Australian School Sacred Heart

Mathematics Worksheets
Year 6/Term 1

Unit: 1. NUMERICAL AND ALGEBRAIC EXPRESSIONS

● Real Number Properties
● Real Number System Anchor Chart
● Exponents
● Exponent Book
● Squares, Cubes, and Roots
● Square Roots and Cube Roots Foldable Notes
● Order of Operations
● Order of Operation Poster
● Project: Numerical and Algebraic Expressions Performance Task A
● Project: Numerical and Algebraic Expressions Performance Task B

1. Write an algebraic expression that illustrates the multiplicative identity.

The property of multiplication is being illustrated below.

⮚ Commutative
⮚ Associative
⮚ Identity
1×2×4=2×1×4

2. The property of addition is being illustrated below.

⮚ Commutative
⮚ Associative
(6 + 7) + 1 = 6 + (7 + 1)
Year 6/Term 3/Unit 1
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 3. Use the distributive property to evaluate the following expression: 9 × (4 +
9)

4. Which property is illustrated below?

1.8 + 7.3 = 7.3 + 1.8

identity property of addition

commutative property of addition

associative property of addition

distributive property

5. Which of the following number sentences illustrates the associative

property of multiplication?

(3 × 8) × 6 = 3 × (8 × 6)

2 × (1 × 9) = (2 × 1) × (2 × 9)

1 × 15 = 15

8×9=9×8

6. April wants to multiply 6 and 42 using the distributive property. Which of

the following number sentences shows how she could do it?

6 × 42 = 42 × 6

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 6 × (40 + 2) = (6 × 40) + 2

(6 × 42) × 1 = 6 × (42 × 1)

6 × (40 + 2) = (6 × 40) + (6 × 2)

7. If a number is raised to a power of 2, it is

⮚ Cubed
⮚ Powered
⮚ Squared

8. In the expression 74 = 2,401, the value of the is 7.

⮚ Power
⮚ Exponent
⮚ Base

9. When using the order of operations to evaluate an expression, you should

complete multiplication before division.

⮚ Never

⮚ Always

⮚ Sometimes

10. Rewrite as a product

× × ×

× ×

Year 6/Term 3/Unit 1

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 × × ×

11. Evaluate 25.

10

16

32

25

12. Choose all the numbers that are perfect squares.

64

24

12

49

144

84

13. Evaluate .

18

Year 6/Term 3/Unit 1

4
 12

14. Evaluate .
3

24

81

15. To simplify the following expression, which operation would you

complete second?
9 + (16 - 2) × 42 ÷ 8
subtract

simplify the exponent

multiply

divide

16. Use the order of operations to find the value of the following expression.

102 - 2 × (8) + 11
795

155

95

15

17. Use the order of operations to find the value of the following expression.
Year 6/Term 3/Unit 1
5
3+ ÷ 3 - (1 × 4)

12

20

Unit: 1. NUMERICAL AND ALGEBRAIC EXPRESSIONS

● Variables
● Variables Worksheet
● Expressions
● Making expressions
● Simplifying Algebraic Expressions
● Collecting Like Terms
● More Simplifying Algebraic Expressions
● More Simplifying Algebraic Expressions

18. Choose a value for n, and then evaluate n2

19. y + 8 can be translated as "the of a number and eight."

⮚ Quotient
⮚ Sum
⮚ Product
⮚ Difference
Year 6/Term 3/Unit 1
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 20. All of the following represent three multiplied by six except:
3(6)

3:6

3·6

3×6

21. Which of the following phrases translates to m - 7?

the difference between seven and a number

seven minus a number

a number decreased by seven

a number subtracted from seven

22. Rewrite the following phrase as a mathematical expression: twice a

number increased by eighteen.
2n + 18

18n + 2

2 + 18

2(18n)

23. What is the value of b - a if a = 18, b = 27, and c = 11?

7

16

11

Year 6/Term 3/Unit 1

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 24. Translate the following phrase to a mathematical expression and then
evaluate the expression for n = 5.
the quotient of twenty and a number
n ÷ 20; 4

20 ÷ n; 4

20n; 100

20 - n = 15

25. Elisha is traveling with her family in the car. If the car is moving at an
average speed of 45 miles per hour, how many miles can they travel in 3
hours? Use the formula r · t, where r represents the rate, or speed, and t
represents the time.
453 miles

15 miles

135 miles

150 miles

26. Simplify the following expression.

(3 + 8x) + 7x
3 + 15x

18x

18 + x

11x + 7

27. Simplify the following expression.

4 · (x · 3)

Year 6/Term 3/Unit 1

8
 x12

7x

x7

12x

28. Which of these expressions is not equivalent to the others?

(4n + 3) + 5n + 8 - 6

(4n + 5n) + (3 + 8 – 6)

9n + 3 + 2

9n + 11

29. Simplify.
(4w + 3) – 2w + 7
2w + 10

2w - 10

6w + 10

6w – 10

30. Simplify.

12d • d
12d

6d 2

6d

Year 6/Term 3/Unit 1

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 12d 2

31. Simplify.

2k 2 + 12

14k 2

2k + 12

14k

32. Explain how to simplify this expression: (7a + 9) + (4a – 7).

33. Identify an expression that is equivalent to 0.3(12y).

Year 6/Term 3/Unit 1

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Unit: 1. NUMERICAL AND ALGEBRAIC EXPRESSIONS
● The Distributive Property
● The Distributive Property
● Factoring Expressions
● Geometric Shapes Art Project
● Equations and Mental Math
● Equations and Mental Math

34. Write an equation whose solution is x = 7.

35. Simplify the following expression using the distributive property.

8(m + 11)
8m + 11

19m

8m + 88

88m

36. Which of the following questions could be used to represent the equation 4
· x = 28?

What number when multiplied by 28 is equal to 4?

