what makes you tap your feet? - davis school · pdf filewhat makes you tap your feet? ......

Chapter 2 Assignments • 27

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What Makes You Tap Your Feet?Introduction to Direct Variation

1. In 2010, Chevrolet produced 12,194 Corvettes. That means they made Corvettes at a rate of about

34 cars per day.

a. How many Corvettes did Chevrolet produce in 7 days? Show your work.

b. How many days did it take Chevrolet to produce 1190 Corvettes? Show your work.

c. Complete the table.

Time (days) Number of Corvettes

7

21

1 __ 2

1190

952

Lesson 2.1 Assignment

Name ________________________________________________________ Date _________________________

28 • Chapter 2 Assignments

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Lesson 2.1 Assignment page 2

d. Use the data in the table to complete the graph.

y

x4 8 12 16 20 24 28 32 36

Time (days)

120

240

360

480

600

720

840

960

1080

Num

ber

of C

orve

ttes

Corvette Production

e. Is the data in the graph discrete or continuous? Explain your reasoning.

f. Does it make sense to connect the points in this graph? If so, connect them.

Explain your reasoning.

g. What is the ratio of Corvette production to time?

h. Does the number of Corvettes vary directly with time? Explain your reasoning.


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Name ________________________________________________________ Date _________________________

Building Bird Feeders Is for the Birds!Determining Equivalent Ratios

The student council at Camp Creek Middle School determine that 3 out of 4 students prefer that all

school assemblies be held on Friday afternoon.

1. If 200 students are surveyed, how many will prefer that school assemblies be held on Friday

afternoon? Explain how you determined your answer.

2. If 747 students prefer that school assemblies be held on Friday afternoon, how many students

were surveyed? Explain how you determined your answer.


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Analyze each table shown. Determine if the relationship is proportional. If the relationship is

proportional, calculate the equivalent ratio to justify your answer.

3. Of the 75 boys in the 7th grade class, 25 participate in at least one sport. Of the 120 girls in the

7th grade class, 30 participate in at least one sport.

7th Grade Class Plays Sports Total

Boys 25 75

Girls 30 120

4. Of the 210 boys in the 8th grade, 190 have a cell phone. Of the 168 girls in the 8th grade,

152 have a cell phone.

8th Grade Class Cell Phones Total

Boys 190 210

Girls 152 168

7718A_C2_Assign_CH02_027-048.indd 30 12/03/14 2:48 PM


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Name ________________________________________________________ Date _________________________

5. Of the 250 sixth graders, 75 said they went to the movies over the weekend. Of the 180 seventh

graders, 54 said they went to the movies over the weekend. Of the 200 eighth graders, 65 said

they went to the movies over the weekend.

Class Attended a Movie Total

6th Graders 75 250

7th Graders 54 180

8th Graders 65 200

6. In the town of Clover, 3 out of 5 citizens who are eligible to vote did so in the spring election.

a. Write an equation showing the relationship between the citizens who voted (v) and the citizens

who are eligible to vote (e) and the equivalent ratio.

b. Use the equation from part (a) to determine the number of citizens that voted in the spring

election if 400 citizens were eligible to vote.



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c. Use the equation from part (a) to determine the number of citizens that were eligible to vote in

the spring election if 180 actually voted.



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Name ________________________________________________________ Date _________________________

Kids Just Wanna Have Fun!Determining and Applying the Constant of Proportionality

1. Shilo is riding her bicycle across the state of Georgia to raise money for her favorite charity. The

distance (d ) in miles that she can travel varies directly with the length of time (t) in hours she

spends riding.

Assumethatherconstantofproportionalityis18.

a. Write an equation showing the proportional relationship between d and t using the

information given.

b. If Shilo rides for 3 hours, how far will she travel? Use your equation to show the

relationship between distance and time.

c. How long does it take Shilo to ride 6 miles? Use your equation to show the relationship

between distance and time.


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d. What does the constant of proportionality represent in this problem?

2. Maya’s construction company builds brick houses. The table shows the relationship between the

time Maya works and the number of bricks she can install.

Hours Worked Bricks Installed

8 1680

7 1470

6 1260

a. Define variables for the quantities that are changing in this problem situation.

b. Analyze the table to determine if the relationship is proportional. Explain your reasoning and

state a constant of proportionality if possible.

c. What does the constant of proportionality represent in this problem?

d. Write an equation showing the relationship between the number of hours worked, the number

of bricks installed, and the constant of proportionality.


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Name ________________________________________________________ Date _________________________

e. Use your equation from part (d) to determine how many bricks Maya can install in 5.5 hours.

Show your work.

f. Use your equation from part (d) to determine how many hours it will take Maya to install

840 bricks. Show your work.


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Solve each using the equation for the constant of proportionality, y __ x  5 k.

3. k 5 2 __ 7

and x 5 21 4. k 5 0.3 and y 5 18



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Name ________________________________________________________ Date _________________________

Stop that Speeding Snail?Using the Constant of Proportionality to Solve Proportions

1. Dudley and Bob monitored the distance their pet turtle could walk in a certain amount of time.

Their results are shown in the table. The table of values represents a proportional relationship.

