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

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

Learn to 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.

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) 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)

Additional Example 1A: Using Properties to Add and Multiply Whole Numbers 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

Additional Example 1B: Using Properties to Add and Multiply Whole Numbers 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

Check It Out: Example 1A 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

Check It Out: Example 1B 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 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

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 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 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. 5  34 7. 3  71 50 150 70 96 90 170 213

Patterns and Sequences 1-7 Patterns and Sequences Course 1 Warm Up Problem of the Day Lesson Presentation

Warm Up Determine what could come next. 1. 3, 4, 5, 6, ___ 2. 10, 9, 8, 7, 6, ___ 3. 1, 3, 5, 7, ___ 4. 2, 4, 6, 8, ___ 5. 5, 10, 15, 20, ___ 7 5 9 10 25

Problem of the Day How can you place the numbers 1 through 6 in the circles so that the sums along each side are equal? 6 2 1 4 3 5

Learn to find patterns and to recognize, describe, and extend patterns in sequences.

Vocabulary perfect square term arithmetic sequence

Each month, Eva chooses 3 new DVDs from her DVD club. Eva’s DVDs Month 1 3 2 4 Position Value + 3 6 + 3 9 + 3 12 The number of DVDs Eva has after each month shows a pattern: Add 3. This pattern can be written as a sequence. 3, 6, 9, 12, 15, 18, …

A sequence is an ordered set of numbers A sequence is an ordered set of numbers. Each number in the sequence is called a term. In this sequence, the first term is 3, the second term is 6, and the third term is 9. When the terms of a sequence change by the same amount each time, the sequence is an arithmetic sequence.

Look for a relationship between the 1st term and the 2nd term Look for a relationship between the 1st term and the 2nd term. Check if this relationship works between the 2nd term and the 3rd term, and so on. Helpful Hint

Additional Example 1A: Extending Arithmetic Sequences Identify a pattern in each sequence and then find the missing terms. 48, 42, 36, 30, , , , . . . –6 –6 –6 –6 –6 –6 Look for a pattern. A pattern is to subtract 6 from each term to get the next term. 30 – 6 = 24 24 – 6 = 18 18 – 6 = 12 So 24, 18, and 12 will be the next three terms.

Additional Example 1B: Extending Arithmetic Sequences Position 1 2 3 4 5 6 Value of Term 9 22 35 48 +13 +13 +13 +13 +13 A pattern is to add 13 to each term to get the next term. 48 + 13 = 61 61 + 13 = 74 So 61 and 74 will be the next terms in the arithmetic sequence.

Check It Out: Example 1A Identify a pattern in each sequence and name the next three terms. 39, 34, 29, 24, , , , . . . –5 –5 –5 –5 –5 –5 Look for a pattern. A pattern is to subtract 5 from each term to get the next term. 24 – 5 = 19 19 – 5 = 14 14 – 5 = 9 So 19, 14, and 9 will be the next three terms.

1 2 3 4 5 6 7 16 25 34 Check It Out: Example 1B Position Value of Term +9 +9 +9 +9 +9 A pattern is to add 9 to each term to get the next term. 34 + 9 = 43 43 + 9 = 52 So 43 and 52 will be the next terms in the arithmetic sequence.

Additional Example 2A: Completing Other Sequences Identify a pattern in the sequence. Name the missing terms. 24, 34, 31, 41, 38, 48, , , ,… +10 –3 +10 –3 +10 –3 +10 –3 A pattern is to add 10 to one term and subtract 3 from the next. 48 – 3 = 45 45 + 10 = 55 55 – 3 = 52 So 45, 55, and 52 are the missing terms.

Additional Example 2B: Completing Other Sequences Position 1 2 3 4 5 6 7 8 Value of Term 16 32  4 ÷2 A pattern is to multiply one term by 4 and divide the next by 2. 8 ÷ 2 = 4 4  4 = 16 16 ÷ 2 = 8 8  4 = 32 So 4 and 8 will be the missing terms in the sequence.

Check It Out: Example 2A Identify a pattern in each sequence and name the missing terms. 6, 12, 14, 28 , 30, , ,. . .  2 + 2  2 + 2  2 + 2 A pattern is to multiply one term by 2 and add 2 from the next. 30  2 = 60 60 + 2 = 62 So 60 and 62 are the missing terms.

A pattern is to multiply one term by 6 and divide the next by 2. Check It Out: Example 2B Position 1 2 3 4 5 6 7 8 Value of Term 18 54 162  6 ÷2  6 ÷2  6 ÷2  6 A pattern is to multiply one term by 6 and divide the next by 2. 18 ÷ 2 = 9 9  6 = 54 54 ÷ 2 = 27 27  6 = 162 So 9 and 27 will be the missing terms in the sequence.

Lesson Quiz Identify a pattern in each sequence, and then find the missing terms. 1. 12, 24, 36, 48, , , , … 2. 75, 71, 67, 63, , , ,… Identify a pattern in each sequence. Name the missing terms. 3. 1000, 500, , 125,… 4. 100, 50, 200, , 400, ,… add 12; 60, 72, 84 subtract 4; 59, 55, 51 divide by 2; 250 divide by 2 then multiply by 4; 100, 200