Project Title: Proportional Reasoning in Real-Life Stories
Challenge Brief
In this investigation, you will determine whether three real-life stories describe proportional or
non-proportional relationships by creating and examining tables of data and the related equation
and graph that represent each story.
Project Requirements:
1. Every group is complete the following for each story:
 Construct a data table
 Create a graph of the data
 Write an equation that corresponds with the data in the table and graph
 Answer the guiding questions
2. Creative Display of Work: Chart Paper
Each group will be assigned one story to do the following:
 Write your scenario in large print.
 Include the data table, graph, and equation.
 In your own words, explain if the real-life scenario represents a proportional or nonproportional relationship.
3. Participation in Class Discussion
 Complete, ‘What Do You Think?’
Standards
7th Grade:
(7.3) Patterns, relationships, and algebraic thinking. The student solves problems involving direct
proportional relationships. The student is expected to
(B) estimate and find solutions to application problems involving
proportional relationships such as similarity, scaling, unit cost,
and related measurement units.
(7.5) Patterns, relationships, and algebraic thinking. The student uses equations to solve
problems. The student is expected to
(B) formulate problem situations when given a simple equation and
formulate and equation when given a problem situation.
th
8 Grade:
(8.3) Patterns, relationships, and algebraic thinking. The student identifies proportional or nonproportional linear relationships in problem situations and solves problems. The student is
expected to
(A) compare and contrast proportional and non-proportional linear
Relationships.
Scenarios
1. Your principal has asked you to participate in a Race for the Cure, a fund-raising event to
collect money for research to fight cancer. Your middle school will donate $20 for each
mile you walk or run.
2. Your school plans to buy new computers at $525 per computer. The total number of
computers that can be purchased depends on the amount of money in the budget allocated
for the computers.
3. You are helping your mom plan a birthday party for your brother at a bowling alley. The
shoe rental is $5 and each game costs$2.50.
Race for the Cure
Your principal has asked you to participate in a Race for the Cure, a
fund-raising even to collect money for research to fight cancer. Your
middle school will donate $20 for each mile you walk or run.
a. Construct a table to determine the total amount of money you can raise depending
on how many miles you will walk or run. Show how you determined the amount
of the donation by recording the process you used to calculate the amount in a
column labeled “Process”.
b. Create a graph of your data. Describe how the graph is a representation of the
table. (graph paper)
c.
Determine an equation that could be used to calculate the amount of money you
can raise if you were to walk x miles.
d. Does your equation represent the data in your graph? Explain your reasoning.
e. In what way is the $20 per mile donation represented in the data table? In the
equation? In the graph of the equation?
f. a proportion to determine the money raised for walking or running 4 miles.
Running or walking 8 miles? Running or walking 10 miles? Show your work.
g. Were your answers for each problem already in the table, the equation, and your
graph? Explain why or why not?
h. Does the real-life problem represent a proportional relationship? Use the data
from your table, equation, and graph to explain why or why not?
Computer Purchases
Your school plans to buy new computers at $525 per computer. The
total number of computers that can be purchased depends on the amount
of money in the budget allocated for the computers.
a. Create a table to determine the cost of computers depending on the number of
computers.
b. Determine an equation that could be used to budget x computers.
c. Use your equation to buy six additional computers. Enter the data in your
table and graph the data.
d. Does your equation represent the data in your graph? Explain your reasoning.
e. In what way is the price of a computer represented in the data table? In the
equation? In the graph of the equation?
f. Set up a proportion to determine the cost of computers if the school bought 5
computers, eight computers, and ten computers. Show your work.
g. Were your answers for each computer already in the table, the equation, and
in your graph? Explain why or why not?
h. Does this situation represent a proportional relationship? Why or why not?
Use the data from your table, equation, proportion, and graph to explain.
Party at the Bowling Alley
You are helping your mom plan a birthday party for your brother at a bowling
alley. The shoe rental is $5 and each game costs $2.50.
a. Create a table to record what could be the cost per person for a
different number of bowling games.
b. Determine an equation that could be used to calculate the cost per person for x
games.
c. Use your equation to buy five additional games. Enter your data in the table and
graph all the data.
d. Does your equation represent the data you graphed? Explain your reasoning.
e. Can you use a proportion to determine the cost of bowling 8 games? Explain your
reasoning.
f. In what way is the cost per game represented in the data table? In the equation? In
the graph of the equation?
g. In what way is the shoe rental price represented in the data table? In the equation?
In the graph of the equation?
h. Does this situation represent a proportional relationship? Why or why not?
What Do You Think?
1. Compare and contrast data tables, equations, and graphs for the three
stories you investigated.

What is similar and what is different for the three tables?

What is similar and what is different for the three graphs?

What is similar and what is different for the three equations?
2. Identify characteristics of proportional and non-proportional relationships by analyzing
the three data tables, graphs, and equations.

Describe the properties of data in a table that represent a proportional relationship.

Describe the properties of a graph that represents a proportional relationship.

Describe the properties of an equation that represent a proportional relationship.
Proportional Reasoning in Real-Life Stories
Rubric
4
Explanation
Use of Visuals
Display of
Work (chart
paper)
Mechanics
Demonstrated
Knowledge
A complete
response with a
detailed
explanation in all
three scenarios.
Clear data table,
graph, and
equation with
detail in all three
scenarios.
Includes scenario,
data table, graph,
equation, &
detailed
explanation of
proportional or
non-proportional
reasoning.
Completes all
three scenarios
with no math
errors or flaws in
reasoning.
Shows complete
understanding of
the scenarios,
questions,
proportional
reasoning, and
processes.
Criteria
3
Good solid response
with clear
explanation in two
out of the three
scenarios.
Clear data table,
graph, & equation in
all three scenarios.
2
Points
1
Explanations are
unclear in any of the
scenarios.
Misses Key
Points in all
scenarios.
Unclear data table,
graph, & equation in
any or all of the three
scenarios.
Missing data
table, graph, or
equation in any
or all of the three
scenarios.
Includes scenario,
data table, graph,
equation &
explanation of
proportional or nonproportional
reasoning.
Includes scenario,
data table, graph and
equation.
No product.
No major math
errors or serious
flaws in reasoning.
Some serious math
errors or flaws in
reasoning.
Major errors or
serious flaws in
reasoning.
Shows substantial
understanding of the
three scenarios,
questions,
proportional
reasoning, and
processes.
Response shows
some understanding
of the scenarios.
Response or no
response shows
complete lack of
understanding.