So, this morning was the first day back in school after the inspirational conference this past weekend.  I arrived to find that my classes were all less than half full due to the scheduled AP Environmental Science test (our most popular AP class)

So I told the remaining students we were just going to explore some things in geometry, and that if we found anything interesting we’d try to confirm our theories and prove them if possible.  And if we just messed about all day, that would be OK too as half of the class were missing.

Here’s the exploration.  I gave them sheets of paper with a 3 inch line marked.  I told them that represented a soccer goal.  Then I passed out different angles cut out of construction paper.  These, I said, represented the accuracy of different soccer players:  good shooters had very tight angles  because the ball would be sure to go pretty much where they shot at.  Weaker players had very large angles because they didn’t have such good control.

Their job was to make a “map” for each player (different angles) that showed the region of the field the player could shoot from and be certain to score a goal (we were ignoring the goalkeeper)

I’m going to write up the results of the day to share with you all, but give this exploration a try first.  It’s a lot of fun and leads to accessable, interesting proofs.