Lesson 9

In this lesson, students use linear functions to model real-world situations (MP4). In the candle activity, 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. In the shadow activity, it is difficult to tell from the information given if a linear model is appropriate, but when they are given more information, it becomes clear that the relationship is not linear. In the garbage recycling activity, different linear models apply to different time periods.

None of the given data are perfectly fit by a linear function, and students have to determine whether a linear approximation is reasonable and for which values it would be reasonable. Students should start to see both the value of linear models and their limitations. The garbage recycling activity leads into the next lesson, which is about modeling with piece-wise linear functions.

Provide access to straightedges to each student.