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Sharing Ideas & Making Bad Math Puns on the Internet Since 2012 My non-AP calc students have truly blown me away with the ease at which they've taken to derivative rules this unit. I went into this unit with a relatively open idea of pacing- what my AP kids can do in a day might take 3-4 with these kiddos. But, they're killing and the struggle became very, very real as we started implicit differentiation. With that in mind, I write this sorting activity to I have students identify the initial problem, then work on whiteboards to determine the next steps. They had great conversations and asked even better questions. Once this was finished, I saw a lot more independence as we solved implicit differentiation problems without Recursion has always been a weird topic for me- one where I try all sorts of different things to try to get kids to tie the relatively basic conceptual idea to the funky notation that is sometimes as*ociated with it. I've taught it at the middle school level (next=now blah blah blah), in Algebra 1, in Algebra 2, and in Pre-Calculus and I inevitably always have some kids who struggle make the transition from the idea to the notation and requirements. So, yet again, I tried tweaking this year. Here's what I did.  Students had 30 seconds in groups to tell me the exact sequence about which I was thinking....this obviously caused some unrest. Some groups were prepared with random guesses, some got indignant that they didn't have enough information, some argued among themselves about which side to take. I let groups guess and every time I said WRONG! until someone finally pointed out that this was rigged.  I let them know that I'd allow the clas* to ask 2 questions to try to get it right. They needed to prioritize those questions in their groups and then we continued the discussion. The 2 questions they asked: We discussed- was this strong enough to give me the EXACT sequence I was thinking about? Nope!  That's it! We need to know where to start and how to proceed from there! Those 2 magical ingredients of a recursive formula were just