I decided with my non AP class that I would do only a very quick review of graphing and then jump right into the Calculus. We spent today remembering how to write equations of lines, manipulate them a bit, and then used the motion detector to start to build the conceptual framework of he derivative. I asked students what slope meant in a graph and (surprisingly) not many really could say anything. Then, I had someone walk in front of the motion detector to make a linear graph. They all noted that the person walked at a constant speed. Then I asked the person to walk to make a steeper graph. Immediately, everyone shouted out to walk faster. So they all intuitively knew exactly what was going on – the experience with the motion detector just allowed us to put intuition into words. This was basic, but I’m okay with that because we are going to use complicated versions of all these EXACT same ideas in the next couple of days. My plan is to bring out the motion detector again to explore some more Calculus-y style graphs to build he idea of a derivative, and then to use @thinkthankthunk ‘s idea to figure out how the motion detector works in order to get at the limit definition.