1. Properties (Answers)  Commutative Property  Associative Property  Distributive Property  Additive Identity  Additive Inverse  Multiplicative Identity  Multiplicative Inverse  Substitution  Symmetric Equality  Transitive Equality  Addition Property of Equality  Multiplication Property of Equality  Zero Product Property Game 2

2. Definitions: Choose the property that matches the definition

3. Two numbers that add to 0

4. Switch sides with 2 equations

5. Two numbers that multiply to 1

6. “Great cheese comes from happy cows. Happy cows come from California.” Therefore great cheese comes from California.

7. Multiply equal amounts to both sides.

8. Replace a variable with a number.

9. Change order of the numbers from left to right side.

10. Add equal amounts to both sides.

11. If the product of 2 numbers is 0, then one of the numbers being multiplied must equal 0.

12. Multiply by 1

13. Multiply a parenthesis by an outside number

14. Add and subtract the same number.

15. Add zero

16. Reciprocal

17. Positive and Negative of the same number.

18. 5B - B = 4B Replace B with Bananas, so this means: Eat 1 Banana out of a bunch of 5 Bananas and 4 are left

20. Properties with Variables Examples

21. a + b + c = b + a + c

22. If a = b, then 4a = 4b

23. If a = b and b = c, then a = c.

24. (a + b) + c = a + (b + c)

25. If ab = 0, then a = 0 or b = 0

26. a(b + c) = ab + ac

27. a + 0 = a

28. a + (-a) = 0

29. a * 1 = a

30. a x 1/a = 1

31. If a = b, then a + 2 = b + 2

32. If a + b = c and b = 2, then a + 2 = c

33. If 12 = b, then b = 12

35. Examples from Block 1

36. If x = 6 Then x + 8 = 14

37. 10 + 0 = 10

38. 3 equations. The middle of the first two are equal. The ends create the third. Example: If 4 = x and x = y, then 4 = y

39. x 2/5 becomes x 5/2

40. 1 * 15 = 15

41. If (x + 8)(x - 9) = 0, then (x + 8) = 0 or (x - 9) = 0 So (x + 8) gives x = -8 And (x – 9) gives x = 9

42. -57 + 57 = 0 -57 + 57 = 0

43. 6(x - 5) = 6x - 30

44. If 5 + 6 = 11, then 11 = 5 + 6

45. y = 5 + x when x = 4, then y = 9

46. 2 * 1 = 2

47. 4 * 5 * 7 = 7 * 5 * 4

48. If 10 = x Then 20 = 2x

49. 7 * 1/7 = 1

50. (1 * 2) * 3 = 1 * (2 * 3)

51. When you volunteer to wash Mr. Burkholder’s car but send your younger sibling to do it instead.

53. Properties Examples 2 Block 5 Shown Bl 1 7

54. 3 * 5 * 4 * 8 = 8 * 4 * 5 *3

55. ( 6 * 3) * 5 = 6 * (3 * 5)

56. 3(x - 8) = 3x - 24

57. 5 + 0 = 5

58. -12 + 12 = 0 -12 + 12 = 0

59. 72 * 1 = 72 Or 1 * 72 = 72

60. Multiplicative Inverse  Inverse means Opposite  Multiply and Divide the same number are opposites  OR Do reciprocal  numbers multiply to 1  Example: 8 * 1/8 = 1 8 * 1/8 = 1 Or Or * 3/4 becomes * 4/3 * 3/4 becomes * 4/3

61. Substitution  Replace a letter with a number  Example: 5 + x = y where x = 8 5 + x = y where x = 8 y = 13 y = 13

62. Symmetric Equality  2 Equations  Switch sides  Example: If 2 + 3 = 5, If 2 + 3 = 5, then 5 = 2 + 3 then 5 = 2 + 3

63. Transitive Equality  3 equations  The middle of the first two are equal.  The ends create the third.  Example: If 4 = x and x = y, then 4 = y If 4 = x and x = y, then 4 = y

64. Addition Property of Equality  Add Equal things to both sides.  Example: If 9 = x If 9 = x then 12 = x + 3 (Add 3 to both sides.) then 12 = x + 3 (Add 3 to both sides.)

65. Multiplication Property of Equality  Multiply Equal things to both sides.  Example: If 7 = x If 7 = x Then 28 = 4x (Multiply both sides by 4.) Then 28 = 4x (Multiply both sides by 4.)

