Teaser
Open class with an online game, either Gimme Friction or Taberinos. Play for ten minutes. Have your students write down their highest scores. Create a classroom leaderboard.
What can you do with this now?
Spoiler
I’ll try to limit myself to broad strokes here. There are a lot of interesting trees but the forest — the framework for turning an interesting thing into a challenging thing — is what interests me most.
1. Freeze gameplay in time and space.
2. Ask the students to make an intuitive prediction about where the ball will hit the ceiling.
3. Show them the answer.
4. Formalize the math.
You can print out the previous picture and pass it around. Have students measure everything. Measuring things is a useful thing to do when you don’t know what to do.
Don’t just tell them to measure the angles. “Measure the angles,” is too helpful. Who will narrow down the scope of a problem like that for them after they graduate?
Eventually reach the (useful) conclusion that in a frictionless system like this, the incoming angle equals the outgoing angle.
5. Practice
Screengrab a few more scenarios like #1 above and have them determine where the ball will end up. Ideally, you’ll have the answer videos queued up so that the question of correctness isn’t answered by the authority figure in the room, rather by the world itself.
6. Play the game again.
Are scores higher or lower? Does an appreciation of the math undergirding the game even matter? Does it matter if it matters?
7. Iterate
Gimme Friction beats out Taberinos and the usual miniature golf-style application of this concept because, eventually, you’re firing cannon balls
8. More practice.
Good questions here include:
“Is it possible to hit all three targets?”
“What cannon angles are ‘safe’?”
9. Extensions
Can you imagine the exceptional grasp of coordinate geometry, trigonometry, and vector math it took to program this game? We haven’t even gone into the way the cannon ball slides to a stop and then expands until it reaches a boundary.
So lay a coordinate grid over a screenshot. The only variable here is the angle of the cannon. If a student could develop an algorithm to describe the final position and size of the first shot fired for every angle from -90° to 90°, I’d assign her an A for the first semester of Trigonometry, no hesitation.
20 Comments
Steven Peters
April 5, 2010 - 10:35 am -I can’t help but think of curling when I see this game, although having a fixed initial speed does change the gameplay drastically.
Since the gameplay is physics-based, with collisions (elastic I think) and friction opposing the velocity of the cannon ball, I can imagine this game being useful in a physics class. With regard to safety, the ball basically travels a fixed distance before stopping (if the collisions are elastic). Thus, you would have to search over the different input angles for resulting paths that are long enough without bouncing back to the bottom. It kind of seems like a ray-tracing problem in that sense. It could also fall under the category of “path planning” which is useful for determining the path of mobile robots. Perhaps you could imagine the ball as a roomba that drives around bouncing off things (they actually have a more random algorithm than that).
Nice catch, Dan.
grace
April 5, 2010 - 5:28 pm -I would have loved a lesson like this in my Geometry class! It also reminds me of countless practice problems in the physics class I took in high school. Thanks for sharing.
I think your questions are some of the most powerful elements of your lessons in that they’re provocative and compelling, yet clearly focused on the objective and the topic at hand rather than just being fuzzy or purely exploratory– this is often a difficult balance to strike, particularly in extension questions when it’s so tempting to just have students do the worksheet or otherwise practice. If students don’t respond right away to something like “is it possible to hit all three targets,” to what extent do you scaffold by breaking that down into more manageable chunks? I’d love to hear both your theoretical answer– what you believe, on principle– and your practical answer– what you actually find yourself doing– if they’re different!
And your footnote made me laugh out loud.
Dan Meyer
April 7, 2010 - 9:32 pm -At this point it’s all theoretical, since I haven’t taught the lesson, but I’ll try to flex my imagination here.
I’m pretty sure my remedial students would say “I dunno.” to the “Is it possible to hit all three targets?” question. I would ask the student to play. Pick a point on the first circle. What will happen when you shoot there? How do you want to adjust? Is that better? How do you know? Could you make your shot even better? Okay, now see where it hits the second target. Etc.
I can imagine a lot of great conversations. Most of them, I think, would prioritize “play” over “correctness.” They’d also define errors not as failure but as valuable information.
