The goal of this lesson is for students to understand that we can generally approach equations of the form \(px+q=r\) by \(q\) subtracting from each side and dividing each side by \(p\) (or multiplying by \(\frac{1}{p}\)). Students only work with examples where \(p\) , \(q\), and \(r\) are specific numbers, not represented by letters. This is accomplished by considering what can be done to a hanger to keep it balanced.
Students are solving equations in this lesson in a different way than they did in the previous lessons. They are reasoning about things one could “do” to hangers while keeping them balanced alongside an equation that represents a hanger, so they are thinking about “doing” things to each side of an equation, rather than simply thinking “what value would make this equation true” or reasoning with situations or diagrams.
Lesson overview
 7.1 Warmup: Hanger Diagrams (10 minutes)
 7.2 Activity: Hanger and Equation Matching (15 minutes)
 7.3 Activity: Use Hangers to Understand Equation Solving (15 minutes)
 Lesson Synthesis
 7.4 Cooldown: Solve the Equation (5 minutes)
Learning goals:
 Compare and contrast (orally) different strategies for solving an equation of the form \(px+q=r\).
 Explain (orally and in writing) how to use a balanced hanger diagram to solve an equation of the form \(px+q=r\).
 Interpret a balanced hanger diagram, and write an equation of the form \(px+q=r\) to represent the relationship shown.
Learning goals (student facing):

Let’s see how a balanced hanger is like an equation and how moving its weights is like solving the equation.
Learning targets (student facing):
 I can find an unknown weight on a hanger diagram and solve an equation that represents the diagram.
 I can write an equation that describes the weights on a balanced hanger.
 I can explain how a balanced hanger and an equation represent the same situation.
Glossary:
 Access the complete Grade 7 glossary.
Standards:
 This lesson builds towards the standard: CCSS.7.EE.B.4.aMS.7.EE.4aMO.7.EEI.B.4b
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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