Year 6/Term 3/Unit 1
11
 The product of 4 and what number is equal to 28?

The quotient of 4 and what number is equal to 28?

What number when added to 4 is equal to 28?

37. Solve this equation.

28 - k = 22
k=

38. Solve this equation.

w÷9=9
w=

39. Simplify.
6(4m + 5)
24m + 5

4m + 30

24m + 30

64m + 65

40. Simplify.
10y(3x – 7z)
30xy – 70yz

103xy – 107yz

30xy – 7z

3x – 70yz

41. Simplify.

Year 6/Term 3/Unit 1

12
p(17 + 24r)
17 + 24pr

17p + 24pr

17p + 24r

17 + 24r

42. Find the greatest common factor of the terms in the following expression:
10x + 12xy.
x

2x

2xy

43. Find the greatest common factor of the terms in the following expression:
6ab + 18a.
6a

3a

2a

44. Factor the following expression using the GCF.

4dr – 16r
r(4d – 16)

2r(2d – 8)

4(dr – 4r)

Year 6/Term 3/Unit 1

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 4r(d – 4)

45. Factor the following expression using the GCF.

25st + 30t
5t(2s + 6)

5t(5s + 6)

5t(5 + 6t)

5t(s + 6)

46. Look at the student work shown below.

Simplify: 4t(2s – 7).
(4t)(2s) – 7
8st - 7
Did the student correctly simplify the expression? If “yes,” explain the steps the
student followed. If “no,” explain what the student did wrong and what should
have been done.

47. Factor this expression using the GCF and then explain how you can verify
your answer.
6ab + 8a

Year 6/Term 3/Unit 1

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 48. Write a question that matches this equation.
45 – n = 15

Unit: 2. FRACTIONS
● Divisibility and Prime Factorization
● Prime Factorization
● Greatest Common Factor
Year 6/Term 3/Unit 1
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 ● Greatest Common Factor
● Fractions
● Fraction Flower
● Equivalent Fractions
● Hanging Equivalent Fractions Project

49. A.) Write a four digit whole number that is divisible by 2.

B.) Based on the divisibility tests, how do you know that your number is
divisible by 2?

50. Write a proper fraction where the whole is divided into an even number of
equal parts, and an odd number of those parts exist.

51. In the fraction , the is 7.

⮚ Denominator
⮚ Numerator

52. The number 37 is .

⮚ Composite

Year 6/Term 3/Unit 1

16
 ⮚ Prime

53. Choose all the numbers that are factors of 16.

10

12

16

54. What is the prime factorization of 48?

4 × 12

23 × 6

24 × 3

23 × 32

55. Which fraction is modeled below?

Year 6/Term 3/Unit 1

17
 56. What is the value of the point on the number line?

57. In history class, students could either make a timeline of World War II or
interview someone that lived through World War II. Nine of the students
chose to make a timeline, and eleven of the students chose to interview
someone. Which fraction represents the part of the class that interviewed
someone?

Year 6/Term 3/Unit 1

18
 58. Which pair of fractions is not equivalent fractions?

59. Find the GCF of 28 and 30.

60. Find the GCF of 14 and 15.

61. Write in simplest form. Use / for the fraction line.

62. Write a fraction that is equivalent to . Use / for the fraction line.

63. Rewrite 48 + 60 using the distributive property

Year 6/Term 3/Unit 1

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 64. Rewrite the expression 26 + 8 as the product of the GCF and a sum. Then,
simplify the expression. Show all of your steps.

Unit: 2. FRACTIONS
● Least Common Multiple
● Least Common Multiple Activity
● Project: Fractions Performance Task A
● Comparing and Ordering Fractions
Year 6/Term 3/Unit 1
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 ● Comparing Fractions with Diagrams
● Fractions on The Number Line
● Improper Fractions and Mixed Numbers
● Mixed Number to Improper Fraction
● Fractions and Decimals
● Geometric Shapes Art Project

65. A) Describe the mixed numbers that come between 1 and 2 on the number
line.
B) Write a mixed number that comes between 1 and 2 on the number line.

66. Write two proper fractions whose denominators are not the same, but
whose least common denominator is 12.

67. Rewrite 8 as an improper fraction. Use / for the fraction line.

65. Rewrite 2 as an improper fraction. Use / for the fraction line.

Year 6/Term 3/Unit 1
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 66. Find the LCM of 20 and 18.

67. Find the LCM of 6 and 5.

68. All of the following are multiples of 6 except _____.

54

30

40

12

69. Which of the following is a multiple of 8?

18

22

30

48

70. Plastic cups come in packages of twenty-four, and straws come in

packages of twenty. If you want to end up with the same total number of
straws as cups, what is the smallest total number you should buy?

120

200

240

480

Year 6/Term 3/Unit 1

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 71. Complete the inequality statement.

