280 10 m 140 m2 - 140 140 10 m 140 m2 - 140 0
46. 46. @MathletePearcewww.tapintoteenminds.com YO UR TURN A pool has a width of 14 m and an area of 700 m2. What is the length? 14 m 140 m2 10 m 140 m2 700 - 140 560 10 m 140 m2 - 140 420 10 m 140 m2 - 140 280 10 m 140 m2 - 140 140 10 m 140 m2 - 140 0 50 m 700 m2
47. 47. @MathletePearcewww.tapintoteenminds.com
48. 48. @MathletePearcewww.tapintoteenminds.com
49. 49. @MathletePearcewww.tapintoteenminds.com A pool has a width of 3 m and an area of 12 times a number. What is the length?
50. 50. @MathletePearcewww.tapintoteenminds.com 1 1 1 A pool has a width of 3 m and an area of 12 times a number. What is the length? 12x
51. 51. @MathletePearcewww.tapintoteenminds.com 1 1 1 12x x A pool has a width of 3 m and an area of 12 times a number. What is the length?
52. 52. @MathletePearcewww.tapintoteenminds.com 1 1 1 12x x x x x A pool has a width of 3 m and an area of 12 times a number. What is the length?
53. 53. @MathletePearcewww.tapintoteenminds.com 1 1 1 9x x x x x A pool has a width of 3 m and an area of 12 times a number. What is the length? 12x - 3x 9x
54. 54. @MathletePearcewww.tapintoteenminds.com 1 1 1 9x x x x x x A pool has a width of 3 m and an area of 12 times a number. What is the length? 12x - 3x 9x
55. 55. @MathletePearcewww.tapintoteenminds.com 1 1 1 6x x x x x x x x x A pool has a width of 3 m and an area of 12 times a number. What is the length? 12x - 3x 9x - 3x 6x
56. 56. @MathletePearcewww.tapintoteenminds.com 1 1 1 6x x x x x x x x x x A pool has a width of 3 m and an area of 12 times a number. What is the length? 12x - 3x 9x - 3x 6x
57. 57. @MathletePearcewww.tapintoteenminds.com 1 1 1 3x x x x x x x x x x x x x A pool has a width of 3 m and an area of 12 times a number. What is the length? 12x - 3x 9x - 3x 6x - 3x 3x
58. 58. @MathletePearcewww.tapintoteenminds.com 1 1 1 3x x x x x x x x x x x x x x x x x A pool has a width of 3 m and an area of 12 times a number. What is the length? 12x - 3x 9x - 3x 6x - 3x 3x - 3x 0x
59. 59. @MathletePearcewww.tapintoteenminds.com 1 1 1 3x x x x x x x x x x x x x x x x x A pool has a width of 3 m and an area of 12 times a number. What is the length? 12x - 3x 9x - 3x 6x - 3x 3x - 3x 0x 4x
60. 60. @MathletePearcewww.tapintoteenminds.com A pool has an area of 3x2 + 11x + 6. What are the dimensions?
61. 61. @MathletePearcewww.tapintoteenminds.com A pool has an area of 3x2 + 11x + 6. What are the dimensions? x2 x2 x2 x x x x x x x x x x x 11 1 11 1
62. 62. @MathletePearcewww.tapintoteenminds.com A pool has an area of 3x2 + 11x + 6. What are the dimensions? x2 x2 x2 x x x x x x x x x x x 11 1 11 1
63. 63. @MathletePearcewww.tapintoteenminds.com A pool has an area of 3x2 + 11x + 6. What are the dimensions? x2 x2 x2 x x x x x x x x x x x 1 1 1 1 1 1
64. 64. @MathletePearcewww.tapintoteenminds.com A pool has an area of 3x2 + 11x + 6. What are the dimensions? x2 x2 x2 x x x x x x x x x x x 1 1 1 1 1 1
65. 65. @MathletePearcewww.tapintoteenminds.com A pool has an area of 3x2 + 11x + 6. What are the dimensions? x x 1 1 1 1 1 1 x2 x2 x2 x x x x x x x x x
66. 66. @MathletePearcewww.tapintoteenminds.com A pool has an area of 3x2 + 11x + 6. What are the dimensions? x 1 1 1 1 1 1 x2 x2 x2 x x x x x x x x x x
67. 67. @MathletePearcewww.tapintoteenminds.com A pool has an area of 3x2 + 11x + 6. What are the dimensions? x x2 x2 x2 x x x x x x x x x x 1 1 1 1 1 1
68. 68. @MathletePearcewww.tapintoteenminds.com A pool has an area of 3x2 + 11x + 6. What are the dimensions? x 1 1 1 x2 x2 x2 x x x x x x x x x x 1 1 1
69. 69. A pool has an area of 3x2 + 11x + 6. What are the dimensions? x 1 1 1 x2 x2 x2 x x x x x x x x x x 1 1 1
70. 70. x x A pool has an area of 3x2 + 11x + 6. What are the dimensions? x 1 1 1 x2 x2 x2 x x x x x x x x x x 1 1 1
71. 71. x x x A pool has an area of 3x2 + 11x + 6. What are the dimensions? x 1 1 1 x2 x2 x2 x x x x x x x x x x 1 1 1
72. 72. x x x x A pool has an area of 3x2 + 11x + 6. What are the dimensions? x 1 1 1 x2 x2 x2 x x x x x x x x x x 1 1 1
73. 73. x 1x x x A pool has an area of 3x2 + 11x + 6. What are the dimensions? x 1 1 1 x2 x2 x2 x x x x x x x x x x 1 1 1
74. 74. x 1 1x x x A pool has an area of 3x2 + 11x + 6. What are the dimensions? x 1 1 1 x2 x2 x2 x x x x x x x x x x 1 1 1
75. 75. x 1 1 1 x x x A pool has an area of 3x2 + 11x + 6. What are the dimensions? x 1 1 1 x2 x2 x2 x x x x x x x x x x 1 1 1
76. 76. x 1 1 1 x 1 x x A pool has an area of 3x2 + 11x + 6. What are the dimensions? x 1 1 1 x2 x2 x2 x x x x x x x x x x 1 1 1
77. 77. x 1 1 1 1 x 1 x x A pool has an area of 3x2 + 11x + 6. What are the dimensions? x 1 1 1 x2 x2 x2 x x x x x x x x x x 1 1 1
78. 78. x 1 1 1 1 x 1 x x A pool has an area of 3x2 + 11x + 6. What are the dimensions? x 1 1 1 x2 x2 x2 x x x x x x x x x x 1 1 1 (x + 3)(3x + 2)
79. 79. Concreteness Fading 1 2 3Enactive Concrete Iconic Visual Symbolic Abstract x 1 1 1 1 x 1 x x 1 1 1 x2 x x x x x x x 1 1 1 x2 x 3 6x 6 2x2 2x 2 2x = (2x + 2)(x + 3) 2x2 + 8x + 6 Factor: