Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Find each sum or product. 1. 17 + 15 2. 29 + 39 3. 8(24) 4. 7(12) 5. 3(91) 6. 6(15) 32 68 192 84 273 90

Problem of the Day Determine the secret number from the following clues: The number is a multiple of 5. It is divisible by 3. It is less than 200. Its tens digit equals the sum of its other two digits. 165

We will use number properties to compute mentally.

Vocabulary Commutative Property Associative Property Distributive Property

Mental math means “doing math in your head.” Many mental math strategies use number properties that you already know to make equivalent expressions that may be easier to simplify.

COMMUTATIVE PROPERTY (Ordering) Words Numbers You can add or multiply numbers in any order. It will not change the answer. 18 + 9 = 9 + 18 15  2 = 2  15

ASSOCIATIVE PROPERTY (Grouping) Words Numbers When adding or multiplying you can change the grouping of the numbers. It will not change the answer. (17 + 2) + 9 = 17 + (2 + 9) (12  2)  4 = 12  (2  4)

Caution! The Commutative and Associative Properties do not apply to subtraction or division.

Additional Example 1A: Using Properties to Add and Multiply Whole Numbers Simplify 17 + 5 + 3 + 15. Look for sums that are multiples of 10 17 + 5 + 3 + 15 Use the Commutative Property. 17 + 3 + 5 + 15 Use the Associative Property to make groups of compatible numbers. (17 + 3) + (5 + 15) 20 + 20 Use mental math to add. 40

Additional Example 1B: Using Properties to Add and Multiply Whole Numbers Simplify 4  13  5. Look for products that are multiples of 10 4  13  5 13  4  5 Use the Commutative Property. Use the Associative Property to group compatible numbers. 13  (4  5) 13  20 Use mental math to multiply. 260

The expressions in each row of example 1B are equivalent because they have the same value. Helpful Hint

Check It Out: Example 1A Simplify 12 + 5 + 8 + 5. Look for sums that are multiples of 10 12 + 5 + 8 + 5 Use the Commutative Property. 12 + 8 + 5 + 5 Use the Associative Property to make groups of compatible numbers. (12 + 8) + (5 + 5) 20 + 10 Use mental math to add. 30

Look for products that are multiples of 10. 8  3  5 Check It Out: Example 1B Simplify 8  3  5. Look for products that are multiples of 10. 8  3  5 3  8  5 Use the Commutative Property. Use the Associative Property to group compatible numbers. 3  (8  5) 3  40 Use mental math to multiply. 120 STOP HERE

DISTRIBUTIVE PROPERTY Words Numbers To multiply a number by a sum, multiply by each number in the sum and then add. 6  (10 + 4) = (6  10) + (6  4) = 60 + 24 = 84 You can remove the parenthesis in an expression. Next you multiply the value outside the parenthesis to each of the terms inside the parenthesis.

When you multiply two numbers, you can “break apart” one of the numbers into a sum and then use the Distributive Property.

Additional Example 2A: Using the Distributive Property to Multiply Use the Distributive Property to find the product. 6  35 “Break apart” 35 into 30 + 5. 6  35 = 6  (30 + 5) Use the Distributive Property. = (6  30) + (6  5) Use mental math to multiply. = 180 + 30 = 210 Use mental math to add.

Additional Example 2B: Using the Distributive Property to Multiply Use the Distributive Property to find the product. 9  87 “Break apart” 87 into 80 + 7. 9  87 = 9  (80 + 7) Use the Distributive Property. = (9  80) + (9  7) Use mental math to multiply. = 720 + 63 = 783 Use mental math to add.

Check It Out: Example 2A Use the Distributive Property to find the product. 4  27 “Break apart” 27 into 20 + 7. 4  27 = 4  (20 + 7) Use the Distributive Property. = (4  20) + (4  7) Use mental math to multiply. = 80 + 28 = 108 Use mental math to add.

Check It Out: Example 2B Use the Distributive Property to find the product. 6  43 “Break apart” 43 into 40 + 3. 6  43 = 6  (40 + 3) Use the Distributive Property. = (6  40) + (6  3) Use mental math to multiply. = 240 + 18 = 258 Use mental math to add.

Lesson Quiz # 1 Simplify. 1. 18 + 24 + 2 + 6 2. 10  5  3 3. 13 + 42 + 7 + 8 Use the Distributive Property to find each product. 4. 8  12 5. 6  15 6. 5  34 7. 3  71 50 150 70 96 90 170 213

Lesson Quiz # 2 1. Evaluate 16 + 23 + 4 + 7. A. 50 B. 40 C. 30 D. 20

Lesson Quiz for Student Response Systems 2. Evaluate 3  7  10. A. 140 B. 170 C. 190 D. 210

Lesson Quiz for Student Response Systems 3. Evaluate 15 + 56 + 5 + 4. A. 86 B. 80 C. 77 D. 70

Lesson Quiz for Student Response Systems 4. Use the Distributive Property to find the product. 7  15 A. 135 B. 125 C. 115 D. 105

Lesson Quiz for Student Response Systems 5. Use the Distributive Property to find the product. 4  73 A. 292 B. 282 C. 272 D. 262