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 Tshirt 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.
Learning Targets
Student Facing
 I can solve percent increase and decrease problems by writing an equation to represent the situation and solving it.
Glossary Entries

percentage decrease
A percentage decrease tells how much a quantity went down, expressed as a percentage of the starting amount.
For example, a store had 64 hats in stock on Friday. They had 48 hats left on Saturday. The amount went down by 16.
This was a 25% decrease, because 16 is 25% of 64.

percentage increase
A percentage increase tell how much a quantity went up, expressed as a percentage of the starting amount.
For example, Elena had \$50 in the bank on Monday. She had \$56 on Tuesday. The amount went up by \$6.
This was a 12% increase, because 6 is 12% of 50.