Properties. Properties (Answers) Commutative Property Associative Property Distributive Property Additive Identity Additive Inverse Multiplicative.

PropertiesProperties

Properties (Answers)Properties (Answers) Commutative PropertyCommutative Property Associative PropertyAssociative Property Distributive PropertyDistributive Property Additive IdentityAdditive Identity Additive InverseAdditive Inverse Multiplicative IdentityMultiplicative Identity Multiplicative InverseMultiplicative Inverse

SubstitutionSubstitution Symmetric EqualitySymmetric Equality Transitive EqualityTransitive Equality Addition Property of Addition Property of

EqualityEquality Multiplication Property Multiplication Property

of Equalityof Equality Zero Product PropertyZero Product Property

Hr. 6: Hr. 6: 3 * 1 = 33 * 1 = 3 Hr. 6:Hr. 6: 1 * 5 = 51 * 5 = 5 Hr. 7: Hr. 7: 7 * 1 = 77 * 1 = 7 Hr. 7:Hr. 7: 1 * 6 = 61 * 6 = 6

5B - B = 4B5B - B = 4B

Replace B with BananasReplace B with Bananas

(So this means: Eat 1 Banana out of a bunch of 5 Bananas (So this means: Eat 1 Banana out of a bunch of 5 Bananas

and 4 Bananas are left.)and 4 Bananas are left.)

Hr. 6: Hr. 6: If x = 7, then 5x = 35If x = 7, then 5x = 35 Hr. 6: Hr. 6: If x = 8, then 6x = 48If x = 8, then 6x = 48 Hr. 7: Hr. 7: x = p, then 2x = 2px = p, then 2x = 2p Hr. 7: Hr. 7: ab = c, then (a)ab = acab = c, then (a)ab = ac Hr. 7: Hr. 7: ab = c, then 8ab = 8cab = c, then 8ab = 8c

Hr. 6: Hr. 6: 3(X + 1) = 3x + 33(X + 1) = 3x + 3 Hr. 6:Hr. 6: 7(X + 2) = 7x + 147(X + 2) = 7x + 14 Hr. 7 : Hr. 7 : 4(X - 7) = 4x - 284(X - 7) = 4x - 28 Hr. 7Hr. 7 4(B + -2) = 4B - 8 4(B + -2) = 4B - 8

Hr. 6: Hr. 6: Y = 22 +X. When X = 4, then Y = 26.Y = 22 +X. When X = 4, then Y = 26. Hr. 6: Hr. 6: F(a) = a + 1. F(2) = 3F(a) = a + 1. F(2) = 3 Hr. 7 : Hr. 7 : y = 1 + a, when a = 2, y = 3y = 1 + a, when a = 2, y = 3 Hr. 7 Hr. 7 f(x) = 8x, then f(1) = 8f(x) = 8x, then f(1) = 8

Hr. 6: Hr. 6: 3 + 0 = 3 3 + 0 = 3 Hr. 6:Hr. 6: 37 + 0 = 37 37 + 0 = 37 Hr. 7: Hr. 7: 4 + 0 = 44 + 0 = 4 Hr. 7:Hr. 7: 6 + 0 = 66 + 0 = 6

Hr. 6: Hr. 6: 3 = x, then 9 = x + 63 = x, then 9 = x + 6 Hr. 6: Hr. 6: if x = 1, then x + 8 = 9if x = 1, then x + 8 = 9

Hr. 7: Hr. 7: x = q, then x + 1 = q + 1x = q, then x + 1 = q + 1

Hr. 7: Hr. 7: X = 3, then x + 5 = 8X = 3, then x + 5 = 8

Hr. 6: Hr. 6: 5P = 0, then P = 05P = 0, then P = 0 Hr. 6: Hr. 6: If A(J+1) = 0, then A = 0 or (J+1) = 0If A(J+1) = 0, then A = 0 or (J+1) = 0 Hr. 7: Hr. 7: 4X = 0, then X =04X = 0, then X =0 Hr. 7: Hr. 7: 6Y = 0, then Y =06Y = 0, then Y =0 Hr. 7: Hr. 7: AB = 0, then either A = 0 or B = 0AB = 0, then either A = 0 or B = 0

