1-4 Properties and Mental Math Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

1-4 Properties and Mental Math Warm Up Find each sum or product (24) 4. 7(12) 5. 3(91) 6. 6(15)

1-4 Properties and Mental Math 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

1-4 Properties and Mental Math Learn to use number properties to compute mentally.

1-4 Properties and Mental Math Vocabulary Commutative Property Associative Property Distributive Property

1-4 Properties and Mental Math 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.

1-4 Properties and Mental Math COMMUTATIVE PROPERTY (Ordering) WordsNumbers You can add or multiply numbers in any order =  2 = 2  15

1-4 Properties and Mental Math ASSOCIATIVE PROPERTY (Grouping) WordsNumbers When you are only adding or only multiplying, you can group any of the numbers together. (17 + 2) + 9 = 17 + (2 + 9) (12  2)  4 = 12  (2  4)

1-4 Properties and Mental Math The Commutative and Associative Properties do not apply to subtraction or division. Caution!

1-4 Properties and Mental Math Additional Example 1A: Using Properties to Add and Multiply Whole Numbers Simplify Look for sums that are multiples of Use the Commutative Property (17 + 3) + (5 + 15) Use mental math to add Use the Associative Property to make groups of compatible numbers.

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

1-4 Properties and Mental Math The expressions in each row of example 1B are equivalent because they have the same value. Helpful Hint

1-4 Properties and Mental Math Check It Out: Example 1A Simplify Look for sums that are multiples of Use the Commutative Property (12 + 8) + (5 + 5) Use mental math to add Use the Associative Property to make groups of compatible numbers.

1-4 Properties and Mental Math Check It Out: Example 1B Simplify 8  3  5. 8  3  5 Look for products that are multiples of Use the Commutative Property. 3  8  5 3  (8  5) Use mental math to multiply. 3  40 Use the Associative Property to group compatible numbers.

1-4 Properties and Mental Math DISTRIBUTIVE PROPERTY WordsNumbers To multiply a number by a sum, multiply by each number in the sum and then add. 6  (10 + 4) = (6  10) + (6  4) = = 84

1-4 Properties and Mental Math When you multiply two numbers, you can “break apart” one of the numbers into a sum and then use the Distributive Property.

1-4 Properties and Mental Math Additional Example 2A: Using the Distributive Property to Multiply Use the Distributive Property to find the product. 6  35 6  35 = 6  (30 + 5) “Break apart” 35 into = 210 Use the Distributive Property. = (6  30) + (6  5) Use mental math to add. = Use mental math to multiply.

1-4 Properties and Mental Math Additional Example 2B: Using the Distributive Property to Multiply Use the Distributive Property to find the product. 9  87 9  87 = 9  (80 + 7) “Break apart” 87 into = 783 Use the Distributive Property. = (9  80) + (9  7) Use mental math to add. = Use mental math to multiply.

1-4 Properties and Mental Math Check It Out: Example 2A Use the Distributive Property to find the product. 4  27 4  27 = 4  (20 + 7) “Break apart” 27 into = 108 Use the Distributive Property. = (4  20) + (4  7) Use mental math to add. = Use mental math to multiply.

1-4 Properties and Mental Math Check It Out: Example 2B Use the Distributive Property to find the product. 6  43 6  43 = 6  (40 + 3) “Break apart” 43 into = 258 Use the Distributive Property. = (6  40) + (6  3) Use mental math to add. = Use mental math to multiply.

1-4 Properties and Mental Math Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

1-4 Properties and Mental Math Lesson Quiz Simplify  5  Use the Distributive Property to find each product    

1-4 Properties and Mental Math 1. Evaluate A. 50 B. 40 C. 30 D. 20 Lesson Quiz for Student Response Systems

1-4 Properties and Mental Math 2. Evaluate 3  7  10. A. 140 B. 170 C. 190 D. 210 Lesson Quiz for Student Response Systems

1-4 Properties and Mental Math 3. Evaluate A. 86 B. 80 C. 77 D. 70 Lesson Quiz for Student Response Systems

1-4 Properties and Mental Math 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

1-4 Properties and Mental Math 5. Use the Distributive Property to find the product. 4  73 A. 292 B. 282 C. 272 D. 262 Lesson Quiz for Student Response Systems