I started doing an itty-bitty bit of related rates with my kids today, and it was totally fun! I only did very basic problems with them so far, because they've been asking about where we would encounter chain rule. My goal this month/early next month is to finish off all the basic differentiation rules and skills, then to come back to related rates later to do a thorough study, so I gave them only the first few problems (Level 1) from Bowman today, just enough to wet their appetite.
And I gave them this grid to help them organize their thinking. I tried doing all the problems (up through Sam's problem on the two flies on the inflatable earth, which I consider Level 4), and they all fit into this grid pretty well. I hope that helps!
I LOVE RELATED RATES!!!!!
By the way, some of my kids solved for rate of change in radius like this:
dr/dt = dr/dA * dA/dt
dA/dt = dA/dr * dr/dt and divided both sides by dA/dr.
I like this! It's a good opportunity for us to come together as a class tomorrow to discuss equivalence of equations involving derivatives, so that they can learn to think more flexibly about the Chain Rule already.
I am also instituting very structured group work this term, which has been very helpful in approaching new tasks, at least in this class (and also in my Alg 2 classes). The kids haven't really commented on it, but I find that their discussions are more productive now that we are into our second grouping and they are more used to the idea of working with people and having assigned leadership roles. Excited about the promise of the rest of the year!!!