Saturday, April 14, 2012

Rolling Tires

It started a little over a month ago when I had to get my car tires aligned. As my car was being worked on, I killed 30 minutes worth of time walking around the industrial park with my son and came across this goldmine:
a dumpster full of used and abandoned tires 

Mentally, I started mapping out some math application(s) for the tires and figured Spring Break would be a prime opportunity to record a 3Act lesson for my geometry class. I'm proudly addicted to Dan Meyer's 3 Act lesson format. I can only hope I'm doing it justice. After trial and error, self reflection, and feedback from both students and online colleagues I'm starting to see the strength in 3 Act lessons, if done correctly. It requires planning, objectives, patience, and of course... time.

Have an objective, a lesson in mind, a real-world example, (maybe use a word problem from a textbook to jumpstart your direction), start training your eye to always look for lessons you can bring to your students...

Make sure it's measurable: Yes, it's fun to throw a picture at students and ask them, "What's the first question that comes to mind?" Both you and your students might agree on the same perplexing question, but if there isn't measurable data or a realistic solution, your media might simply reduce to a fun picture you both were perplexed by, predicted an answer to, and discussed a path to the solution. That fact alone might be valuable enough without the actual construction and implementation of a class activity/lesson.
This Lego pic I snapped is a great example of something difficult to measure: it might open up a discussion, students might make a prediction, but measuring it would be very difficult because of the numerous variables. However, something like my JUMBO and mini stop sign staging is very measurable and a lesson can be constructed beyond the discussion and prediction arena. Therefore, with Rolling Tires, I made sure everything was measurable before pressing record.

Act 1: A video of me rolling a tire (a friend was disappointed it wasn't a supermodel in a bikini). What's the first question that comes to mind? Hitting the initial mark during Act 1 is imperative to the overall success of the lesson.

Act 2: A keynote and/or video to reveal information my students might find necessary to solve the question agreed upon.

Act 3: The video payoff to see how the calculated (theoretical) answers compare to the actual (practical) results.

Please feel free to download and use all three videos. Give me some feedback. Ask me some questions. The necessary information is included in Act 2. I thought, great an actual way to apply circumference. I will try to post any handouts or graphic organizers used. Lastly, if time permits I might make a sequel to include a couple different scenarios.

Possible Sequel: I heard a long time ago that some taxi drivers put smaller wheels on their cabs so the car tires would produce more revolutions, yielding a higher cab fare. Check the tires of that cab before you get in it.



  1. This is sick, Mr. Stadel, I love it! Will definitely steal it for later this year, already have a folder for 3Act lessons. Same here, everywhere I go, I'm always looking for possibilities. But you're right on about it being measurable - how do you have Act3 without it? I like what I'm seeing on, but they are more for inspiration, really can't use them if they're not quantitative. (Stealing your stop signs images too!)

    I actually did a very similar "Rolling Tires" lesson around Pi Day two years ago when I brought in my bicycle and my daugther's. I rode the bikes (one at a time :) down the school hallway a marked distance and asked the same question of how many rotations.

    What I sorely lack is the skill to do all the add-ons to the videos, so until I learn how, Act 2 will be filled in by hand!

    (Nathan Kraft already left a comment on vimeo about the stopping point of the two tires, I noticed this too.)

    Thank you, thank you, thank you for sharing!

    1. Thanks Fawn,

      Glad you'll be using the stop signs pictures too. I have measurements for that setup and will hopefully post the keynote soon. Let me know if you're interested.

      I love your bicycle lesson idea. I always get a kick out of seeing little kids ride their bikes and how hard they have to pedal just to go a decent speed. Smaller tire = more work. There's nothing wrong with filling in Act 2 by hand! The kids have to do it!

      Re: stopping point. This is what I told Nathan Kraft:
      I used Keynote and exported the presentation as a movie so I could insert it into iMovie (the poor man's version of Adobe After Effects I guess, ha!).
      I purposely staged Act 3 as you saw it. I'm expecting some viewers to initially ask if the tire hits the target in Act 1. I want to encourage nonlinear thinking in my class and by doing so I am proposing situations where a tire hits the target and the other one doesn't. Therefore, my students might have to do four calculations before viewing Act 3. Then before watching Act 3, I'll rouse the class up for predictions in hitting the target. After seeing the results, it allows room for more discussion and if I'm lucky, a desire to see more. I have video of both tires missing and hitting the target. This allows for a 'sequel' or 'outtakes' part of the lesson (hope that makes sense).
      Thanks for the feedback and glad you enjoyed it. Not sure I will post the 'outtakes' video, but if you're interested, let me know. That way you have 4 possible situations to discuss with students.

  2. I want EVERYTHING you have, Mr. Stadel, please deliver by Friday. Only slightly kidding.

    Lovely, I'd appreciate the stop signs' measurements (I promise not to look and see if I can answer my own questions based on your pics alone). I'd also love the 'outtakes' for the tires too if not too much trouble. I definitely sense the questions coming with my geometry kids. Thank you for explaining the ending, and yes, the best lessons are ones that encourage us to think outside-the-box. I think "linear" is spelled B-O-R-I-N-G.

    Luckily I have a group of geometry 8th graders who are wonderful thinkers and problem-solvers (actually we all have them in ALL our classes, don't we?), they motivate me to always extend a problem, so rarely do we end with, "Oh, here is the answer."

    However, I'll admit there are occasions when a kid keeps asking so many WHAT-IFs that I'm thinking, Damn it, child, let's move on already!:) But instead I say something like, "Well, what do YOU think? Let us know when you have a conjecture." The class sighs with relief.

    1. I'll gladly post what outtakes I can before Friday. I'll throw out a tweet when they're posted. You're a great speller :P I agree and like your response to your students with the never-ending hypotheticals. As for the Stop signs, check my comments on that blog post for very restricted measurements. I hope it's enough to compare the areas of the signs... :D

  3. Maybe this could be a non-example. It's what came to mind when I saw your rolling tires. :)

  4. In Act 3, it should say 24% of a fifth rotation, not fourth. Right?