Hr. 6: Hr. 6: If a = b and b = d, then a = dIf a = b and b = d, then a = d Hr. 6: Hr. 6: x = y and y = z, so x = zx = y and y = z, so x = z Hr. 7: Hr. 7: If x = 2 and 2 = y, then x = y If x = 2 and 2 = y, then x = y Hr. 7 Hr. 7 If x = k and k = y, then x = yIf x = k and k = y, then x = y Hr. 7 Hr. 7 If 1+4 = 5 and 5 = 3 + 2, If 1+4 = 5 and 5 = 3 + 2, then 1 + 4 = 3 + 2then 1 + 4 = 3 + 2

Hr. 6:Hr. 6: 63 * 1/63 = 163 * 1/63 = 1 Hr. 6:Hr. 6: 3/7 * 7/3 = 13/7 * 7/3 = 1 Hr. 7Hr. 7 7 * 1/7 = 1 7 * 1/7 = 1 Hr. 7Hr. 7 4/7 * 7/4 = 14/7 * 7/4 = 1

Hr. 6:Hr. 6: 6 + 4 = 4 + 66 + 4 = 4 + 6 Hr. 6:Hr. 6: A + B + C = B + C +AA + B + C = B + C +A Hr. 7:Hr. 7: 9 + 2 = 2 + 99 + 2 = 2 + 9 Hr. 7:Hr. 7: 1+2+3 = 2+1+31+2+3 = 2+1+3

Hr. 6: Hr. 6: If 93 = a, then a = 93If 93 = a, then a = 93 Hr. 6: Hr. 6: If x + 4 = y, then f(x) = x + 4 If x + 4 = y, then f(x) = x + 4 Hr. 7Hr. 7 If 8 = x, then x =8 If 8 = x, then x =8 Hr. 7Hr. 7 If x + 7 = y, then y = x + 7 If x + 7 = y, then y = x + 7

Hr. 6:Hr. 6: 6 + 4 = 4 + 66 + 4 = 4 + 6 Hr. 6:Hr. 6: A + B + C = B + C +AA + B + C = B + C +A Hr. 7:Hr. 7: 9 + 2 = 2 + 99 + 2 = 2 + 9 Hr. 7:Hr. 7: 1+2+3 = 2+1+31+2+3 = 2+1+3

Hr. 6: Hr. 6: -4 + 4 = 0 -4 + 4 = 0 Hr. 6:Hr. 6: 5 - 5 = 05 - 5 = 0 Hr. 7 : Hr. 7 : 2 + -2 = 0 2 + -2 = 0 Hr. 7Hr. 7 6 + -6 = 06 + -6 = 0

PropertiesPropertiesExamplesExamples

Block 6/7 2011Block 6/7 2011

Properties (Answers)Properties (Answers) Commutative PropertyCommutative Property Associative PropertyAssociative Property Distributive PropertyDistributive Property Additive IdentityAdditive Identity Additive InverseAdditive Inverse Multiplicative IdentityMultiplicative Identity Multiplicative InverseMultiplicative Inverse

SubstitutionSubstitution Symmetric EqualitySymmetric Equality Transitive EqualityTransitive Equality Addition Property of Addition Property of

EqualityEquality Multiplication Property Multiplication Property

of Equalityof Equality Zero Product PropertyZero Product Property

Game 1

Hr. 7Hr. 7 7 * 1/7 = 1 7 * 1/7 = 1

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Hr. 6: Hr. 6: If x = 8, then 6x = 48If x = 8, then 6x = 48

Answer a different property than Answer a different property than Substitution.Substitution.

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Hr. 7: Hr. 7: 6Y = 0, then Y =06Y = 0, then Y =0

.