___

<

>

Complete the inequality statement.

___

<

>

72. Complete the inequality statement.

9 ___ 9

<

>

73. Which of the following is listed from smallest to largest?

, ,

, ,

, ,

Year 6/Term 3/Unit 1

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 , ,

74. Rewrite as a mixed number.

75. Rewrite as a mixed number.

76. Is 17 to the right or left of 17 on the number line? Explain your answer.

Year 6/Term 3/Unit 1

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 77. A green bottle holds 8 ounces of water. A blue bottle holds 8 ounces of
water. Which bottle holds more? Write an inequality that compares the
fractions.

78. Write a fraction that can be used to represent the same value of the
decimal number 0.45

79. Rewrite as a decimal number.

80. Rewrite 7.25 as a mixed number in lowest terms.

Year 6/Term 3/Unit 1

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 7

Unit: 2. FRACTIONS
● Estimating with Fractions
● Multiplying Fractions
● Multiplying Fractions
● Multiplying Fractions
● Multiplying Mixed Numbers
● Project: Fractions Performance Task B

81. Round 14 to the nearest whole number.

82. Which of the following is closest to?

83. Round each mixed number to the nearest whole number and then estimate
the product.

3 ×5

15

18

20

Year 6/Term 3/Unit 1

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 24

84. Find of 12. Express your answer in simplest form.

85. Multiply. Express your answer in simplest form.

86. Mari Kere borrowed 15 books from the library last month. She's already

read of them. How many of the 15 books has she read?

Year 6/Term 3/Unit 1

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 87. Evaluate the following expression. Express your answer in simplest form.

+ ×

88. Multiply. Express your answer in simplest form.

11 ×4

47

44

47

44

89. Find the product of 3 and . Express your answer in simplest form.

90. Explain how to round 14 to the nearest whole number, using the number
line as a tool. Use complete sentences in your answer.

Year 6/Term 3/Unit 1

28
 91. Explain how to estimate the product of 12 x6 . Use complete
sentences in your answer.

92. Explain how to find the product of x . Use complete sentences in your
answer.

93. Find the product of and . Express your answer in simplest form.

94. Ongelica swims 14 hours per month. If she swims the same amount
every month, how many hours does she swim in 6 months?

85 hours

86 hours

86 hours

86 hours

Year 6/Term 3/Unit 1

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 95. A city lot is 20 meters wide. It is 2 times as long as it is wide. How long
is the city lot? Express your answer in simplest form.

52 meters

54 meters

52 meters

54 meters

Unit: 3. DIVIDING FRACTIONS

● Dividing with Unit Fractions
● Dividing Whole Numbers by Fractions
● Dividing Fractions by Whole Numbers
● Dividing Fractions by Fractions
● Project: Dividing Fractions Performance Task A
● Ratios Project

96. Write an expression so that when you divide ¼ by a number the quotient
will be greater than 1/4.

Year 6/Term 3/Unit 1

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 97. Divide.

20

10

98. Write a division problem with as the dividend and 3 as the divisor. Then,
find the quotient.

99. Select all proper fractions.

Year 6/Term 3/Unit 1

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 100.

101. A pitcher of juice holds 6 cups. How many -cup servings of juice
are in the pitcher?

102. For the following word problem, explain which number is the
dividend, which is the divisor. Then write a division problem and find the
quotient.

If each person gets -pound of squash, how many people can evenly split a 9-pound
basket of squash from the farmer's market?

103. Find the quotient. If necessary, use / for the fraction bar.

Year 6/Term 3/Unit 1

32
 =

104. Divide.

105. Frances read of an article in three minutes. How much of the

article did she read each minute?

106. Write a word problem that must be solved with division and

includes as the dividend and 4 as the divisor.

Year 6/Term 3/Unit 1

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 107. Write a division problem such that the quotient is the same
as 3
/8 ÷ 3/5

108. Use a model to divide. Express the answer in simplest terms. If

necessary, use / for the fraction bar.

109. Divide. Express the answer in simplest terms. If necessary, use / for
the fraction bar.

110. Ryan needs pound of chicken to make one cup of chicken dip. He

has pound of chicken. Ryan calculated that he can make exactly three
cups of dip. Is he correct? Use complete sentences to explain your answer.

Year 6/Term 3/Unit 1

34
Unit: 3. DIVIDING FRACTIONS
● Alternate Quiz—Form A: Dividing with Fractions Using a Visual Model
● Alternate Quiz—Form B: Dividing with Fractions Using a Visual Model
● Dividing Fractions
● Dividing Mixed Numbers
● Dividing Mixed Numbers Worksheet
● Division in Real Life
● Division in Real Life
● Project: Dividing Fractions Performance Task B

111. Write a whole number between 1 and 10, and then write its
reciprocal.

112. Divide.
Year 6/Term 3/Unit 1
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 3

113. A recipe calls for 3 cups of flour, evenly divided into two different
bowls. How much flour should be put into each bowl?

1 cups

1 cups

1 cups

2 cups

114. Evaluate the expression.

÷ -

115. Find the quotient.

6 ÷3
Year 6/Term 3/Unit 1
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 23

116. Find the product of 3 and . Express your answer in simplest

form.

