Box Volume
This is a classic calculus problem, although it is often introduced as early as a basic algebra course. This version is based on the sketch of the same name from the Calculus section of Sketchpad's Samples.
The problem involves trying to maximize (or minimize) the volume of the box made by cutting the corners out of a piece of paper and folding up the sides, given an original paper size. Here you can vary both the size of the paper and the size of the corner to cut out.