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M A N E U V E R I N G T H E M I D D L E .C O M

PA G E T W O

PAGE TOPIC RESOURCE4 Sample Pacing Guide

5-6 Ideas for Implementation & Helpful Hints

7-16 Binder Covers, Dividers, and Spine Labels

17-18 Ratios and Rates Student Handout 1

19 Ratios and Rates Homework 1

21-22 Constant of Proportionality Student Handout 2

23 Constant of Proportionality Homework 2

25-26 Proportionality and Tables Student Handout 3

27 Proportionality and Tables Homework 3

29-30 Proportionality and Graphs Student Handout 4

31 Proportionality and Graphs Homework 4

33-34 Proportional Relationships Student Handout 5

35 Proportional Relationships Homework 5

37-38 Proportional Relationships Quiz Quiz 1

39-40 Fractional Unit Rates Student Handout 6

41 Fractional Unit Rates Homework 6

43-44 Comparing Unit Rates Student Handout 7

45 Comparing Unit Rates Homework 7

47-54 Proportional Relationship Unit Study Guide Study Guide

55-57 Proportional Relationship Unit Test Test

PROPORTIONAL RELATIONSHIPS UNITTable of Contents

©Maneuvering the Middle LLC, 2016

DAY 1 DAY 2 DAY 3 DAY 4 DAY 5

Rates and Ratios Constant of Proportionality

Proportionality and Tables

Proportionality and Graphs

ProportionalRelationships

Student Handout 1Homework 1





DAY 6 DAY 7 DAY 8 DAY 9 DAY 10

Proportional Relationships Quiz

Fractional Unit Rates Comparing Unit Rates ProportionalRelationships Unit

Study Guide

Proportional Relationships Unit

Test

Quiz Student Handout 6Homework 6


Unit Study Guide Unit Test

NOTES


PROPORTIONAL RELATIONSHIPSPACING GUIDE

*NOTE: This file has been organized for double-sided printing. Any blank pages were left so intentionally to make printing easy.

Ideas for Implementation: This bundle has all of the notes, homework, quizzes, and tests to make your life easier and help your students to be successful with proportional relationship concepts. A sample pacing guide is included for those of you who do not have a district scope and sequence or if it is very general. Additionally, an answer key is included.

If you notice any discrepancies in the documents or have any questions, please email me at: [email protected].

STANDARDS7.RP.1 Compare unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.

7.RP.2 Recognize and represent proportional relationships between quantities.

• 7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

• 7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

• 7.RP.2c Represent proportional relationships by equations.

• 7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation with special attention to the points (0, 0) and (1, r) where r is the unit rate.

PROPORTIONAL RELATIONSHIPSStudent Handouts


HELPFUL HINTS

A few ideas for organizing your curriculum and keeping things nice and neat:

Keep each unit in a separate binder and use the spine labels and covers to keep them looking nice and easy to find. I personally love 1.5” binders.


Student Handouts

BINDERS

I place my originals in page protectors in chronological order. Any extra copies from that lesson, I hole punch and place behind that page. When I need an extra or a student is missing something from weeeeeeeeks ago, I can simply pull out a copy.

PAGE PROTECTORS

I highlight the edges of my answer keys or if I am really good, print them on colored paper. It helps them to stand out and makes them easy to find on my desk, in a binder, by the document camera, etc. Plus, highlighter doesn’t show up if you make a copy.

ANSWER KEYS

Card stock in a page protector makes an awesome divider. When I set up my dividers, I include one for handouts, activities, assessments, and answer keys. Binder covers and spine labels have been included. J

CARD STOCK

Happy Teaching!

PROPORTIONALRELATIONSHIPS

s e v e n t h G r a d e C u r r i c u l u m

U n i t t w o : 7 . R P . 1 7 . R P . 2

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RATE• A rate is a specific _________________ of two quantities with different

units.

Ex: ________________________________________________________________

RATIO

• A ratio is a _________________ of _____numbers. It can be written

______different ways.

• The order in which you write the ratio is _______________to the

meaning. Ratios, like fractions, can be simplified.

Name _____________________________________Date ______________________________Pd______

Unit: Proportional RelationshipsStudent Handout 1

RATIOS AND RATES

TEETH TO NO TEETH

SMILES TO TOTAL

BIG EYES TO TEETH

SMILES TO TONGUE

TONGUE TO TOTAL ANGRY TO SMILES

SILLY FACE TO ANGRY FACE

TINY EYES TO NO SMILE


Hunter jogs four miles in 30 minutes. Ryan jogs seven miles in 48 minutes. What is each person’s rate of speed? Who jogs the fastest?

Use the pictures below to practice writing ratios.

WAYS TO SOLVE

PROPORTIONS

• Scaling

• Cross multiplication

When two ratios are _____________,they can be referred to as _______________.

Summarize today’s lesson:


The _______________can help us determine the better value for our money.

