In this lesson, students use linear functions to model real-world situations (MP4). In the Warm-up, they are given data for an almost linear relationship and develop a linear model. They use their model to make predictions and discuss the reasonableness of the model. Then students consider a situation, the amount of the moon that appears illuminated from Earth over time, that they can make a linear model for, but it isn’t very accurate. In the garbage recycling activity, different linear models apply to different time periods.

When given data isn’t perfectly linear, students have to determine if a linear model is reasonable and what types of restrictions the model might need. The work here leads to future work modeling with piecewise linear functions.

The third activity is optional and offers additional practice with a situation that seems linear at first glance but is not. This activity works best when each student has access to a device that can run the applet, which allows students to plot values accurately.