content.njctl.orgcontent.njctl.org/courses/math/5th-grade-math/algebraic... · Web viewA company rents bicycles for a fee of $10 plus $4 per hour of use. Write an algebraic expression

5th Grade PMIAlgebraic Concepts Classwork and Homework

Order of Operations

ClassworkSimplify by using the Order of Operations.

1. 14 – 7 x 22. 8 + 9 – 23. 9 – 5 – 8 ÷ 24. 4 x 13 + 51 ÷ 3

5. 8 x 2 – 2 – 7 6. 28 – 4 ÷ 27. 4 + 11 x 5 - 48. 17 + 48 ÷ 3 – 7

HomeworkSimplify by using the Order of Operations.

9. 20 + 7 x 1510. 7 x 5 + 311. 12 – 3 + 10 x 312. 67 – 3 x 19 – 4

13. 7 - 7 + 9 x 1014. 38 – 6 ÷ 215. 5 x 9 – 10 ÷ 516. 58 – 8 – 10 ÷ 10 – 6

Grouping Symbols

ClassworkSimplify by using the Order of Operations.

17. (12 – 7) x 218. 8 + (9 – 2)19. (9 – 5) – (8 ÷ 2)20. 4 x 13 + 51 ÷ 321. (8 x 2 – 2) – 7 22. [(28 – 4) ÷ 2]

23. [4 x (11 – 5)] + 424. [(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)

NJ Center for Teaching and Learning ~ 1 ~ www.njctl.org

HomeworkSimplify by using the Order of Operations.

30. (20 + 7) – 1531. 7 x (5 + 3)32. (12 – 3) + (10 x 3)33. 67 – 3 x 19 – 434. (7 x 7 – 9) – 1035. [(38 – 2) ÷ 6]

36. [5 x (9 – 4)] – 537. [(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)] + 1441. {[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

ClassworkWrite the algebraic expression for each phrase.43. 16 less than 444. the sum of 3 and 1545. the quotient of 36 and 1846. ten increased by nine47. seven times two and a half48. 21 divided by 349. 50 decreased by 2950. 20 divided by 451. 17 less than the product of 3 and 252. the quotient of 8 divided by two minus four

Write a phrase for each algebraic expression.

53. 90 – 4454. 279 + 355. 30 ÷ 656. 36 – 457. 2(1/4)

HomeworkWrite the algebraic expression for each phrase.NJ Center for Teaching and Learning ~ 2 ~ www.njctl.org

58. 4 subtracted from 8259. 1 plus 9960. the quotient of 400 and 2061. sixteen increased by five62. double one-half63. 20 divided by 564. forty-five decreased by forty65. 55 divided by 1166. six times the sum of three and two67. The quotient of twenty-one and by seven minus ten

Write a phrase for each algebraic expression.

68. 100 – 7269. 457 + 1470. 24 ÷ 871. 98 – 072. 3(5)

Writing & Interpreting Expressions Application Problems

Classwork73. 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 +190c. 190 – c

b. c–190d.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 + 5c. 125 x 5

b. 125 – 5d. 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 TablesClassworkComplete each input(x) output(y) table using rule given.

81. Rule: Add 8

Input (x) Output (y)0 81 92


3 114

82. Rule: Multiply 4


Input (x) Output (y)1 4

1668 321012 48

83. Rule: Divide by 5

Input (x) 40 30 20 10Output (y) 8 6 4

84. Rule: Subtract 9

Input (x) 10 14 30 9Output (y) 1 5

85. Rule: Multiply 2, then Add 3

Input (x) 3 5 7 9 11 13Output

(y)9 17 25

Homework

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

86. Rule: Subtract 4

Input (x) Output (y)20 1625 213035 31

87. Rule: Divide by 10


Input (x) Output (y)10 120 2

340


Input (x) 1 3 5 7Output (y) 24 56 72

89. Rule: Add 12

Input (x) 3 6 9 12 15Output

(y)15 18 24 30

90. Rule: Divide by 3, then Subtract 2

Input (x) 30 60 90 120 150 180Output

(y)8 18 28 48


Input (x) 2 9 7 10Output

(y)40 100 180 60 140

ClassworkStudy the table; choose the correct function.

92.

X Y1 133 155 17

7 19

A. y = x + 2B. y = x + 12C. y = 2x

93.

