Lesson 6: Using Equations to Solve Problems
About this lesson
In the previous two lessons students learned to represent proportional relationships with equations of the form \(y=kx\). In this lesson they continue to write equations, and they begin to see situations where using the equation is a more efficient way of solving problems than other methods they have been using, such as tables and equivalent ratios.
The activities introduce new contexts and, for the first time, do not provide tables; students who still need tables should be given a chance to realize that and create tables for themselves. The activities are intended to motivate the usefulness of representing proportional relationships with equations, while at the same time providing some scaffolding for finding the equations.
As students use the abstract equation \(y=kx\) to reason about quantitative situations, they engage in MP2.
Lesson overview
 6.1 Warmup: Number Talk: Quotients with Decimal Points (5 minutes)
 6.2 Activity: Concert Ticket Sales (15 minutes)

6.3 Activity: Recycling (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 6.4 Cooldown: Granola (5 minutes)
Learning goals:
 Generate an equation for a proportional relationship, given a description of the situation but no table.
 Interpret (orally) each part of an equation that represents a proportional relationship in an unfamiliar context.
 Use an equation to solve problems involving a proportional relationship, and explain (orally) the reasoning.
Learning goals (student facing):
 Let’s use equations to solve problems involving proportional relationships.
Learning targets (student facing):
 I can relate all parts of an equation like \(y=kx\) to the situation it represents.
 I can find missing information in a proportional relationship using the constant of proportionality.
Required materials:
 fourfunction calculators
Glossary:
 Access the complete Grade 7 glossary.
Standards
 This lesson builds on the standards: CCSS.5.NBT.B.7MS.5.NBT.7MO.5.NBT.A.8 CCSS.6.RP.A.2MS.6.RP.2MO.6.RP.A.2
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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