117. What is the reciprocal of 2 ?

118. Divide. Express your answer in simplest form.

119. Divide. Express your answer in simplest form.

8÷2

120. Which fraction would make this equation true using the multiplicative
inverse?

Year 6/Term 3/Unit 1

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 121. Using complete sentences, explain how to find the quotient

of . Make sure to include the quotient in your answer.

122. Write a word problem that can be represented by the

expression .

123. Ari mixed 2 cups of red grapes with cups of green grapes. He

then divided the grapes into bags with cup of mixed grapes in each.
How many bags of grapes will Ari have?

124. Sabrina and three friends share pizzas. If they all ate the same
amount, which expression could be one of the steps in determining how
much pizza each person ate?

Year 6/Term 3/Unit 1

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 125. Which of the following situations can be represented by the

expression ? Select all that apply.

Four friends equally share pizzas.

yards of material is cut into four sections.

A baker adds cups of flour to 4 cups of flour.

An electrician cuts yards of wire from a strip 4 yards long.

Year 6/Term 3/Unit 1

39
 Australian School Sacred Heart
Mathematics Worksheets
Year 6/Term2

Unit: 5. RATIOS
 Ratios

 Ratios Poster

 Equivalent Ratios

 Solving Ratio Problems Worksheet

 Solving Ratio Problems

 Solving Ratio Problems Worksheet

 More Ratio Problems

 Project: Ratios Performance Task A

1. Sacred's basketball team won 9 games this season and lost 5 games.
Write the win-loss ratio in simplest form.

5:9

9:5

5:1

1:5

2. Heart's basketball team won 9 games this season and lost 5 games.
Write the ratio of wins to total games in simplest form.

3. Which situations accurately describe a ratio of ? Select all that apply.

Tussel picked five daisies and eight roses.

1
Year 6/Term 2/Unit 1
 Shaula found five green fruit loops in her cereal bowl, out of every thirteen pieces.

Arren painted eight trees for every three birds.

For every eight shots, Maiden made five baskets.

4. Match the description with the ratio.

1. There are three silver bows for every four red bows in a bag. 3:4

2. There are four red bows out of ten bows. 4:10

3. There are six blue bows and ten silver bows. 3:10

4. There are three black bows out of a bag of ten bows. 6:10

5. Use the tape diagram to find the ratio.

Mr. Mids' art class used blue paint and purple paint for a school mural. Find the part-
to-whole ratio of purple paint to the total. Write the ratio using a colon and no spaces.

6. Use the tape diagram to find the ratio.

Mr. Mids' art class used blue paint and purple paint for a school mural. Find the part-
to-part ratio of purple paint to blue paint. Write the ratio using a colon and no spaces.

7. Use the tape diagram to find the ratio.

2
Year 6/Term 2/Unit 1
Mr. Mids' art class used blue paint and purple paint for a school mural. Find the ratio
of blue paint to the total. Write the ratio using a colon and no spaces.

8.

Find the equivalent ratios of blue marbles to total marbles. Select all that
apply.

2 to 3

4 to 7

4 to 8

8 to 14

9.

Find the ratio of red marbles to total marbles. Write the ratio in simplest form.

3
Year 6/Term 2/Unit 1
 10.

Find the ratio of blue marbles to red marbles. Write the ratio in simplest form.

11. Write a ratio that can be expressed in lowest terms as 5:1

12. All of the following represent the same ratio except _____.

4:3

3 to 4

13. What is the ratio of yellow sections to blue sections, in lowest terms?

4
Year 6/Term 2/Unit 1
 5 to 3

3 to 4

3 to 5

1 to 2

14. What is the ratio of red sections to total sections, in lowest terms?

15. In a crowd, the ratio of men to women is 5 to 6. If there are 90 men, how many
women are there? Use the ratio table to help you find the number of women.

5
Year 6/Term 2/Unit 1
 Men 5 10 30 90

Women 6 12

women

16. Use the image below to describe at least three different ratios, written in simplest
form. Include at least one part-to-part ratio and one part-to-whole ratio.

17. Use the word CHATTAHOOCHEE to match each ratio.

1. 3:2 the ratio of E's to H's

2. 2:3 the ratio of H's to O's

3. 2:2 the ratio of O's to letters

4. 13:3 the ratio of T's to E's

5. 2:13 the ratio of letters to H's

18. Micah mixed 3 ounces of yellow paint with 5 ounces of blue paint. What is the
ratio of blue paint to the total amount of paint that Micah used? Write the ratio
using a colon and no spaces.

6
Year 6/Term 2/Unit 1
 a0

19.

Sydney bought two packages of grapes and noticed that the amount of purple grapes to
green grapes was a ratio, as shown in the tape diagram above. Which of the following
ratios are equivalent to the ratio of purple grapes to green grapes? Select all that apply.

18 to 15

25 to 30

35 to 42

48 to 40

20. The ratio of students polled in 6th grade who prefer lemonade to iced tea is 8:4.
If there were 39 students in 6th grade polled, explain how to find the number of
students that prefer lemonade and the number of students that prefer iced tea
using a ratio table. If you wish, you may upload a copy of your ratio table.

21. Melissa’s mom is making waffles and pancakes for a class party. The ratio of
students who want waffles to pancakes is 4:6. Which of the following tape
diagrams represent the given ratio? Select all that apply.