A 12-pack of Orange Crush is priced at $3.00. A six-pack is priced at $1.75. Which is the better value?

$3.00UNITPRICE

PEROZ

A small university enrolls in-state and out-of-state students. The number of students enrolled in their most recent freshman class was 243. The school reported that it enrolled seven in-state students for every two out-of-state students. How many of each type of student was enrolled in the freshman class?

Name _____________________________________Date ______________________________Pd______

Unit: Proportional RelationshipsHomework 1

Answer the following questions. Be sure to justify your response.


1. At the ice cream shop, there are 14 shakes sold for every 6 malts. What is the ratio of malts to shakes?

2. Eight out of 10 dentists prefer Crest toothpaste. What is the ratio of dentists who do not prefer Crest to those who do?

3. An animal shelter currently only has 30 dogs and 20 cats. What is the ratio of cats to animals?

4. Folgers Coffee is priced at $12.88 for 80 cups of coffee, and Seattle’s Best is priced at $9.00 for 50 cups. Which brand of coffee is the better value for each cup?

5. Anna can type 123 words in 3 minutes. Caroline can type 220 words in 5 minutes. Who can type the fastest?

6. An amusement park sells child and adult tickets at a ratio of 8:1. On Saturday, they sold 147 more child tickets than adult tickets. How many tickets did the amusement park sell on Saturday?

7. Northside High School is having a spaghetti dinner fundraiser. In order to advertise, students place flyers on neighborhood doors. Margie hands out 120 flyers in 2 hours. Jaxon hands out 18 flyers in 15 minutes. Who is able to pass out flyers at a faster rate? Defend your thinking.

8. Stan’s Steakhouse has a server to cook ratio of 5 to 2. The total number of servers and cooks is 42. How many servers does Stan’s Steakhouse employ?

RATIOS AND RATES

4. Examine the table below. Describe the patterns that are true.

1. Mario travels 180 miles in 2.5 hours. If Mario travels at the same rate, how far can Mario travel in 5 hours?

2. Using the information about Mario’s rate, complete the table below.

3. How many miles does Mario travel in one hour? Explain your solution.

CONSTANT OFPROPORTIONALITY

• The value of the ratio of two proportional quantities.

• Represented by the equation _____________, where y represents the

y-values in a table/graph and x, represents the x-values in the

table/graph.

Name _____________________________________Date ______________________________Pd______


CONSTANT OF PROPORTIONALITYTwo quantities are _________________ if the ratio between the quantities is

_______________.


HOURS 2.5 5 7.5 10 12.5

MILES

FEET (X) INCHES (Y)Y

X

1 12

2 24

3 36

4 48

5 60

a. How do you know that the number of feet is proportional to the number of inches?

b. Using x, the number of feet, how do you find y, the number of inches?

HOURS MILES WALKED Y/X

2 3

4 6

6 9

8 12

5. While training for a marathon, Keith’s watch reported how many calories he burned at each mile marker. The data is shown below.

a. Is the number of calories proportional to the number of miles? Explain your thinking.

b. The next day, Keith ran 7.5 miles. How many calories did he burn?

c. What is the constant of proportionality?

d. Write an equation to explain the relationship between the number of miles and the calories burned.

MILES 1 2 3 4 5

CALORIES BURNED 117 234 351 468 585

Use the information below to determine the constant of proportionality in each situation.



y = k = x =

Apply your understanding of the constant of proportionality to the questions below.

k: _________________k: _________________ k: _________________

CUPS OF OIL

CUPS OF

WATERY/X

1.5 6

4 16

5.5 22

7.5 30

FEET INCHES Y/X

3 36

5 60

6 72

8 96

A student reads at a constant rate in her chapter book, Where the Red Fern Grows. This can

be described by the equation y=12

x . Complete the chart below.

A gym employee is paid monthly. After working for three months, he had earned $4,500. To determine how much money he will make over a six-month period, he created the table below.

MONTH TOTAL EARNINGS

Y

X

1

2

3

4

5

6

Use the situation below to complete the table and answer the questions.


1. If he continues to earn at the same rate, how much will he have earned after working 5 months?

2. After how many months will the gym employee have made $19,500?

3. Write an equation to represent the constant of proportionality.

4. The teacher recommends that students read for 20 minutes each night. How many pages will the student complete?

5. In a really exciting part of the book, the student read 18 pages in one sitting. For how many minutes did she read?

6. If the book is 245 pages, how many minutes will it take her to finish?

Name _____________________________________Date ______________________________Pd______

7. Describe any patterns you notice when working with proportional relationships.


MINUTES PAGES READ

Y

X

1

2

3

4

5

6

CONSTANT OF PROPORTIONALITY

1. There are two coffee shops in town that charge different prices. The prices are proportional, but some of the information is missing from their price lists.

a. What do you notice that is different about the two tables?

b. What proves that both coffee shops sell their drinks at proportional rates?

c. If you purchased nine cups of coffee at Houndstooth Coffee, how much more would you

spend than if you purchased nine cups at Seattle Coffee Works?

d. A third coffee shop is opening up in a busy

business district. What do you notice about their

pricing structure?

e. What would be the benefit to this structure?

Name _____________________________________Date ______________________________Pd______


Relationships are _________________ if they can be represented by the equation

_________________ , where k represents the constant of proportionality.

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CUPS OF COFFEE

TOTAL COST

Y

X

1

2

3 $8.25

4

5 $13.75

6

CUPS OF COFFEE

TOTAL COST

Y

X

1

2 $5.60

3

4

5

6 $16.80

SEATTLE COFFEE WORKS HOUNDSTOOTH COFFEE

CUPS OF COFFEE

TOTAL COST

Y

X

1 $2.90

2 $5.70

3 $8.40

4 $11.00

5 $13.50

6 $15.90

STUMPTOWN COFFEE

PROPORTIONALITY AND TABLES

Complete the tables and use the information to answer the questions below.

Each table shows a proportional relationship. Fill in the missing values and determine k.

______________________________________

Use your understanding of the constant of proportionality to determine k. If the relationship does not have a constant of proportionality, label it non-proportional.


What is the constant of proportionality in the table above?

X Y

2 6.8

5 17

8 27.2

11 37.4

x y

3 18

5 30

7 42

9 54

x y

1 3

4 9

7 15

10 21

7

42

63

28 84

35

6 15

18 45

60

75

4

8

15 12

25 20

1

24

42

10

13 78


A _________________ can also represent k in a proportional relationship.

FEET 1 2 3 4 5

YARDS1

3

2

3

33

= 14

3

5

3

K = _______ K = _______ K = _______ K = _______

___________________

Name _____________________________________Date ______________________________Pd______


Savannah, Greg, and Kevin all take part-time jobs for the summer. Their hourly wages are shown in the tables below. Use the information to answer the questions below.


HOURS$

EARNED

2 $19.00

4 $38.00

6 $57.00

8 $76.00

10 $95.00

12 $114.00

14 $133.00

HOURS$

EARNED

3 $27.00

6 $54.00

9 $81.00

12 $108.00

15 $135.00

18 $162.00

21 $189.00

SAVANNAH GREG

HOURS$

EARNED

2 $16.50

5 $41.25

8 $66.00

11 $90.75

14 $115.50

17 $140.25

20 $165.00

KEVIN

PROPORTIONALITY AND TABLES

1. What is the constant of proportionality, k, of Kevin’s wage? Greg’s? Savannah’s?

2. Which person has the highest hourly wage? How do you know?

3. If all three friends worked 20 hours during

the week, how much would each person earn?

4. Savannah earns $247.00. How many hours did she work?

5. How long will it take Greg to earn $500.00? Round to the nearest hour.

A bike rider cycles 18 miles in 1 hour.

Name _____________________________________Date ______________________________Pd______


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Compare the two graphs below. Jot down your observations in the table below.

PROPORTIONALITY AND GRAPHSUse the information below to create a table and determine the constant of proportionality, k.

HOURS TOTAL MILES

K = _______EQUATION: ___________________

ORDERED PAIRS

GRAPH CHARACTERISTICS

PROPO

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ROPO

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-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8

87654321

-8-7-6-5-4-3-2-1

-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8

87654321

-8-7-6-5-4-3-2-1 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8

87654321

-8-7-6-5-4-3-2-1

-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8

87654321

-8-7-6-5-4-3-2-1

Proportional relationships are _________________ and pass through the _____________.


Graph the tables below. Explain if they are proportional or not.

EXAMPLE 1 EXAMPLE 2 EXAMPLE 3

Example 1 is _______________

___________________________

___________________________

___________________________

Example 2 is _______________

___________________________

___________________________

___________________________

Example 3 is _______________

___________________________

___________________________

___________________________

X 1 2 3 4 5

Y 1 3 5 7 9

X -3 -1 1 3 5

Y -6 -2 2 6 10

X 2 4 6 8 10

Y 1 2 3 4 5

87654321

-8-7-6-5-4-3-2-1

87654321

-8-7-6-5-4-3-2-1-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8

87654321

-8-7-6-5-4-3-2-1

Use your understanding of proportional graphs and tables to answer the questions below.

4. The number of feet in a yard can be represented by a graph. Which of the following graphs best represents y, the number of feet in x yards?

A. B. C. D.

5. Which of the situations best describes the graph at right?

A. Each smoothie costs $3.00.B. A runner can run 6 miles in an hour.C. There are twelve cookies in a dozen.D. It takes 6 hours to travel a mile.

