The Reel Deal : A Lesson by Mathalicious

Lately it seems that popular movies have gotten longer and longer. In fact, the average top-grossing movie’s runtime has steadily increased over the past 30 years. Why might this be, and will that trend continue in the future?

In this lesson students use scatterplots to examine linear and nonlinear patterns in data and make predictions about the future. They also bump up against some limitations of the linear model and the dangers of extrapolation.

Students will

Interpret a scatterplot to describe how the length of top-grossing movies has changed over time
Informally fit a line to data and interpret its rate of change in the context of movie length
Extrapolate from known data to make a prediction for the future and consider its reasonableness
Refine predictions based on new data and compare linear vs. nonlinear patterns of association
Discuss the potential problems of extrapolation from a limited data set

Before you begin

Students need two basic skills for the majority of this discussion: the ability to plot points from a table, and the ability to use a line to calculate the rate of change between two variables.