# Happy kindergarten surprises

I was at a table full of kindergartners playing with triangles, trapezoids, and concave hexagons. We were building and chatting. They wanted to know if I wanted to hear them sing in French. I said yes. The sweetest two minutes ensued as this table’s Frere Jacques spread to the next and then the next, and soon the whole classroom was singing and doing math.

A few minutes later I made this.

And then I went scrambling for my notebook.

Yup. Sure enough. $(a-b)^2+4(ab)=4(\frac{1}{2}ab)+c^2$ is equivalent to the Pythagorean Theorem.

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### 2 responses to “Happy kindergarten surprises”

1. Monica C.

Love this! My advanced fifth graders have recently learned the Pythagorean theorem – this will challenge them to see how you came up with your equation. Thank you!

2. Imagine the children have a large sheet of red paper and they have paper triangles they can move around atop the sheet of red paper.

Then the Pythagorean theorem ‘pops out’ even more clearly.