# Lesson 7

Reasoning about Solving Equations (Part 1)

### Lesson Narrative

The goal of this lesson is for students to understand that we can generally approach equations of the form $$px+q=r$$ by subtracting $$q$$ 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.

### Learning Goals

Teacher Facing

• 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.

### Student Facing

Let’s see how a balanced hanger is like an equation and how moving its weights is like solving the equation.

### Student Facing

• I can explain how a balanced hanger and an equation represent the same situation.
• 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.