Unrelatable Related Rates

Let’s face it–we all hate related rates.  Even I, a girl with a love affair of calculus, hate them.  They’re so contrived and boring…NO ONE CARES about the salt falling into a perfect cone and–gasp!–the radius is magically equal to the height so that the problem is easier!  How convenient.

I put my cards on the table for my calc kids.  “Calculus can be a very powerful tool for analyzing real-word phenomena.  The related rates problems in your textbook and on the AP exam do not highlight this.  But, I want you to do well on the exam, so we’re going to do these types of problems.  Feel free to laugh at the absurdity of each scenario.”

I felt like I needed to get that out there.  Otherwise, you’re throwing pretty hard problems at them AND the problems are stupid, so…double whammy.  At least this way, we’ve covered the stupid part.

Anyway, I think I actually had more buy-in giving this caveat than I have before.  I was honest, and the kids seemed to appreciate that.

But, that’s not my one good thing…

A really tricky thing for kids is knowing when to substitute numbers for variables.  I encourage them not to label anything on their picture with numbers unless that piece is constant.  But, still, this is a hard concept to wrap your mind around when you have a bajillion words you’re trying to decipher.  And it’s your first day ever dealing with related rates.

As I was walking around, I heard a group of girls working on a pretty challenging problem.  They were doing surprisingly well (again, Day 1).  I heard one of the girls say, “Can’t we just plug in 150 for x?”  To which another responded, “No, x is changing, so we can’t plug that in until we differentiate.”

Maybe it doesn’t sound like an amazing thing to you.  But, let me tell you…this was absolute music to my ears…

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