We started Optimizing today in my AP class. I gave them all a one meter long string and asked them to capture the largest rectangular area on their desk that they could (using one edge of the desk as a side). I gave them about 5 minutes… Most kids settled on the square because they didn't really try anything else, so I was glad to kind of have blown their mind a bit when the answer turned out to not be a square. This is a screen shot of the GeoGebra applet I used. Overall, I felt like this was a solid introduction, though perhaps a bit time consuming.