Polynomials and Roller Coasters

by Rebekah Cook

In my Honors Pre-Calculus class last semester, I had the opportunity to teach a STEM unit using polynomial functions to design roller coasters. The overall goal of the unit was for students to work in teams to design a portion of a roller coaster that would meet the needs of a client and their customers in hopes of being chosen as the final design team, experiencing the same process as someone in the field of architecture or structural engineering might in competing for a job.

While learning about the behavior of polynomial functions, students researched different types of roller coasters and surveyed the needs and wants of potential customers. They then had to come up with an algebraic and graphical model capturing the height verses time of the first 30 seconds of a roller coaster ride, keeping in mind the constraints set by the client and customers. The design teams did a gallery presentation of their graphical representations and analysis of their coasters for their first rounds of interviews, after which half of the teams were eliminated.  Using the feedback from this, the final teams created 3-dimensional models to capture the first 30 seconds of the ride and provide a visual for the client to understand the behavior of the coaster. They presented these on the last day of finals to a group of professionals including district personnel, engineers, and architects, acting on behalf of the client who chose two final groups they would hire to design their roller coaster. The feedback from all interviewers was tremendous as they were very impressed by the hard work put into the presentations and models and the level of understanding the students demonstrated in using all types of functions, not just polynomials, to model real-life situations. 

In my 15 years of teaching mathematics I have always struggled with helping students understand and be able to analyze the behavior of algebraic functions, especially at the higher levels. After students completed this project, I feel they not only had a great time creating their roller coasters, but they also felt more comfortable talking about the behavior of functions than I have ever experienced before.