3. Expanded Area Model for Multiplication

We saw previously that drawing pictures is a good way to think about multiplication.

Multiplying is really just adding a whole bunch of things together, as long as they’re the same size. The little boxes showed that, but it got a little crazy once we used bigger numbers.

So, let’s keep on with the pattern of pretending, by trying out 14 x 7. Since I don’t actually know 14 x 7, I will break it down: 14 is really just 10 and 4. So I’ll split that side length in my picture. Then I have two little rectangles…10×7 and 4×7! I can do that!
(and if you want to get really fancy/technical, we did just demonstrate the distributive law!)

unnamedWow, that was WAY easier than expected! Maybe we can apply that same logic to our original problem?

So…
867 = 800 + 60 + 7
and
39 = 30 + 9

expanded-area-model

BAM! Still annoying…but addition is better than multiplication.

Now…how does this all help with the lattice model? That ugly beast of multiplication…

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