Ever since Riley and I had this exchange, I've been dissatisfied with my classroom's plain door that is not covered in spikes. Well, like, lo:
This took three days of class time (129 minutes) for a non-honors Geometry class of almost all tenth graders. Many students also needed some additional time outside of class. The goal was for students to get hands-on grokking for the meanings of height, slant height, surface area, and volume. They designed the net of a pyramid and labeled dimensions, calculated the total surface area and volume of their design, and constructed and decorated the model.
I offered a bonus for a base that was not a square. I also suggested making a cone instead, but none of them chose to make a cone, so next time I should make the cone worth a bonus as well. I specified a target range for the area of the base, and a target range for the volume, mostly so that the door would look cool.
Here is the project description and scoring sheet.
In order to make grading less ultimately-annoying, since they were given lots of flexibility in choosing measurements, I programmed my TI to do calculations for me (link goes to TI-Nspire .tns file.) The vast majority made a square pyramid, and just about every student first decided on the length of a base edge and the slant height, and went from there, so the program takes these measurements as inputs, and returns all the other values they were supposed to calculate. This way, if their numbers match my numbers, I can just move on, and only have to spend more time inspecting their work if there is a discrepancy.
Here is an example of what a student turned in. Since they had to organize their work, I had to say things like "Label EVERYTHING! Make it REALLY EASY for me to grade! I am VERY LAZY and I DON'T CARE if you get a good grade!" That sounds awful but it's funny only because they know neither of those things are true. It would be easier to grade these if you gave them like a template where they had to fill in stuff, but I think there's a ton of value in them deciding how to present their work sometimes. This is hard for me to explain, but when they are in filling-in-blanks mode it's different from figuring-stuff-out mode.
This was pretty fun and a nice break from the usual. I believe the goal of reliably distinguishing both slant height from height, and volume from surface area was achieved. And my door is looking pretty badass. I'd do this again.
Shoulders this project stands on: