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.