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

2. 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

3. 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

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

5. Course 1 1-5 Mental Math Vocabulary Commutative Property Associative Property Distributive Property

6. Course 1 1-5 Mental Math Mental math means “doing math in your head.” Many mental math strategies use number properties that you already know.

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

8. Course 1 1-5 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)

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

10. Course 1 1-5 Mental Math Additional Example 1B: Using Properties to Add and Multiply Whole Numbers Evaluate 4  13  5. 4  13  5 Look for products that are multiples of 10 260 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.

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

12. Course 1 1-5 Mental Math Check It Out: Example 1B Evaluate 8  3  5. 8  3  5 Look for products that are multiples of 10 120 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.

13. Course 1 1-5 Mental Math DISTRIBUTIVE PROPERTY WordsNumbers 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

14. 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

15. Course 1 1-5 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 30 + 5. = 210 Use the Distributive Property. = (6  30) + (6  5) Use mental math to add. = 180 + 30 Use mental math to multiply.

16. Course 1 1-5 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 80 + 7. = 783 Use the Distributive Property. = (9  80) + (9  7) Use mental math to add. = 720 + 63 Use mental math to multiply.

17. Course 1 1-5 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 20 + 7. = 108 Use the Distributive Property. = (4  20) + (4  7) Use mental math to add. = 80 + 28 Use mental math to multiply.

18. Course 1 1-5 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 40 + 3. = 258 Use the Distributive Property. = (6  40) + (6  3) Use mental math to add. = 240 + 18 Use mental math to multiply.

19. Course 1 1-5 Mental Math 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  125. 6  15 6. 5  347. 3  71 15050 70 96 90 170213