[IAEP] [NaturalMath] Re: Looking for Concrete "Fraction Experiences"

[David Corking]

Rebecca wrote:
> So David you're saying that if you consider:
>  3 divided by 2/3, the quotient will be 4.5 because 2/3 of that is 3?
> That's nice.  Can you give us a concrete example for that?

Yes.

(1) A student made a scale model of the classroom, using a scale of
1/60. Using a ruler, she measured the diagonal of the model as 25 cm.
To calculate the diagonal of the classroom, I reverse the scaling
operation, so I divide by 1/60. When I divide 25 by a sixtieth, the
quotient will be 1500, because a sixtieth of 1500 is 25 (to me, "of"
means "scaled by" which means "multiplied by".) The diagonal of the
classroom is 1500 cm or 15 m.

(2) The toy car covers the five foot track in three-quarters of a
second. To divide five by three-quarters, I want a number that, when
scaled by three-quarters, gives five. So I would estimate that the
speed is bigger than five, probably seven or eight feet per second. I
can use this estimate to check a more accurate calculation, which I
can do with a calculator, or with the algorithm of divide by the
numerator ( 5 / 3 ) then multiply by the denominator ( 4 * five-thirds
which is twenty thirds or six and two-thirds feet per second.)

(3) Electrical calculations are practical, but not concrete for
everyone. 14 year olds might want to try this one:
Q:A circuit has a resistance, R, of 0.66 ohms, and is powered by a 3
volt battery. Make a mental estimate of the current, I, in amperes,
using the formula I = V / R.
A: 0.66 is about two-thirds, so I want 3 divided by 2/3. What number
would I scale by 2/3 to get 3? 4.5, so V is about 4.5 amperes.

The above text is a bit dense. I suspect it is easier to find the
inverse scaling model by guided discovery, than to absorb it from a
lecture or textbook.

Maria wrote:
> Do you teach division by decimals through division by fractions?

I don't teach, so I hope I didn't respond out of turn.  I try to help
with Etoys, and I am a volunteer classroom assistant, but with an age
group that hasn't encountered fraction multiplication yet. My
suggestions are merely from my own knowledge of applied math, rather
than teaching experience.

Hope that helps, David