1 2 3 4 5 6 7 8 9 10

30

27

0

3

6

9

12

15

18

21

24

1 2 3 4 5

15

13.5

0

1.5

3

4.5

6

7.5

9

10.5

12

3 6 9 12 15 18 21 24 27 30

60

54

0

6

12

18

24

30

36

42

48

60

54

0

6

12

18

24

30

36

42

48

1 2 3 4 5

1 2 3 4 5

60

54

0

6

12

18

24

30

36

42

48

-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8

K = _______EQUATION: ___________________

Concert tickets go on sale for $34.00 each.

1. If the venue needs to sell 86 tickets to break even, then how much money have they invested

in the concert?

2. The venue has a maximum capacity of 200 people. If it sells out, how much revenue will the

concert earn?

3. Describe how you know that this is a proportional relationship.

4. What does the ordered pair (0, 0) represent in this situation?

5. What does the ordered pair (6, 204) represent in this situation?

Read the scenario below. Then, complete the table, graph the ordered pairs, and write an equation. Use the information to answer the questions below.


Name _____________________________________Date ______________________________Pd______


TICKETS SOLD

TOTAL REVENUE

ORDERED PAIRS

PROPORTIONALITY AND GRAPHS

[GRAPH] [TABLE]

[VERBAL DESCRIPTION] [PROPORTIONALITY]

Name _____________________________________Date ______________________________Pd______


The number of miles a white-tailed deer travels is shown in the table below. Complete the missing information and answer the question.

[EQUATION]

PROPORTIONAL RELATIONSHIPS

HOURS MILES

1

2

3 84

4

5

6

7 196

8

9



• Represents a _______________________________________________.

• Two things will be true about a graph that is proportional:

1) The graph will be a ______________ _______.

2) The graph will pass through the ____________.

• In a table, we want to check for equivalent ratios. In other words, in

a proportional table, the ratio of yx

will always be _________________.

[GRAPH] [TABLE]

[VERBAL DESCRIPTION]

2. The student council is selling t-shirts to raise awareness for the local animal shelter. For each t-shirt they sell, they will donate $7.00.

[PROPORTIONALITY]

[EQUATION]

5

10

15

20

25

30

35

40

45

Read each scenario below. Determine if the situation is proportional or not. If it is proportional, then write an equation to represent it.


3. A restaurant charges $10.00 for a medium pizza and $1.00 for each topping. ______________

_______________________________________________________________________________________

4. A restaurant has an all-you-can-eat buffet. They charge $8.75 per person. ______________

_______________________________________________________________________________________

5. A restaurant charges $1.50 for a fountain drink with free refills. _________________________

_______________________________________________________________________________________

6. A restaurant has a build-your-own salad option. It is $3.80 per pound of salad. ____________

_______________________________________________________________________________________

6. A vehicle travels at a rate of 65 miles per hour. ________________________________________

_______________________________________________________________________________________


[GRAPH] [TABLE]

[VERBAL DESCRIPTION] [PROPORTIONALITY]

Complete the missing information in the chart below. Then, answer the questions.

HOURS RENTED

TOTALCOST

0

1

2 $24.00

3

4

5

6

7 $84.00

8

9

1. The bike rental company has determined that they will charge based on the nearest half

hour. If Michael rented the bike for 5.5 hours, how much would that cost?

2. What does the point (7, 84) represent in this situation?

3. If a customer has $50.00 to spend, for how many hours can they rent the bicycle?

[EQUATION]


Name _____________________________________Date ______________________________Pd______



5. During the fall a pumpkin patch advertises four pumpkins for $11.00. Which equation below represents this proportional relationship?

A. y = 411

x B. y = 2.75x

C. y = 0.36x D. 11y = 4x

6. The table below shows the relationship between the number of miles traveled, x, and the number of gallons of gas used, y.

Which of the following equations best represents the relationship?

A. y = 7.6x B. y = 684xC. y = 0.13x D. y = 76x

Answer the following questions. Be sure to show your thinking.

Name _____________________________________Date ______________________________Pd______

Unit: Proportional RelationshipsQuiz 1

Use the table below to answer questions 1-4.

1. Kenny is practicing for a typing test to obtain a job as a paralegal. The number of words he can type is proportional to the number of minutes. If the test is 18 minutes long, how many words will Kenny be able to type?

2. What number is missing in the table above?


Answers

1. ______________

2. ______________

3. ______________

4. ______________

5. ______________

6. ______________

7. ______________

8. ______________

9. ______________

10. _____________

QUIZ: PROPORTIONAL RELATIONSHIPS

MINUTES 0 3 6 9 12

WORDS TYPED 0 120 ? 360 480

3. Which number represents k, the constant of proportionality?

A. 120B. 60C. 40D. 12

4. Kenny types 280 words. How long did he type for?

A. 4B. 5C. 6D. 7

X 3 5 7 11

Y 228 380 532 836

A movie theater has increased their ticket prices. They are shown below.

7. The graph shows the proportional relationship of the cost of movie tickets. Using the graphdetermine the constant of proportionality, k.

