5th Grade PMI Algebraic Concepts Classwork and Homework

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5th Grade PMI

Algebraic Concepts Classwork and Homework

Order of Operations

Classwork

Simplify by using the Order of Operations.

1. 14 – 7 x 2

2. 8 + 9 – 2

3. 9 – 5 – 8 ÷ 2

4. 4 x 13 + 51 ÷ 3

5. 8 x 2 – 2 – 7

6. 28 – 4 ÷ 2

7. 4 + 11 x 5 - 4

8. 17 + 48 ÷ 3 – 7

Homework


9. 20 + 7 x 15

10. 7 x 5 + 3

11. 12 – 3 + 10 x 3

12. 67 – 3 x 19 – 4

13. 7 - 7 + 9 x 10

14. 38 – 6 ÷ 2

15. 5 x 9 – 10 ÷ 5

16. 58 – 8 – 10 ÷ 10 – 6

Grouping Symbols

Classwork


17. (12 – 7) x 2

18. 8 + (9 – 2)

19. (9 – 5) – (8 ÷ 2)

20. 4 x 13 + 51 ÷ 3

21. (8 x 2 – 2) – 7

22. [(28 – 4) ÷ 2]

23. [4 x (11 – 5)] + 4

24. [(48 – 3) + 5] ÷ (17 – 7)

25. 2 x [(14 – 5) + (10 ÷ 2)]

26. {3 + [(15 x 2) – 11]}

27. {[6 x (20 – 5 x 3)] + 9}

28. {[9 x (2 + 9) – 5]} x 4

29. Which expression equals 132?

(12 x 2) + 8 or 12 x (2 + 8)

Homework


30. (20 + 7) – 15 31. 7 x (5 + 3)


32. (12 – 3) + (10 x 3)

33. 67 – 3 x 19 – 4

34. (7 x 7 – 9) – 10

35. [(38 – 2) ÷ 6]

36. [5 x (9 – 4)] – 5

37. [(58 – 8) – 10] ÷ (10 – 6)

38. 5 x [(10 – 4) + (15 ÷ 3)]

39. {2 + [(20 x 2) – 10]}

40. {[7 x (10 – 5 x 2)] + 14

41. {[10 x ( 7 – 5 + 1)]} – 15

42. Which expression equals 142

(50 – 5) x 3 + 7 or 50 – 5 x (3 + 7)

Writing & Interpreting Expressions

Classwork

Write the algebraic expression for each phrase.

43. 16 less than 4

44. the sum of 3 and 15

45. the quotient of 36 and 18

46. ten increased by nine

47. seven times two and a half

48. 21 divided by 3

49. 50 decreased by 29

50. 20 divided by 4

51. 17 less than the product of 3 and 2

52. the quotient of 8 divided by two minus four

Write a phrase for each algebraic expression.

53. 90 – 44

54. 279 + 3

55. 30 ÷ 6

56. 36 – 4

57. 2(1/4)

Homework

Write the algebraic expression for each phrase.

58. 4 subtracted from 82

59. 1 plus 99

60. the quotient of 400 and 20

61. sixteen increased by five


62. double one-half

63. 20 divided by 5

64. forty-five decreased by forty

65. 55 divided by 11

66. six times the sum of three and two

67. The quotient of twenty-one and by seven minus ten

Write a phrase for each algebraic expression.

68. 100 – 72

69. 457 + 14

70. 24 ÷ 8

71. 98 – 0

72. 3(5)

Writing & Interpreting Expressions Application Problems

Classwork

73. A company rents bicycles for a fee of $10 plus $4 per hour of use.

Write an algebraic expression for the total cost in dollars for renting a

bicycle for eight hours.

