Q&A #286

Teachers' Lounge Discussion: Teaching conversion of units of measurement

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From: Tom Hibbs

To: Teacher2Teacher Public Discussion
Date: 2001111914:32:00
Subject: Re: metric conversions

I would go a bit further.

   1km/1000m = 8.32km/X m  then the units seem to cancel(divide out,
divide to 1, etc)just like the numbers and solves to X = 8320 m.

Your method of ratios and the previous teacher's method of unit
fractions can fit together.  The idea in teaching conversion of units
of measurement is to give the student a basis for unit conversions in
physics, chemistry, business, and other applications without having to
unlearn a method that was not general enough.

We are constantly looking at km/h, miles/hour, ft/sec, and m/s and
trying to see what a rate with one combination of units equals using
the other combination of units.  The units are dictated by the

8 miles/hr = X ft/sec is solved with unit fractions as 

(8 miles/1 hr)(1hr/60 min)(1 min/60sec)(5280 ft/1mile) = X ft/sec

This is visualized better with numerator over denominator type style. 
The units "cancel" in numerators and denominators except ft/sec and
the resulting "rate" is 8x1x1x5280 ft / 1x60x60x1 sec.  The decision
to multiply or divide is decided by the unit fractions.

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