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Do kids get most units?

August 24, 2008 pm31 10:03 pm

I don’t think so. I don’t think they have a very good sense of distance, of rate, of volume, of area, as expressed in most standard units (traditional or metric).

Can we do anything about this in math class? Does it matter?

Yes, and yes.

It matters in the real world. There’s a piece of literacy that’s missing if I kid knows 5 miles is far, but can’t get more specific. How much is 2 gallons of soup? Adults don’t get square feet. And move to metric in the US, and lots of people are lost. We encounter the terms daily. We should understand how much, how far, how long, how fast, in terms that make sense.

And it matters in math class. All those annoying word problems, in context, with answers in cubic feet or meters per second. Shouldn’t kiddies know if their answers make sense? What good is the context if they don’t sense the scale?

Teach them to convert

So there’s two pieces here. There are a number of ways to convert. I like what I call factor-label. Example. I want to know how fast 100 meters in 9.69 seconds is in miles per hour. Look at this:

\frac{100 meters}{9.69 seconds} \times \frac{60 seconds}{1 minute} \times \frac{60 minutes}{1 hour} \times \frac{1 kilometer}{1000 meters} \times \frac{5 miles}{8 kilometers}

Now, ‘cancel’ the units (it’s not really math, but it works) as if we were canceling common factors in fractions, multiply across, and presto: 23 point something miles per hour (the bad 8:5 conversion limits my significant digits, but no matter. I can’t perceive the difference between 23 and 24 mph. Does 23.2 vs 23.3 really matter to the kids?)

There’s other ways to convert units, but the kids must be armed with some tool.

Teach them human-scale reference units

Miles per hour. Sounds so natural. Rolls off the tongue. But I am fairly confident that most of my students don’t have a good grasp of how fast 2 mph, 10 mph, 20 mph, 50 mph, 100 mph, etc, really are.

good ideas, below the fold — >

Time is okay, but it is worth teaching them to count out seconds. Really.

Distance is tougher. Little distances? Put rulers in front of them. Ask kids to show with their fingers, for example, 3 inches, 2 centimeters, one foot, 5 centimeters, one inch. Drill it a little here and there. They will get better, but they need practice. From feet, once they are down, get some estimates of heights of ceilings, widths of classrooms, lengths of hallways. Estimate, measure, estimate again. They will get better.

Bigger distances? In New York I use blocks (I specify short Manhattan blocks). Twenty blocks (approximately) make a mile. Reexpress them in meters, in kilometers, in feet, in yards. But let “block” be a good unit, one that they can refer back to.

Area? Estimate, measure and multiply, estimate more. Classrooms. Desktops. Sheet of paper. The classroom makes a good standard, human-scale unit.

Volume. You know, this is tough. I fall back on liters (thank you Coke!), but I don’t work much with it. Do the volume of the teacher’s desk, shock them with the answer, and that’s pretty much it. It helps if they have an inch cube or a foot cube in front of them. The centimeter cube is too small and they don’t ‘feel’ the relationship. I haven’t seen a meter cube, but I think it would be too big. Textbook volume wouldn’t be bad, but it’s different for each book, and the cover can throw things off.

Rate. That’s the big one. Miles per hour is foreign. I start with seconds per block. We estimate normal walk, slow walk, brisk walk, run, bicycle/skates/skateboard, slow car, fast car, and then take the reciprocal and convert to miles per hour. Can do kph, too. And meters per second. Seconds and parts of minutes they get. Blocks they learn. And that gives them something to hang their hats on for the harder (but more common) units.

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7 Comments leave one →
  1. August 26, 2008 am31 12:29 am 12:29 am

    You could make a meter cube out of pieces of foam, perhaps. I know a lot of craft stores sell slabs of foam that are sizes like 24″x36″x2″. You could put some of these together and trim appropriately to make a meter cube that would be quite light. If you made it with a removable top, then it wouldn’t be too awkward to store since it would be hollow.

  2. August 26, 2008 am31 7:51 am 7:51 am

    I don’t think they really get units, either. Unit rates and unit conversion are on the to-revamp list this year.

    I think the more you can do with representing quantities as lengths and measuring things, the better. The discussion of why measurements in centimeters are easier than inches is ever-illuminating.

    Any hints for helping them wrap their heads around the technique you described, where you multiply by the conversion factor and cancel units? I love to convert this way, so simple, but I’ve had trouble getting them to retain it.

    Also, check these out:
    http://tinyurl.com/5vqptq
    http://tinyurl.com/6rapph

  3. August 26, 2008 am31 8:52 am 8:52 am

    Those are very nice links (little unit conversion puzzles using factor/label, with some, but not all, conversions supplied.)

    I don’t have a good way of getting them to remember the method, except they seem to like canceling…

  4. August 28, 2008 am31 4:43 am 4:43 am

    Hey you are right. Kids don’t get units. I remember thinking of them as grownup stuff. Centimetres and millilitres were okay, but rates are hard, and so are sizes larger than small humans. Even now I think sqft (and square metres) are not easy, and acres/hectares I don’t get at all. Wish I had a good way to figure those.

    Incidentally, I never found it hard to learn both metric and imperial systems. We learned metric in school, but adults often use (still) imperial for cooking and for weight and height.

    Volume: canning jars, if that’s familiar to students. Juice boxes? Ours are 200 or 250 mL, so 4 or 5 to a litre.

  5. August 28, 2008 am31 6:44 am 6:44 am

    and length and time are much easier than area, volume, or rate.

    Angles, while we’re at it, are very hard to estimate, except in geometry text type drawings.

  6. Miss Aileen permalink
    September 9, 2008 pm30 8:28 pm 8:28 pm

    I agree about students in today’s high schools have a difficult time grasping the conversion scale between SI, metric, the way us Americans do it (I guess we had to be different). I think we just need to spend a little extra time explain the conversion formula to help students to become comfortable with it.

    I had a chemistry teacher show us the conversion formula you provided as an example.

    m/s to miles/km

    And it was one of the easiest things that I had learned, and I could transfer it over through all math, science, and etc courses through my high school and college career. I will definately be stressing this for my future students.

  7. brenda johnstone permalink
    September 21, 2008 am30 7:31 am 7:31 am

    i dont get this at all and this isn’t much help.

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