Shoe Boxes

My calculus kids are working on their shoe box projects. Today, their problem statements and solutions were due. I was so impressed with both their creativity and accuracy. Not only were they solving some of the most difficult problems in AP Calculus, they were actually creating these problems themselves. To top it off, the situations they were modeling were a whole lot more entertaining than many of the problems I’ve seen on AP Exams. (Seriously, College Board, water entering and leaving again?) Some of the ones I remember (mind you, I’ve fallen asleep once already writing this post)…

  • The rate of cat litter being poured into and out of a litter box
  • The rate at which M&M’s are being produced in and shipped out of a factory
  • The rate at which graduates enter and leave the stage
  • The rate at which a slushie is poured into and leaked out of a dispenser
  • The rate at which a balls fly to a pitcher and the rate at which he hits them
  • The rate at which bowling balls go in and out of a lane
  • The rate at which shoppers enter and leave a mall
  • The rate at which bees enter and leave a hive

There are other great ones I’m missing, but–needless to say–I was impressed. I’m excited for presentation day next week, when we get to see their decked out shoe boxes. 

Mostly, though, I’m just so proud of this group for how far they’ve come this year. I remember when these problems were such a struggle, and now they’re solving them–and applying them to “real life” situations–like it’s nothing. Using these rates, they can tell you how fast a quantity is entering, leaving, or changing; they can tell you how much of the quantity has entered and left; they can tell you how much of the quantity exists at any time; they can tell you what the maximum and minimum amount of the quantity is. They can calculate the rates of these rates and explain what those mean. 

They can do it all. They’re rockstars. 

I hope they’ll carry with them a love of calculus for the rest of their lives…


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