8. If the movie theater seats 328 people, what is the maximum amount of money the theater can bring in during a showing?

9. A kitchen sink holds 24 gallons of water. A full sink drains at 3 gallons per minute. Which of the following tables best represents the situation?

A. B.

C. D.

10. Which of these does NOT represent the number of minutes in a hour?

A. B.

Use the graph below to answer questions 7-8. Be sure to show your thinking.

MOVIE TICKET SALES

DO

LLA

RS

NUMBER OF TICKETS

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1 2 3 4 5 6 7 8 9 10

100

90

10

20

30

40

50

60

70

80

X 1 2 3 4

Y 24 48 72 96

X 1 2 3 4

Y 21 18 15 12

X 0 2 4 6

Y 24 21 18 15

X 1 2 3 4

Y 24 21 18 15

TIME(HOURS)

TIME(MINUTES)

2 120

5 300

6 360

8 4801 2 3 4 5

600540

060

120180240300360420480

TIME (HOURS)

TIM

E (M

INU

TES)

C. y = 60x, where x represents the time in hours and y represents the time in minutes

D. There are 240 minutes in 4 hours.

UNIT RATE

• A rate is a specific _________________ of two quantities.

• Unit rate is the value when the __________________ is one, or the

amount per one. It is the same _________________ as the constant of

proportionality and can be represented with fractions.

Ex: ________________________________________________________________

1.

11

2 · 6 =

2.

21

2÷ 6 =

3.

22

3 ·

1

4 =

4.

13

4÷

2

3 =

Name _____________________________________Date ______________________________Pd______


FRACTIONAL UNIT RATES


Practice finding the unit rates of the following problems.

What do you notice about the unit rate?

In order to work with fractional unit rates, you must be comfortable multiplying and dividing fractions.

NICK’S FITNESS TEST UNIT RATE

78 sit-ups in 2 minutes

42 push-ups in 3 minutes

40 jumping jacks in 1 minute

The fitness test results of other students are shown below. Determine their unit rates.



FITNESS TEST RESULTS X Y Y/X UNIT RATE

112

miles in 15 minutes

2 miles in 12 minutes

213

miles in 20 minutes

5. Gabby measures out 512

pounds of

almonds at the grocery store bulk section. At checkout the total cost is $20.90. What is the price per pound?

6. A car travels 117 miles in 214

hours. How

fast does the car travel in an hour?

7. A baker’s dozen (13) of cookies is on sale for $4.94. What is the cost of an individual cookie?

8. At the fabric store, Marisela spends $9.00

on 118

yards of fabric. How much does one

yard of fabric cost?

Use your understanding of unit rates to answer the questions below.

Name _____________________________________Date ______________________________Pd______



1. A recipe for banana bread requires 3 cups

of bananas for every 112

cups of sugar used.

At this rate, how many cups of sugar should be used if 2 cups of bananas are used?

2. Emma pays $108 every six weeks for tennis lessons. What is the price per year for tennis lessons?

3. If34

gallon of paint covers13

of the wall,

then how much paint is needed for the entire wall?

4. Jeremy can row 13

of a mile in 14

of an hour.

What is the unit rate?

5. Four bottles of Powerade cost $3.88. Find the unit price of each bottle.

6. Art mows 18

acre in 14

hour. How many

acres does Art mow per hour?

FRACTIONAL UNIT RATESAnswer the following questions. Be sure to justify your response.

The price of a gallon of organic chocolate milk is $6.40. The price of six cartons of organic chocolate milk is $2.88.

1. What does the unit rate of the gallon of organic chocolate milk represent?

2. What does the unit rate of organic chocolate milk cartons represent?

3. What is the cost per ounce of the gallon variety?

4. What is the cost per carton in each six-pack?

5. What is the cost per ounce of the carton variety, if each carton contains eight ounces?

6. If the gallon variety was poured into cartons, how many cartons would it fill? How much would each carton cost?

Name _____________________________________Date ______________________________Pd______



Unit rates are helpful when comparing quantities, as long as the units are _____________.

ONE GALLON OF ORGANIC CHOCOLATE MILK

NUMBER OF OUNCES

COSTY

X

SIX CARTONS OF ORGANIC CHOCOLATE MILK

NUMBER OF CARTONS

COSTY

X

COMPARING UNIT RATES

The Moore family is adding a brick patio to their back yard. Mr. Moore is determining how many square bricks he needs for his rectangular patio, as well as the cost. His sketch is shown below and is not drawn to scale. Use the formula A=bh to help answer the questions below.

7. How much does each brick paver cost?

8. How many square inches will each paver cover?

9. What is the cost per square inch of the pavers?

10. How many square feet will each paver cover?

11. How many square feet is the patio?

12. How many pavers are needed to cover the patio? How much will that cost?

PATIO

12 feet

10 f

eet

8 in

8 in

BRICK PAVER

SOLD IN A BOX OF 12 PAVERS FOR $15.36


Use the following information to answer the questions below.

