[IAEP] multiplication and division as scaling (was Re: [NaturalMath] Looking for Concrete "Fraction Experiences")

[Maria Droujkova]

On Mon, Jul 18, 2011 at 12:04 PM, David Corking <lists at dcorking.com> wrote:

> Maria Droujkova  wrote:
> > I think scaling can correspond both to division and to multiplication.
> You can scale up and
> > down - also by numbers over and under one if you think more
> algebraically.
>
> Absolutely. In my observation, many 7-year-olds are able to think
> algebraically about multiplication and division of natural numbers
> (1,2,3,...). Since they simultaneously discover common fractions,
> place value, and decimal money, it won't be long before they have all
> the building blocks in place to confidently multiply by various kinds
> of fractions.
>

And with babies and toddlers, you can introduce scaling qualitatively or
"semi-qualitatively" - especially with software. The plus is that they
explore grounding for multiplication, division and fractions all together,
within one connected conceptual field. This can be easily extended into
place value systems (as a way to keep track of exponentiation) and then
decimals.

The minus is they won't get the big surprise in their life from their first
"multiplication makes smaller" example :-)


Cheers,
Maria Droujkova
919-388-1721

Make math your own, to make your own math.
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