# Lesson 8

Percent Increase and Decrease with Equations

### Lesson Narrative

In this lesson, students represent situations involving percent increase and percent decrease using equations. They write equations like $$y = 1.06x$$ to represent growth of a bank account, and use the equation to answer questions about different starting amounts. They write equations like $$t - 0.25t = 12$$ or $$0.75t=12$$ to represent the initial price $$t$$ of a T-shirt that was \\$12 after a 25% discount. The focus of this unit is writing equations and understanding their connection to the context. In a later unit on solving equations the focus will be more on using equations to solve problems about percent increase and percent decrease.

When students repeatedly apply a percent increase to a quantity and see that this operation be expressed generally by an equation, they engage in MP8.

### Learning Goals

Teacher Facing

• Explain (orally and in writing) how to calculate the original amount given the new amount and a percentage of increase or decrease.
• Generate algebraic expressions that represent a situation involving percent increase or decrease, and justify (orally) the reasoning.

### Student Facing

Let’s use equations to represent increases and decreases.

### Student Facing

• I can solve percent increase and decrease problems by writing an equation to represent the situation and solving it.

Building On