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26 Oct 2005 - 19:27

Doug's distributive property graphic

this is beautiful!


In my next life, I want to come back as a graphic designer.

distributive property manipulatives?

Any thoughts on whether distributive property manipulatives might be a good idea?

I'm thinking something extremely simple, maybe a large grid and those round plastic number 'counters' (they look a little like thin Poker chips). Or you could just use paper, or pennies or buttons. Anything.

You could ask the child to show you:

3 ( 2 + 4)

as an array like Doug's, or possibly as the two different arrays, which might be best. The child would see the equivalence because he or she had just made the equivalence with his own hands.

Temple on using your hands

I talked to Temple (Grandin) again last night. She had lots of horror stories of professional architects who can't make scale drawings. These are all young people who learned to do scale drawings on the computer.

She is adamant that there is a motor component to seeing. She thinks you can't get your visual processing right if you haven't....done things with your hands (can't be more specific than that).

The mistakes these people made were all perceptual mistakes, not cattle handling mistakes. (We're talking about the meatpacking industry.)

I really think there's something to this. (It's making me curious about that strange-looking Borenson fellow with his hands-on algebra, I must say....)

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I don't have any great manipulative in mind myself, but I do have a suggestion for those working to construct them. The examples you've posted so far are rather arbitrary applications of the distributive property. I would like something that ties in specifically with the mental math use of the property.

For example, the easiest way for me to simplify

21 * 8

in my head is to think of it as

20 * 8 + 1 * 8.

Here, I've taken advantage of the distributive property to actually make the problem more manageable.

An even harder thing to illustrate with a manipulative, I think, is a problem like

19 * 12.

Here, I want to solve it as

20 * 12 - 1 * 12.

A manipulative that supports that would be great.

-- DanK - 26 Oct 2005


Singapore Math teaches this CONSTANTLY.

That was the big breakthrough the other night, when Christopher told me to use the distributive property to do a mental multiplication.

But it turns out he has fragmented knowledge; he only knows the distributive property in the context of mental multiplication!

-- CatherineJohnson - 26 Oct 2005

Title: Doug's distributive property graphic
TopicType: WebLog
SubjectArea: MathManipulatives, MiddleSchoolMath
LogDate: 200510261526