Next up with my ninth grade math class: solving rational equations. I’ve been having fun with combined rate problems such as, “How long does it take Timmy and Marsha to mow the grass if it takes Timmy 2 hours on his own and Marsha 1.5 hours on her own?”

I, therefore, with great pride present you my first Vimeo video (Edit: Filling the Sink):

How I’m using it:

  1. Put it out there as a warmup — how long do you think it’ll take to fill this sink? Show about 10 seconds of the video.
  2. Put it out there in the lesson — what about when I combine the faucet and pitcher?  Teach them combined rate problems as a specific case of rational equations.
  3. Watch “Trial 1 (faucet only)” and “Trial 2 (pitcher only)”, then compute time to fill the sink with both working together.
  4. Play “Trial 3” and compare your experimental results to my actual results.
  5. Close class with this: Assuming your computed time to fill the sink is different from the actual time, discuss what you think is the most significant source of error and how I could fix it in “Filling the Sink, Part II”.

Side note that’s aggravating but true: I’ve struggled with finding great applications of the concepts I teach because they’re rarely as complex as the stuff we’re expected to work with. With rational equations, I’m still looking for something where I’ll need to factor the numerator and denominator, cancel some terms out, and move along. My gut tells me this thing doesn’t exist.

Georgia Performance Standards: MM1A3d Solve simple rational equations.