Accelerated
7th
Module 2A: Proportional Relationships
Grade Mathematics
Additional Problems
1. There are 2 cups of kiwi juice for every 5 cups of strawberry juice in Catie’s punch recipe. Paul’s
punch recipe calls for 7 cups of strawberry juice for every 3 cups of kiwi juice. Whose recipe has a
stronger kiwi flavor? Justify your answer.
2. What are three ratios equivalent to “2 to 6?” Explain how you know they are equivalent.
3. What is one way that you encounter or use ratios in your life?
4. If 2 pounds of beans cost $5, how much will 15 pounds of beans cost? Show your work and explain
your reasoning.
5. A fourth-grade class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would they
need each day for 12 caterpillars? Use drawings, words, or numbers to show how you got your
answer.
6. Bonita had a leaky faucet, which dripped 6 ounces of water in 8 minutes.
If Bonita’s faucet is dripping at a constant rate, how much water dripped in 4 minutes?
Show 2 different ways that Bonita could use to find the answer to the question.
Crystal places a bucket under a faucet and collects 19.5 ounces in 26 minutes. Was Crystal’s faucet
dripping equally as fast as Bonita’s faucet or was one dripping faster than the other?
Need Help? Check out these related resources.
 Learnzillion: Solve ratio problems using tables and multiplication
http://learnzillion.com/lessons/588-solve-ratio-problems-using-double-number-lines
Introduction to use of tables and multiplication for problem solving.

Learnzillion: Solve ratio problems using double number lines
http://learnzillion.com/lessons/588-solve-ratio-problems-using-double-number-lines
Introduction to use of a double number line for problem solving.
7. The grocery store sells beans in bulk. The grocer’s sign above the beans says, “5 pounds for $4.” At
this store, you can buy any number of pounds of beans at this same rate, and all prices include tax.
Alberto said, “The ratio of number of dollars to the number of pounds is 4:5. That’s $0.80 per pound.”
Beth said, “The sign says the ratio of the number of pounds to the number of dollars is 5:4. That’s 1.25
pounds per dollar.”
A. Are Alberto and Beth both correct? Explain.
B. Claude needs two pounds of beans to make soup. Show Claude how much money he will need.
C. Dora has $10 and wants to stock up on beans. Show Dora how many pounds of beans she can buy.
Accelerated
7th
Module 2A: Proportional Relationships
Grade Mathematics
Additional Problems
D. Do you prefer to answer parts (B) and (C) using Alberto’s rate of $0.80 per pound, using Beth’s rate
of 1.25 pounds per dollar, or using another strategy? Explain.
8. If a person walks ½ mile in ¼ hour, compute the two unit rates that may be found.
9. A ½ gallon of paint was used to paint a mural. The mural covered ¾ of the wall. When you need to
repaint the wall years later, about how much paint will you need to cover the whole wall? Show your
work and explain your reasoning.
1
1
5
2
10. If the temperature is raising degree in hour, what would be the increase in temperature per hour?
1
1
11. If Monica read 7 2 pages in 4 hour, what is her average reading rate in pages per hour?
12. John mows a third of a lawn in one sixth of an hour. Marcia mows a quarter of a lawn is one tenth of
an hour. (The lawns are the same size and mowing difficulty.) A student claims that Marcia is moving
1
1
faster, because she only worked for 10 of an hour while John worked for 6 of an hour. Is the student’s
reasoning correct? Why or why not?
Need Help? Check out these related resources.
 Learnzillion: Define unit rate using double number line
http://learnzillion.com/lessons/842-define-unit-rate-using-double-number-line
Introduction to definition of and use of unit rate for comparing two rates.