Hr. 6: Hr. 6: 3 + 0 = 3 3 + 0 = 3

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Hr. 7Hr. 7 6 + -6 = 06 + -6 = 0

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Hr. 7: Hr. 7: (2 + 3) + 5 = 2 + (3 + 5)(2 + 3) + 5 = 2 + (3 + 5)

Hr. 7Hr. 7 4(B + -2) = 4B - 8 4(B + -2) = 4B - 8

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Hr. 6: Hr. 6: if x = 1, then x + 8 = 9if x = 1, then x + 8 = 9

Answer a different property than Substitution.Answer a different property than Substitution.

.

Hr. 7: Hr. 7: 7 * 1 = 77 * 1 = 7

.

Hr. 7:Hr. 7: 1+2+3 = 2+1+31+2+3 = 2+1+3

Hr. 6: Hr. 6: If a = b and b = d, then a = dIf a = b and b = d, then a = d

.

Hr. 7Hr. 7 If 8 = x, then x =8 If 8 = x, then x =8

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Hr. 7 Hr. 7 f(x) = 8x, then f(1) = 8f(x) = 8x, then f(1) = 8

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Properties (Answers)Properties (Answers) Commutative PropertyCommutative Property Associative PropertyAssociative Property Distributive PropertyDistributive Property Additive IdentityAdditive Identity Additive InverseAdditive Inverse Multiplicative IdentityMultiplicative Identity Multiplicative InverseMultiplicative Inverse

SubstitutionSubstitution Symmetric EqualitySymmetric Equality Transitive EqualityTransitive Equality Addition Property of Addition Property of

EqualityEquality Multiplication Property Multiplication Property

of Equalityof Equality Zero Product PropertyZero Product Property

Game 2

Hr. 6: Hr. 6: 3 = x, then 9 = x + 63 = x, then 9 = x + 6

Not SubstitutionNot Substitution

.

9 + 2 = 2 + 99 + 2 = 2 + 9 Hr. 7:Hr. 7:

Hr. 6:Hr. 6: 37 + 0 = 37 37 + 0 = 37

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Hr. 7: Hr. 7: If x = 2 and 2 = y, then x = y If x = 2 and 2 = y, then x = y

.

Hr. 7: Hr. 7: ab = c, then 8ab = 8cab = c, then 8ab = 8c

.

Hr. 7 : Hr. 7 : y = 1 + a, when a = 2, y = 3y = 1 + a, when a = 2, y = 3

.

Hr. 7Hr. 7 If x + 7 = y, then y = x + 7 If x + 7 = y, then y = x + 7

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Hr. 7 : Hr. 7 : 2 + -2 = 0 2 + -2 = 0

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Hr. 7 : Hr. 7 : 4(X - 7) = 4x - 284(X - 7) = 4x - 28

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Hr. 6:Hr. 6: 1 * 5 = 51 * 5 = 5

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5B - B = 4B5B - B = 4B

Replace B with Bananas.Replace B with Bananas.

(So this means: Eat 1 Banana out of a bunch of 5 Bananas (So this means: Eat 1 Banana out of a bunch of 5 Bananas

and 4 Bananas are left.)and 4 Bananas are left.)

Hr. 7: Hr. 7: (a + b) + c + d = a + b + (c + d)(a + b) + c + d = a + b + (c + d)

Hr. 6:Hr. 6: 3/7 * 7/3 = 13/7 * 7/3 = 1

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Hr. 6: Hr. 6: If A(J+1) = 0, then A = 0 or (J+1) = 0If A(J+1) = 0, then A = 0 or (J+1) = 0

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Properties (Answers)Properties (Answers)

Commutative Commutative PropertyProperty

Associative PropertyAssociative Property Distributive PropertyDistributive Property Additive IdentityAdditive Identity Additive InverseAdditive Inverse Multiplicative IdentityMultiplicative Identity Multiplicative InverseMultiplicative Inverse

SubstitutionSubstitution Symmetric EqualitySymmetric Equality Transitive EqualityTransitive Equality Addition Property of Addition Property of