I’d appreciate anything you could add to my thinking here.
grace
April 8, 2010 - 7:38 am -I like your hands-on approach to having students figure it out through a very concrete experience. My intuition would have been to break down the questions I was asking and adding the following to some of yours:
“What would the perfect path have to look like if it was going to hit all three targets? Can you draw me a rough sketch of what you’d hope to see? How do you know that your path is reasonable/possible?”
“What would you have to do to make the cannon ball follow that path? Where would it have to start?
“Did what you do work? Why not?”
My concerns would be around doing too much of the thinking for students, or around breaking it down so far that they lose sight of the big picture. I’ve kind of been obsessed with questioning lately, which is why I was so excited to see your link to David Cox’s recent post.
Steven Peters
April 8, 2010 - 8:01 am -It would be nice if there was an undo option in the game so you could take the same shot multiple times. That’s how you deal with the question of is it possible to do something, you let them try multiple times. Unfortunately the game isn’t set up like that, but the game could probably be cloned for educational purposes such as these.
Dan Meyer
April 8, 2010 - 9:01 am -I felt the same way about the NLOS Cannon game.
breetai
April 9, 2010 - 12:17 pm -As long as we’re talking about Flash games, WCYDWT?
http://www.swfme.com/view/1046212
Dan Meyer
April 10, 2010 - 1:36 pm -Someone turned the XKCD comic into a game! Awesome.
Cramer
April 11, 2010 - 7:49 pm -Thanks Dan. I lost 3 hours of grading assessments on Friday night because I couldn’t stop playing !!
Stacy
April 17, 2010 - 5:43 pm -Beyond the questions of collisions, I’m also tossing around something for the circle unit we’ll be hitting soon at the end of this year. Give students the coordinates and radii of several circles already played in the field. Then give the final resting place for a fired circle. What will the final radius of the circle be? Still tossing it around, but that’s what I’ve got so far.
Dan Meyer
April 18, 2010 - 6:56 am -@Stacy, if they can answer for a given set of pre-existing circles and a given cannon angle the location and size of the next circle, I’d say they’ve done something enormous. I shudder to think about scaffolding that task, though.
tonypa
April 18, 2010 - 7:35 am -Why are all your screen shots from Gimme Friction Baby game? (I am joking, thank you for mentioning Taberinos)
I wish you would use original link instead of driving traffic toward big portal. Gimme Friction Baby was designed by Wouter Visser for Game Design Competition run at JayIsGames
http://jayisgames.com/archives/2007/08/gimme_friction_baby.php
And while I am here, you can find many more games at my own site too :)
Steven Kimmi
May 18, 2010 - 11:19 am -Just wondering if you’ve seen this? http://www
Dan Meyer
May 18, 2010 - 11:38 am -Yep. Love it. Tickles my math fancy.
DaoudaW
May 19, 2010 - 1:48 am -How do you create the multiple exposure screen shots? I’ve tried different things, but there must be an easier way!
Kris Kramer
May 19, 2010 - 6:59 am -Any suggestions for kids that don’t have computers in the room?
Dan Meyer
May 19, 2010 - 5:12 pm -I recorded the screen using ScreenFlow and converted it into a screencast. I used QuickTime Pro to turn the screencast into an image sequence. Then I imported all the layers into Photoshop and selectively masked out the little ball in each frame.
In other words, if there’s any easy (or cheap) way to do this, you won’t find it here. Sorry.
Sure. This particular case demands a lot of practice so you’d have to print out a lot of mini-examples like in step eight above. You’d also have to have the actual videos for each practice example queued up so students could check their predictions for the path of the ball. I apologize I haven’t provided those resources. One of these days.
Paul E. Black
May 20, 2010 - 5:10 am -In step 4 you say, “… in a frictionless system like this, the incoming angle equals the outgoing angle.” The system has friction. Maybe the way to put that is “… in a system without outside forces …”
Jeff Trevaskis
May 26, 2010 - 4:42 am -Gimme Friction is a great game Dan. Simple to play but very addictive. If you can extract some Maths from it then you are on a winner. Keep up the great WCYDWT posts. I am plucking up my courage to post a few of my ideas on my Webmaths blog.
Cheers, Jeff.