74. The female lion at a zoo weights 190 pounds more than the female cheetah. Let c represent the weight in pounds of the cheetah. Which expression gives the weight in pounds of the lion? a. c +190 c. 190 – c

b. c–190 d.190c

75. Tickets to a play cost $8 each. Which expression gives the ticket cost

in dollars for a group of g girls and b boys? a. 8+(g+b) c. 8+(gxb)

b. 8x(g+b) d. 8x(gxb)

76. Write a scenario that can be represented by the expression 2 (8 + 4).

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Homework

Choose the correct expression to solve the problem. 77. Mark is 71 inches tall. Suzanne is 7 inches shorter than Mark. Write

an expression that represents Suzanne’s height in inches.

78. A subway train has 5 cars. Each car can carry 125 passengers. Which

expression gives the number of passengers the train can carry? a. 125 + 5 c. 125 x 5

b. 125 – 5 d. 125 ÷ 5

79. Nessa and Lisa share lemonade and an order of nachos. Lemonade

costs $2 and nachos cost $6. Which expression gives the amount in dollars each girl will pay if they split the cost evenly? a. 2 + (6 x 2) b. (2 + 6) x 2

c. 2 + (6 ÷ 2) d. (2 + 6) ÷ 2

80. Write a scenario that can be represented by the expression 2 (8 + 4).

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Function Tables

Classwork

Complete each input(x) output(y) table using rule given.

81. Rule: Add 8

Input (x) Output (y)

0 8

1 9

2

3 11

4

82. Rule: Multiply 4


1 4

16

6

8 32

10

12 48


83. Rule: Divide by 5

Input (x) 40 30 20 10

Output (y) 8 6 4

84. Rule: Subtract 9

Input (x) 10 14 30 9

Output (y) 1 5

85. Rule: Multiply 2, then Add 3

Input (x) 3 5 7 9 11 13

Output (y)

9 17 25

Homework

Complete each input (x) output (y) table using rule given.

86. Rule: Subtract 4


20 16

25 21

30

35 31

87. Rule: Divide by 10


10 1

20 2

3

40


Input (x) 1 3 5 7

Output (y) 24 56 72

89. Rule: Add 12

Input (x) 3 6 9 12 15

Output (y)

15 18 24 30

90. Rule: Divide by 3, then Subtract 2

Input (x) 30 60 90 120 150 180

Output (y)

8 18 28 48



Input (x) 2 9 7 10

Output (y)

40 100 180 60 140

Classwork

Study the table; choose the correct function.

92.

X Y

1 13

3 15

5 17

7 19

A. y = x + 2

B. y = x + 12

C. y = 2x

93.

X Y

6 1

12 2

18 3

24 4

A. y = x ÷ 6

B. y = x + 1

C. y = 6x

94.

x Y

9 18

7 14

6 12

3 6

A. y = x – 6

B. y = 2x

C. y = x ÷ 2

95.

x 20 24 28 32 36

y 17 21 25 29 33

A. y = x – 3

B. y = x + 3

C. y = x + 4

96.

x 4 10 2 7 2

y 14 32 8 23 8

A. y = 10x – 4

B. y = 3x + 2

C. y = 2x + 3


Write an equation using the table, and answer the question.

97.

Equation: __________________________________

If each gift box contained 4 stuffed animals, what would be the number

of animals in ten gift boxes? ___________________________

98.

Equation: __________________________________

Redbox video rental charges $5 to rent a video. What is the total cost to

rent six videos? _________________________

99. The table below shows the

number of cards in Flipe’s

baseball card collection each

week.

Given the rule add 2 and

starting at zero complete the

table below.

0

2

The table below shows the

number of cards in Ryan’s

baseball card collection each

week.

Given the rule add 4 and starting

at zero complete the table below.

0

2

Boxes (b) Animals (a)

1 4

2 8

3 12

4 16

5 20

10 ?

Videos (v) 1 2 4 5 6

Cost (c) 5 10 20 25 ?


Look at both of the tables once they are complete. Explain the

relationship between the corresponding terms, and how you can use

that to compare Flipe and Ryan’s baseball card collections.

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Homework

Study the table; choose the correct function.

