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:
- 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.
- 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.
- Watch “Trial 1 (faucet only)” and “Trial 2 (pitcher only)”, then compute time to fill the sink with both working together.
- Play “Trial 3” and compare your experimental results to my actual results.
- 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.
Megan Hayes-Golding 
Really excellent, Megan. Great work.
Solid.
Where is the link to the vimeo video? Am I totally missing it?
OK. It’s showing up now (with Chrome). When I watched it at work (with Firefox and IE), the video wasn’t showing up.
Do any of the kids ever mention the fact that the water out of the pitcher is not being poured at a constant rate?
@Touzel – excellent question! Some of my students did point that out. They also didn’t like in the 3rd video when I ran out of water from the pitcher but the sink was still filling — both are strong reasons I included discussion on sources of error.
Thanks @Dan and @Jason. My kids really dug the lesson.
Thanks Megan! I used this with my freshmen last week – they had a great time estimating how long it would take to fill the sink and it was a perfect lead in to solving work problems.
Maybe some extensions to this:
How long does it take for the sink to drain? Then, if the sink is full, open the drain but keep the water running. How long will it take for all of the water to drain then? (Subtraction problem)
Also, with the pitcher: if you start adding water from the pitcher after the water has been running (like 20 seconds), how long then? That adds a little more complication to the variables, and gives some good discussion on setup and the meaning of variables (do you use t +20 or t – 20? What does t represent for both cases?)
Definitely good stuff.
I totally agree with your “aggravating but true” side-note. It’s my current hang-up with implementing this 3-Act inquiry stuff completely…