1-5 Mental Math Warm Up Problem of the Day Lesson Presentation Course 1 Warm Up Problem of the Day Lesson Presentation

1-5 Mental Math Warm Up Find each sum or product. 1. 17 + 15 Course 1 1-5 Mental Math 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

1-5 Mental Math Problem of the Day Course 1 1-5 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

1-5 Mental Math Learn to use number properties to compute mentally. Course 1 1-5 Mental Math Learn to use number properties to compute mentally.

Insert Lesson Title Here Course 1 1-5 Mental Math Insert Lesson Title Here Vocabulary Commutative Property Associative Property Distributive Property

Course 1 1-5 Mental Math Mental math means “doing math in your head.”

COMMUTATIVE PROPERTY (Ordering) Course 1 1-5 Mental Math COMMUTATIVE PROPERTY (Ordering) Words Numbers You can add or multiply numbers in any order. 18 + 9 = 9 + 18 15  2 = 2  15

ASSOCIATIVE PROPERTY (Grouping) Course 1 1-5 Mental Math ASSOCIATIVE PROPERTY (Grouping) Words Numbers 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)

Course 1 1-5 Mental Math Additional Example 1A: Using Properties to Add and Multiply Whole Numbers A. Evaluate 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

Course 1 1-5 Mental Math Additional Example 1B: Using Properties to Add and Multiply Whole Numbers B. Evaluate 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

1-5 Mental Math Try This: Example 1A A. Evaluate 12 + 5 + 8 + 5. Course 1 1-5 Mental Math Try This: Example 1A A. Evaluate 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

1-5 Mental Math Try This: Example 1B B. Evaluate 8  3  5. Course 1 1-5 Mental Math Try This: Example 1B B. Evaluate 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

DISTRIBUTIVE PROPERTY Course 1 1-5 Mental Math DISTRIBUTIVE PROPERTY Words Numbers When you multiply a number times a sum, you can find the sum first and then multiply, or multiply by each number in the sum and then add. 6  (10 + 4) = 6  14 = 84 6  (10 + 4) = (6  10) + (6  4) = 60 + 24 = 84

Course 1 1-5 Mental Math When you multiply two numbers, you can “break apart” one of the numbers into a sum and then use the Distributive Property. Break the greater factor into a sum that contains a multiple of 10 and a one-digit number. You can add and multiply these numbers mentally. Helpful Hint

Additional Example 2A: Using the Distributive Property to Multiply Course 1 1-5 Mental Math Additional Example 2A: Using the Distributive Property to Multiply Use the Distributive Property to find the product. A. Evaluate 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 Course 1 1-5 Mental Math Additional Example 2B: Using the Distributive Property to Multiply Use the Distributive Property to find the product. B. Evaluate 9 x 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.

1-5 Mental Math Try This: Example 2A Course 1 1-5 Mental Math Try This: Example 2A Use the Distributive Property to find the product. A. Evaluate 4 x 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.

1-5 Mental Math Try This: Example 2B Course 1 1-5 Mental Math Try This: Example 2B Use the Distributive Property to find the product. B. Evaluate 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.

Insert Lesson Title Here Course 1 1-5 Mental Math Insert Lesson Title Here Lesson Quiz Evaluate. 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. Angie wants to buy 3 new video games. How much will she need to save if each game costs $27? 50 150 70 96 90 $81