Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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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
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• 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
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Sunshine State Standards
MA.6.EE.1.1-3 Apply the Commutative, Associative,
and Distributive Properties to show that two
expressions are equivalent.
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Vocabulary
Commutative Property Associative
Property Distributive Property
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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.
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COMMUTATIVE PROPERTY (Ordering) COMMUTATIVE PROPERTY (Ordering)
Words Numbers
You can add or multiply numbers in any order. 18 9 9 18 15 ? 2 2 ? 15
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ASSOCIATIVE PROPERTY (Grouping) 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)
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Caution!
The Commutative and Associative Properties do
not apply to subtraction or division.
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Additional Example 1A Using Properties to Add
and Multiply Whole Numbers Simplify 17 5 3
15.
17 5 3 15
17 3 5 15
Use the Associative Property to make groups of
compatible numbers.
(17 3) (5 15)
20 20
40
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Additional Example 1B Using Properties to Add
and Multiply Whole Numbers Simplify 4 ? 13 ? 5.
4 ? 13 ? 5
13 ? 4 ? 5
13 ? (4 ? 5)
13 ? 20
260
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Check It Out Example 1A Simplify 23 8 12
7.
23 8 12 7
23 7 8 12
30 20
50
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Check It Out Example 1B Simplify 49 17 51.
49 17 51
49 51 17
100 17
117
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Check It Out Example 1C Simplify 6 33 5.
6 33 5
6 5 33
30 33
990
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Check It Out Example 1D Simplify 2 69 5.
2 69 5
2 5 69
10 69
690
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DISTRIBUTIVE PROPERTY 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
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When you multiply two numbers, you can break
apart one of the numbers into a sum and then use
the Distributive Property.
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Additional Example 2A Using the Distributive
Property to Multiply Use the Distributive
Property to find the product. 6 ? 35
6 ? 35 6 ? (30 5)
(6 ? 30) (6 ? 5)
180 30
210
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Additional Example 2B Using the Distributive
Property to Multiply Use the Distributive
Property to find the product. 9 ? 87
9 ? 87 9 ? (80 7)
(9 ? 80) (9 ? 7)
720 63
783
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Check It Out Example 2A Use the Distributive
Property to find each product. 6 ? 71
6 ? 71 6 ? (70 1)
6 ? 70 6 ? 1
420 6
426
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Check It Out Example 2B Use the Distributive
Property to find each product. 28 ? 5
28 ? 5 (20 8) ? 5
20 ? 5 8 ? 5
100 40
140
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Check It Out Example 2C Use the Distributive
Property to find each product. 8 ? 44
8 ? 44 8 ? (40 4)
8 ? 40 8 ? 4
320 32
352
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Lesson Quiz
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
150
50
70
90
96
170
213
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Lesson Quiz for Student Response Systems
1. Evaluate 16 23 4 7. A. 50 B. 40 C. 30
D. 20
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Lesson Quiz for Student Response Systems
2. Evaluate 3 ? 7 ? 10. A. 140 B. 170 C. 190
D. 210
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Lesson Quiz for Student Response Systems
3. Evaluate 15 56 5 4. A. 86 B. 80 C. 77
D. 70
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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
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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