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

[Maria Droujkova]

On Thu, Jul 14, 2011 at 9:46 AM, David Corking <lists at dcorking.com> wrote:

>
>
> > In practice, nurses, pizza cooks, carpenters and so
> > on don't "really" divide by fractions - they work with numerators and
> > denominators separately.
>
> This may not be the case when dealing with decimal fractions or
> percentages, when they might wish to crank a formula, or hit the
> division key on a calculator.


I agree completely, and I should have specified this case.

People conceptualize decimals as "single numbers" for all operations, unlike
fractions that are considered "pairs of numbers" for many purposes.


> Therefore I think it is worthwhile to
> give students a chance to develop a mental picture of division by a
> fraction, even if they choose to forget it later, and rely on the
> algorithm.
>

Do you teach division by decimals through division by fractions? Maybe some
parts of it, e.g. why division by 0.01 is the same as multiplication by 100?


> I see from your wiki page that you might not agree with me that
> percentages and decimals are special cases of fractions. However, at
> least in some curricula, fraction arithmetic is taught first, and the
> others follow.
>
> A couple of examples:
> (1) if a toy car completes a five foot track in three-quarters of a
> second, what is its speed?
> (2) if you want to take 20% sales tax, or value added tax, off an
> invoice to find the pre-tax price, then you divide by 1.2
> (3) devise a formula to convert lap times measured in problem (1) into
> speeds in miles per hour, or kilometres if you prefer.
>
> I think we will find numerous other examples in science, engineering
> and finance.
>

Yes, grown-ups divide by decimals (as you said, usually using computers) all
the time.


Cheers,
Maria Droujkova
919-388-1721

Make math your own, to make your own math.
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