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.