Lesson 3 Properties of Operations Unit 3A Expressions Lesson 3 Properties of Operations

Lesson 3: Properties of Operations Objective: Swbat identify properties of operations. Do Now: Worksheet

Lesson 3: Properties of Operations Definitions A property is a statement that is true for any number. A counterexample shows that a conjecture is false.

Lesson 3: Properties of Operations Properties of Operations Commutative Property a + b = b + a a ∙ b = b ∙ a Associative Property a + (b + c) = (a + b) + c a ∙ (b ∙ c) = (a ∙ b) ∙ c Additive Identity Property a + 0 = a Multiplicative Identity a ∙ 1 = a Multiplicative Property of Zero a ∙ 0 = 0

Lesson 3: Properties of Operations Do the properties apply to subtraction or division? If you can find a counterexample that shows it is false, the property does not apply. Examples: Commutative Property under Subtraction: a – b ≠ b – a 3 – 4 ≠ 4 – 3 Commutative Property under Division: a/b ≠ b/a 6/ 2 ≠ 2/6

Lesson 3: Properties of Operations Name the property. 1.) 2 ∙ (5 ∙ n) = (2 ∙ 5) ∙ n 2.) 42 + x + y = 42 + y + x 3.) 3x + 0 = 3x

Lesson 3: Properties of Operations Simplify the expression and justify each step using properties. Example 1: (7 + g) + 5 = (g + 7) + 5 _________________ = g + (7 + 5) _________________ = g + 12 simplified Example 2: 4 ∙ (3c ∙ 2) = 4 ∙ (2 ∙ 3c) _________________ = (4 ∙ 2) ∙ 3c _________________ = 8 ∙ 3c simplify = (8 ∙ 3) ∙ c _________________ = 24c simplifies

Classwork Guided Practice #1 – 5 Independent Practice #1 – 10 Problem Solving #1 - 7

Closure Question: Why are the properties important? Exit Ticket Homework: Practice # 1 - 12

Exit Ticket Give an example using the Associative Property and Commutative Property.

Homework