1. Welcome to: A “Hands-On” Approach to the Distributive Property Presenter: Dave Chamberlain Math Curriculum Specialist, Capistrano USD Past President, Orange County Math Council Creator, TEAM UP! For Common Core Learning

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 x^2 + 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. When/How is the Distributive Property Important? Content standards which include the word “distributive”: 3.OA.5 3.MD.7c Grade 4 Critical Area 1 - They apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. 6.NS.4 6.EE.3 7.NS.2.a 8.NS.7b N-CN-2 N-VM-9

5. What is 14 x 13?

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

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

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

9. What is 14 x 13?

10. 14

11. What is 14 x 13? 14 x 13

12. What is 14 x 13? 14 x 13

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

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

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

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

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

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

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

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 +

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

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

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

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

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

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

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

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

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

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

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

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

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

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

37. 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?

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

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

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

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

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

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

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

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

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

47. At this point you may be thinking…

48. Dave, that’s kind of…

49. brilliant

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

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

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

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

54. Dave, that’s kind of… brilliant semi-interesting useless and/or soooo NOT “Hands-On”…...I’m looking through my program now for another session.

55. Wait! Let’s go back to 14 x 13…

56. 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...

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

58. Just kidding!

59. What is 11 x 13?

60. What is 15 x 14?

61. What is 16 x 15?

62. What is 19 x 19?

63. What is 21 x 21?

64. What is 99 x 98?

65. What is 21 x 12?

66. What is 31 x 22?

67. What is 101 x 11?

68. At this point you may be thinking…

69. Dave, that’s kind of…

70. genius

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

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

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

74. Dave, that’s kind of… genius semi-genius still useless and/or a cool bar trick, but how would this help a kid in, oh I don’t know, an Algebra 1 class?

75. Well, does… (x + 4)(x + 3) pique your interest?

76. Well, does… (x + 4)(x + 3) pique your interest? I thought so…

77. Well, 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...

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

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

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

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

82. Now let’s FACTOR…

83. x + 5x + 4 2

84. Now let’s FACTOR… x + 6x + 9 2

85. Now let’s FACTOR… x - 6x + 9 2

86. Now let’s FACTOR… x - 2x - 8 2

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

88. At this point you may be thinking…

89. Dave, the session has been…

90. life-changing

91. Dave, the session has been… life-changing worth the 60 minutes of my life I’ll never get back

92. Dave, the session has been… life-changing bearable…I’m still here! worth the 60 minutes of my life I’ll never get back

93. Dave, the session has been… life-changing bearable…I’m still here! and/or worth the 60 minutes of my life I’ll never get back

94. Dave, the session has been… life-changing bearable…I’m still here! and/or OK, OK…I’m going to update my Facebook page when I get home! worth the 60 minutes of my life I’ll never get back