1. Welcome to: A “Hands-On” Approach to the Distributive Property (Session 538) Presenter: Dave Chamberlain djchamberlain@capousd.org Math Curriculum Specialist, Capistrano USD President, Orange County Math Council

2. When/How is the Distributive Property Important?

3. When/How is the Distributive Property Important? Math Practice Standard 7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well-remembered 7 x 5 + 7 x 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

4. What is 14 x 13?

5. Convince me… Write down as many different ways to prove that 14 x 13 = 182

6. What is 14 x 13? What was the most efficient method? What was the least efficient method?

7. What is 14 x 13? How is the “standard algorithm” taught?

8. What is 14 x 13?

9. 14

10. What is 14 x 13? 14 x 13

11. What is 14 x 13? 14 x 13

12. What is 14 x 13? 14 x 13 2

13. What is 14 x 13? 14 x 13 2 1

14. What is 14 x 13? 14 x 13 2 1 4

15. What is 14 x 13? 14 x 13 2 1 4 0

16. What is 14 x 13? 14 x 13 2 1 4 x

17. What is 14 x 13? 14 x 13 2 1 4 0

18. What is 14 x 13? 14 x 13 2 1 4 0 4

19. What is 14 x 13? 14 x 13 2 1 4 0 4 1

20. What is 14 x 13? 14 x 13 2 1 4 0 4 1 +

21. What is 14 x 13? 14 x 13 2 1 4 0 4 1 +

22. What is 14 x 13? 14 x 13 2 1 4 0 4 1 2 +

23. What is 14 x 13? 14 x 13 2 1 4 0 4 1 2 8 +

24. What is 14 x 13? 14 x 13 2 1 4 0 4 1 2 8 1 +

25. What is 14 x 13? What are the advantages of teaching the “standard algorithm”? What are the disadvantages of teaching the “standard algorithm”?

26. What is 14 x 13? Let’s look at the “partial products” method…

27. What is 14 x 13? (10 + 4)

28. What is 14 x 13? (10 + 4) x

29. What is 14 x 13? (10 + 4) x (10 + 3) =

30. What is 14 x 13? (10 + 4) x (10 + 3) = 100

31. What is 14 x 13? (10 + 4) x (10 + 3) = 100 + 30

32. What is 14 x 13? (10 + 4) x (10 + 3) = 100 + 30 + 40

33. What is 14 x 13? (10 + 4) x (10 + 3) = 100 + 30 + 40 + 12 =

34. What is 14 x 13? (10 + 4) x (10 + 3) = 100 + 30 + 40 + 12 = 182

35. What is 14 x 13? What are the advantages of teaching the “partial products” method? What are the disadvantages of teaching the “partial products” method?

36. What is 9 x 8… …using “partial products”?

37. What is 9 x 8… …using “partial products”? (10 - 1)

38. What is 9 x 8… …using “partial products”? (10 - 1) x

39. What is 9 x 8… …using “partial products”? (10 - 1) x (10 - 2) =

40. What is 9 x 8… …using “partial products”? (10 - 1) x (10 - 2) = 100

41. What is 9 x 8… …using “partial products”? (10 - 1) x (10 - 2) = 100 - 20

42. What is 9 x 8… …using “partial products”? (10 - 1) x (10 - 2) = 100 - 20 - 10

43. What is 9 x 8… …using “partial products”? (10 - 1) x (10 - 2) = 100 - 20 - 10 + 2 =

44. What is 9 x 8… …using “partial products”? (10 - 1) x (10 - 2) = 100 - 20 - 10 + 2 = 72

45. At this point you may be thinking…

46. Dave, that’s kind of…

47. brilliant

48. Dave, that’s kind of… brilliant semi-interesting

49. Dave, that’s kind of… brilliant semi-interesting useless

50. Dave, that’s kind of… brilliant semi-interesting useless and/or

51. Dave, that’s kind of… brilliant semi-interesting useless and/or soooo NOT “Hands-On”…

52. Dave, that’s kind of… brilliant semi-interesting useless and/or soooo NOT “Hands-On”…...I’m rating this session a “0”!

53. Wait! Let’s go back to 14 x 13…

54. Wait! Let’s go back to 14 x 13… For now, let’s make each of your wrists worth 10 and your fingers worth 1 each...

55. Too bad that this “hand multiplication” trick only works for 14 x 13.

56. Just kidding!

57. What is 15 x 14?

58. What is 16 x 15?

59. What is 19 x 19?

60. What is 21 x 21?

61. What is 99 x 98?

62. What is 21 x 12?

63. What is 31 x 22?

64. What is 101 x 11?

65. At this point you may be thinking…

66. Dave, that’s kind of…

67. genius

68. Dave, that’s kind of… genius semi-genius

69. Dave, that’s kind of… genius semi-genius still useless

70. Dave, that’s kind of… genius semi-genius still useless and/or

71. Dave, that’s kind of… genius semi-genius still useless and/or irrelevant…I teach Algebra…

72. Dave, that’s kind of… genius semi-genius still useless and/or irrelevant…I teach Algebra…...I’m rating this session a “0”!

73. Wait! Does… (x + 4)(x + 3) pique your interest?

74. Wait! Does… (x + 4)(x + 3) pique your interest? I thought so…

75. Wait! Does… (x + 4)(x + 3) pique your interest? This time, let’s make each of your wrists worth x and your fingers worth 1 each...

76. What is (x + 5)(x + 2)?

77. What is (x + 3)(x - 2)?

78. What is (x - 4)(x - 4)?

79. What is (x + 5)(x - 5)?

80. Now let’s FACTOR…

81. x + 5x + 4 2

82. Now let’s FACTOR… x + 6x + 9 2

83. Now let’s FACTOR… x - 6x + 9 2

84. Now let’s FACTOR… x - 2x - 8 2

85. Now let’s FACTOR… x + x + x + 1 2 3

86. At this point you may be thinking…

87. Dave, the session has been…

88. life-changing

89. Dave, the session has been… life-changing worth the 90 minutes of my life I’ll never get back

90. Dave, the session has been… life-changing bearable…I’m still here! worth the 90 minutes of my life I’ll never get back

91. Dave, the session has been… life-changing bearable…I’m still here! and/or worth the 90 minutes of my life I’ll never get back

92. Dave, the session has been… life-changing bearable…I’m still here! and/or OK, OK… worth the 90 minutes of my life I’ll never get back

93. Dave, the session has been… life-changing bearable…I’m still here! and/or OK, OK… I’m rating this session a “333”! worth the 90 minutes of my life I’ll never get back