I love quadratic functions.  There are so many real-world applications that it is difficult to choose just one, and of course, I don't.  As part of our quadratics unit, I offer several project options for students choose from that apply quadratic functions.

A popular project amongst my students is the roller coaster project.  Students explore the time and distance required for an actual roller coaster to fall from its tallest hill and then design their own roller coasters.

I start by having students use data from a real-world roller coaster to determine the time it will take for the coaster to go from the tallest hill to the bottom.  This is our "warm-up."  Students have already seen quadratic functions and are essentially applying a quadratic function to solve a problem.

In part two, students explore the design of roller coasters.  We take time to actually design roller coasters online.  My students like the simulation from the Jason Learning and this one from Discovery kids.  The programs are different enough that it is valuable to have students work with both of them.  Students have time to explore the challenges in designing a roller coaster as well as thinking about what kind of roller coaster they would like to create i.e. scary, fast, slow, tame, etc.

In part three, students get to the really fun part.  Students design their own roller coasters.  They develop their own models for their roller coasters, sketch the roller coasters, and write about them.  As I am reminded again and again with project-based learning, students will do amazing work when given broad parameters and lots of freedom.

This project works well because:
1. Students work with an example of what they will develop a model for.
2. Students are given ample time to explore the concepts.
3. Students have broad parameters to guide them with an open-ended project that provides significant freedom.
Have a favorite tip for working with quadratic functions or open-ended projects?  Post it in the comments section below.

Math Mondays
is a bi-weekly blog post (2nd and 4th Monday of each month) sharing tips, ideas, resources, and products for teaching math.  If you have questions or think there is something I should include, you can leave me a message in the comments section below or at the store in the question and answer section.