As an introduction to Integration in my Calculus class, I gave them the task of determining the volume of various buildings on campus. I wanted them to get comfortable with the idea of splitting something up into much smaller pieces in order to find the area and also wanted them to get an idea of good and bad approximations. Each group was given two similarly sized buildings and was asked to figure out which one was larger. It ended up being a great project – one that is a very simple question on the outset, but still provides quite a bit of challenge, a large problem that needs to be attacked with lots of smaller ones, and something that actually spits out a fairly interesting answer at the end.

The other nice thing about student directed learning like this is that they come up with stuff that you would never expect. Most groups used the same method of determining the heights of the buildings – using something in a picture that they know the size of and then creating some sort of scale to measure everything else. One group created a really nice visual for this by stacking members of their group that has been one of my favorite pieces of student work all year. It’s nothing groundbreaking, and it’s fairly simple, but for some reason I just found it absolutely hilarious. Check it out…