Name _____________________________________Date ______________________________Pd______


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Two girl scout troops are completing a wilderness campout. Use the information to answer the questions.

The Blue Troop hikes 23

mile every 12

hour. The Yellow Troop hikes 34

mile every 13

hour.

BLUE TROOP YELLOW TROOP

CABIN TO THE RESTROOMS

RESTROOMS TO THE CAMPFIRE

CAMPFIRE TO THE CABIN

COMPARING UNIT RATES

12

mile

34

mile

112

miles

Name _____________________________________Date ______________________________Pd______

Unit: Proportional RelationshipsReview - CCSS

Solve each of the problems below. These represent the types of questions on your test. Be sure to ask questions if you need more help with a topic.

PROPORTIONAL RELATIONSHIPS UNIT STUDY GUIDE

I CAN DETERMINE IF A RELATIONSHIP IS PROPORTIONAL. 7.RP.2

1. Determine if the representations below are proportional (P) or non-proportional (NP).

a. _______

b. _______

I CAN FIND THE CONSTANT OF PROPORTIONALITY. 7.RP.2A

2. Determine the constant of proportionality in each of the problems below.

a. ___________

y = 112x

d. ___________

b. ___________

c. ___________

A restaurant has an all you can eat buffet. They charge $13.95 per person.

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X 2 4 6 8 10

Y 5 9 13 17 21

X 3 5 7 9 11

Y 1.5 2.5 3.5 4.5 5.5

c. _______

y = 9x + 12

d. _______

y = 34x

e. _______

1 2 3 4 5 6 7 8 9 10

200

180

20

40

60

80

100120

140

160

X 2 4 6 8 10

Y 190 380 570 760 950

AUTO REPAIR

MIL

ES

NUMBER OF HOURS1 2 3 4 5 6 7 8 9 10

500

450

50

100

150

200

250300

350

400

I CAN USE TABLES TO REPRESENT PROPORTIONAL RELATIONSHIPS. 7.RP.2B

3. Complete the table below. Use the information to answer a-c.

I CAN WRITE EQUATIONS TO REPRESENT PROPORTIONAL RELATIONSHIPS. 7.RP.2B

4. An app developer projects that he will earn $20.00 for every 8 apps downloaded. Write an equation to represent the proportional relationship between the number of apps and the total earnings.

5. It takes Esther 12 minutes to ride a roller coaster four times. Write an equation to represent the proportional relationship between the number of rides and the total amount of time.

6. Use the table below to write an equation to represent the constant of proportionality.

7. Write an equation to represent the constantof proportionality.


BABYSITTING WAGES

DO

LLA

RS

HOURS

# OF TEXTBOOKS

TOTAL SALES ($)

4 $64.00

7 $112.00

9 $144.00

13 $208.00

20 $320.00

100

90

80

70

60

50

40

30

20

10

1 2 3 4 5 6 7 8 9 10

HOURSTOTAL

RAINFALL (IN)

0

1

2

3 10.5

4

5 17.5

a. After how many hours will the amount of rainfall be 28 inches?

b. Write an equation to represent the rainfall.

c. If it continues at this rate, how many inches of rain will fall after 6 hours?

I CAN USE A GRAPH TO REPRESENT PROPORTIONAL RELATIONSHIPS. 7.RP.2B,7.RP.2C

Use the graph to answer the questions below.

12. In this situation what does the ordered pair (0, 0) represent?

13. How many gallons of gas are required for a 500 mile road trip?


14. Which ordered pair above can be used to determine the unit rate?



GAS MILEAGE

GA

LLO

NS

MILES

BIRTHDAY CUPCAKES

DO

ZE

NS

OF

CU

PCA

KE

S

HOURS

10

9

8

7

6

5

4

3

2

1

50 100 150 200 250

20

18

16

14

12

10

8

6

4

2

1 2 3 4 5 6 7 8 9 10

I CAN USE VERBAL DESCRIPTIONS TO REPRESENT PROPORTIONAL RELATIONSHIPS. 7.RP.2C

8. Write a situation to represent the equation y = 5x.

__________________________________________

__________________________________________

__________________________________________

9. Dannie sells beach towels for $12.50 each. Write an equation to represent the situation.

10. Margie saves $7.25 of her allowance each week. Write an equation to represent the situation.

11. Write a situation to represent the equation y = 0.5x.

__________________________________________

__________________________________________

__________________________________________


I CAN COMPUTE UNIT RATES. 7.RP.1

16. A baker’s dozen (13) of cookies is on sale for $2.08.

17. 123

yards of chain cost $9.00.

18. The cost of two pounds of cherries is $8.58. What is the unit rate that describes the cost per pound of cherries?

19. Jeremy can row23

of a mile in 14

of an

hour. What is the unit rate that describes the miles per hour?

