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.

• Something that has always interested me!

I asked my remedial 7th and 8th graders “If I’m in my car driving at 60 miles per hour, how far away will I be in one hour?” And the majority of them don’t know.
Granted they are language learners BUT I don’t think they understand ‘miles per hour’ at any level. They hear it, maybe, as one word “milesperour” and because they have limited vocabularies, it’s just another word they don’t understand.

I usually can talk them through it, often by having them discuss it with a partner.

And as you said, it really isn’t very meaningful to them. The speed limit in front of the school is 25 mph (when children are present). But that doesn’t mean anything. I mean no one is driving for an hour – they’re just going a couple of hundred yards in front of the school.

I’m also interested in what people say about miles per hour and other unit rates.

• This [http://wyrmath.wordpress.com/2013/08/15/would-you-rather-9/] seems like it could be a pretty nice task that leads to some rich conversations re: your concerns here. Plus, it utilizes many of the standards for mathematical practice in addition to the mathematical content.

• Jasper

Her explanation is excellent.

I would ask her how long she thought she could run at her top speed. Then I would tell her about relay races, where people pass a baton, so that each runner can go their top speed. Suppose she said that she could go her top speed for 10 seconds. I would ask her to imagine a relay with hundreds of girls, just as fast as she is. How far could the baton travel in one hour?