Lesson 8

Reasoning about Solving Equations (Part 2)

Lesson Narrative

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.

Learning Goals

Teacher Facing

  • 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.

Student Facing

Let’s use hangers to understand two different ways of solving equations with parentheses.

Learning Targets

Student Facing

  • I can explain how a balanced hanger and an equation represent the same situation.
  • I can explain why some balanced hangers can be described by two different equations, one with parentheses and one without.
  • 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.

CCSS Standards

Building On


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