# 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.

### Learning Targets

### 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.