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Comparing Relationships with Tables: IM 7.2.7
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1. Lesson 7.2.7
- IM 7.2.7 Lesson: Comparing Relationships with Tables
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2. Practice 7.2.7
- IM 7.2.7 Practice: Comparing Realtionships with Tables
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Comparing Relationships with Tables: IM 7.2.7
IM 6 – 8 Math, GeoGebra Classroom Activities, Jul 30, 2020
“Comparing Relationships with Tables” from IM Grade 7 by Open Up Resources and Illustrative Mathematics. Licensed under the Creative Commons Attribution 4.0 license.
Table of Contents
- Lesson 7.2.7
- IM 7.2.7 Lesson: Comparing Relationships with Tables
- Practice 7.2.7
- IM 7.2.7 Practice: Comparing Realtionships with Tables
IM 7.2.7 Lesson: Comparing Relationships with Tables
A lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey. Invent four new versions of this lemonade recipe:
One that would make more lemonade but taste the same as the original recipe.
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One that would make less lemonade but taste the same as the original recipe.
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One that would have a stronger lemon taste than the original recipe.
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One that would have a weaker lemon taste than the original recipe.
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Entrance to a state park costs $6 per vehicle, plus $2 per person in the vehicle. Complete the table and answer the questions below.
For each row in the table, if each person in the vehicle splits the entrance cost equally, how much will each person pay?
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How might you determine the entrance cost for a bus with 50 people?
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Is the relationship between the number of people and the total entrance cost a proportional relationship?
Explain how you know.
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What equation could you use to find the total entrance cost for a vehicle with any number of people?
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Han and Clare were running laps around the track. The coach recorded their times at the end of laps 2, 4, 6, and 8. Complete the table of Han's run.
Now complete the table of Clare's run and answer the questions below.
Is Han running at a constant pace? How do you know?
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Is Clare running at a constant pace? How do you know?
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Write an equation for the relationship between distance and time for anyone who is running at a constant pace.
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IM 7.2.7 Practice: Comparing Realtionships with Tables
Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would the constant of proportionality be?
How loud a sound is depending on how far away you are:
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The cost of fountain drinks at Hot Dog Hut.
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A taxi service charges $1.00 for the first ⅒ mile then $0.10 for each additional ⅒ mile after that. Fill in the table with the missing information and answer the question below.
Is this relationship between distance traveled and price of the trip a proportional relationship? How do you know?
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A rabbit and turtle are in a race. Is the relationship between distance traveled and time proportional for either one? If so, write an equation that represents the relationship.
| Turtle’s run: | Rabbit’s run: |
 |  |
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For each table, answer: What is the constant of proportionality?
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Kiran and Mai are standing at one corner of a rectangular field of grass looking at the diagonally opposite corner. Kiran says that if the the field were twice as long and twice as wide, then it would be twice the
distance to the far corner. Mai says that it would be more than twice as far, since the diagonal is even longer than the side lengths. Do you agree with either of them? Why or why not?
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