66. Zero Product Property  Product is multiply  If 2 numbers multiply to 0, then one of the numbers must be 0.  Example: Question: If (x + 6)(x - 4) = 0, then Question: If (x + 6)(x - 4) = 0, then Answer: (x + 6) = 0 or (x - 4) = 0 Answer: (x + 6) = 0 or (x - 4) = 0 So (x + 6) gives x = -6 So (x + 6) gives x = -6 And (x – 4) gives x = 4 And (x – 4) gives x = 4

68. Properties Examples 2 Block 7 Shown Bl 1 5

69. Commutative Property  1 Equation  CO = Change order;  move numbers; “commute”  Example: 3 * 2 * 1 = 1 * 2 * 3 3 * 2 * 1 = 1 * 2 * 3

70. Associative Property  1 Equation  SO = Same Order.  Change groups or ( )  Example: ( 3 * 6 ) * 15 = 3 * ( 6 * 15) ( 3 * 6 ) * 15 = 3 * ( 6 * 15)

71. Distributive Property  1 Equation  Multiply the outside by everything in the inside.  Example: 4 (x - 7) = 4x - 28 4 (x - 7) = 4x - 28

72. Additive Identity  Add ZERO  Identity means stays the same  Example: 21 + 0 = 21 21 + 0 = 21

73. Additive Inverse  Inverse means Opposite  Add and Subtract the same number or  Positive and Negative  Adds to ZERO.  Example: +8 - 8 = 0 +8 - 8 = 0

74. Multiplicative Identity  Multiply by 1  Identity means stays the same  Example: 7 * 1 = 7 7 * 1 = 7 Or Or 1 * 8 = 8 1 * 8 = 8

75. Multiplicative Inverse  Inverse means Opposite  Multiply and Divide the same number are opposites  OR Do reciprocal  numbers multiply to 1  Example: 10 * 1/10 = 1 10 * 1/10 = 1 Or * 7/8 becomes * 8/7 Or * 7/8 becomes * 8/7

76. Substitution  Replace a letter with a number  Example: 5 + x = y where x = 7 5 + x = y where x = 7 y = 12 y = 12

77. Symmetric Equality  2 Equations  Switch sides  Example: If 3 + 4 = 7, If 3 + 4 = 7, then 7 = 3 + 4 then 7 = 3 + 4

78. Transitive Equality  3 equations  The middle of the first two are equal.  The ends create the third.  Example: If 4 = x and x = y, then 4 = y If 4 = x and x = y, then 4 = y

79. Addition Property of Equality  Add Equal things to both sides.  Example: If 8 = x If 8 = x then 15 = x + 7 (Add 7 to both sides.) then 15 = x + 7 (Add 7 to both sides.)

80. Multiplication Property of Equality  Multiply Equal things to both sides.  Example: If 3 = x If 3 = x then 21 = 7x (Multiply both sides by 7) then 21 = 7x (Multiply both sides by 7)

81. Zero Product Property  Product is multiply  If 2 numbers multiply to 0, then one of the numbers must be 0.  Example: If (x + 2)(x - 7) = 0, then If (x + 2)(x - 7) = 0, then (x + 2) = 0 or (x - 7) = 0 (x + 2) = 0 or (x - 7) = 0 So (x + 2) gives x = -2 So (x + 2) gives x = -2 And (x – 7) gives x = 7 And (x – 7) gives x = 7

83. Properties Examples 2 Block X Template

84. Commutative Property  1 Equation  CO = Change order;  move numbers; “commute”  Example:

85. Associative Property  1 Equation  SO = Same Order.  Change groups or ( )  Example:

86. Distributive Property  1 Equation  Multiply the outside by everything in the inside.  Example: (x -) = x – (x -) = x – (x + -) = x + - (x + -) = x + -

87. Additive Identity  Add ZERO  Identity means stays the same  Example: + 0 = + 0 =

88. Additive Inverse  Inverse means Opposite  Add and Subtract the same number or  Positive and Negative  Adds to ZERO.  Example: + = 0 + = 0

89. Multiplicative Identity  Multiply by 1  Identity means stays the same  Example: * 1 = ??? * 1 = ??? Or 1 * = Or 1 * =

90. Multiplicative Inverse  Inverse means Opposite  Multiply and Divide the same number are opposites  OR Do reciprocal  numbers multiply to 1  Example: * 1/ = 1 * 1/ = 1 Or * / becomes * / Or * / becomes * /

91. Substitution  Replace a letter with a number  Example: 5 + x = y where x = 5 + x = y where x = y = y =

92. Symmetric Equality  2 Equations  Switch sides  Example: If + =, If + =, then then

93. Transitive Equality  3 equations  The middle of the first two are equal.  The ends create the third.  Example: If 4 = x and x = 2y, then ??? If 4 = x and x = 2y, then ???

94. Addition Property of Equality  Add Equal things to both sides.  Example: If 5 = x, then 9 = ??? If 5 = x, then 9 = ???

95. Multiplication Property of Equality  Multiply Equal things to both sides.  Example: If 5 = x, then 9 = ??? If 5 = x, then 9 = ???

96. Zero Product Property  Product is multiply  If 2 numbers multiply to 0, then one of the numbers must be 0.  Example: If (x + )(x - ) = 0, then If (x + )(x - ) = 0, then (x + ) = 0 or (x - ) = 0 (x + ) = 0 or (x - ) = 0 So (x + ) gives x = So (x + ) gives x = And (x – ) gives x = And (x – ) gives x =