I presented the labs for the first-year calculus course at my school this past semester, and as a bit of an experiment I decided to try giving the students some less “ordinary” problems to work on at the end of the labs (partly inspired by this problem). I only ended up doing it for the first four weeks of the semester due to a combination of it taking much too long to create them and a general lack of interest by most of the students, but they were fun to make anyway so I might as well share them in case anyone else would like to present these or similar problems in their own labs or course. PDF as well as TeX files are provided, so you can edit out my name and all that jazz.
Lab #1: Intervals with Braid
The first week’s problem was based off the video game Braid. This problem ended up not working too well due to about 10 people in the class of ~600 having played of the game, and the rest being very confused by the idea of the cloud platform moving along with the main character (it makes sense if you’ve played the game, honest!).
Lab #2: The Bat Man
The next week I decided to go a bit more mainstream and have the problem based on Batman chasing the Joker. The question doesn’t make a lick of sense if you think about it physically (the cars have negative acceleration for one thing), but this being a math class I decided not to care. I feel like this was the most successful of the weekly problems because the Batman/Joker stuff was completely incidental and the question was still easy enough for the students to understand and tackle.
Lab #3: Calvin Reaches his Limit
By this point I had learned that even if I am going to sugar-coat the question under a picture of Calvin and Hobbes, it’s a good idea to include a sentence at the end summarizing what the heck it is I’m asking them to compute or prove. I think this is a fun question no matter how advanced of a mathematician you are, and it was probably a bit mean of me to present it to first-year students.
The last of these problems that I presented was a (very) simple continuity question based on Super Mario World. I originally wanted to use Super Metroid for this question since it would allow for more varied movements from the hero, but I decided that (as I learned in Lab #1) it would be best to stick with a more recognizable game. It was a pain to come up with a semi-nice-looking branch function that resembled Mario’s movement in a believable way and led to simple (i.e., non-fractional) limits at the points of interest.