proportional relationships - webnode...7.4b calculate unit rates from rates in mathematical and...

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Stations Students will be able to represent proportional relationships in various forms and compute unit rates.

Ideas for Implementation: Stations are a perfect activity that incorporates movement and cooperative learning. Use this for a full day lesson or set them up and have students work on them throughout the unit. Instructions: Print on cardstock or place in a page protector to help them last. Each student needs a recording sheet as well. 1.  Place stations in various locations around the room 2.  Divide students into groups of 2-4. 3.  Set timer to a specific time (5-7 minutes) and have students work with their group to complete

the station. When time is up, students switch locations.

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Proportional relationships

7.4C Represent constant rates of change in mathematical and real world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d=rt.

7.4B Calculate unit rates from rates in mathematical and real-world problems.

7.4C Determine the constant of proportionality (k=y/x) within mathematical and real-world problems.

7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measure 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.

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Determine whether the relationship is proportional or not. Justify your answer.

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A D

B E

C F

X 4 8 12 16 20

y 3 6 9 12 15

X 1 2 3 4 5

y 1 3 5 7 9

X 2 4 6 8 10

y 12 24 36 48 60

v  v  

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Determine the constant of proportionality in each of the representations below.

A c

B d

e

X 2 4 6 8 10

y 7 14 21 28 35 y = 2.75x

1

Zoo Admission

Dolla

rs

Number of Tickets

2 3 4 5 6 7 8 9 10

10

20

30

40

50

60

70

80

90

100

X 0 3 6 9 12

y 0 12 24 36 48

A video game developer projects that he will earn $65.00 for every 5

games purchases. Write an equation to represent the proportional

relationship between the number of games and the total earnings.

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Use the graph to answer the questions below.

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

b How can the constant of proportionality be represented with an ordered pair?

c Write an equation to represent the gas mileage of the Toyota Corolla.

Toyota Corolla (mpg)

Gallons

Mile

s

2 4 6 8 10

50

100

150

200

250

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Use the table to answer the questions below.

aThe store manager earns $310.50 in one week. How many hours did the manager work?

bDuring November, sales are at their peak. The store manager must work 40 hours that week. How much will the manager earn?

cWrite an equation to represent the proportional relationship between the hours worked and the total earnings.

Hours $ earned

2 $27.00

4 $54.00

6 $81.00

8 $108.00

10 $135.00

12 $162.00

14 $189.00

Starbucks Store Manager Wages

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Write an equation to represent the proportional relationships below.

The cost of a 4 pack of apple juice is $2.24. Write an equation that relates the cost in dollars, y, to the number

of apple juice cartons, x.

A marathon runner is able to run 15 miles in 3 hours. Write an equation that relates the number of miles, y, to

the number of hours, x.

A 12 ounce latte costs $3.00. Write an equation that relates the cost in dollars, y, to the number of ounces, x.

Compute the unit rate for each of the items below.

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50 oz $6.00

32 oz $3.84

44 oz $5.72

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Compute the unit rate for each member of the football team below.

76 91 44

runs of a mile

every hour

1

3 1

4

runs of a mile

every hour

5

6 3

4

runs of a mile

every hour

3

4 1

2

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Change the recipe below, so that it serves one.

Chicken Pot Pie

1

4

21

4

21

2

11

2

cups of pastry dough cups vegetables, chopped cup of butter

salt and pepper to taste cups of chicken *serves four  

A

B

C

D

E

Show all your work in the appropriate box below.

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Name _____________________________________   Date ____________________________  Pd ______  

Unit: Proportional Relationships Stations

Proportional Relationships Stations

A d

B e

C f

Station 1

Station 2 Station 3 A

B

C

Station 4

A

B

C

Station 5

A B C

Station 6

Soda Popcorn Lemonade

Station 7

#79 #91 #44

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Station 8

A 3.5

B 15

C 2.75

D 13

E 4

Show all your work in the appropriate box below.

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Name _____________________________________   Date ____________________________  Pd ______  

Unit: Proportional Relationships Stations

Proportional Relationships Stations

A proportional d proportional

B not proportional e not proportional

C proportional F not proportional

Station 1

Station 2 Station 3 A traveled 0 miles, used 0

gallons of gas

B (1, 30)

C y=30x

Station 4

A 23 hours

B $540.00

C y=13.5x

KEY  

unlike  unlike  like  unlike  unlike  

     9/16 cups of pastry dough 5/8 cups of vegetables, chopped 1/16 cups of butter 3/8 cups of chicken, chopped

Station 5

A y=0.56x B y=5x C y=0.25x

Station 6

Soda Popcorn Lemonade

$0.13 per ounce $0.12 per ounce $0.12 per ounce

Station 7

#79 #91 #44

1 1/3 miles per hour

1 1/9 miles per hour

1 1/2 miles per hour

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Station 8