7
Year 6/Term 2/Unit 1
 22. The ratio of blue marbles to red marbles in a bucket is 63 to 45. If there are 648
marbles, how many marbles are blue and how many are red? Complete the given
ratio table to solve the problem.

Blue 63

Red 45

Total 108 216 648

270 blue marbles, 378 red marbles

378 blue marbles, 270 red marbles

315 blue marbles, 225 red marbles

385 blue marbles, 263 red marbles

23. Recipe A calls for 2 cups of sugar and makes 48 cookies. Recipe B calls for 3 cups
of sugar and makes 54 of the same-sized cookies. Determine which recipe
contains more sugar in each cookie. Use complete sentences to explain your
reasoning.

8
Year 6/Term 2/Unit 1
 24.

A bag is filled with small and large marbles. The ratio of small to large marbles is 1:3. On
your own sheet of paper, draw a tape diagram to represent this situation.

There are eight more large marbles than small marbles. On your diagram, how many
marbles does each bar represent? [Type your answer as a number.]

marbles

25.

A bag is filled with small and large marbles. The ratio of small to large marbles is 1:3. On
your own sheet of paper, draw a tape diagram to represent this situation.

There are eight more large marbles than small marbles. How many total marbles are in
the bag? [Type your answer as a number.]

marbles

9
Year 6/Term 2/Unit 1
Unit: 5. RATIOS
 The Value of a Ratio
 The Value of Ratios
 Comparing Ratios
 Comparing Ratios
 Double Number Lines
 Equations Project
 Equations
 Area of Triangles
 Project: Ratios Performance Task B

26. The value of a ratio is __________.

the sum of the two quantities in the ratio

the difference of the two quantities in the ratio

the product of the two quantities in the ratio

the quotient of the two quantities in the ratio

27. If necessary, use / for the fraction bar.

The diagram shows a green to pink ratio value of a0

.

28. A class has 7 boys and 10 girls. Select all associated ratios for this
class.

7:3

7:10

10:7

17:5

7:17

10:17

10
Year 6/Term 2/Unit 1
 3:7

10:3

29. Which of the following ratios has the same ratio value as 4:6?

5:10

4:12

6:9

4:16

30. Write a ratio value comparing 3 to a number, where the value of the ratio
is greater than 3:5.

31. Dalia's smoothie recipe has 4 cups of yogurt and 8 cups of fruit. Arturo's
smoothie recipe has 3 cups of yogurt and 9 cups of fruit.

Which recipe has a larger fruit to yogurt ratio?

Dalia's recipe

Arturo's Recipe

The fruit to yogurt ratios are the same.

32. Three friends went apple picking and then counted the apples they picked.

Red Apples Green Apples

Carmen 20 12

Dylan 12 10

Eli 16 20

11
Year 6/Term 2/Unit 1
Who had the largest red to green apple ratio? Use complete sentences to
explain how you got your answer.

33.

If necessary, use / for the fraction bar. Please reduce to simplest terms

What ratio value is shown by the following double number line? Use / for the fraction
bar and do not use spaces. a0

34. A recipe calls for 2 carrots for every 3 stalks of celery. Walter is
preparing the recipe for a group and uses 15 stalks of celery. How many
carrots should he use? [Type your answer as a number.]

Use the double number line to solve.

carrots

12
Year 6/Term 2/Unit 1
 35.
Shira is decorating a room with green and purple balloons. She wants to use 4
green balloons for every 5 purple balloons. How many purple balloons will she
need if she uses 20 green balloons? Use a double number line to solve.

purple balloons

36. Explain how to draw a double number line representing a 1:4 ratio.

37. For any ratio, the second quantity in the ratio by the ratio
value to get the first quantity.

38. During his summer vacation, Alex spent 6 minutes riding his bike for
every minute he spent watching television. If he rode his bike for 780
minutes, how many minutes did he spend watching television? Use an
equation to solve. [Type your answer as a number.]

a0
minutes

39. Grace is organizing a snack for her friends. Each person will get 4 apple
slices and 6 pretzels. If Grace used 18 pretzels, how many apple slices
did she use? [Type your answer as a number.]

a0
apple slices

13
Year 6/Term 2/Unit 1
 40. If there are three sleds for every five children, which equation shows the
correct relationship between the number of sleds (S) and the number of
children (C)?

C= ×S

S= ×C

=S×C

S= ÷C

Unit: 6. RATES AND PERCENT

 Rates
 Real Life Unit Rates
 Rates and Ratios
 Rates and Ratios Worksheet
 Solving Rate Problems
 Solving Rates Problems

41. Express the following relationship as a rate.

$4.60 for 4 attempts

$1.25 per attempt

$1.75 per attempt

$0.75 per attempt

$1.15 per attempt

42. A train travels 120 miles in 3 hours. At this same rate, how many miles
will it travel in 8 hours?

400 miles

450 miles

14
Year 6/Term 2/Unit 1
 500 miles

320 miles

43. Express the following rate as a rate.

36 jumping jacks in 3 minutes

a0
jumping jacks per minute

44. Which of the following describes a rate?

growing 12 inches in 3 years

writing 4 pages in 1 hour

picking 80 apples in 30 minutes

45. What is the rate unit of running 4 miles in one hour?

miles per hour

miles

hours

46. Express the following relationship as a rate.

60 goals in 20 games

6 goals per game

3 goals per game

30 goals per game

goal per game

15
Year 6/Term 2/Unit 1
 47.
What is the ratio value associated with the rate of beats per minute?

80

60

40

20

48. Use the double number line to answer the question.

How many heartbeats are there in 4 minutes?

