Try the fish tank problem. You have a fish tank 20 in x 10 in x 10 in (easy
numbers to start with, but then it gets complicated).
How many fish can it hold on the basis of 5 fish to a gallon? (Different
answers for UK and US gallons).
How much would the tank weigh? (Ignore the weight of the empty tank.)
If the shelf on which it rests can JUST support your weight, and the tank must
weigh no more than than half your weight, what is the maximum weight of the
tank? (Again ignore the weight of the empty tank.)
I can’t even think of doing this problem in imperial/USC units.
Now do it in metric.
Tank is 50 cm x 20 cm x 20 cm. Fish at the rate of one fish per liter.
Volume = 50 x 20 x 20 cm = 20 000 cm³ = 20 L = 20 fish.
20 L weighs 20 kg. I weigh 66 kg, so well within the maximum 33 kg safe limit.
Metric wins in this kind of problem every time.
John F-L
From: Martin Vlietstra
Sent: Sunday, October 13, 2013 7:22 AM
To: U.S. Metric Association
Subject: [USMA:53320] RE: Presenting the metric system to the innumerate
Try finding the average height of the students in your class using feet and
inches, then using metric units.
Next try them with a problem that a friend and I had a few years ago –what
should the approximate diameter of a sphere be if it is to accommodate 2000
tons of water. (They may assume that one long ton (2240 lbs) equals one short
ton (2000 lbs) equals one tonne). I did this problem mentally when it was
presented to me. My reasoning was:
One tonne of water has a mass of one cubic metre.
We need to construct a sphere of volume 2000 cubic metres
If we work in units of 10 metres, we need to find the radius
and therefore the diameter of a sphere with volume 2 units.
If you made it simpler, by requiring a cube rather than a sphere, the answer
works out at 10*(2)^0.333 metres or approximately 13 metres.
I had the answer, while my friend, who was working out the same problem had
started off : 2000*2240/62.5 to get the volume. (BTB, I am a Brit, so used
tones of 2240 lbs – another good reason for the metric system).
You might also like to warn your students about the hazards of drinking in the
UK – our pints are larger than yours.
Martin
From: [email protected] [mailto:[email protected]] On Behalf Of
Paul Rittman
Sent: 12 October 2013 18:25
To: U.S. Metric Association
Subject: [USMA:53319] Presenting the metric system to the innumerate
I like to present the metric system to college students by first getting them
to see the value of a decimalized system of accounting. I tell them that Thomas
Jefferson asked Congress in the 1790s (as Sec of State, not as Prez) to
decimalize the dollar when it was adopted as the nation’s currency, as opposed
to the 1 pound=20 shillings=240 pence system used by Britain. I’ve typically
let them see the utility of this system of counting, by taking our year (2013),
and asking them if we had 2013 pennies, how much money would we have, expressed
in terms of dollars and cents? The exercise is designed to show people how easy
it is, to recon 2013 pennies in blocks of 100. You don’t even have to do any
multiplication or division, you just move the decimal and arrive at $20.13. I
then tell them how easy it is to convert 1000 grams to kilograms, etc.
The last time I tried this, I received a shock. I had 3 students volunteer an
answer, and the first two got it wrong. Fortunately, the third student did
state that 2013 cents was equal to 20 dollars and 13 cents, but I was shocked
that the rest of the class was either silent or guessed wrong. I’m wondering if
this is symptomatic of the group of students as a whole (college freshmen). Now
I’m sure that some knew, but simply didn’t feel like voicing their opinion in a
large group of people; some others might have been bored (has been known to
happen in classes!)—but I’m still thinking that quite a few didn’t know.
I think in the spring, I’ll give my students a short, anonymous survey to see
if they can understand mathematical concepts like this.
But in the meantime, my suspicions remain strong that many adults are close to
being innumerate, if not already there.
And I’m wondering how to present the metric system to them—to students who have
no desire or ability to convert inches to feet to yards to miles, etc. If they
don’t even bother with that, what difference would the metric system make to
them? What attracted me to it was the standardization of it (there was only one
kilometer, one gram, etc.), which made remembering statistics much easier. Of
course students wouldn’t see this as much of an advantage.
But apart from the ease of converting among units, what other benefits can be
presented to the man in the street?
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