Numbers & Operations 8th Grade

Unit 2 – 7th Grade Star

Converting Repeating Decimals to Fractions and Decimal Expansion – Quiz 1

Classwork

  1. Write each repeating decimal as a fraction in simplest form*
  1. Find the decimal expansion of the following*:

Homework

  1. Write each repeating decimal as a fraction in simplest form*
  1. Find the decimal expansion of the following[*]:

Squares, Square Roots & Perfect Squares – Quiz 2

Classwork

  1. A square has an area of 9 units2.
  2. What is the side length of a square of this area?
  1. Draw a square with an area of 9 units2.
  1. What is the square root of 9?
  1. Explain why your answers in parts (a) and (c) are the same.
  1. Fill in the following table:

Side Length of a square
(units) / Area of the square
(units2)
1
2
3
4
5
6
7
8
9
10
11
12
13
  1. Explain how the table above helps you find the square root of 121?
  1. Simplify each square root.

Homework

  1. A square has an area of 36 units2.
  2. What is the side length of a square of this area?
  1. Draw a square with an area of 36 units2.
  1. What is the square root of 36?
  1. Explain why your answers in parts (a) and (c) are the same.
  1. Fill in the following table:

Side Length of a square
(units) / Area of the square
(units2)
14
15
16
17
18
19
20
  1. Simplify each square root.

Squares of Numbers Greater Than 20

Classwork

  1. Fill in the following table:

Side Length of a square
(units) / Area of the square
(units2)
10
20
30
40
50
60
70
80
90
100
  1. If you compare that to the table of side lengths from 1-10, what pattern do you notice?

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  1. Simplify each square root.

Homework

  1. Simplify each square root.

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Simplifying Perfect Square Radical Expressions – Quiz 3

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Classwork

  1. Simplify each square root.

Homework

  1. Simplify each square root.
  2. -
  3. -

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Approximating Square Roots – Quiz 4

Classwork

  1. What two integers do the following square roots fall between?
  1. Draw and label a number line from 0 to 10. Place the following square roots on the number line.
  1. Estimate the following square roots.
  2. Approximate the square root to the nearest integer
  1. For what integer x is closest to 7.42?[*]
  1. For what integer x is closest to 5.1?*
  1. For what integer x is closest to 3.9?*

Homework

  1. What two integers do the following square roots fall between?
  1. Draw and label a number line from 0 to 10. Place the following square roots on the number line.
  1. Estimate the following square roots.
  1. Approximate the square root to the nearest integer

a.
b.
c.
d.
e.

  1. For what integer x is closest to 5.2?[*]
  1. For what integer x is closest to 6.1?*
  1. For what integer x is closest to 6.9?*

Rational & Irrational Numbers – Quiz 4

Classwork.

  1. Circle the numbers below that are rational
  2. 3.5
  3. π
  4. 0.25
  5. 0.
  1. Given the statement “If x is a rational number then is irrational.” Which values of x make the statement false?* A) 15 B) 24 C) 4 D) 20
  1. Given the statement “If x is a rational number then is irrational.” Which values of x make the statement false?* A) 25 B) 49 C) 5 D) 59

Homework

  1. Circle the numbers below that are irrational.
  2. 6.75
  3. π
  4. 0.
  1. Given the statement “If x is a rational number then is irrational.” Which values of x make the statement false?[*]

A) 36 B) 8 C) 16 D) 121

  1. Given the statement “If x is a rational number then is irrational.” Which values of x make the statement false?*

A) 144 B) 12 C) 48 D)30

Properties of Exponents – Quiz 5

Classwork

  1. Complete each equation for the missing value:
  1. (52)(55) = 5?
  2. (127)(123) = 12?
  3. (3-2)(35) = 3?
  4. (49)(4-3) = 4?
  5. (54)(5?) = 512
  6. (107)(10?)(10-6) = 103
  7. 34 ÷ 32 = 3?
  8. = 5?
  9. = 9?
  10. 124 ÷ 126 = 12?
  11. 108 ÷ 10? = 103
  12. = 24
  1. A rectangle has a length of mm and a width of mm. Write an expression for the area of the rectangle as a power of 5.[*]
  1. Express the volume of a cube with a side length of inches as a power of 7.*
  1. a) Write an exponential expression for the area of a rectangle with a length of meters and a width of meters. b) Evaluate the expression to find the area of the rectangle.*

Homework

  1. Complete each equation for the missing value:

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  1. (122)(127) = 12?
  2. (25)(22) = 2?
  3. (5-3)(55) = 5?
  4. (158)(15-5) = 15?
  5. (67)(6?) = 615
  6. (11-6)(11?)(118) = 115
  7. 77 ÷ 73 = 7?
  8. = 11?
  9. 37 ÷ 39 = 3?
  10. = 2?
  11. = 132
  12. 5? ÷ 56 = 53
  13. 3
  14. 7

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  1. A rectangle has a length of mm and a width of mm. Write an expression for the area of the rectangle as a power of 4.[*]
  1. Express the volume of a cube with a side length of inches as a power of 2.*
  1. a) Write an exponential expression for the area of a rectangle with a length of meters and a width of meters. b) Evaluate the expression to find the area of the rectangle.*

Unit 2 Review

Determine whether the given numbers are perfect squares. Circle your answer.

