1 3 Properties of Numbers Warm Up Problem

1 -3 Properties of Numbers Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

1 -3 Properties of Numbers Warm Up Evaluate. 1. 2 + 5 3 – 7 10 2. 5(3 – 1) ÷ (3 + 2) 2 3. (4 + 1)2 – 8 ÷ 2 21 4. 12 ÷ 3 6 – 20 4

1 -3 Properties of Numbers Problem of the Day Daniel usually buys 6 bottles of water and 3 apples when he goes to the grocery store. Next time he goes, he will buy three times as many of each. How many items will Daniel buy? 27

1 -3 Properties of Numbers Sunshine State Standards Prep for MA. 7. A. 3. 4 Use the properties of equality…to show that two equations are equivalent in a given context. Review MA. 6. A. 3. 5

1 -3 Properties of Numbers Vocabulary Commutative Property Associative Property Identity Property Distributive Property

1 -3 Properties of Numbers

1 -3 Properties of Numbers Additional Example 1: Identifying Properties of Addition and Multiplication Tell which property is represented. A. (2 6) 1 = 2 (6 1) Associative Property The numbers are regrouped. B. 3 + 0 = 3 3+0=3 Identity Property The sum of 0 and any number is the number. C. 7 + 9 = 9 + 7 7+9=9+7 Commutative Property The order of the numbers is switched.

1 -3 Properties of Numbers Check It Out: Example 1 Tell which property is represented. A. 7 1 = 7 7 1=7 One of the factors is 1. Identity Property B. 3 + 4 = 4 + 3 3+4=4+3 Commutative Property The order of the numbers is switched. C. (5 1) 2 = 5 (1 2) (5 1) 2 = 5 ( 1 2) Associative Property The numbers are regrouped.

1 -3 Properties of Numbers Additional Example 2: Using Properties to Simplify Expressions Simplify each expression. Justify each step. A. 21 + 16 + 9 = 16 + 9 + 21 = 16 + (9 + 21) = 16 + 30 = 46 Commutative Property. Associative Property. Add. B. 20 9 5 = 20 5 9 = 20 (5 9) = 20 45 = 900 Commutative Property. Associative Property. Multiply.

1 -3 Properties of Numbers Check It Out: Example 2 A & B Simplify each expression. Justify each step. A. 17 + 14 + 3 = 14 + 17 + 3 = 14 + (17 + 3) B. 12 3 5 = 14 + 20 = 34 12 3 5 = 3 5 12 = 3 (5 12) = 3 60 = 180 Commutative Property. Associative Property. Add. Commutative Property. Associative Property. Multiply.

1 -3 Properties of Numbers You can use the Distributive Property to multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.

1 -3 Properties of Numbers Additional Example 3: Using the Distributive Property to Multiply Mentally Use the Distributive Property to find 6(54). Method 1: 6(54) = 6(50 + 4) Rewrite 54 as 50 + 4. = 300 + 24 Use the Distributive Property. Multiply. = 324 Add. = (6 50) + (6 4) Method 2: 6(54) = 6(60 – 6) = (6 60) – (6 6) = 360 - 36 = 324 Rewrite 54 as 60 – 6. Use the Distributive Property. Multiply. Subtract.

1 -3 Properties of Numbers Check It Out: Example 3 Use the Distributive Property to find 8(19). Method 1: 8(19) = 8(10 + 9) = (8 10) + (8 9) Method 2: Rewrite 19 as 10 + 9. Use the Distributive Property. = 80 + 72 Multiply. = 152 Add. 8(19) = 8(20 – 1) = (8 20) – (8 1) = 160 – 8 = 152 Rewrite 19 as 20 – 1. Use the Distributive Property. Multiply. Subtract.

1 -3 Properties of Numbers Lesson Quizzes Standard Lesson Quiz for Student Response Systems

1 -3 Properties of Numbers Lesson Quiz Tell which property is represented. 1. 17 1 = 17 Identity Property Associative Property 3. 2 16 = 16 2 Commutative Property 2. (12 + 14) + 5 = 12 + (14 + 5) Simplify each expression. Justify each step. 4. 4 12 25 1, 200 5. 48 + (15 + 2) 65 Use the Distributive Property to find each product. 6. 6 (12 + 5) 7. (20 – 7) 9 102 117

1 -3 Properties of Numbers Lesson Quiz for Student Response Systems 1. Identify the property that is represented. (21 + 16) + 7 = 21 + (16 + 7) A. Identity Property B. Associative Property C. Commutative Property D. Distributive Property

1 -3 Properties of Numbers Lesson Quiz for Student Response Systems 2. Identify the property that is represented. 17 · 9 = 9 · 17 A. Associative Property B. Commutative Property C. Distributive Property D. Identity Property

1 -3 Properties of Numbers Lesson Quiz for Student Response Systems 3. Simplify the expression 20 · 11 · 5. Then identify the correct justification for each step. A. 20 · 11 · 5 = 20 · 5 · 11 Commutative Property = (20 · 5) · 11 Associative Property = 100 · 11 Multiply. = 1, 100 B. 20 · 11 · 5 = 11 · 20 · 5 Commutative Property = (11 · 20) · 5 Associative Property = 110 · 5 Multiply. = 550

1 -3 Properties of Numbers Lesson Quiz for Student Response Systems 4. Simplify the expression 53 + (11 + 7). Then identify the correct justification for each step. A. 53 + (11 + 7) = 11 + (53 + 7) Associative Property = (11 + 53) + 7 Commutative Property = 60 + 7 Add. = 67 B. 53 + (11 + 7) = 53 + (7 + 11) Commutative Property = (53 + 7) + 11 Associative Property = 60 + 11 Add. = 71

1 -3 Properties of Numbers Lesson Quiz for Student Response Systems 5. Use the Distributive Property to identify the product of 8(20 + 2). A. 196 B. 113 C. 176 D. 85