100.

x Y

10 6

12 8

14 10

16 12

A. y = x – 4

B. y = x + 2

C. y = x – 2

101.

X Y

2 1

4 2

6 3

8 4

A. y = x + 1

B. y = x ÷ 2

C. y = 2x

102.

X Y

1 4

4 16

9 36

12 48

A. y = 3x

B. y = 4x

C. y = x + 4

103.

x 3 6 9 12 15

y 13 16 19 22 25

A. y = x - 10

B. y = x + 3

C. y = x + 10

104.

x 4 15 7 10 30

y 4 26 10 16 56

A. y = 4x – 2

B. y = 2x – 4

C. y = 2x


105. Write an equation using the table, and answer the question.

Equation:

______________________

If one tricycle has 3 wheels, how

many wheels are there for five

tricycles?

106.

Equation: __________________________________

The table shows the relationship between the length of a phone call

in minutes and the cost of the call. What is the cost of one minute?

107. The table below shows the

number of minutes until the

next #33 city bus arrives.

Given the rule add 12 and

starting at 0, complete the

pattern below.

0, ____, ____, ____, …

The table below shows the

number of minutes until the next

#24 city bus arrives.

Given the rule add 6 and starting

at 0, complete the pattern below.

0, ____, ____, ____, …

Number of Tricycles (t)

Number of Wheels (w)

1 3

2 6

3 9

4 12

5 ?

6 18

Length of call in minutes (L)

1 2 3 4 5

Cost of call (C)

? $2.50 $3.75 $5.00 $6.25


Look at both of the patterns once they are complete. Explain the

relationship between the corresponding terms, and how you can use

that to compare the frequency of each bus’ arrival.

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Graphing Patterns & Relationships in the Coordinate Plane

Classwork

108. Which ordered pair is on the graph of the function represented by this

table?

Week (x) 0 1 2 3

$ Saved (y) 25 30 35 40

A (25, 0)

B (35, 2)

C (2, 35)

109.


110.

111.


112.

113. Which best describes the relationship between the cost of cooling a

home and the outside temperature?

A. Horizontal line

B. An increasing straight line

C. A decreasing straight line

D. Vertical line

114. Graph the following points on line a and b. Label each line.

Line a Line b

(1,2) (1,3)

(2,4) (2,4)

(3,6) (3,5)

(4,8) (4,6


115. Compare line a and line b from the previous problem. Explain the

difference between the rule for line a and the rule for line b.

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Homework

Complete the following.

116. Which ordered pair is on the graph of the function represented by

this table?

Gallon of gas (x) 0 1 2 3

Distance in miles (y) 0 5 50 75

A. (3, 50)

B. (1, 25)

C. (75, 3)

117.


118.

119.


120. Graph the following points on line a and b. Label each line.

Line a Line b

(1,2) (1,0.5)

(2,4) (2,1)

(3,6) (3,1.5)

(4,8) (4,2)

121. Compare line a and line b from the previous problem. Explain the

relationship between the y-coordinates in line a to the corresponding

coordinates in line b.

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Algebraic Concepts Unit Review

Multiple Choice Questions

1. Evaluate (7 - 3) + 18 a. -14 b. 22 c. -8 d. 4 2. Evaluate 25 - (4 ÷ 2) a. 10.5 b. 27 c. 23 d. 19 3. Evaluate (9 x 8) + (3 x 7) a. 93 b. 693 c. 83 d. 35 4. Evaluate 1 x (5 + 13) x 3 a. 54 b. 18 c. 44 d. 28 5. Evaluate 63 ÷ (3 + 4) a. 19 b. 25 c. 7 d. 9 6. According to order of operations, what would come first? a. multiplication b. subtraction 7. According to order of operations, what would come first?