Time (minutes) Distance (inches)

5 14.5

14 40.8

19 55.1

25 72.5

a. Define variables for the quantities that are changing in this problem situation.

b. How can you determine the constant of proportionality using the values in the table?

c. What is the constant of proportionality?



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2. Analyze each table or problem situation to determine if the relationship is proportional. State a

constant of proportionality if possible. Show your work.

a. Girls Boys

7 14

9 21

11 22

b. A baby blue whale weighed 5520 pounds at birth. After two days, the baby weighed 5710. After

14 days, the baby weighed 8180 pounds. Is there a constant of proportionality?


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Name ________________________________________________________ Date _________________________

The Man Who Ran from Marathon to AthensGraphing Direct Proportions

1. Tony is going into sixth grade in the fall. During the summer, he is required to read at least two

books from an approved reading list and to complete a mini-project to accompany each book.

Suppose the number of pages ( p) that Tony can read varies directly with the amount of time

(t) in hours he spends reading. Suppose the constant of proportionality relating the variables

p and t is 30.

a. Write an equation showing the relationship between the number of pages read and the time

spent reading. Assume that Tony always maintains the same rate of reading.

b. What does the constant of proportionality represent in this problem?

c. Complete the table showing the amount of time spent reading and the number of pages read

using your equation from part (a).

Time (in hours) Number of Pages Read

t p

0.5

37.5

60

2.5

3


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d. Graph the values in the table from part (c) on the coordinate plane shown. Graph the values of t

on the x-axis and the values of p on the y-axis.

1

20

40

60

80

2 3 4

90

10

30

50

70

Time (in hours)

Num

ber

of P

ages

Rea

d

p

t

e. Explain how the graph verifies that the number of pages Tony reads is directly proportional to

the amount of time he spends reading.

f. Interpret the meaning of the point (2.5, 75) on the graph.


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Name ________________________________________________________ Date _________________________

g. For each of the following points on the graph, form the ratio y-coordinate

____________ x-coordinate

in the table.

Then, simplify the ratio. What do you notice? What is significant about what you noticed?

x-coordinate y-coordinate y-coordinate

_____________ x-coordinate

0.5

37.5

60

2.5

3

2. Mariah is trying to improve her math skills over the summer. When she reads her math book, the

number of pages she can read depends on the difficulty of the concept being studied. Mariah

keeps track of the amount of time and the number of pages read during several study sessions

in the table.

Time (in hours) Number of Pages Read

0.5 5

0.75 7

1 10

1.5 8

2 12



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a. Graph each point from the table on the graph shown. Label the x- and y-axis and name

your graph.

1

4

8

12

16

2 3 4

18

2

6

10

14

b. What do you notice about the points you plotted?

c. Determine if there is a constant of proportionality. Pick two points from the graph to form

the ratio y-coordinate

____________ x-coordinate

.


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Name ________________________________________________________ Date _________________________

Racing to the Finish Line!Using Direct Proportions

1. Jameer works in a men’s clothing store. The amount of money (m) he makes is directly proportional

to the number of hours (h) he works.

a. Complete the table to show the amount of money Jameer earns for the different amounts of

time that he works.

Hours (h)Money (m)(in dollars)

3

56.25

6 75.00

7.5

b. Determine the constant of proportionality and interpret it in the context of the problem.

c. Write an equation showing the relationship between m and h.

d. How many hours does Jameer have to work to make $100?


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e. How much money does Jameer earn if he works 40 hours?

2. Henry knows that whenever he buys something he is charged a sales tax. This sales tax (t) varies directly with the amount of money (m) he spends on the item.

a. Write an equation representing the direct proportional relationship between the sales tax and

the amount of money spent. Use the variable k as the constant of proportionality.

b. If Henry pays $1.76 in sales tax on an item that costs $22, what is the value of the constant

of proportionality?

c. What does the constant of proportionality represent in this problem?



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Name ________________________________________________________ Date _________________________

d. If Henry buys an item that costs $76, how much is the sales tax? Use the constant of

proportionality you calculated in part (b).

e. How much does an item cost if the sales tax is $1.04? Use the constant of proportionality

you calculated in part (b).


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Connecting Representations of Proportional RelationshipsInterpreting Multiple Representations of Direct Proportions

1. Millie is cutting out stars to decorate the gym for the school dance. The number of stars (s) she can

cut out varies directly with the time (t) in minutes she spends cutting out the stars.

a. Write an equation showing the relationship between s and t.

b. Complete the table to show the number of stars Millie is able to cut out for various amounts of

time. Explain how you completed the table.

Time (t)(in minutes)

Number of Stars (s) s __ t  5 k

0 ------

12 6

15

44

50


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c. Write the equation representing the relationship between s and t using the value of k you

determined from the table.

d. Graph the data. Label the x- and y-axes and name your graph.

e. Did the graph turn out as you expected? Explain.

f. Determine the constant of proportionality in two different ways by using the graph.

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