40

80

120

160

49. Use the double number line to answer the question.

16
Year 6/Term 2/Unit 1
How many minutes until the heart beats 120 times?

120

10

50. Use the following table to answer the question. Mireya wants to buy 4
avocados. The local market sells avocados at the rate shown in the
table. The store down the road is advertising 4 avocados for $4.20.
Which has the better rate?

Avocados Price

1 $1.15

2 $2.30

5 $5.75

10 $11.50

51. Use the table to answer the question.

Avocados Price

1 $1.15

2 $2.30

5 $5.75

17
Year 6/Term 2/Unit 1
 10 $11.50

How much will 4 avocados cost?

$1.15

$3.45

$4.45

$4.60

52. A soccer team scores an average of 12 goals per season. A double

number line is drawn to figure out the average number of goals the team
scores in 6 seasons. Which of the following statements is true about the
diagram?

One number line increases by 12, and the other increases by 6.

One number line increases by 1, and the other increases by 6.

One number line increases by 12, and the other increases by 1.

One number line increases by 2, and the other increases by 1.

53. Select all that apply.

Zack is taking a test in which he answers questions at a rate of question per

minute. If Q represents questions and M represents minutes, which of the
following equations describe this rate relationship? Select all that apply.

M= ×Q

Q=3×M

Q= ×M

M=3×Q

54. Zack is taking a test in which he answers questions at a rate

of question per minute. How many questions can he answer in 6

minutes?

2
18
Year 6/Term 2/Unit 1
 3

18

55. Write an equation to solve and find the answer to the following rate
problem. Show all of your work.

A gardening store sells 6 plants per hour. How many plants they will sell in 7
hours?

Close

Course Information

Course: SHAS Mathematics 600 Semester 1

Unit: 6. RATES AND PERCENT

Assignment: 16. Quiz: Applying Ratios and Rates

QUIZ: APPLYING RATIOS AND RATES

Question #1FillInBlank

Answer KeyShow

Convert 40.64 centimeters to inches. [Type your answer as a number.]

1 inch ≈ 2.54 centimeters

a0 inches
Question #2MultipleChoice

Answer KeyShow

Complete the inequality.

6 gallons ___ 50 pints

19
Year 6/Term 2/Unit 1
 >

<

Question #3FillInBlank

Answer KeyShow

Alice ran 8 miles over the weekend. How many kilometers did she run? [Type
your answer as a number.]

1 mile ≈ 1.6 kilometers

a0 kilometers
Question #4FillInBlank

Answer KeyShow

Complete the statement. [Type your answer as a number.]

7 pounds × 16 ounces = a0 pound(s)

Question #5MultipleSelect

Answer KeyShow

Select all that apply.

Two different clothes detergents are on sale at Shop Mart. Clean White is
priced at $8.63 for 32 fluid ounces. Clean Bright is priced at $7.20 for 24 fluid
ounces. Which ratio tables are correct?

Clean White

cost $8.63 0.27

fluid ounces 32 1

Clean White

cost $8.63 1

fluid ounces 32 0.27

20
Year 6/Term 2/Unit 1
Clean Bright

cost $7.20 1

fluid ounces 24 0.30

Clean Bright

cost $7.20 0.30

fluid ounces 24 1

56. Price-club sells a 12-ounce package of spaghetti noodles for $3.44 and

Shop Mart sells a 2 -pound box of spaghetti noodles for $8.35.

The unit price per ounce at Price-Club is $ , and the unit price per
ounce at Shop Mart is $

57. Crafter’s Warehouse sells 6 yards of solid color fleece for $16.49. They
sell 16 feet of patterned fleece for $15.40. Which fleece is the better
price?

Both the solid color and patterned fleeces have the same unit price.

The solid color fleece is a better price.

The patterned fleece is a better price.

58. Which paint costs the most per quart?

 Glide Paint: 1 gallon for $28.92
 Smooth Paint: 3 quarts for $22.75
 One-Coat Paint: 4 pints for $15.00
Glide Paint

Smooth Paint

One-Coat Paint

21
Year 6/Term 2/Unit 1
 59. A train travels with a constant speed of 86 kilometers per hour. How far
can it travel in 4 hours? [Type your answer as a number.]

a0 kilometers

60. Which runs faster: a mule deer that can run 80 feet in 6 seconds or a
gazelle that can run 140 feet in 10 seconds?

A mule deer runs faster

A gazelle runs faster

They run at the same speed

61. A marketing company is hiring two college students to hand out

brochures near an event.Marshall hands out 300 brochures in 2 hours.
Silas hands out 240 brochures in 90 minutes. Who handed out more
brochures per minute?

Marshall

Silas

Neither. They handed out brochures at the same rate.

62. A 6th grade student can complete 20 multiplication facts in 1 minute. If

he works at the same rate, how long should it take him to complete 35
multiplication facts? [Type your answer as a decimal number.]

a0 minutes

63. Which of the following measurements is larger: 4.3 liters or 562

milliliters? Explain your reasoning.

