Lesson plan

Lesson 1: Relationships between Quantities

Lesson 1: Relationships between Quantities

In this introductory lesson, students encounter some engaging contexts characterized by relationships that are not proportional. The goal is simply to see that we need some new strategies—it is the work of the upcoming unit to develop strategies for efficiently solving problems about contexts like some of the ones in this lesson. In this lesson, is not expected that students write expressions or equations, or use any specific representation. Students may choose to make diagrams or tables or reason in some other way.

Lesson overview

  • 1.1 Warm-up: Pricing Theater Popcorn (10 minutes)
  • 1.2 Activity: Entrance Fees (10 minutes)
  • 1.3 Optional Activity: Making Toast (10 minutes)
    • Includes "Are you Ready for More?" extension problem
  • Lesson Synthesis
  • 1.4 Cool-down: Movie Theater Popcorn, Revisited (5 minutes)

Learning goals:

  • Determine unknown values in a relationship that is not proportional, and explain (orally and in writing) the solution method.
  • Interpret and describe (orally and in writing) relationships that are predictable, but not proportional.
  • Justify (orally) that a given relationship is not proportional.

Learning goals (student facing):

  • Let’s try to solve some new kinds of problems.

Learning targets (student facing):

  • I can think of ways to solve some more complicated word problems.


  • Access the complete Grade 7 glossary. 


  • This lesson builds on the standards: CCSS.7.RP.A.2 CCSS.7.RP.A.2.aMS.7.RP.2aMO.7.RP.A.2aMS.7.RP.2
  • This lesson builds towards the standards: CCSS.7.EE.B CCSS.7.EE.B.4CCSS.7.EE.B.4.aMS.7.EE.4aMO.7.EEI.B.4bMS.7.EE.4






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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