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NJ Center for Teaching and Learning ~ 1 ~ www.njctl.org
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
Simplify by using the Order of Operations.
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
Simplify by using the Order of Operations.
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
Simplify by using the Order of Operations.
30. (20 + 7) – 15 31. 7 x (5 + 3)
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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
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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
Input (x) Output (y)
1 4
16
6
8 32
10
12 48
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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
Input (x) Output (y)
20 16
25 21
30
35 31
87. Rule: Divide by 10
Input (x) Output (y)
10 1
20 2
3
40
88. Rule: Multiply 8
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
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91. Rule: Multiply 20
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
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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 ?
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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
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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
NJ Center for Teaching and Learning ~ 10 ~ www.njctl.org
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.
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110.
111.
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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
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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.
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118.
119.
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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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NJ Center for Teaching and Learning ~ 16 ~ www.njctl.org
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?
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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
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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)
19. Which of the following points is on the line?
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a. (-1,-3) b. (-3, -1) c. (1, 3) d. (-1, 3)
20. Which of the following points is on the line?
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)]
NJ Center for Teaching and Learning ~ 20 ~ www.njctl.org
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
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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)]}
NJ Center for Teaching and Learning ~ 22 ~ www.njctl.org
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.
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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
*Indicated problem derived from Engage NY NJ Center for Teaching and Learning 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
53. 90 decreased by 44
54. 279 and 3 more
55. The quotient of 30 and 6
56. 36 decreased by 4
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
71. 98 decreased by 0
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
*Indicated problem derived from Engage NY NJ Center for Teaching and Learning www.njctl.org
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.
*Indicated problem derived from Engage NY NJ Center for Teaching and Learning www.njctl.org
c. The y-coordinates in Table B
are 4 times bigger than those in
Table A.