POD

basic advanced

4b + 6

b= 5, c= 3, d=7

(10c ÷b)2 + d

4(5) + 620 + 6

26

(10(3) ÷5)2 + 7(30 ÷5)2 + 7(6)2 + 736 + 7

43

PODb= 5, c= 3, d=7

basic advanced

b + 4c × d (b2 × 4 + 44) ÷ (4c)

5 + 4(3) × 75 + 12 × 7

5 + 84 89

(52 × 4 + 44) ÷ (4 × 3)(25 × 4 + 44) ÷ (4 × 3)

(100 + 44) ÷ (4 × 3)

(144) ÷ (4 × 3)(144) ÷ (12)

12

POD

State whether the conjecture is true or false. If false, provide a counterexample.

Subtraction of whole numbers is associative

False

(8−5) − 3 ≠ 8 − (5−3)

Properties of OperationsThe Commutative Property states that the order in which numbers are added or multiplied does not change the sum or product.

a + b = b + a a × b = b × a

The Associative Property states that the way in which numbers are grouped when they are added or multiplied does not change the sum or product.

a + (b+c) = (a+ b) + c a × (b×c) = (a × b) × c

The Additive Identity Property states that when 0 is added to any number, the sum is the number.

a + 0 = a 0 + a = a

The Multiplicative Identity Property states that when any number is multiplied by 1, the product is the number.

a × 1 = a 1 × a = a

The Multiplicative Property of Zero states that when any number is multiplied by 0, the product is 0.

a × 0 = 0 0 × a = 0

The Distributive Property states that to multiply a sum or difference by a number, multiply each term inside the parenthesis by the number outside the parenthesis.

a( b + c ) = ab + ac a( b – c ) = ab − ac

2 ( y + 2) = 2(y) +2(2)

= 2y + 4

The expressions 2(y+2) and 2y+4 are equivalent expressions. No matter what y is, these expressions have the same value.

Whiteboard time

Name the property shown by the statement:

2 × (5 × n) = (2 × 5) × n

Associative Property

Whiteboard time

Name the property shown by the statement:

42 + b + y = 42 + y + b

Commutative Property

Whiteboard time

Name the property shown by the statement:

3c + 0 = 3c

Additive Identity Property

Whiteboard time

Name the property shown by the statement:

3m × 0 × 5m = 0

Multiplicative Property of Zero

Whiteboard time

Name the property shown by the statement:

7c + 0 = 7c

Additive Identity Property

Whiteboard time

Name the property shown by the statement:

(3 × m) × 2 = 2 × (3 × m)

Commutative Property

Whiteboard time

Name the property shown by the statement:

8(-9 + 4) = 8(-9) + 8(4)

Distributive Property

Whiteboard time

Use the distributive property and evaluate:

5(-9 + 11)

5(-9) + 5(11)

-45 + 55 10

Whiteboard time

Use the distributive property and evaluate:

7(10 − 5)

7(10) − 7(5)

70 − 35 35

Whiteboard time

Use the distributive property and evaluate:

6(p − 5)

6(p) − 6(5)

6p − 30

Simplify each expression

(7 + g) + 5(7 + g) + 5 = (g + 7) + 5

= g + (7 + 5) = g + 12

Commutative Property of Multiplication

Associative Property of Multiplication

Simplify each expression

(m × 11) × m(m × 11) × m = (11 × m) × m

= 11 × (m × m)

= 11 × m2

Commutative Property of Multiplication

Associative Property of Multiplication

= 11m2

Simplify each expression

a (9 b) a (9 b) = (a 9) b (9 a) b

9 (a b)

Associative Property of Multiplication

commutative Property of Multiplication

= 9ab

Associative Property of Multiplication

Simplify each expression

9c + (8+3c)9c + (8+3c) = 9c + (3c +8)

(9c + 3c) +8

12c +8

Associative Property of Multiplication

commutative Property of Multiplication

Simplify each expression

6 + (d + 8)6 + (d + 8)= 6 + (8 + d)

(6 + 8) +d

14 + d

Associative Property of Multiplication

commutative Property of Multiplication

Simplify each expression

4 × (3c × 2)4 × (3c × 2)= 4 × (2 × 3c)

(4 × 2) × 3c

8 × 3c

Associative Property of Multiplication

commutative Property of Multiplication

(8 × 3) × c

24 × c 24c

Associative Property of Multiplication