This year I wanted to make explicitly clear the connections between AROC, IROC, and the derivative, so we used the same four functions as examples for each of them. We did AROC for each of them one day, IROC for each of them one day, and derivatives for each of them one day. This is my third year teaching AP Cal and my first time to organize the information this way. I definitely like this best, and I like how the pocket that holds these sheets also holds the formulas.
Between AROC and IROC, I used another advanced organizer and a desmos graph to help develop the concept behind the limit formula for IROC, and I think that worked well. Post coming soon with more details.
In a very sinister way, I love teaching students to find a derivative using the limit definition, watching them struggle, knowing that very soon, we will be learning the power rule, and they'll hate my guts for making them do it "the long way." ;) I explain that while we'll rarely, if ever, use "the long way" again, they have to recognize for AP purposes when they see it that they are being asked to find a derivative.
Between AROC and IROC, I used another advanced organizer and a desmos graph to help develop the concept behind the limit formula for IROC, and I think that worked well. Post coming soon with more details.
In a very sinister way, I love teaching students to find a derivative using the limit definition, watching them struggle, knowing that very soon, we will be learning the power rule, and they'll hate my guts for making them do it "the long way." ;) I explain that while we'll rarely, if ever, use "the long way" again, they have to recognize for AP purposes when they see it that they are being asked to find a derivative.