64. Which brand of rice is the better buy? Explain your reasoning.

22
Year 6/Term 2/Unit 1
  Brand A: 12 ounces of rice for $2.24
 Brand B: 18 ounces of rice for $3.19

65. Michael drove his car for 150 minutes at a constant speed of 75 miles
per hour and then for another 2 hours at a constant speed of 81 miles
per hour. How far did Michael drive? Show or explain how you got your
answer.

Unit: 6. RATES AND PERCENT

 Percents and Fractions
 Clock Fractions-Percentages
 Percents and Decimals
 Percent Patterns
 Percent of a Number
 Percent of a Number
 Solving Percent Problems
 Project: Job, Salary, and Lifetime Income
 Project: Rates and Percent Performance Task B

66. Write a fraction with a denominator of 9 whose equivalent percent is

less than 100%. B.) Explain why the fraction is less than 100%.

23
Year 6/Term 2/Unit 1
 67. Which of the following are in order from smallest to largest?

60%, 0.2, 1/2

0.2, 1/2 60%

1
/2, 0.2, 60%

1
/2, 60%, 0.2

68. Express 64% as a fraction in simplest form.

69. Three out of every five students wore green on St. Patrick's Day. What
percent of the students wore green?

35%

60%

80%

75%

70. Complete the inequality.

9% ___ 0.4

<

24
Year 6/Term 2/Unit 1
 >

71. Express 0.52 as a percent.

0.52%

52%

520%

0.0052%

72. Which of the following is the best estimate for 31% of 9?

73. What is 46% of 22? Use a fraction and express your answer in simplest
form.

10

11

10

74. Rewrite as a percent. Make sure to label your answer with %.

75. Rewrite 4% as a decimal.

25
Year 6/Term 2/Unit 1
 76. Find 140% of 15.

77. Use the diagram to complete the statement. [Type your answer as a
number.]

60% 0f 20 is a0
.

78. Colleen spent 60 minutes online. If she spent 24 minutes on local news
sites, what percent of her online time did she spend on local news
sites?

24%

30%

40%

60%

79. Marie and her family are on a trip. So far, they have traveled 175 miles
and are 25% of the way to their destination. How many total miles will
they travel?

44 miles

200 miles

700 miles

875 miles

80. Each month, Ellie spends 4 hours in tap class at her dance studio. If
each month she spends 20% of her class time in tap class, what is the

26
Year 6/Term 2/Unit 1
 total number of hours she spends in dance classes each month?
Explain or show how you find your answer.

Unit: 7. GEOMETRY AND MEASUREMENT

 Polygons
 Polygon Creature Project
 Area of a Parallelogram
 Area of Parallelogram
 Area of Triangles
 Area of Composite Figures
 Area of Composite Figures
 Area of Composite Figures
 Project: Geometry and Measurement Performance Task A

81. What type of triangle can a right triangle be?

scalene

acute

obtuse

isosceles

82. What type of triangle is this?

acute

scalene

27
Year 6/Term 2/Unit 1
 equilateral

right

83. All rectangles are _____.

parallelograms

rhombuses

squares

quadrilaterals

84. A quadrilateral has no right angles, and two pair of congruent, parallel
sides. What is the figure?

square

rectangle

rhombus

parallelogram

85. What is the area of parallelogram ABDC?

7 cm 2

9 cm 2

12 cm 2

12.25 cm 2

86. What is the area of triangle ABD?

28
Year 6/Term 2/Unit 1
 7 cm 2

3.5 cm 2

6 cm 2

4.5 cm 2

87. If the area of the parallelogram is 15 cm 2, what is the area of the green
triangle?

30 cm 2

15 cm 2

7.5 cm 2

8 cm 2

88. What is the height of the triangle?

2 units

3 square units

3 units

can't be determined

29
Year 6/Term 2/Unit 1
 89. The area of a triangle is 18 square feet. If the base is 3 feet, what is the
height of the triangle?

6 feet

3 feet

12 feet

9 feet

90. The area of a rectangle is 51 square inches. If the width of the rectangle
is 6 inches, what is the length?

19.5 inches

13 inches

9 inches

8.5 inches

91. Steve is adding wallpaper to a living room wall and he needs to know
how much wallpaper to buy. If the wall is 8.5 feet tall and 12.5 wide, how
much wallpaper should he buy?

106.25 ft 2

96.25 ft 2

42 ft

108 ft 2

92. What is the area of the triangle?

15 cm 2

14 cm 2

12 cm 2
30
Year 6/Term 2/Unit 1
 24 cm 2

93. What is the area of the trapezoid?

88 in 2

128 in 2

96 in 2

48 in 2

94. What is the area of the composite figure?

84 m 2

72 m 2

108 m 2

96 m 2

95. What is the area of the hexagon?

31
Year 6/Term 2/Unit 1
 60 m 2

80 m 2

100 m 2

120 m 2

96. What is the measurement for this angle?

30 degrees

150 degrees

34 degrees

155 degrees

97. Explain how to determine the angle measurement for this angle.

32
Year 6/Term 2/Unit 1
Unit: 7. GEOMETRY AND MEASUREMENT
 Solid Figures
 Solid Figures Around You
 Volume
 More Volume
 Finding Volumes

98. Which solid figure has one polygon base?

pyramid

cone

cylinder

prism

99. Which solid figure has seven vertices?

heptagonal prism
33
Year 6/Term 2/Unit 1
 hexagonal pyramid

triangular prism

octagonal pyramid

100. What is the name of this solid figure?

rectangular pyramid

cylinder

triangular prism

rectangular prism

101. Which solid figure has nine edges?

rectangular pyramid

octagonal pyramid

rectangular prism

triangular prism

102. What is the volume of the rectangular prism?

64 m3

128 m3

256 m3
34
Year 6/Term 2/Unit 1
 288 m3

103. A rectangular prism is 4 inches long, 6 inches wide, and has a

height of 5 inches. What is its volume?

