If I were in Harry Potter World, I would expand time between when I teach Volumes of Revolution and the AP Exam. This way, I could do a hands on project to actually embed the knowledge in the student brains. But alas, I'm just stuck with regular old days and a time-crunched teacher and students who are teenagers.
This year, I had my students do this project for the days they were in class.
It's the first time I've done it, so I made notes in my document for when the inevitable things went wrong this year that I want to improve upon for next attempt of this project:
You'll be shocked to learn that students can't convert between ruler tick marks and decimal numbers. SHOCKED, I tell you. You will also be floored by the fact that directions are for "other people", when you are doing a project, you should just keep asking about the next step.
Anyway, I liked how they turned out:
It was a good mix of freedom for their creativity, an in-depth practice of regression and degrees of polynomials and piecewise functions and graphing. It was a sad awareness of just how shallow some of the students' knowledge was of how to find a volume of revolution. I don't have a grading rubric (everyone is a winner!), but I think I may add one next time.