In geometry I put this up on the board as they walked in.

# 1, 4, 9, 16, 25…

I asked ’em what patterns they saw.

- Perfect Squares
- First difference is always odd
- Constant second difference of 2
- y = x²

I was wondering if they would come up with this:

I eventually put the pattern up and asked if any square multiplied by 4 is always a square. They said yes and talked about the shape a dot representation of the number would make when multiplied by 4.

Then a student asked **“Is a perfect square multiplied by a perfect square also always a perfect square?” **

Well **(a²)(b²) = (ab)²**

We had a great 5 minute discussion about this, I had never thought of the product of two perfect squares, it is always fun when I learn along with them. I don’t talk enough about number theory, this was a great exercise in developing both number theory and sense.

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