Notes-Ratios and Proportions Lesson 4: Identifying Proportional and Non-Proportional Relationships in Tables
Name _________________________Date _______________Period _____
Independent/Group Work: You will complete the tables below, independently. Then, you will discuss your results
with a small group.
Example: Which Team Will Win the Race?
You have decided to run in a long distance race. There are two teams that you can join. Team A runs at a constant
rate of 2.5 miles per hour. Team B runs 4 miles the first hour and then 2 miles per hour after that.
Task: Create a table for each team showing the distances that would be run for times of 1, 2, 3, 4, 5, and 6 hours.
Team A
Time (hours)
Distance (miles)
1
2.5
Time (hours)
1
Team B
Distance (miles)
4
2
5
2
6
3
7.5
3
8
4
10
4
10
5
12.5
5
12
6
14
6
14
Now, discuss the questions below in your groups. I will choose people from each group to answer some of these
questions to the class-so be sure everyone in your group participates in the discussion and understands the
answers.
a.) For which team is distance proportional to time? Explain your reasoning. Team A.
b.) Explain how you know distance for the other team is not proportional to time. They ran at different speeds
throughout the rsace.
c.) If the race were 2.5 miles long, which team would win? Be ready to explain. Team B because they took 1
hour to run 4 miles (or 36 minutes to run 2.5 miles) and Team A took 1 hour to run 2.5 miles.
d.) If the race were 3.5 miles long, which team would win? Be ready to explain. Team B because they took 1
hour to run 4 miles (52.5 minutes to run 3.5 miles and Team A took over an hour to run 3.5 miles.
e.) If the race were 4.5 miles long, which team would win? Be ready to explain. Team B because at the time of
the race that both teams passed the 4.5 mile mark, Team B had still traveled farther faster.
f.) For what length race would it be better to be on Team B than Team A? Explain your reasoning. Any race
less than 10 miles in length.
g.) Using this relationship, if the members on the team ran for 10 hours, how far would each member run on
each team? Team A would have run 24 miles in 10 hours, while Team B would have run 22 miles in 10 hours.
h.) Will there always be a winning team, no matter what the length of the course? Why or why not? No. if
the race was 4 miles long, Team A and Team B would have tied.
Notes-Ratios and Proportions Lesson 4: Identifying Proportional and Non-Proportional Relationships in Tables
i.) If the race is 12 miles long, which team should you choose to be on if you wish to win? Why would you
choose this team? Team A because they finished 12.5 miles at the time Team B finished 12 miles, so they
passed the 12 mile mark before Team B.
j.) How much sooner would you finish on that team compared to the other team? It depends on the length of
the race.