**Submitting Organization:** Illustrative Mathematics

**Grade Levels: **9th Grade

**Subject Area:** Math

**Standards Alignment: **Common Core Standards Math

F-IF.B.6 This connects to high school content standard HSF-IF.B.6, about calculating and interpreting rates of change, and to mathematical practice standard MP.6: Model with mathematics.

**Description of the Activity: **

In this problem, students use given data points to calculate the average rate of change of a function over a specific interval, foreshadowing the idea of limits and derivatives to students. Indeed, teachers of advanced classes could closely mirror this idea by starting with the average rate of change for the year and then shrinking the interval to approximate the line tangent to the curve at a specific point. Exposing students to these ideas early on is good preparation for calculus.

**Discussion Questions:**

- When do you think the EPA started its intervention?
- At the rate the population was declining 3 months after the first observation, when would the mathemafish population have disappeared? What about 6 months after the first observation?

**Resources Needed:**

None

**Link to further resources:**

https://www.illustrativemathematics.org/content-standards/tasks/686