Embed Size (px)
DESCRIPTION
1-2 Properties of Numbers Problem of the Day Daniel usually buys 6 bottles of water and 3 apples when he goes to the grocery store. Next time he goes, he will buy three times as many of each. How many items will Daniel buy? 27
Citation preview
1-2 Properties of Numbers
Warm UpWarm Up
Lesson PresentationLesson PresentationProblem of the DayProblem of the Day
Lesson Quizzes
1-2 Properties of Numbers
Warm UpEvaluate.
1. 2 + 5 3 – 72. 5(3 – 1) ÷ (3 + 2)3. (4 + 1)2 – 8 ÷ 24. 12 ÷ 3 6 – 20
10
2214
1-2 Properties of Numbers
Problem of the DayDaniel usually buys 6 bottles of water and 3 apples when he goes to the grocery store. Next time he goes, he will buy three times as many of each. How many items will Daniel buy? 27
1-2 Properties of Numbers
Learn how to identify properties of numbers and use them to simplify numerical expressions.
1-2 Properties of Numbers
VocabularyCommutative PropertyAssociative PropertyIdentity PropertyDistributive Property
1-2 Properties of Numbers
1-2 Properties of Numbers
1-2 Properties of Numbers
1-2 Properties of NumbersAdditional Example 1: Identifying Properties of Addition
and MultiplicationTell which property is represented.A. (2 6) 1 = 2 (6 1)
B. 3 + 0 = 3
C. 7 + 9 = 9 + 7
(2 6) 1 = 2 (6 1) The numbers are regrouped.Associative Property
3 + 0 = 3 One of the factors is 0.Identity Property
7 + 9 = 9 + 7 The order of the numbers is switched.Commutative Property
1-2 Properties of NumbersCheck It Out: Example 1
Tell which property is represented.A. 7 1 = 7
B. 3 + 4 = 4 + 3
C. (5 1) 2 = 5 (1 2)
7 1 = 7 One of the factors is 1.Identity Property
3 + 4 = 4 + 3 The order of the numbers is switched.Commutative Property
(5 1) 2 = 5 ( 1 2) The numbers are regrouped.Associative Property
1-2 Properties of NumbersAdditional Example 2: Using Properties to Simplify
ExpressionsSimplify each expression. Justify each step.A. 21 + 16 + 9
B. 20 9 5
21 + 16 + 9 = 16 + 9 + 21 Commutative Property.= 16 + (9 + 21)= 16 + 30
Associative Property.
= 46Add.
20 9 5 = 20 5 9 Commutative Property.= 20 (5 9)= 20 45
Associative Property.
= 900Multiply.
1-2 Properties of NumbersCheck It Out: Example 2A & B
Simplify each expression. Justify each step.A. 17 + 14 + 3
B. 12 3 5
17 + 14 + 3 = 14 + 17 + 3 Commutative Property.= 14 + (17 + 3)= 14 + 20
Associative Property.
= 34Add.
12 3 5 = 3 5 12 Commutative Property.= 3 (5 12)= 3 60
Associative Property.
= 180Multiply.
1-2 Properties of Numbers
You can use the Distributive Property to multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.
1-2 Properties of NumbersAdditional Example 3: Using the Distributive Property
to Multiply MentallyUse the Distributive Property to find 6(54).Method 1:
Method 2:
= (6 50) + (6 4)
Rewrite 54 as 50 + 4.
= 300 + 24= 324
Use the Distributive Property.Multiply.
6(54) = 6(60 – 6) Rewrite 54 as 60 – 6.
= (6 60) – (6 6)= 360 - 36
Use the Distributive Property. Multiply.
= 324 Subtract.
Add.
6(54) = 6(50 + 4)
1-2 Properties of NumbersCheck It Out: Example 3
Use the Distributive Property to find 8(19).Method 1:
Method 2:
= (8 10) + (8 9)Rewrite 19 as 10 + 9.
= 80 + 72= 152
Use the Distributive Property.Multiply.
8(19) = 8(20 – 1) Rewrite 19 as 20 – 1.
= (8 20) – (8 1)= 160 – 8
Use the Distributive Property. Multiply.
= 152 Subtract.
Add.
8(19) = 8(10 + 9)
1-2 Properties of Numbers
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
1-2 Properties of NumbersLesson Quiz
Tell which property is represented.
1. 17 1 = 172. (12 + 14) + 5 = 12 + (14 + 5)3. 2 16 = 16 2
Simplify each expression. Justify each step.4. 4 12 255. 48 + (15 + 2)
Use the Distributive Property to find each product.6. 6 (12 + 5)7. (20 – 7) 9
Identity PropertyAssociative Property
Commutative Property
1,20065
102117
1-2 Properties of Numbers
1. Identify the property that is represented.(21 + 16) + 7 = 21 + (16 + 7)
A. Identity PropertyB. Associative PropertyC. Commutative PropertyD. Distributive Property
Lesson Quiz for Student Response Systems
1-2 Properties of Numbers
2. Identify the property that is represented.17 · 9 = 9 · 17
A. Associative PropertyB. Commutative PropertyC. Distributive PropertyD. Identity Property
Lesson Quiz for Student Response Systems
1-2 Properties of Numbers
3. Simplify the expression 20 · 11 · 5. Then identify the correct justification for each step.
A. 20 · 11 · 5 = 20 · 5 · 11 Commutative Property= (20 · 5) · 11 Associative Property= 100 · 11 Multiply.= 1,100
B. 20 · 11 · 5 = 11 · 20 · 5 Commutative Property= (11 · 20) · 5 Associative Property= 110 · 5 Multiply.= 550
Lesson Quiz for Student Response Systems
1-2 Properties of Numbers4. Simplify the expression 53 + (11 + 7). Then
identify the correct justification for each step.
A. 53 + (11 + 7) = 11 + (53 + 7) Associative Property
= (11 + 53) + 7 Commutative Property
= 60 + 7Add.
= 67B. 53 + (11 + 7) = 53 + (7 + 11) Commutative
Property= (53 + 7) + 11 Associative
Property= 60 + 11
Add.= 71
Lesson Quiz for Student Response Systems
1-2 Properties of Numbers
5. Use the Distributive Property to identify the product of 8(20 + 2).
A. 196B. 113C. 176D. 85
Lesson Quiz for Student Response Systems
