Here’s a short mistake that I came across today that I found interesting.

I was chatting with a 5th Grader. The question was, “What do you think is your top speed?”

Her: I don’t know how fast I run.

Me: Well, you know here is how fast I walk. [Walks.] I think that’s about 3 miles per hour.

Her: OK, well maybe I can run 6 miles an hour.

Other Kid: You can run way faster than that. You can run 15 miles an hour.

Her: Well, yeah, for a little bit. But I couldn’t run 15 miles in one hour. I’d get tired.

I don’t give enough thought to miles per hour. It’s really an abstraction of realistic rates, rates that you could actually use. Like, if it takes me 3.9 seconds, on average, to add a paperclip to a chain, then I can use that to realistically figure out how many paperclips I could chain together in 5 minutes. But miles per hour — at least in the context of running — isn’t realistic in that way. It’s a concept that imagines a world that pays attention to my current speed but strips away all the reality of exhaustion and physical limits.

In the future I’m going to try to be more sensitive and explicit about this when talking about miles per hour with little kids.

Thoughts about rates and the units we use would be very, very welcome. Share interesting anecdotes in the comments, please.

We here at the MathMistakes world headquarters got today’s mistake via email submission:

Question:  If you are driving 60 km/h, how far would you go in 20 minutes?
Student’s answer: 1200 km

Since we don’t have much to work with, in terms of diagnosing the students’ error,  let’s do two things in the comments today.  First, leave a note if you have about the specific question and student answer. Second, let’s use the comments as a place to discuss strategies for helping students form an intuition for rates.