1. Warm Up
Evaluate.
 3 – 7
2. 5(3 – 1) ÷ (3 + 2)
3. (4 + 1)2 – 8 ÷ 2
4. 12 ÷ 3  6 – 20

2. ANSWERS Warm Up Evaluate. 1. 2 + 5  3 – 7 2. 5(3 – 1) ÷ (3 + 2)
3. (4 + 1)2 – 8 ÷ 2
4. 12 ÷ 3  6 – 20
ANSWERS 10 2 21 4

3. What are we doing today? Tell which property is represented.
1. 17  1 = 17
2. ( ) + 5 = 12 + (14 + 5)
3. 2  16 = 16  2
Simplify each expression. Justify each step.
4. 4  12  25
(15 + 2)
Use the Distributive Property to find each product.
6. 6  (12 + 5)
7. (20 – 7)  9

4. I will…
Learn how to identify properties of numbers and use them to simplify numerical expressions.

5. Vocabulary Commutative Property Associative Property Identity Property
Distributive Property

6. THINK about these…
DISCUSS…
Ask Questions!

7. and these…
DISCUSS…
Ask Questions!

8. AND these, too…
DISCUSS…
Ask Questions!

9. What will HELP you Remember?
NOW…Write HINTS
Associate
Commute
Identity
THINK!!!
What will HELP you Remember?

10. Example 1: Identifying Properties of Addition and Multiplication
Tell which property is represented.
A. (2  6)  1 = 2  (6  1)
B = 3
C = 9 + 7
(2  6)  1 = 2  (6  1)
The numbers are regrouped.
Associative Property
3 + 0 = 3
One of the addends is 0.
Identity Property
7 + 9 = 9 + 7
The order of the numbers is switched.
Commutative Property

11. I try! Practice 1a: 7  1 = 7 1b: 3 + 4 = 4 + 3

12. Tell which property is represented. A. 7  1 = 7
Practice 1
Tell which property is represented.
A. 7  1 = 7
B = 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

13. Is there ANOTHER way to simplify?
Example 2:
Using Properties to Simplify Expressions
Simplify each expression. Justify each step. A
B. 20  9  5
Is there
ANOTHER
way to simplify? =
Commutative Property.
= 16 + (9 + 21)
Associative Property. =
Add.
= 46
20  9  5 = 20  5  9
Commutative Property.
= 20  (5  9)
Associative Property.
= 20  45
Multiply.
= 900

14. Find two DIFFERENT ways to simplify each expression!
I try!
Practice
2a:
2b:  3  5
Find two DIFFERENT ways to simplify each expression!

15. Simplify each expression. Justify each step. A. 17 + 14 + 3
Practice 2
Simplify each expression. Justify each step. A
B. 12  3  5 =
Commutative Property.
= 14 + (17 + 3)
Associative Property. =
Add.
= 34
12  3  5 = 3  5  12
Commutative Property.
= 3  (5  12)
Associative Property.
= 3  60
Multiply.
= 180

16. THINK about this… DISCUSS… Ask Questions!
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.
DISCUSS…
Ask Questions!

17. Example 3: Using the Distributive Property to Multiply Mentally
Use the Distributive Property to find 6(54).
Method 1:
Method 2:
6(54) = 6(50 + 4)
Rewrite 54 as
Use the Distributive Property.
= (6  50) + (6  4)
Multiply. =
Add.
= 324
6(54) = 6(60 – 6)
Rewrite 54 as 60 – 6.
Use the Distributive Property. Multiply.
= (6  60) – (6  6) =
Subtract.
= 324

18. Use the Distributive Property to find 8(19). Method 1:
Practice 3
Use the Distributive Property to find 8(19).
Method 1:
Method 2:
8(19) = 8(10 + 9)
Rewrite 19 as
Use the Distributive Property. Multiply.
= (8  10) + (8  9) =
Add.
= 152
8(19) = 8(20 – 1)
Rewrite 19 as 20 – 1.
Use the Distributive Property. Multiply.
= (8  20) – (8  1)
= 160 – 8
Subtract.
= 152

19. 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?

20. 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?
Daniel will buy 27 items in all.

21. Lesson
Quiz

22. Tell which property is represented.
1. 17  1 = 17
2. ( ) + 5 = 12 + (14 + 5)
3. 2  16 = 16  2
Simplify each expression. Justify each step.
4. 4  12  25
(15 + 2)
Use the Distributive Property to find each product.
6. 6  (12 + 5)
7. (20 – 7)  9

23. Lesson Quiz ANSWERS Identity Property Associative Property
Tell which property is represented.
1. 17  1 = 17
2. ( ) + 5 = 12 + (14 + 5)
3. 2  16 = 16  2
Simplify each expression. Justify each step.
4. 4  12  25
(15 + 2)
Use the Distributive Property to find each product.
6. 6  (12 + 5)
7. (20 – 7)  9
Identity Property
Associative Property
Commutative Property
1,200 65
102
117