Saturday, 5 December 2015

Fractions of a square

I liked this tweet:
and saw there was at least one ingenious way to solve it:

I looked at it like this:
and it reminded me of this:
(The yellow square is one fifth of the big square. There's a proof here.)
So, I could see here that the diagonal was divided into thirds. After a bit of thrashing around, I could also see that the green triangle must be ⅙ of the whole square.

I like the way the square is divided so simply up into fractions. There are halves and quarters:
and all sorts of other possibilities:

Oh - that would make a good Which One Doesn't Belong?
It strikes me that it would make a good shape for students to divide up in different ways like this.
In the same way that they have here:

And then there's the one fifth square...

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