This lesson is optional. Its goal is to remind students about what they know of percent change and the different ways of expressing it (a topic from grade 7), in preparation for the situations they will encounter in upcoming lessons. A repeated percent increase or decrease is an exponential change.
One key idea being reinforced is that there are different ways to express the new amount after a quantity increases or decreases by a certain percentage. For instance, if a shirt costs \(x\) dollars and is discounted by 20%, the discounted price can be expressed as \(x - 0.2x\), as \(x \boldcdot (1-0.2)\), or as \(x \boldcdot (0.8)\). Knowing how to describe the new amount using the last expression is going to help students represent exponential change in the context of compounded interest, population changes, etc. (where the growth factor is not a whole number). Looking for equivalent ways to express percentage change is largely about strategically using the distributive property (MP7).
This lesson could be bypassed if the pre-unit diagnostic assessment indicates that students don't need to review these concepts and skills.
- Given a starting amount and a percent increase or decrease, calculate a final amount.
- Write expressions using only multiplication to represent a percent increase or decrease.
Let's find the result of changing a number by a percentage.
- I can find the result of applying a percent increase or decrease on a quantity.
- I can write different expressions to represent a starting amount and a percent increase or decrease.