1)1 Yes No

2)8 Yes No

3)16 Yes No

4)25 Yes No

5)82 Yes No

Circle the simplified version of each square root:

6)

  1. 14
  2. 12
  3. 72
  4. 21

7)

a. 10

b. 6

c. 0.6

d. 18

8)

a. -7

b. 0.7

c. 0.07

d. -0.07

Circle whether the given number is rational or irrational

9) π rational irrational

10) 0.875 rational irrational

11)) rational irrational

12)Between what two integers does the following square root fall?

  1. 4 & 5
  2. 6 & 7
  3. 7 & 8
  4. 5 & 6

13)(47)(43) = 4?

  1. 10
  2. 24
  3. 4
  4. 5

14)Approximate ______

15)Find the missing value 114 ÷ 116 = 11? ______

16) ______

17) (67)(6-2) = 6? ______

18)A rectangle has a length of cm and a width of cm. What is the area of the rectangle written as a power of 4? ______

19)Draw and label a number line from 0-10. Place the following numbers on the number line:[*],,

20)Write as a fraction in simplest form.*

21)Write as a fraction in simplest form.*

22) Write two exponential expressions with like bases. Leave all answers in simplified exponential form.

  1. Expression 1:

Expression 2:

  1. Multiply your expressions.
  1. Divide your expressions.
  1. Raise your first expression to the 5th power.

Answer Key

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  1. 7
  2. 4
  1. 3 units
  1. 3
  2. Area of a Square = Side2 and 9 = 32

Side Length of a Square
(units) / Area of the square
(units2)
1 / 1
2 / 4
3 / 9
4 / 16
5 / 25
6 / 36
7 / 49
8 / 64
9 / 81
10 / 100
11 / 121
12 / 144
13 / 169
  1. Since Area of a square = side2, the square root of the area = side. So, √121 = 11.
  2. 5
  3. 8
  4. 9
  5. 7
  6. 4
  7. 6 units
  1. 6
  2. Area = Side2 and 36 = 62

Side Length of a square
(units) / Area of the square
(units2)
14 / 196
15 / 225
16 / 256
17 / 289
18 / 324
19 / 361
20 / 400
  1. 17
  2. 20
  3. 14
  4. 19
  5. 12

Side Length of a square
(units) / Area of the square
(units2)
10 / 100
20 / 400
30 / 900
40 / 1600
50 / 2500
60 / 3600
70 / 4900
80 / 6400
90 / 8100
100 / 10,000
  1. Each answer in this table is 100 times greater than the corresponding answer in the other table. (or 102 times greater).
  2. 53
  3. 89
  4. 22
  5. 80
  6. 45
  7. 15
  8. 29
  9. 97
  10. 31
  11. 66
  12. 71
  13. 36
  14. 92
  15. 55
  16. 61
  17. 83
  18. 24
  19. 49
  20. 50
  21. 17
  22. 5
  23. 8
  24. -9
  25. No real solution
  26. 7
  27. No real solution
  28. ½
  29. – ½
  30. 0.8
  31. 0.09
  32. -0.5
  33. 0.04
  34. No real solution
  35. 17
  36. -20
  37. 8
  38. 19
  39. No real solution
  40. 1/3
  41. ½
  42. No real solution
  43. -3/4
  44. 1/10
  45. No real solution
  46. -0.14
  47. 0.7
  48. 0.19
  49. 0.5

a.

b.

c.

d.

e.

  1. 2.45
  2. 8.37
  3. 7.42
  4. 3.74
  5. 10.29
  6. 6.4
  7. 8.94
  8. 8.06
  9. 2.83
  10. 15.26
  11. 7
  12. 6
  13. 8
  14. 3
  15. 9
  16. 55
  17. 26
  18. 15

a.

b.

c.

d.

e.

  1. 8.83
  2. 2.65
  3. 7.94
  4. 5.39
  5. 6.48
  6. 11.75
  7. 17.32
  8. 12.17
  9. 4.58
  10. 7.21
  11. 4
  12. 6
  13. 4
  14. 6
  15. 7
  16. 27
  17. 37
  18. 48
  19. Rational
  20. Irrational
  21. Irrational
  22. Rational
  23. Irrational
  24. Rational
  25. Irrational
  26. Rational
  27. Rational
  28. Rational
  29. c
  30. a,b
  31. Rational
  32. Irrational
  33. Rational
  34. Rational
  35. Rational
  36. Rational
  37. Irrational
  38. Irrational
  39. Rational
  40. Rational
  41. a,c,d
  42. a
  43. 7
  44. 10
  45. 3
  46. 6
  47. 8
  48. 2
  49. 2
  50. 3
  51. -3
  52. -2
  53. 5
  54. 7
  55. mm2
  56. in3
  57. a. x b. m2
  58. 9
  59. 7
  60. 2
  61. 3
  62. 8
  63. 3
  64. 4
  65. 4
  66. -2
  67. -4
  68. 4
  69. 9
  70. mm2
  71. in3
  72. a. x b. in2

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Review answers

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  1. Yes
  2. No
  3. Yes
  4. Yes
  5. No
  6. B
  7. C
  8. D
  9. Irrational
  10. rational
  11. irrational
  12. b
  13. a
  14. ~7
  15. -2
  16. 4
  17. 5
  18. cm2
  19. =5.29

=5.48

=9.1

  1. Expressions will vary

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[*] From Engage NY

[*] From Engage NY

[*] From Engage NY

[*] From Engage NY

[*] From Engage NY

[*] From Engage NY

[*] From Engage NY