60 in3

120 in3

148 in3

240 in3

104. A cube is 6 feet on each side. What is its volume?

36 ft3

96 ft3

108 ft3

216 ft3

105. Which right rectangular prism does not have a volume of 48 cubic
centimeters?
l = 4 centimeters, w = 3 centimeters, h = 4 centimeters

l = 12 centimeters, w = 2 centimeters, h = 2 centimeters

l = 2 centimeters, w = 4 centimeters, h = 6 centimeters

l = 3 centimeters, w = 4 centimeters, h = 6 centimeters

106. Suppose each cube in this figure is a -inch cube. Select all that
are true.

35
Year 6/Term 2/Unit 1
 The dimensions of this prism are 3 inches × 2 inches × 2 inches.

There are 96 cubes in the prism.

The volume of this prism with -inch unit cubes is the volume of the prism with 1-
inch cubes.

The volume of this prism is 15 cubic inches.

107. Morgan works for a company that ships packages and must
measure the size of each box that needs to be shipped. Morgan
measures a box and finds the length is 4.5 inches, the width is 9 inches,
and the height is 6.5 inches. What is the volume of the box? [Type your
answer as a number. Do not round.]

a0
cubic inches

108. The cargo area of a truck is 8 feet long, 6 feet wide, and 10

feet high. The volume of the cargo area is cubic feet.

109. What is the volume of a shipping cube with dimensions of 2

feet?

6 cubic feet

15 cubic feet

36
Year 6/Term 2/Unit 1
 8 cubic feet

110. Identify this prism and describe it using the following vocabulary
terms: base, edge, face, and vertex.

111. Describe or show two different ways to find the volume of a right
rectangular prism with dimensions of 9 centimeters by 7 centimeters by
12 centimeters.

112. Explain the difference between finding the volume of this right

rectangular prism with whole unit cubes and with -unit cubes.

37
Year 6/Term 2/Unit 1
Unit: 7. GEOMETRY AND MEASUREMENT
 Surface Area of Rectangular Prisms
 Finding Surface area of Rectangular Prism Object
 Surface Area of Triangular Prisms
 Surface Area of A Triangular Prism Object Around You
 Surface Area of Pyramids
 Surface Area of Pyramid Object Around You
 Project: Geometry and Measurement Performance Task B

113. What is the surface area of the rectangular prism?

38
Year 6/Term 2/Unit 1
 128 m2

144 m2

256 m2

288 m2

114. A rectangular prism is 3 inches long, 5 inches wide, and has a

height of 6 inches. What is its surface area?

63 in2

90 in2

120 in2

126 in2

115. In the net of a rectangular prism, each square of the grid is 1

square meter. What is the surface area of the prism?

172 m2

96 m2

108 m2

216 m2

116. A certain rectangular prism has a height of 6 m, a length of 5 m,

and a width of 4 m. Give the dimensions of a second rectangular prism
that will have the same surface area of the first one.

39
Year 6/Term 2/Unit 1
 117. Which expressions will help you find the surface area of this right
triangular prism? Select all that apply.

5 × 11

11 × 3

4 × 11

×3×5

118. Find the surface area of this triangular prism.

144 square centimeters

138 square centimeters

40
Year 6/Term 2/Unit 1
 156 square centimeters

132 square centimeters

119.
The base of this prism is triangle.

120. Find the lateral surface area of this prism.

40 square meters

3 square meters

60 square meters

25 square meters

121. Find the total surface area of this prism. [Type your answer as a
number.]
a0
square meters

41
Year 6/Term 2/Unit 1
 122. Which of the following best describes the pyramid represented by
this net?

square pyramid

rectangular pyramid

triangular pyramid

tetrahedron

42
Year 6/Term 2/Unit 1
 123. Find the surface area of the pyramid represented by this net.
[Type your answer as a number.]

a0
square centimeters

124. A toy pyramid has the dimensions shown below. The base of the
pyramid is an equilateral triangle. What is the area of the base of this
pyramid?

21 cm 2

42 cm 2

31.5 cm 2

27 cm 2

43
Year 6/Term 2/Unit 1
 125. A toy pyramid has the dimensions shown below. The base of the
pyramid is an equilateral triangle. What is the surface area of this
pyramid?

48 cm2

129 cm2

102 cm2

81 cm2

126. Using complete sentences, describe the net of a rectangular

prism with a length of 12 centimeters, a width of 9 centimeters, and a
height of 5 centimeters.

127. Use complete sentences to describe the net of a triangular

pyramid with an equilateral triangle for a base.

44
Year 6/Term 2/Unit 1
 45
Year 6/Term 2/Unit 1