Khan Academy: Finding unit rates
http://www.khanacademy.org/math/arithmetic/rates-and-ratios/rates_tutorial/v/finding-unit-rates
Calculation of unit rate using equivalent ratios.
13. A student is making trail mix. Create a graph to determine if the quantities of nuts and fruit are
proportional for each serving size listed in the table.
Serving Size
Cups of nuts (x)
Cups of fruit (y)
1
1
2
2
2
4
3
3
6
4
4
8
If the quantities are proportional, what is the constant of proportionality or unit rate that defines the
relationship? Explain how the constant of proportionality was determined and how it relates to both
the table and the graph.
Accelerated
7th
Module 2A: Proportional Relationships
Grade Mathematics
Additional Problems
14. The average American eats approximately 1.5 pounds of dirt over 3 years. At this rate, how many
pounds of dirt does a person eat in 1 year, 5 years, 10 years, and 12 years?
Make a table and graph that shows the proportional relationship.
Need Help? Check out these related resources.
 Learnzillion: Display all possibilities in a proportional relationship by graphing
http://learnzillion.com/lessons/1195-display-all-possibilities-in-a-proportional-relationship-by-graphing
Graphing and describing a proportional relationship.
15. See Video: : “How I Ruined Nana’s Eggs” from “Nana’s Chocolate Milk: The Sequel”
http://threeacts.mrmeyer.com/nana/
Describe the situation. What is the problem? What is a solution to the problem? (Show your work and
explain your reasoning.)
16. “Convince Me” – What value would make the statement a proportion?
For each problem, show two strategies for getting your answer.
a.
b.
c.
5
𝑥
= 18
6
6
𝑏
= 21
14
4
2
= 10
𝑐
Need Help? Check out these related resources.
 Learnzillion: Define unit rate using double number line
http://learnzillion.com/lessons/842-define-unit-rate-using-double-number-line
Introduction to definition of and use of unit rate for comparing two rates.

Khan Academy: Finding unit rates
http://www.khanacademy.org/math/algebra/rational-expressions/ratios_algebra/v/find-an-unknownin-a-proportion
Find an unknown in a proportion (note: first 3 minutes are especially helpful based on
what we’ve learned so far)
Accelerated
7th
Module 2A: Proportional Relationships
Grade Mathematics
Additional Problems
17. Does the following situation represent a proportional relationship? If yes,
describe the constants of proportionality associated with the relationship.
If no, explain why it is not a proportional relationship.
Pounds of
Potatoes
Cost
3
$2.10
5
$3.50
10
$6.00
12
$7.20
18. Susie is preparing for a long Segway trip. Below, show how far she can travel in a given length of
time. Complete the table.
Hours
Miles
4
24
6
8
72
120
a. Find how many miles Susie can travel in 1 hour.
b. Write an equation that Susie can use to find the amount of miles she can travel for any number of
hours.
c. If Susie travels 7 hours, how many miles will she go?
19. Coffee costs $18.96 for 3 pounds.
a. Assuming this is a proportional relationship; represent this relationship in 2 ways (one of which
must be a graph in the coordinate plane).
b. What is the cost per pound of coffee? What vocabulary term does this value represent? Where can
you see the cost per pound of coffee in the graph?
Need Help? Check out these related resources.
 Learnzillion: Analyze a table to determine proportional relationships
http://learnzillion.com/lessons/1865-analyze-a-table-to-determine-find-proportional-relationships

Learnzillion: Analyze a graph to find proportional relationships
http://learnzillion.com/lessons/1867-analyze-a-graph-to-find-proportional-relationships
Determining whether a relationship is proportional by reading graphs.
Accelerated
7th
Module 2A: Proportional Relationships
Grade Mathematics
Additional Problems
20. Megalodon Tooth - http://www.101qs.com/803-megalodon-tooth
Write a scale-related question.
What information do you need in order to answer your question?
Do some research to find the information you need to answer your
question.
Answer your question (show your work and explain your reasoning).
21. A carpenter makes miniature replicas of Victorian furniture. The scale model of a table that he
made is 3 inches long. The full-size table is 36 inches long. What is the model’s scale? Show your
work and explain your reasoning.
22. A 2-foot by 2.5-foot scale drawing is created
from an 8-inch by 10-inch photograph. Which
scale does not belong with the others? Explain
why not.
a. 1 ft : 4 in
b. 2 : 8
c.
d.
3
1
1
4
23. Make a scale drawing of your bedroom. Be
sure to indicate your scale. Your drawing
should include at least 3 pieces of furniture,
also drawn to scale.
24. In the scale in the drawing of the thermostat
gasket the scale is indicated as 1:1. What does
this scale mean?
Need Help? Check out these related resources.
 Learnzillion: Using unit rates to interpret scale maps and scale models
http://learnzillion.com/lessons/646-using-unit-rates-to-interpret-scale-maps-and-scale-models
Accelerated
7th
Module 2A: Proportional Relationships
Grade Mathematics
Additional Problems
25. “Convince Me”: Answer the following questions using two different strategies, one of which must
be a double number line:
Kimberly and Vanessa run a baby-sitting service. Kimberly handles taking
the phone calls and scheduling. They split the profits 60-40, meaning that
Kimberly gets 60% of the profits and Vanessa gets 40% of the profits. Last
week their total profits were $180. How much did Kimberly and Vanessa
each earn?
26. Trevor correctly answered 80% of the questions on his Spanish test. The test had 60 questions.
How many questions did Trevor answer incorrectly? Explain how you found your answer. Check
your answer using a second strategy.
27. Describe and correct the error made in writing the percent as a fraction.
8
2
80% = 100 = 25
28. How much is 76% of $25? Check your answer using a second strategy.
29. Lisa bought a bicycle for $520. She also paid a 5% sales tax on the cost
of the bicycle. What was the sales tax on $520?
30. Is 80% of 80% of 125 the same as 64% of 125? Justify your reasoning
using two different strategies.
31. Your friend spends about 35% of each year sleeping, about 10% eating, about 25% on summer
vacation, about 15% on weekend, and about 5% on grooming. He claims that leaves about 10% of
each year, or about 36 days, to go to school. What is the error in this reasoning?
32. Joe saves 5 out of every $6 of his allowance. What percent of his allowance does Joe save?
Need Help? Check out these related resources.
 Learnzillion: Find the part when the percent and total are known
http://learnzillion.com/lessons/596-find-the-part-when-the-percent-and-total-are-known