X Y 6 1


12 218 324 4

A. y = x ÷ 6B. y = x + 1C. y = 6x

94.

x Y9 187 146 123 6

A. y = x – 6B. y = 2xC. y = x ÷ 2


95.

x 20 24 28 32 36y 17 21 25 29 33

A. y = x – 3B. y = x + 3C. y = x + 4

96.

x 4 10 2 7 2y 14 32 8 23 8A. y = 10x – 4B. y = 3x + 2C. 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.


Boxes (b) Animals (a)1 42 83 124 165 2010 ?

Videos (v) 1 2 4 5 6Cost (c) 5 10 20 25 ?

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

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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HomeworkStudy the table; choose the correct function.

100.

x Y10 612 814 10

16 12

A. y = x – 4B. y = x + 2C. y = x – 2

101.

X Y2 14 26 38 4

A. y = x + 1B. y = x ÷ 2C. y = 2x


102.

X Y1 44 169 3612 48

A. y = 3xB. y = 4xC. y = x + 4


103.

x 3 6 9 12 15y 13 16 19 22 25

A. y = x - 10B. y = x + 3C. y = x + 10

104.

x 4 15 7 10 30y 4 26 10 16 56

A. y = 4x – 2B. y = 2x – 4C. 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, ____, ____, ____, …


Number of Tricycles (t)

Number of Wheels (w)

1 32 63 94 125 ?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

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, ____, ____, ____, …

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 PlaneClasswork

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. NJ Center for Teaching and Learning ~ 15 ~ www.njctl.org

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

this table?

Gallon of gas (x) 0 1 2 3Distance 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. -14b. 22c. -8d. 4

2. Evaluate 25 - (4 ÷ 2)

a. 10.5b. 27c. 23d. 19

3. Evaluate (9 x 8) + (3 x 7)

a. 93b. 693c. 83d. 35

4. Evaluate 1 x (5 + 13) x 3

a. 54


b. 18c. 44d. 28

5. Evaluate 63 ÷ (3 + 4)

a. 19b. 25c. 7d. 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. multiplicationb. exponentsc. 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 3b. 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 NJ Center for Teaching and Learning ~ 23 ~ www.njctl.org

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)

0123

Rule: Multiply by 2


Input (x)

Output (y)

0123

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.

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. 02. 153. 0

4. 695. 126. 267. 558. 269. 125


10. 3811. 3912. 613. 9014. 3515. 4316. 4317.1018.1519.020.6921.722.1223.2824.525.2826.2227.3928.37629.12 x (2 + 8)30.1231.5632.3933.634.3035.136.2037.1038.5539.3240.1441.1542. (50 – 5) x 3 + 743.4 – 1644.3 + 1545.36 ÷ 1846.10 + 947.7(2 ½) 48.21 ÷ 349.50 – 2950.20 ÷ 451. [3(2)] - 17

52. (8 ÷ 2) – 453.90 decreased by 4454.279 and 3 more55.The quotient of 30 and 656.36 decreased by 457.Double one-fourth58.82 – 459.1 + 9960.400 ÷ 2061.16 + 562.2(1/2)63.20 ÷ 564.45 – 4065.55 ÷ 1166.6 x (3 + 2)67. (21 ÷ 7) -1068.100 reduced by 7269.14 more than 45770.The quotient of 24 and 871.98 decreased by 072.3 times 573.10(8) + 474. A75. B76.Answers will vary77. 71 – 778. C79. D80.Answers will vary81.10 / 1282.4 / 24 / 4083.284.21 / 085.13 / 2186.2687.30 / 488.8 / 40 / 989.21 / 27 / 1890.38 / 5891.5 / 3 / 20092.B93.A


94.B95.A96.B97.Y = 4x 4098.Y = 5x 3099.

1 2 3 412

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. A101. B102. B103. C104. B105. Y = 3x 15106. Y = 1.25x $1.25107. 0, 12, 24, 36, …

0, 6, 12, 18, …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. C109. C110. Graph A111. Graph A112. Table A113. B114.

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. B118. A119. 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. b2. c3. a 4. a 5. d6. a7. b8. c9. c10.a11.a12.c 13.b14.a15.a


1 2 3 44 5 6 7

16.b17.a18.c19.a 20.b 21.522.2423.6024.18 25.

a. 53b. 120c. 104

26.3x2127.18 – 928.71 + 1829.2(7) 30.y = x + 6 31.y = 2x - 1 32.y = x/2 + 2 or y = 1/2x + 233. 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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content.njctl.orgcontent.njctl.org/courses/math/5th-grade-math/algebraic... · Web viewA company rents bicycles for a fee of $10 plus $4 per hour of use. Write an algebraic expression