a. multiplication b. exponents c. addition 8. Which expression equals 0? a. 64 ÷ 8 - 2 x 4 b. (64 ÷ 8 - 2) x 4 c. 64 ÷ (8 - 2 x 4) d. 64 ÷ (8 - 2) x 4 9. Which expression equals 16? a. 45 ÷ 9 + (3 x 2) b. 45 ÷ (9 + 3) x 2 c. (45 ÷ 9 + 3) x 2 d. 45 ÷ 9 + 3 x 2 10. What expression equals 33? a. {[5 x (4 + 3) - 2] ÷ 1} b. (5 x 4) + [3 - 2] ÷ 1) c. {5 x [4 + 3 - (2 ÷ 1)]} d. [5 x 4 + {3 - 2} ÷ 1] 11. Which phrase is the correct algebraic expression: five more than 7

a. 7 + 5 b. 5 + 7

c. 7 - 5 d. 5(7)

12. Which phrase is the correct algebraic expression: three times the difference four less

than five

a. 3(4 - 5) b. 3(5) - 4

c. 3(5 - 4) d. 12 - 5

13. The phrase 13 less than four, is the same as 13 - 4.

a. True b. False

14. The phrase 72 ÷ 6 is the same as seventy-two divided by six.

a. True b. False 15. For a school project, 3 students each did the same amount of parts for the project.

There were 12 parts in all. Which expression represents how many parts each student was responsible for?

a. 12 3


b. 3 + 12 c. 3 x 12 d. 12 - 3

16. Which graph shows the correct function? y = x + 3

A. B. 17. Which graph shows the correct function? y = 3x + 1

A. B.

18. Which of the following points is on the line?

a. (4,2) b. (0,1) c. (2,4) d. (3,4)



a. (-1,-3) b. (-3, -1) c. (1, 3) d. (-1, 3)


a. (1, 2) b. (2, 1) c. (0, 2) d. (2, -1)

Short Constructed Response Questions

21. 7 + 2 x (5 - 6) = ___________________ 22. (12 + 3) ÷ 5 x 8 = ___________________ 23. 4 x (22 -11) + 16 =___________________ 24. ( 6 x 4 - 0) - 6 = _____________________ 25. Evaluate the expression. Rewrite each step. a. 81 - [(6 x 3) + (5 x 2)]


b. 6 x [(9 ÷ 3) + 17] c. 20 + {12 x [(17 - 2) - (6 + 2)]} Write an expression to represent the following problems: 26. Sophia bought three of each kind of candy in the sweet shop. If there were 21 kinds

of candy in the sweet shop, how many pieces of candy did Sophia buy? _____________________________________________ 27. In the pizzeria, Lewis sold nine fewer pizzas then Anthony. If Anthony sold 18

pizzas, how many pizzas did Lewis sell? _____________________________________________ 28. Lucky collected 18 new stamps for his collection. If he had 72 yesterday, how many

stamps are in the collection now? _____________________________________________ 29. Kushboo exercised 2 times a day for 1 week. How many times did Kushboo work

out? _____________________________________________ Write a function or rule for the following tables:

30.

x y

1 7

2 8

3 9

4 10

31.

x y

0 0

5 9

8 15

23 45

32.

x y

6 5

12 8

18 11

24 14


Extended Constructed Response Questions 33.

a. What is the correct order of operations? (Include grouping symbols)

b. Simplify. {3 + [(6 + 4) ÷ 2] - 1} - {60 -[22 +4(3 x 3)]}


34.

x y

2

4 14

6 20

8

10 32

a. What are the missing values in the table?

b. What is the rule for this function?

c. Graph the function.


d. What would the value of x be if y was 44?

35. a. Complete the Function Table by folllowing the rules given for each table.

Rule: Multiply by ½

Input (x)

Output (y)

0

1

2

3

Rule: Multiply by 2

Input (x)

Output (y)

0

1

2

3

b. Graph and label the coordinate pairs from Table A. Connect the points and

label the line a. Graph and label the coordinate pairs from Table B. Connect

the points and label the line b.

