PO D basicadvanced 4b + 6 b= 5, c= 3, d=7 (10c ÷b) 2 + d 4(5) (10(3) ÷5) (30 ÷5) (6)

PO D b= 5, c= 3, d=7 basicadvanced b + 4c × d (b 2 × ) ÷ (4c) 5 + 4(3) × × (5 2 × ) ÷ (4 × 3) (25 × ) ÷ (4 × 3) ( ) ÷ (4 × 3) (144) ÷ (4 × 3) (144) ÷ (12) 12

PO D 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)

The Commutative Property states that the order in which numbers are added or multiplied does not change the sum or product. a + b = b + aa × 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) + ca × (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 = a0 + a = a

The Multiplicative Identity Property states that when any number is multiplied by 1, the product is the number. a × 1 = a1 × a = a

The Multiplicative Property of Zero states that when any number is multiplied by 0, the product is 0. a × 0 = 00 × 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 + aca( 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( ) 5(-9) + 5(11)

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 × m 2 Commutative Property of Multiplication Associative Property of Multiplication = 11m 2

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