Lesson plan

In this lesson, students will learn how to compare proportional relationships. Students will use their prior knowledge of proportional relationships to tie into comparisons. Students will work collaboratively to compare proportional relationships represented as a description, equation, table, or graph. You can expect this lesson with additional practice to take one `45`-minute class period.

Grade 7

Rates And Proportional Relationships

7.RP.A.2.B

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Students will be able to compare proportional relationships.

- Teacher Slideshow
- Online Practice

At this point, students will have been exposed to different representations of proportional relationships. Because of this, the warm up acts as an opportunity for students to review the different representations.

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Students might use different strategies to compare the two relationships. Most likely, students will find the unit rate and compare the values. Some students might reason that while Addison can walk `17` miles in `2` hours, Ian can walk `18` miles in the same time ; therefore Ian must be faster.

You can communicate to students that they can use any strategy to justify their answer - however they can always use unit rate as a back-up strategy.

When going over students’ answers, it is important that students explain their reasoning. Consider asking students how their methods for finding the unit rate varied depending on the representation. You can also extend the review by asking students to write equations for each person. You can also ask students to determine who the fastest walker was and how they know. This can help extend what they have already accomplished to include the comparison after discussion.

With the next example, students will be given an equation to compare with a table.

To gain insight on students’ understanding of the equation for proportional relationships, allow them to discuss how they can solve this problem with a partner. As students talk, you can listen to determine if students are recognizing that “`50`” in the equation represents the rate of change, or the cost per cell phone for the first company. **Students may also choose to make graphs or tables to help them represent the information given in an equation.**

Once students have determined the cost for each company and the difference, have students explain the process they used to compare the proportional relationships. Ideally, students will have opted to find the unit rate or write an equation for the table.

With this next example, students will need to compare a verbal description and a graph. Ask students to consider what they should try to find for each representation to help compare them: ideally they will use vocabulary like “constant of proportionality” or “unit rate”, but they may also say something more context-related.

This example is different from others since it has three relationships to compare. You could do this as a class with the students, or include it in their practice.

Allowing students time to work collaboratively can allow them some choice in what they work on. It can also allow them the ability to process the information independently, and then deepen their understanding by explaining how they did it to another student. When reviewing with students, be sure to emphasize that the constant of proportionality is the rate of change. Using this value can make it easier to compare proportional relationships.

After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for comparing proportional relationships. Check out the online practice and assign to your students for classwork and/or homework!

Comparing Proportional Relationships Practice

Problem 1 of 5

<p>Megan is looking for a part-time job. She narrows down her search to the following two positions:</p> <ul> <li>A job as a waitress, which pays a dollar amount (`d`) based on number of hours she works (`h`) as given by the equation `d = 13.25h`</li> <li>A job as pastry chef that pays the amount of `$62` for `4` hours of work.</li> </ul> <p>What are the earnings per hour for each of the positions?</p> <p> What is the difference in the hourly rate of pay between the two positions?</p>

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