This lesson continues the work of developing efficient equation solving strategies, justified by working with hanger diagrams. The goal of this lesson is for students to understand two different ways to solve an equation of the form \(p(x+q)=r\) efficiently. After a warm-up to revisit the distributive property, the first activity asks students to explain why either of two equations could represent a diagram and reason about a solution. The next activity presents four diagrams, asks students to match equations and then solve them. The goal is for students to see and understand two approaches to solving this type of equation.
Lesson overview
- 8.1 Warm-up: Equivalent to 2(x+3) (5 minutes)
- 8.2 Activity: Either Or (15 minutes)
- 8.3 Activity: Use Hangers to Understand Equation Solving, Again (15 minutes)
- Lesson Synthesis
- 8.4 Cool-down: Solve Another Equation (5 minutes)
Learning goals:
- Compare and contrast (orally) different strategies for solving an equation of the form \(p(x+q)=r\).
- Explain (orally and in writing) how to use a balanced hanger diagram to solve an equation of the form \(p(x+q)=r\).
- Interpret a balanced hanger diagram with multiple groups, and justify (in writing) that there is more than one way to write an equation that represents the relationship shown.
Learning goals (student facing):
- Let’s use hangers to understand two different ways of solving equations with parentheses.
Learning targets (student facing):
- I can explain why some balanced hangers can be described by two different equations, one with parentheses and one without.
- I can explain how a balanced hanger and an equation represent the same situation.
- I can write an equation that describes the weights on a balanced hanger.
- I can find an unknown weight on a hanger diagram and solve an equation that represents the diagram.
Glossary:
- Access the complete Grade 7 glossary.
Standards:
- This lesson builds on the standard: CCSS.6.EE.A.4MS.6.EE.4MO.6.EEI.A.3
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.
This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses.