1. Splash Screen

2. Five-Minute Check (over Lesson 1–2) Then/Now New Vocabulary
Key Concept: Commutative Properties
Key Concept: Associative Properties
Key Concept: Number Properties
Example 1: Find a Counterexample
Example 2: Identify Properties
Example 3: Simplify Algebraic Expressions
Example 4: Standardized Test Example
Lesson Menu

3. A B C D Evaluate the expression c + 8 – a if a = 4 and c = 3. A. 15
5-Minute Check 1

4. A B C D Evaluate the expression if a = 4 and c = 3. A. 12 B. 6 C. D.
5-Minute Check 2

5. Evaluate the expression 7a – (2c + b) if a = 4, b = 2, and c = 3.
5-Minute Check 3

6. Translate three feet shorter than the height of the building into an algebraic expression.
A. b – 3
B. 3 – b
C. b + 3
D. 3 ÷ b A B C D
5-Minute Check 4

7. Translate eight more than three times a number into an algebraic expression.
B. 3n + 8 C
D. 3 + n + 8 A B C D
5-Minute Check 5

8. One mile is equal to 1,760 yards
One mile is equal to 1,760 yards. Which expression can you use to find the total number of yards in any number of miles?
A. 1,760 ÷ m
B. 1,760m
C. m + 1,760
D. 1,760 – m A B C D
5-Minute Check 6

9. Identify and use properties of addition and multiplication.
You have already evaluated numerical and algebraic expressions. (Lessons 1–1 and 1–2)
Identify and use properties of addition and multiplication.
Use properties of addition and multiplication to simplify algebraic expressions.
Then/Now

10. properties
counterexample
simplify
deductive reasoning
Vocabulary

11. Concept A

12. Concept B

13. Concept C

14. Division of whole numbers is commutative.
Find a Counterexample
State whether the following conjecture is true or false. If false, provide a counterexample.
Division of whole numbers is commutative.
Write two division expressions using the Commutative Property, and then check to see whether they are equal.
12 ÷ 6 = 6 ÷ 12 State the conjecture. ?
2 ≠ 0.5 Divide.
We found a counterexample. That is, 12 ÷ 6 ≠ 6 ÷ 12. So, division is not commutative.
Answer: The conjecture is false.
Example 1

15. State whether the following conjecture is true or false
State whether the following conjecture is true or false. If false, provide a counterexample. Subtraction of whole numbers is commutative.
A. true
B. false, 7 – 4 = 7 – 4
C. false, 7 – 4 ≠ 4 – 7
D. false, (7 – 4) – 2 ≠ 7 – (4 – 2) A B C D
Example 1

16. A. Name the property shown by the statement. 3 ● 10 ● 2 = 3 ● 2 ● 10
Identify Properties
A. Name the property shown by the statement. 3 ● 10 ● 2 = 3 ● 2 ● 10
Answer: The order of the numbers changed. This is the Commutative Property of Multiplication.
Example 2A

17. B. Name the property shown by the statement. (2 + 5) + m = 2 + (5 + m)
Identify Properties
B. Name the property shown by the statement. (2 + 5) + m = 2 + (5 + m)
Answer: The grouping of the numbers and variables changed. This is the Associative Property of Addition.
Example 2B

18. A. Name the property shown by the statement. (4 ● 6) ● 2 = 4 ● (6 ● 2)
A. Commutative Property of Multiplication
B. Associative Property of Multiplication
C. Multiplicative Identity
D. Multiplicative Property of Zero A B C D
Example 2A

19. A B C D B. Name the property shown by the statement. 12 + 9 = 9 + 12
A. Commutative Property of Addition
B. Associative Property of Addition
C. Additive Identity
D. Distributive Property A B C D
Example 2B

20. Commutative Property of Addition
Simplify Algebraic Expressions
A. Simplify 12 + (x + 18).
Commutative Property of Addition
Associative Property of Addition
Simplify.
Answer: x
Example 3A

21. 5 ● (3 ● r) = (5 ● 3)r Associative Property of Multiplication
Simplify Algebraic Expressions
B. Simplify 5 ● (3 ● r).
5 ● (3 ● r) = (5 ● 3)r Associative Property of Multiplication
= 15r Simplify.
Answer: 15r
Example 3B

22. A B C D A. Simplify (6 ● a) ● 4. A. 10a B. 24 + a C. 2a D. 24a
Example 3A

23. A B C D B. Simplify 7 + (12 + m). A. 19 + m B. 19m C. 5 + m D. 12m + 7
Example 3B

24. You need to identify the correct expression.
Which of the following is an example of the Associative Property of Addition?
A = 18
B 9 + (5 + 3) = (9 + 5) + 3
C =
D 14 ● (5 ● 3) = (14 ● 5) ● 3
Read the Test Item
You need to identify the correct expression.
Example 4

25. Solve the Test Item
The Associative Property shows the grouping of addends. Options A and C can be eliminated. Option D can be eliminated because it shows multiplication.
The answer is B.
Answer: B
Example 4

26. Which of the following is an example of the Multiplicative Identity Property?
B. 15 ● 1 = 15
C. 15 ● (–1) = –15
D. –15 ● 0 = 0 A B C D
Example 4

27. End of the Lesson

28. End of Custom Shows