I CAN COMPARE UNIT RATES. 7.RP.1

20. The recipe below shows the amount of each ingredient required to make four servings of pasta. Based on this information, determine the amount of each ingredient needed to make 10 servings.

• 134

cups of cheese

• 23

cups of milk

• 212

cups of pasta

Name _____________________________________Date ______________________________Pd______

Unit: Proportional RelationshipsReview

Solve each of the problems below. These represent the types of questions on your test. Be sure to ask questions if you need more help with a topic.

PROPORTIONAL RELATIONSHIPS UNIT STUDY GUIDE

I CAN DETERMINE IF A RELATIONSHIP IS PROPORTIONAL.

1. Determine if the representations below are proportional (P) or non-proportional (NP).

a. _______

b. _______

I CAN FIND THE CONSTANT OF PROPORTIONALITY.

2. Determine the constant of proportionality in each of the problems below.

a. ___________

y = 112x

d. ___________

b. ___________

c. ___________

A restaurant has an all you can eat buffet. They charge $13.95 per person.

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X 2 4 6 8 10

Y 5 9 13 17 21

X 3 5 7 9 11

Y 1.5 2.5 3.5 4.5 5.5

c. _______

y = 9x + 12

d. _______

y = 34x

e. _______

1 2 3 4 5 6 7 8 9 10

200

180

20

40

60

80

100120

140

160

X 2 4 6 8 10

Y 190 380 570 760 950

AUTO REPAIR

MIL

ES

NUMBER OF HOURS1 2 3 4 5 6 7 8 9 10

500

450

50

100

150

200

250300

350

400

I CAN USE TABLES TO REPRESENT PROPORTIONAL RELATIONSHIPS.

3. Complete the table below. Use the information to answer a-c.

I CAN WRITE EQUATIONS TO REPRESENT PROPORTIONAL RELATIONSHIPS.

4. An app developer projects that he will earn $20.00 for every 8 apps downloaded. Write an equation to represent the proportional relationship between the number of apps and the total earnings.

5. It takes Esther 12 minutes to ride a roller coaster four times. Write an equation to represent the proportional relationship between the number of rides and the total amount of time.

6. Use the table below to write an equation to represent the constant of proportionality.

7. Write an equation to represent the constantof proportionality.


BABYSITTING WAGES

DO

LLA

RS

HOURS

# OF TEXTBOOKS

TOTAL SALES ($)

4 $64.00

7 $112.00

9 $144.00

13 $208.00

20 $320.00

100

90

80

70

60

50

40

30

20

10

1 2 3 4 5 6 7 8 9 10

HOURSTOTAL

RAINFALL (IN)

0

1

2

3 10.5

4

5 17.5

a. After how many hours will the amount of rainfall be 28 inches?

b. Write an equation to represent the rainfall.

c. If it continues at this rate, how many inches of rain will fall after 6 hours?

I CAN USE A GRAPH TO REPRESENT PROPORTIONAL RELATIONSHIPS.



13. How many gallons of gas are required for a 500 mile road trip?


14. Which ordered pair above can be used to determine the unit rate?



GAS MILEAGE

GA

LLO

NS

MILES

BIRTHDAY CUPCAKES

DO

ZE

NS

OF

CU

PCA

KE

S

HOURS

10

9

8

7

6

5

4

3

2

1

50 100 150 200 250

20

18

16

14

12

10

8

6

4

2

1 2 3 4 5 6 7 8 9 10

I CAN USE VERBAL DESCRIPTIONS TO REPRESENT PROPORTIONAL RELATIONSHIPS.

8. Write a situation to represent the equation y = 5x.

__________________________________________

__________________________________________

__________________________________________

9. Dannie sells beach towels for $12.50 each. Write an equation to represent the situation.

10. Margie saves $7.25 of her allowance each week. Write an equation to represent the situation.

11. Write a situation to represent the equation y = 0.5x.

__________________________________________

__________________________________________

__________________________________________


I CAN COMPUTE UNIT RATES.

16. A baker’s dozen (13) of cookies is on sale for $2.08.

17. 123

yards of chain cost $9.00.

18. The cost of two pounds of cherries is $8.58. What is the unit rate that describes the cost per pound of cherries?

19. Jeremy can row23

of a mile in 14

of an

hour. What is the unit rate that describes the miles per hour?

I CAN COMPARE UNIT RATES.

20. The recipe below shows the amount of each ingredient required to make four servings of pasta. Based on this information, determine the amount of each ingredient needed to make 10 servings.

• 134

cups of cheese

• 23

cups of milk

• 212

cups of pasta

Name _____________________________________Date ______________________________Pd______

Unit: Proportional RelationshipsTest

Solve the problems below. Be sure to show your thinking.

1. Which situation is best described by thegraph shown?

A. JJ purchases chips for $0.75 per bag.B. Mark buys a pack of gum for $1.50 eachC. Paula pays $0.50 per ticket at the fair.D. Franco purchases flowers for $3.00 each.

