Math 7
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Proportional relationships can be identified in both tables and graphs. Today you will have an
opportunity to take a closer look at how graphs and tables for proportional relationships can
help you organize your work to find any missing value quickly and easily.
Think about the following learning goals:
 I can decide whether two quantities are in a proportional relationship (RP2A)
 I can identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams,
and verbal descriptions of proportional relationships (RP2B)
 I can explain what a point (x, y) on the graph of a proportional relationship means (RP2D)
 SMP #4 Model with mathematics
1. Robert’s new hybrid car has a gas tank that holds 12 gallons of gas.
When the tank is full, he can drive 420 miles. Assume that his car uses
gas at a steady rate.
a. Is the relationship between the
number of gallons of gas used and
the number of miles that can be
driven proportional? For example,
does it change like Sonja’s birdseed
prediction, or is it more like
Gustavo’s college savings? Explain
how you know.
.
b. Show how much gas Robert’s car will use at
various distances by copying and completing
the table below.
c. Robert decided to graph the situation, as shown below. The distance Robert can travel using
one gallon of gas is called the unit rate. Use Robert’s graph to predict how far he can drive
using one gallon of gas. That is, find his unit rate.
d. While a graph is a useful tool for estimating, it is often
difficult to find an exact answer on a graph. What do you
need to estimate when finding the point labeled (1, y)?
How can you calculate y exactly?
e. Use the table in part (b) and your answer in part (d) to
find Robert’s unit rate (the gallons used to drive 1 mile).
f. Work with your team to write the equation to find the
exact number of miles Robert can drive with any
number of gallons of gas (use x). Be prepared to share your
strategy.
2. THE YOGURT SHOP
Jell E. Bean owns the local frozen yogurt shop. At her store, customers
serve themselves a bowl of frozen yogurt and top it with chocolate chips,
frozen raspberries, and any of the different treats available. Customers must
then weigh their creations and are charged by the weight of their bowls.
Jell E. Bean charges $32 for five pounds of dessert, but not many people buy that much frozen yogurt.
She needs you to help her figure out how much to charge her customers. She has customers that are
young children who buy only a small amount of yogurt as well as large groups that come in and pay
for everyone’s yogurt together.
a. Is it reasonable to assume that the weight of the yogurt is proportional to its cost? How can you
tell?
b. Assuming it is proportional, make a table that lists the price for at least ten different weights of
yogurt. Be sure to include at least three weights that are not whole numbers.
c. What is the unit rate of the yogurt? (Stores often call this the unit price.) Use the unit rate to write
an equation that Jell E. Bean can use to calculate the amount any customer will pay.
d. If Jell E. Bean decided to start charging $0.50 for each cup before her customers started filling it
with yogurt and toppings, could you use the same equation to find the new prices? Why or why
not?
3. Lexie claims that she can text 34 words in 4 minutes. Her teammates, Kenny and Esther,
are trying to predict how many words Lexie can text in a 35-minute lunch period
if she keeps going at the same rate.
a. Is the relationship between the number of words texted and time in minutes proportional?
Why or why not?
b. Kenny represented the situation using the table shown to the right.
Explain Kenny’s strategy for using the table.
c. Esther wants to solve the problem using an equation. Help her
write an equation to determine how many text messages Lexie
could send in any number of minutes.
d. Find the missing values in Kenny’s table.
e. Solve Esther’s equation. Will she get the same answer as Kenny?
f. What is Lexie’s unit rate
Kenny’s Table
Words texted
34
68
Minutes
1
4
8
16
x