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Solving Problems about Proportional Relationships: IM 7.2.9
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1. Lesson 7.2.9
- IM 7.2.9 Lesson: Solving Problems about Proportional Relationships
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2. Practice 7.2.9
- IM 7.2.9 Practice: Solving Problems about Proportional Relationships
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Solving Problems about Proportional Relationships: IM 7.2.9
IM 6 – 8 Math, GeoGebra Classroom Activities, Jul 30, 2020
“Solving Problems about Proportional Relationships” from IM Grade 7 by Open Up Resources and Illustrative Mathematics. Licensed under the Creative Commons Attribution 4.0 license.
Table of Contents
- Lesson 7.2.9
- IM 7.2.9 Lesson: Solving Problems about Proportional Relationships
- Practice 7.2.9
- IM 7.2.9 Practice: Solving Problems about Proportional Relationships
IM 7.2.9 Lesson: Solving Problems about Proportional Relationships
Consider the problem: A person is running a distance race at a constant rate. What time will they finish the race?
What information would you need to be able to solve the problem?
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Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.
| If your teacher gives you the problem card: | If your teacher gives you the data card: |
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A company is hiring people to read through all the comments posted on their website to make sure they are appropriate. Four people applied for the job and were given one day to show how quickly they could check comments.
- Person 1 worked for 210 minutes and checked a total of 50,000 comments.
- Person 2 worked for 200 minutes and checked 1,325 comments every 5 minutes.
- Person 3 worked for 120 minutes, at a rate represented by , where is the number of comments checked and is the time in minutes.
- Person 4 worked for 150 minutes, at a rate represented by .
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Order the people from greatest to least in terms of how fast they checked the comments.
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Write equations for each job applicant that allow you to easily decide who is working the fastest.
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Make a table that allows you to easily compare how many comments the four job applicants can check.
IM 7.2.9 Practice: Solving Problems about Proportional Relationships
For each situation, explain whether you think the relationship is proportional or not. Explain your reasoning.
The weight of a stack of standard 8.5x11 copier paper vs. number of sheets of paper
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The weight of a stack of different-sized books vs. the number of books in the stack.
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Every package of a certain toy also includes 2 batteries.
Are the number of toys and number of batteries in a proportional relationship? If so, what are the two constants of proportionality? If not, explain your reasoning.
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Use for the number of toys and for the number of batteries to write two equations relating the two variables.
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Lin and her brother were born on the same date in different years. Lin was 5 years old when her brother was 2. Find their ages in different years by filling in the table and answer the question below.
Is there a proportional relationship between Lin’s age and her brother’s age? Explain your reasoning.
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A student argues that does not represent a proportional relationship between and because we need to multiply one variable by the same constant to get the other one and not divide it by a constant. Do you agree or disagree with this student?
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Quadrilateral A has side lengths 3, 4, 5, and 6. Quadrilateral B is a scaled copy of Quadrilateral A with a scale factor of 2. Select all of the following that are side lengths of Quadrilateral B.
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