## Measuring Distance in Time

When was the last time you used an actual unit of distance when answering a question of the type “How far is …”?  For example, Katie knows that her school is 5 minutes away, mom’s work is 10 minutes away, and her cousins live an hour away.  This is what really matters to her, and so the concept of a mile never really comes up (as opposed to inches and feet, which are actually used for measuring things like height or length of a piece of paper).  I never really gave this fact much thought until a few weeks ago we went on a bike ride with my sister’s family.  My sister was keeping track of our progress, and at the end declared to the kids that our trip was 8.5 miles.

Yesterday, the bike ride came up in conversation, and Katie exclaimed, “I can’t believe that I biked for 8.5 miles!”  This made me wonder, does she have any sense of how far 8.5 miles is?   My guess was not, and it was an easy hypothesis to test.  So I asked Katie to name something that she thought was about 8.5 miles from our house. It turned into a fun game that I believe actually did give her some feeling for various distances.

K: My cousins’ house.
Me: Not quite. That one is 50 miles away. Try again.
K: My school.
M: That’s only about 4 miles away.
(It would be way too easy if something that’s 10 minutes away would actually be twice as far as something that’s 5 minutes away!)
K: Oh fine, how about my gymnastics class?
(This one, depending on the traffic is between 15 minutes and half an hour away).
M: Let me check (googlemaps to the rescue). Hey look, it’s exactly 8.5 miles away!

So now I think that when I talk to Katie about how far away something is, I’ll try to mention both the distance in miles and the amount of time it takes to get there.  Maybe I should also have her run/walk a mile to give her a “real” sense for it.  I also see maps making their appearences in future discussions on the topic.

And here’s a picture of Katie after the bike ride:

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.
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### 2 Responses to Measuring Distance in Time

1. bovetsky says:

Katie is only six and a half. Ask the same question in high school, and you will get similar results. I tried many times in my physics and astronomy classes, and most students had no clue on the order of units, let alone meters and kilometers.

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2. Joshua says:

We found that our kids’ senses of distance were stronger when we lived in London, a walking city, than in Bangkok, a stuck-in-traffic city. Here, however, it doesn’t really make sense to talk about the time between two locations because that depends so much on time of day and random traffic disruptions.

Two gadgets that are worth the investment: a step counter and a garmin running gps. Both offer a collection of measurements that can provide new numerical insights and questions for your kids.
Step Counter: steps that day, steps that week, stairs climbed (or flights of stairs), and distance walked (depends on some calibration).
GPS: distance, time, max speed, average speed, ours also has heart rate stats.

The step counter, in particular, was great because it was so small they could easily carry it the whole day and get excited about their results. As side benefits, it was a special event when it was their turn to have the counter for the day and it also encouraged them to be more active (as if ours needed that extra push!) Downside: it didn’t survive getting dropped in the bathtub.

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