1. Mathematical Practices Then/Now New Vocabulary
Five-Minute Check
Mathematical Practices
Then/Now
New Vocabulary
Example 1: Verbal to Algebraic Expression
Example 2: Algebraic to Verbal Sentence
Key Concept: Properties of Equality
Example 3: Identify Properties of Equality
Example 4: Solve One-Step Equations
Example 5: Solve a Multi-Step Equation
Example 6: Solve for a Variable
Example 7: Use Properties of Equality
Lesson Menu

2. A. naturals (N), wholes (W), integers (Z)
B. wholes (W), integers (Z), reals (R)
C. naturals (N), wholes (W), rationals (Q), reals (R)
D. naturals (N), wholes (W), integers (Z), rationals (Q), reals (R)
5-Minute Check 1

3. A. naturals (N), wholes (W), integers (Z)
B. wholes (W), integers (Z), reals (R)
C. naturals (N), wholes (W), rationals (Q), reals (R)
D. naturals (N), wholes (W), integers (Z), rationals (Q), reals (R)
5-Minute Check 1

4. A. naturals (N), wholes (W) B. reals (R) C. rationals (Q), reals (R)
D. integers (Z), reals (R)
5-Minute Check 2

5. A. naturals (N), wholes (W) B. reals (R) C. rationals (Q), reals (R)
D. integers (Z), reals (R)
5-Minute Check 2

6. Name the property illustrated by a + (7 + c) = (a + 7) + c.
A. Associative Property of Addition
B. Distributive Property
C. Substitution Property
D. Commutative Property of Addition
5-Minute Check 3

7. Name the property illustrated by a + (7 + c) = (a + 7) + c.
A. Associative Property of Addition
B. Distributive Property
C. Substitution Property
D. Commutative Property of Addition
5-Minute Check 3

8. Name the property illustrated by 3(4 + 0.2) = 3(4) + 3(.02).
A. Associative Property of Addition
B. Identity Property
C. Distributive Property
D. Substitution Property
5-Minute Check 4

9. Name the property illustrated by 3(4 + 0.2) = 3(4) + 3(.02).
A. Associative Property of Addition
B. Identity Property
C. Distributive Property
D. Substitution Property
5-Minute Check 4

10. Simplify (2c)(3d) + c + 5cd + 3c2.
A. 3c2 + 5cd + c
B. 3c2 + 11cd + c
C. 3c2 + 10cd
D. 3c2 + c
5-Minute Check 5

11. Simplify (2c)(3d) + c + 5cd + 3c2.
A. 3c2 + 5cd + c
B. 3c2 + 11cd + c
C. 3c2 + 10cd
D. 3c2 + c
5-Minute Check 5

12. Which equation illustrates the Additive Identity Property?
B. 5(1) = 5
C. 5 + (–5) = 0 D.
5-Minute Check 6

13. Which equation illustrates the Additive Identity Property?
B. 5(1) = 5
C. 5 + (–5) = 0 D.
5-Minute Check 6

14. Mathematical Processes
A.CED.1 Create equations and inequalities in one variable and use them to solve problems.
Mathematical Practices
3 Construct viable arguments and critique the reasoning of others.
8 Look for and express regularity in repeated reasoning. MP

15. You used properties of real numbers to evaluate expressions.
Translate verbal expressions into algebraic expressions and equations, and vice versa.
Solve equations using the properties of equality.
Then/Now

16. open sentence
equation
solution
Vocabulary

17. Verbal to Algebraic Expression
A. Write an algebraic expression to represent the verbal expression 7 less than a number.
Answer:
Example 1

18. Verbal to Algebraic Expression
A. Write an algebraic expression to represent the verbal expression 7 less than a number.
Answer: n – 7
Example 1

19. Verbal to Algebraic Expression
B. Write an algebraic expression to represent the verbal expression the square of a number decreased by the product of 5 and the number.
Answer:
Example 1

20. Verbal to Algebraic Expression
B. Write an algebraic expression to represent the verbal expression the square of a number decreased by the product of 5 and the number.
Answer: x2 – 5x
Example 1

21. A. Write an algebraic expression to represent the verbal expression 6 more than a number.
A. 6x
B. x + 6
C. x6
D. x – 6
Example 1a

22. A. Write an algebraic expression to represent the verbal expression 6 more than a number.
A. 6x
B. x + 6
C. x6
D. x – 6
Example 1a

