1-4 Properties and Mental Math Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of...
-
Upload
stephany-powers -
Category
Documents
-
view
217 -
download
1
Transcript of 1-4 Properties and Mental Math Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of...
1-4 Properties and Mental Math
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson Quizzes
1-4 Properties and Mental Math
Warm UpFind 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
84273
90
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 PropertyAssociative PropertyDistributive 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)
Words Numbers
You can add or multiply numbers in any order.
18 + 9 = 9 + 1815 2 = 2 15
1-4 Properties and Mental Math
ASSOCIATIVE PROPERTY (Grouping)
Words NumbersWhen 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 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.
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 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.
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 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.
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 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.
1-4 Properties and Mental Math
DISTRIBUTIVE PROPERTY
Words NumbersTo 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
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 30 + 5.
= 210
Use the Distributive Property.= (6 30) + (6 5)
Use mental math to add.
= 180 + 30 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 80 + 7.
= 783
Use the Distributive Property.= (9 80) + (9 7)
Use mental math to add.
= 720 + 63 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 20 + 7.
= 108
Use the Distributive Property.= (4 20) + (4 7)
Use mental math to add.
= 80 + 28 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 40 + 3.
= 258
Use the Distributive Property.= (6 40) + (6 3)
Use mental math to add.
= 240 + 18 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.
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
15050
70
96 90
170 213
1-4 Properties and Mental Math
1. Evaluate 16 + 23 + 4 + 7.
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 15 + 56 + 5 + 4.
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