Of all of the things that frustrate my students in geometry class, theorems and proofs are clearly the top two. This feeling is quite understandable, too. I think that students have a hard time making sense of the stuff I am asking them to prove AND I think that student have a hard time making sense of the method I am asking them to use to prove that stuff.
Enter Dr. James Tanton, who seems to have more fun doing math than most of my students would even think was possible. This video here presents a theorem called the Two Pancake Theorem (I have also seen it called the Ham Sandwich Theorem) along with a proof to support the theorem.
This video impressed me for a couple of reasons. First of all, there is nothing abstract about a pancake… and really… as you watch the video, don’t let yourself get caught up in the mathy-ness of it. Think about pancakes! Also, the proof is very approachable and makes use of excellent deductive reasoning without being overbearing.
Seriously, it is a proof about cutting pancakes in half!
Of course, the theorem does have some more serious applications than pancakes or ham sandwiches (regression lines and data analysis, for example), but that doesn’t mean that it takes an applied mathematician to have some fun with cutting some pancakes in half.