23. B. Write an algebraic expression to represent the verbal expression 2 less than the cube of a number.
A. x3 – 2
B. 2x3
C. x2 – 2
D. 2 + x3
Example 1b

24. B. Write an algebraic expression to represent the verbal expression 2 less than the cube of a number.
A. x3 – 2
B. 2x3
C. x2 – 2
D. 2 + x3
Example 1b

25. A. Write a verbal sentence to represent 6 = –5 + x.
Algebraic to Verbal Sentence
A. Write a verbal sentence to represent 6 = –5 + x.
Answer:
Example 2

26. A. Write a verbal sentence to represent 6 = –5 + x.
Algebraic to Verbal Sentence
A. Write a verbal sentence to represent 6 = –5 + x.
Answer: Six is equal to –5 plus a number.
Example 2

27. B. Write a verbal sentence to represent 7y – 2 = 19.
Algebraic to Verbal Sentence
B. Write a verbal sentence to represent 7y – 2 = 19.
Answer:
Example 2

28. B. Write a verbal sentence to represent 7y – 2 = 19.
Algebraic to Verbal Sentence
B. Write a verbal sentence to represent 7y – 2 = 19.
Answer: Seven times a number minus 2 is 19.
Example 2

29. A. What is a verbal sentence that represents the equation n – 3 = 7?
A. The difference of a number and 3 is 7.
B. The sum of a number and 3 is 7.
C. The difference of 3 and a number is 7.
D. The difference of a number and 7 is 3.
Example 2a

30. A. What is a verbal sentence that represents the equation n – 3 = 7?
A. The difference of a number and 3 is 7.
B. The sum of a number and 3 is 7.
C. The difference of 3 and a number is 7.
D. The difference of a number and 7 is 3.
Example 2a

31. B. What is a verbal sentence that represents the equation 5 = 2 + x?
A. Five is equal to the difference of 2 and a number.
B. Five is equal to twice a number.
C. Five is equal to the quotient of 2 and a number.
D. Five is equal to the sum of 2 and a number.
Example 2b

32. B. What is a verbal sentence that represents the equation 5 = 2 + x?
A. Five is equal to the difference of 2 and a number.
B. Five is equal to twice a number.
C. Five is equal to the quotient of 2 and a number.
D. Five is equal to the sum of 2 and a number.
Example 2b

33. Key concept

34. A. Name the property illustrated by the statement. a – 2.03 = a – 2.03
Identify Properties of Equality
A. Name the property illustrated by the statement. a – 2.03 = a – 2.03
Answer:
Example 3

35. A. Name the property illustrated by the statement. a – 2.03 = a – 2.03
Identify Properties of Equality
A. Name the property illustrated by the statement. a – 2.03 = a – 2.03
Answer: Reflexive Property of Equality
Example 3

36. Identify Properties of Equality
B. Name the property illustrated by the statement. If 9 = x, then x = 9.
Answer:
Example 3

37. Answer: Symmetric Property of Equality
Identify Properties of Equality
B. Name the property illustrated by the statement. If 9 = x, then x = 9.
Answer: Symmetric Property of Equality
Example 3

38. A. Reflexive Property of Equality B. Symmetric Property of Equality
A. What property is illustrated by the statement? If x + 4 = 3, then 3 = x + 4.
A. Reflexive Property of Equality
B. Symmetric Property of Equality
C. Transitive Property of Equality
D. Substitution Property of Equality
Example 3a

39. A. Reflexive Property of Equality B. Symmetric Property of Equality
A. What property is illustrated by the statement? If x + 4 = 3, then 3 = x + 4.
A. Reflexive Property of Equality
B. Symmetric Property of Equality
C. Transitive Property of Equality
D. Substitution Property of Equality
Example 3a

40. A. Reflexive Property of Equality B. Symmetric Property of Equality
B. What property is illustrated by the statement? If 3 = x and x = y, then 3 = y.
A. Reflexive Property of Equality
B. Symmetric Property of Equality
C. Transitive Property of Equality
D. Substitution Property of Equality
Example 3b

41. A. Reflexive Property of Equality B. Symmetric Property of Equality
B. What property is illustrated by the statement? If 3 = x and x = y, then 3 = y.
A. Reflexive Property of Equality
B. Symmetric Property of Equality
C. Transitive Property of Equality
D. Substitution Property of Equality
Example 3b

