2. Lesson Menu Main Idea and New Vocabulary Key Concept:Commutative Properties Key Concept:Associative Properties Key Concept:Number Properties Example 1:Identify Properties Example 2:Find a Counterexample Example 3:Use Mental Math Example 4:Simplify Algebraic Expressions Example 5:Simplify Algebraic Expressions

3. Main Idea/Vocabulary Identify and use mathematical properties to simplify algebraic expressions. property counterexample simplify

4. Key Concept

5. Key Concept 1a

6. Key Concept 1b

7. Example 1 Identify Properties Name the property shown by the statement (3 m) 2 = 2 (3 m). Answer:The grouping of the numbers and variable did not change, but their order did. This is the Commutative Property of Multiplication.

8. Example 1 CYP A.Associative Property of Addition B.Associative Property of Multiplication C.Commutative Property of Addition D.Commutative Property of Multiplication Name the property shown by the statement 4 + (8 + x) = (4 + 8) + x.

9. Example 2 State whether the following conjecture is true or false. If false, provide a counterexample. Subtraction of whole numbers is associative. Find a Counterexample Write two subtraction expressions using the Associative Property. 4 ≠ 10Simplify. (12 – 5) – 3 = 12 – (5 – 3)State the conjecture. ? Answer:The conjecture is false. We found a counterexample: (12 – 5) – 3 ≠ 12 – (5 – 3). So, subtraction is not associative.

10. Example 2 CYP A.true B.false; (16 ÷ 8) ÷ 2 ≠ 16 ÷ (8 ÷ 2) State whether the following conjecture is true or false. If false, provide a counterexample. Division of whole numbers is associative.

11. Example 3 Use Mental Math GARDENS In a museum garden, a decorative pool containing fish is 2 feet deep, 17 feet long, and 5 feet wide. Use mental math to find the volume of water in the pool. Write an expression for the volume. You can rearrange the numbers using the properties of math. Look for products that are multiples of 10. 2 × 17 × 5= 2 × 5 × 17 Commutative Property = (2 × 5) × 17Associative Property = 10 × 17 Multiply. = 170 Simplify. Answer:The volume of the water is 170 cubic feet.

12. Example 3 CYP A.50 pounds B.60 pounds C.70 pounds D.80 pounds ROCKS A landscaper bought four rocks to use in a landscaping project. The rocks weighed 15 pounds, 22 pounds, 8 pounds, and 25 pounds. Use mental math to find the total weight of the rocks.

13. Example 4 Simplify the expression 6 + (d + 8). Justify each step. Simplify Algebraic Expressions Answer: 6 + (d + 8)= 6 + (8 + d) Commutative Property of Addition = (6 + 8) + d Associative Property of Addition = 14 + d Simplify.

14. Example 4 CYP A.5m + 14; Commutative (+) and Associative (+) B.11m + 8; Commutative (×) and Associative (×) C.16m + 3; Commutative (+) and Associative (+) D.16m; Commutative (×) and Associative (×) Simplify the expression 5m + (3 + 11m). Name two properties you can use to justify the steps.

15. Example 5 Simplify Algebraic Expressions Simplify the expression a (9 b). Justify each step. Answer: a (9 b)= (a 9) b Associative Property of Multiplication = (9 a) bCommutative Property of Multiplication = 9ab Simplify.

16. Example 5 CYP A.9t; Commutative (×) and Associative (×) B.14t; Commutative (×) and Associative (×) C.14 + t; Commutative (+) and Associative (+) D.7t + 2; Commutative (×) and Associative (+) Simplify the expression 7 (t 2). Name two properties you can use to justify the steps.