*Indicated problem derived from Engage NY NJ Center for Teaching and Learning www.njctl.org

c. Describe the relationship between the y-coordinates in Table A and Table B

that have the same x-coordinate.

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Answer Key

Algebraic Concepts

1. 0

2. 15

3. 0

4. 69

5. 12

6. 26

7. 55

8. 26

9. 125

10. 38

11. 39

12. 6

13. 90

14. 35

15. 43

16. 43

17. 10

18. 15

19. 0

20. 69

21. 7

22. 12

23. 28

24. 5

25. 28

26. 22

27. 39

28. 376

29. 12 x (2 + 8)

30. 12

31. 56

32. 39

33. 6

http://www.engageny.org/sites/default/files/resource/attachments/math-g5-m2-full-module.pdf

http://www.njctl.org/


34. 30

35. 1

36. 20

37. 10

38. 55

39. 32

40. 14

41. 15

42. (50 – 5) x 3 + 7

43. 4 – 16

44. 3 + 15

45. 36 ÷ 18

46. 10 + 9

47. 7(2 ½)

48. 21 ÷ 3

49. 50 – 29

50. 20 ÷ 4

51. [3(2)] - 17

52. (8 ÷ 2) – 4


54. 279 and 3 more

55. The quotient of 30 and 6


57. Double one-fourth

58. 82 – 4

59. 1 + 99

60. 400 ÷ 20

61. 16 + 5

62. 2(1/2)

63. 20 ÷ 5

64. 45 – 40

65. 55 ÷ 11

66. 6 x (3 + 2)

67. (21 ÷ 7) -10

68. 100 reduced by 72

69. 14 more than 457

70. The quotient of 24 and 8


72. 3 times 5

73. 10(8) + 4

74. A

75. B

76. Answers will vary

77. 71 – 7

78. C

79. D

80. Answers will vary

81. 10 / 12

82. 4 / 24 / 40

83. 2

84. 21 / 0

85. 13 / 21

86. 26

87. 30 / 4

88. 8 / 40 / 9

89. 21 / 27 / 18

90. 38 / 58

91. 5 / 3 / 200

92. B

93. A

94. B

95. A

96. B

97. Y = 4x 40

98. Y = 5x 30

99.

1 2 3 4

12 3 4 5

The values in the 2nd table are 2

more than the corresponding

values in the 1st table. This

means that, each week, Ryan

has 2 more cards in his collection

than Flipe.

100. A

101. B

102. B

103. C

104. B

105. Y = 3x 15

106. Y = 1.25x $1.25

107. 0, 12, 24, 36, …

0, 6, 12, 18, …

1 2 3 4

4 5 6 7




The values in the 2nd pattern are

1/2 of the corresponding values

in the 1st pattern. This means

that, the #24 bus comes twice as

often as the #33 bus.

108. C

109. C

110. Graph A

111. Graph A

112. Table A

113. B

114.

115. The difference is the operation.

The rule for line a is times 2,

while the rule for line b is add 2.

116.

117. B

118. A

119. Graph A

120. 121. The y-coordinates in line b are

¼ the value of the corresponding

coordinates in line a.

122. Table B

Answer Key – Unit Review 1. b

2. c 3. a 4. a 5. d 6. a 7. b 8. c 9. c 10. a 11. a 12. c 13. b 14. a 15. a 16. b 17. a 18. c 19. a 20. b 21. 5 22. 24 23. 60 24. 18 25.

a. 53 b. 120 c. 104

26. 3x21 27. 18 – 9 28. 71 + 18 29. 2(7) 30. y = x + 6 31. y = 2x - 1 32. y = x/2 + 2 or y = 1/2x + 2 33. p md as, 5 34. a = 8

b = 26 rule: y = 3x + 2 graph of rule

35.

a.

b.




c. The y-coordinates in Table B

are 4 times bigger than those in

Table A.



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5th Grade PMI Algebraic Concepts Classwork and Homework