Today, we did an exploratory intro problem for the second half of my non AP Calculus course – estimate the area of this curvy building (I blogged about this here). This ends up being a contest, which we will solve next week with an integral and then see who is closest. I always find this really interesting to see what they do. Lots of groups tried something with the area of a circle, which was interesting but perhaps a waste of time (maybe ill use an even weirder shape next year). I found this group's work super cool. They used triangles, and then kept filling the area left over with more triangles. This is intuitively the limiting process, so I loved talking about this strategy with the class.