Make only one cut, and then assemble the pieces into a square.
This is my new introduction to completing the square. This time around I’m trying to give a strong geometric intuition of what’s going on. I’m hoping to build off of this by excluding the little square, and asking the students how one would figure out the area of the missing square. Then I’ll work up to using variables for the sides, and then finally from that derive a procedure.
Easier said than done, I know. I also have some history I was going to toss in, and I’m hoping to slip in a decent application at the end. Any suggestions of where to look would be appreciated.