How I Teach Calculus: A Comedy (xkcd-Dating Pool, Optimization)

It often starts with something awesome on the Internet. I had no idea how rich this was going to get. My students laughed, they thought, they got frustrated (and liked it), and they actively learned how to program spreadsheets, in addition to the calculus standard that I had in mind: optimization.

Like I need to tell you where this came from. (Obligocredit: xkcd)

This is one of the easiest opening acts I’ve ever used. It plays smoother than a Stevie Wonder LP.

After reading, the kids naturally discussed some points among themselves. This happens a lot, and I think, to most, it looks a lot like kids talking randomly.

I pretty much reject the idea that teachers should guide and focus everything. I bring the kids back to me when I think they can’t make any more progress on their own. Otherwise I just keep my mouth shut and keep Pandora on “no cussing.”

The first thing the students talked about was the standard creepiness rule:

They did a few mental calculations to see if they agreed. They questioned the comic’s upper limit. To a lot of students it should have been, for an 18-year old, 16-20 (+/- 2), not 16-22.

Why? They hashed this out with some pretty killer math thought: No! It’s the minimum of the older person that fixes the upper limit for the younger person. The way we handled that with a function was exciting. The students came up with a max function as:

If you think about that long enough, it’s intuitive, but not at first, which is awesome.

And some graphs where made:

Datee Age vs. Dater Age. Orange – Max dating age; Blue – Min dating age; Pink – Dating Range. All in years.

The students noticed a few things: Below 14 years, you have no dating range (as it should be); These lines really should be piecewise as your max gets above 100 years. There aren’t many people in the 100-110 decile. Finally, this graph tells us very little about what we actually care about…

How does your dating pool change as you age?

They stated that. Awesome. And the other foot drops. this becomes a really interesting problem, how can we add up all the singles that live within your dating range? We’re going to need to know the number of singles at any given age.

Quick, to the Census!

About 45 minutes later, and alot A LOT of math-thought later,¹ we had this spreadsheet going. If you’re running this lesson on a short time scale, you may want to just seed this with mine. We distributed the load to about 4 age bins per student.

WEMADETHISWITHGOOGLEDOCSDOESTHISMAKEUSTECHSAVVY?

Then, things got even more awesome. One of my students put it perfectly:

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