Slate.com’s always entertaining “The Explainer” segment runs an always-even-more entertaining year-end segment on the Unanswered Questions of the Year in which readers are prompted to vote on the question to be answered (aside: say, that’s a pretty awesome activity for a classroom. Students in the middle of a Problem vote on the question the teacher answers.)
This years’ edition contains burning questions such as “When you urinate in a toilet and there’s splashback, is that urine or toilet water?” and “Why do dogs like having their bellies rubbed?”
The one that I’m interested in is the following.
Artifact
13. When parking in a nearly full parking lot, is it quicker to a) park in the first open space you see and walk, or b) drive a few laps around the lot and grab the closest possible spot? In my experience the two ways are about even, since the extra time spent driving for “b)” means a quicker exit when you leave. Please settle this using statistics as my wife has refused to argue anymore regarding this issue.
Tell me this isn’t a dilemma you play out in your head on a near daily basis.
I suppose you could use statistics, but this would make a super modeling project as well. Moreover, I have no idea what “level” of math a problem such as this requires and that’s a good thing. This could be a middle school project or an Algebra 2 project. This could be attempted by your high-flying AP Calculus-bound students as well as your remediated Algebra 1B students who probably hate the subject you’re teaching them.
So how do we pose this problem to students? A video of you driving around looking for a parking spot with your friend/spouse imploring you to “just park and we’ll walk!” might work. A few simple diagrams might work:
Does your school have parking issues? Particularly in the afternoon? Grab some footage. Or shoot, even the simple question posed in The Explainer may be interesting enough as is.
Guiding Questions
- Does the size of the parking lot have anything to do with the decision to Park and Walk or to Keep Searching?
- Do the number of parking spaces have anything to do with our decision?
- How fast do people walk through parking lots?
- How often are cars vacating their parking spots?
This is a good example of a problem that A) could potentially be immediately interesting to students (or at least could be posed in an interesting way), B) doesn’t necessarily have a correct solution, C) offers multiple routes through the problem, and D) can be accessed regardless of prior mathematics expertise.
What are some potential “next steps” students could take to engage in the problem? What are some potential mathematical routes to a solution? This is something to think about over the break, and as you’re vigorously searching for a parking space at the mall to buy that last-minute gift you’ve been putting off.
emergent math 
In regards to how often cars vacate their parking spots, it is also interesting to contrast the case of a shopping mall, where departure times might be expected to be random and follow a normal Gaussian distribution, with a movie theater where departure times would bunch together, and a school where there might not be a significant chance of departures until lunchtime and/or the end of the day.
I think this is a good problem for computer science students to write a Monte Carlo simulation to explore the problem space.