2. Find the constant of proportionality in thegraph below.

A. 9 B. 4.5 C. 3D. 1.5

3. Jeremy can row38

of a mile in 14

of an hour.

What is the unit rate that describes the miles per hour?

A. 112

miles per hour

B. 34

miles per hour

C. 112

hours per mile

D. 34 hours per mile

4. A bag of popcorn contains 483 calories andserves 3.5 people. How many calories are in each serving?

___________________

5. An app developer projects that he will earn$230.00 for every 100 apps downloaded. Which of the following equations can be usedto represent the proportional relationship between the number of apps, x, and the total earnings, y.

A. y = 100x + 230 B. y = 230x + 100

C. x = 2.30y D. y = 2.30x

6. Based on the information in the table, whatis the constant of proportionality?

A. k = 8 B. k = 20

C. k = 5 D. k = 10

PROPORTIONAL RELATIONSHIPS UNIT TEST

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2 4 6 8 10

15

3

6

9

12

NUM

BER

OF

MIL

ES

HOURS

1 2 3 4 5 6 7 8 9 10

20

18

2

4

6

8

10

12

14

16

X 5 10 15 20 25

Y 25 50 75 100 125

7. The graph below shows the relationship between the amount of money in Sarah’s savings account over a period of time. Which of the following statements is NOT true about the relationship?

A. After 5 weeks, Sarah has $100 in her account.

B. If Sarah has a balance of $60, then 7 weeks have passed.

C. The relationship is proportional.D. The situation can be represented by the

equation y = 200 – 20x.

8. The table below shows the relationship between the number of miles traveled, x, and the number of gallons of gas used, y.

Which of the following equations best represents the relationship?

A. y= 1

35x B. y = 35x

C. 35 = 1x D. y = 3.5x

9. The graph shows the amount of money that Terrance saves each week from his lawn moving job. Which best represents the unit rate?

A. (0, 0)B. (1, 200)C. (200, 1)D. (2, 200)

10. Which of the following does NOT represent the number of months in a year?

A. B.

11. Which situation best represents the equation below?

y = 2.5x

A. Each day 2.5 inches of water evaporates from the experiment.B. Two cartons of eggs ring up at the register for $2.50.C. A bank account is opened with a balance of $5, and $2.50 is deposited each day.D. John is 2.5 times as big as his brother Sam.

12. Which of the following situationsrepresents a proportional relationship?

A. A cheeseburger is $7.95 plus $1.00 for each additional topping.

B. A pool fills at a rate of 90 gallons per hour.C. A health club charges a $40.00

membership fee plus $25.00 per month.D. A bank account begins with $350.00 and

gains $30.00 per month.

X 35 70 105 140 175

Y 1 2 3 4 5

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1 2 3 4 5 6 7 8 9 10

200

180

20

40

60

80

100

120

140

160

ACCO

UNT

BALA

NCE

NUMBER OF WEEKS

TIME(YEARS)

TIME(MONTHS)

2 24

4 48

6 60

8 721 2 3 4 5

6054

06

12182430364248

NUMBER OF YEARS

NUM

BER

OF

MONTH

S

C. y = 12x, where x represents the number of years and y represents the number of months

D. There are 96 months in 8 years.

1 2 3 4 5 6 7 8 9 10

2000

1800

0

200

400

600

800

1000

1200

1400

1600

WEEKS TO

TAL

SAVIN

GS

($)

13. The following graph shows the relationship between the number of times a gear can rotate in a period of time. Which of the following statements is true?

14. Which of the following tables best represents the relationship between p and f in the equation p = 3.5f?

A. B. C. D.

Calvin is starting a new job this summer. He has created a table to represent his earnings, which are dependent on the number of hours he works. Use the table below to answer questions 15-16.

15. ___________________Write an equation to represent y, Calvin’s total earnings based on x the number of hours he works.

16. ___________________How much will Calvin earn if he works 21 hours?

f p

3 3.5

5 7

8 10.5

10 14

14 17.5


f p

3.5 1

5.5 2

8.5 3

10.5 4

14.5 5

f p

2 7

5 17.5

9 31.5

11 38.5

14 49

f p

1 3.5

2 7

3 10.5

4 14

5 17.5

1 2 3 4 5 6 7 8 9 10

100

90

0

10

20

30

40

50

60

70

80

NUMBER OF MINUTES

NUM

BER

OF

ROTA

TIO

NS

A. If the gear rotates 30 times, then it has been rotating for 1.5 minutes.

B. The graph satisfies the equation y = 10x.

C. If the machine rotates for 15 minutes, then it will make 350 rotations.

D. The relationship is non-proportional.

HOURS WORKED 3 7 15 24 30

TOTAL EARNINGS $46.50 $108.50 ? $372.00 $465.00

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