42. Key Concept

43. A. Solve m – 5.48 = 0.02. Check your solution.
Solve One-Step Equations
A. Solve m – 5.48 = Check your solution.
m – 5.48 = 0.02 Original equation
m – = Add 5.48 to each side.
m = 5.5 Simplify.
Check m – 5.48 = 0.02 Original equation
5.5 – 5.48 = 0.02 Substitute 5.5 for m. ?
0.02 = 0.02 Simplify. 
Answer:
Example 4

44. A. Solve m – 5.48 = 0.02. Check your solution.
Solve One-Step Equations
A. Solve m – 5.48 = Check your solution.
m – 5.48 = 0.02 Original equation
m – = Add 5.48 to each side.
m = 5.5 Simplify.
Check m – 5.48 = 0.02 Original equation
5.5 – 5.48 = 0.02 Substitute 5.5 for m. ?
0.02 = 0.02 Simplify. 
Answer: The solution is 5.5.
Example 4

45. Solve One-Step Equations
Original equation
Simplify.
Example 4

46. Check Original equation
Solve One-Step Equations
Check Original equation ?
Substitute 36 for t. 
Simplify.
Answer:
Example 4

47. Check Original equation
Solve One-Step Equations
Check Original equation ?
Substitute 36 for t. 
Simplify.
Answer: The solution is 36.
Example 4

48. A. What is the solution to the equation x + 5 = 3?
B. –2
C. 2
D. 8
Example 4a

49. A. What is the solution to the equation x + 5 = 3?
B. –2
C. 2
D. 8
Example 4a

50. B. What is the solution to the equation
C. 15
D. 30
Example 4b

51. B. What is the solution to the equation
C. 15
D. 30
Example 4b

52. 53 = 3(y – 2) – 2(3y – 1) Original equation
Solve a Multi-Step Equation
Solve 53 = 3(y – 2) – 2(3y – 1).
53 = 3(y – 2) – 2(3y – 1) Original equation
53 = 3y – 6 – 6y + 2 Apply the Distributive Property.
53 = –3y – 4 Simplify the right side.
57 = –3y Add 4 to each side.
–19 = y Divide each side by –3.
Answer:
Example 5

53. 53 = 3(y – 2) – 2(3y – 1) Original equation
Solve a Multi-Step Equation
Solve 53 = 3(y – 2) – 2(3y – 1).
53 = 3(y – 2) – 2(3y – 1) Original equation
53 = 3y – 6 – 6y + 2 Apply the Distributive Property.
53 = –3y – 4 Simplify the right side.
57 = –3y Add 4 to each side.
–19 = y Divide each side by –3.
Answer: The solution is –19.
Example 5

54. What is the solution to 25 = 3(2x + 2) – 5(2x + 1)?B. C.
D. 6
Example 5

55. What is the solution to 25 = 3(2x + 2) – 5(2x + 1)?B. C.
D. 6
Example 5

56. Subtract πr 2 from each side.
Solve for a Variable
Surface area formula
Subtract πr 2 from each side.
Simplify.
Example 6

57. Divide each side by πr. Simplify. Answer: Solve for a Variable
Example 6

58. Solve for a Variable
Divide each side by πr.
Simplify.
Example 6

59. GEOMETRY The formula for the perimeter of a rectangle is where P is the perimeter, and w is the width of the rectangle. What is this formula solved for w? A. B. C. D.
Example 6a

60. GEOMETRY The formula for the perimeter of a rectangle is where P is the perimeter, and w is the width of the rectangle. What is this formula solved for w? A. B. C. D.
Example 6a

61. Use Properties of Equality
A B
C D
Read the Test Item
You are asked to find the value of the expression 4g – 2. Your first thought might be to find the value of g and then evaluate the expression using this value. Notice that you are not required to find the value of g. Instead, you can use the Subtraction Property of Equality.
Example 7

62. Subtract 7 from each side.
Use Properties of Equality
Solve the Test Item
Original equation
Subtract 7 from each side.
Simplify.
Answer:
Example 7

63. Subtract 7 from each side.
Use Properties of Equality
Solve the Test Item
Original equation
Subtract 7 from each side.
Simplify.
Answer: C
Example 7

64. If 2x + 6 = –3, what is the value of 2x – 3?
B. 6
C. –6
D. –12
Example 7

65. If 2x + 6 = –3, what is the value of 2x – 3?
B. 6
C. –6
D. –12
Example 7