Calculate the part using the percent and total with a double number line.
Learnzillion: Convert fractions into percents
http://learnzillion.com/lessons/596-find-the-part-when-the-percent-and-total-are-known
Using multiplication by “1”
Accelerated
7th
Module 2A: Proportional Relationships
Grade Mathematics
Additional Problems
33.
Is the percent increase from 50 to 70 the same as the percent of decrease from 70 to 50? Why or
why not?
34.
The price of an iPod increased by $18, which represents a 9% increase. What was the iPod’s
original price? Check your answer using a second strategy.
35.
Clyde was directed to weigh a 500 g mass on the balance. He weighed it
quickly and reported that the object weighed 458 g. Find the percent
error involved, using two different strategies.
36.
You measured the skateboard ramp using a ruler and got a measurement
of 7.5 feet. According to the plan specifications, the ramp is 8 feet in length. What is the percent of
error in your measurement?
37.
Jamal needs to purchase a countertop for his kitchen. Jamal measured the countertop as 5 ft. The
actual measurement is 4.5 ft. What is Jamal’s percent error?
38.
There were 24 boys and 20 girls in a chess club last year. This year the
number of boys increased by 25%, but the number of girls decreased by
10%. Was there an increase or decrease in the overall membership? Find
the overall percent change in membership of the club.
39.
The sales team at an electronics store sold 48 computers last month. The manager at the store
wants to encourage the sales team to sell more computers and is going to give all the sales team
members a bonus if the number of computers sold increases by 30% in the next month. How
many computers must the sales team sell to receive the bonus? Explain your reasoning.
40.
After eating at a restaurant, Mr. Jackson’s bill before tax is $52.50. The sales tax rate is 8%. Mr.
Jackson decides to leave a 20% tip for the waiter based on the pre-tax amount. How much is the
tip Mr. Jackson leaves for the waiter? How much will the total be, including the tax and tip?
41.
A sweater is marked down 33% off the original price. The original price was $27.50. What is the
sale price of the sweater (before sales tax)? If the sales tax rate is 6%, how much will the sweater
cost?
42.
A salesperson set a goal to earn $2,000 in May. He receives a base salary of $500 per month as
well as a 10% commission for all sales in that month. How much merchandise will he have to sell
to meet his goal?
43.
A cookie company makes 4-ounce bags of chocolate chip cookies. The allowable margin of error
for the cookie bags is ±5%. If a bag is found to weigh 3.8 ounces, should it be removed or be
allowed to ship out? Justify your answer.
44.
The following price reductions are available.
Three for
Accelerated
7th
Module 2A: Proportional Relationships
Grade Mathematics
Additional Problems
a. Which of these four offers gives you the biggest price reduction? Explain your reasoning.
b. Which of these four offers gives you the smallest price reduction? Explain your reasoning.
45.
Helen and Julie are out shopping and see the sign for a clearance rack of shoes that reads “30%
off” and a sign that says “additional 70% off”. Helen says, “These shoes must be free if they are
100% off!” Julie disagrees. Help Julie to correct Helen’s reasoning.