5. Lesson 6 CA Standard 25.0 Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements.

6. Lesson 6 KC1

7. Lesson 6 KC2

8. Lesson 6 Ex2 Use Multiplication Properties Evaluate 2 ● 8 ● 5 ● 7 using properties of numbers. Name the property used in each step. You can rearrange and group the factors to make mental calculations easier. Answer: 560 2 ● 8 ● 5 ● 7 = 2 ● 5 ● 8 ● 7 Commutative ( × ) = (2 ● 5) ● (8 ● 7) Associative (×) = 10 ● 56 Multiply mentally. = 560 Multiply mentally. BrainPop: The Commutative Property

10. Lesson 6 KC3 BrainPop: The Associative Property

11. Lesson 6 Ex3 Write and Simplify an Expression A. Use the expression three times the sum of 3x and 2y added to five times the sum of x and 4y. Write an algebraic expression for the verbal expression. Answer: 3(3 x + 2 y ) + 5( x + 4 y ) Words three times five times the sum of the sum 3 x and 2 y added to of x and 4 y Variable Let x and y represent the numbers. Equation 3(3 x + 2 y ) + 5( x + 4 y )

12. Lesson 6 Ex3 Write and Simplify an Expression B. Simplify the expression and indicate the properties used. 3 (3 x + 2 y ) + 5 ( x + 4 y ) = 3 (3 x ) + 3 (2 y ) + 5 ( x ) + 5 (4 y ) Distributive Property = 9 x + 6 y + 5 x + 20 y Multiply. = 9 x + 5 x + 6 y + 20 y Commutative (+) = (9 x + 5 x ) + (6 y + 20 y ) Associative (+) = (9 + 5) x + (6 + 20) y Distributive Property Answer: = 14 x + 26 y Substitution