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Lesson plan

Lesson 6: Using Equations to Solve Problems

teaches Common Core State Standards MP8 http://corestandards.org/Math/Practice/MP8
teaches Common Core State Standards 7.RP.A.2.c http://corestandards.org/Math/Content/7/RP/A/2/c
teaches Common Core State Standards 7.RP.A.2 http://corestandards.org/Math/Content/7/RP/A/2
teaches Common Core State Standards MP2 http://corestandards.org/Math/Practice/MP2

Lesson 6: Using Equations to Solve Problems

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 Warm-up: 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 Cool-down: 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:

  • four-function calculators


  • Access the complete Grade 7 glossary.


  • 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 2017-2019 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/math-curriculum/.

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).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

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