EqualityEquality Multiplication Property Multiplication Property

of Equalityof Equality Zero Product PropertyZero Product Property

Game 3

Hr. 6: Hr. 6: (3 x 4) x 2 = 3 x (4 x 2) (3 x 4) x 2 = 3 x (4 x 2)

Hr. 6: Hr. 6: 3 * 1 = 33 * 1 = 3

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Hr. 6: Hr. 6: F(a) = a + 1. F(2) = 3F(a) = a + 1. F(2) = 3

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Hr. 6: Hr. 6: If x + 4 = y, then f(x) = x + 4 If x + 4 = y, then f(x) = x + 4

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Hr. 7: Hr. 7: x = q, then x + 1 = q + 1x = q, then x + 1 = q + 1

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Hr. 6: Hr. 6: x = y and y = z, so x = zx = y and y = z, so x = z

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Hr. 7: Hr. 7: AB = 0, then either A = 0 or B = 0AB = 0, then either A = 0 or B = 0

.

Hr. 6:Hr. 6: 5 - 5 = 05 - 5 = 0

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Hr. 6:Hr. 6: 7(X + 2) = 7x + 147(X + 2) = 7x + 14

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Hr. 7Hr. 7 4/7 * 7/4 = 14/7 * 7/4 = 1

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Hr. 7: Hr. 7: x = p, then 2x = 2px = p, then 2x = 2p

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Hr. 7: Hr. 7: 4 + 0 = 44 + 0 = 4

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Hr. 6:Hr. 6: A + B + C = B + C +AA + B + C = B + C +A

Properties (Answers)Properties (Answers) Commutative PropertyCommutative Property Associative PropertyAssociative Property Distributive PropertyDistributive Property Additive IdentityAdditive Identity Additive InverseAdditive Inverse Multiplicative IdentityMultiplicative Identity Multiplicative InverseMultiplicative Inverse

SubstitutionSubstitution Symmetric EqualitySymmetric Equality Transitive EqualityTransitive Equality Addition Property of Addition Property of

EqualityEquality Multiplication Property Multiplication Property

of Equalityof Equality Zero Product PropertyZero Product Property

Game 4

Hr. 7:Hr. 7: 1 * 6 = 61 * 6 = 6

.

Hr. 6: Hr. 6: -4 + 4 = 0 -4 + 4 = 0

..

Hr. 6: Hr. 6: If 93 = a, then a = 93If 93 = a, then a = 93

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Hr. 6: Hr. 6: If x = 7, then 5x = 35If x = 7, then 5x = 35

NOT SUBSTITUTIONNOT SUBSTITUTION

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Hr. 6:Hr. 6: 6 + 4 = 4 + 66 + 4 = 4 + 6

Hr. 7: Hr. 7: X = 3, then x + 5 = 8X = 3, then x + 5 = 8

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Hr. 6:Hr. 6:

9 + (3 + 8) = (9 + 3) + 89 + (3 + 8) = (9 + 3) + 8

Hr. 7 Hr. 7 If x = k and k = y, then x = yIf x = k and k = y, then x = y

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Hr. 7: Hr. 7: ab = c, then (a)ab = acab = c, then (a)ab = ac

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Hr. 6: Hr. 6: 5P = 0, then P = 05P = 0, then P = 0

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Hr. 6: Hr. 6: 3(X + 1) = 3x + 33(X + 1) = 3x + 3

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Hr. 6:Hr. 6: 63 * 1/63 = 163 * 1/63 = 1

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Hr. 6: Hr. 6: Y = 22 +X. When X = 4, then Y = 26.Y = 22 +X. When X = 4, then Y = 26.

..

Hr. 7 Hr. 7 If 1+4 = 5 and 5 = 3 + 2, If 1+4 = 5 and 5 = 3 + 2, then 1 + 4 = 3 + 2then 1 + 4 = 3 + 2

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Hr. 7:Hr. 7: 6 + 0 = 66 + 0 = 6

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Hr. 7: Hr. 7: 4X = 0, then X =04X = 0, then X =0

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