## What You Can’t Do With This: NLOS Cannon Challenge

This is a classic game. It’s been around in various forms longer than I’ve been alive. Choose your velocity, choose your angle, cross your fingers, and fire. Discovery has simplified the game nicely, removing some noisy variables like wind speed, which you’ll find in other versions.

I first saw Discovery’s incarnation several weeks ago and have been on-and-off obsessed ever since by the question: what can I do with this? The point of this post is to throw up my hands and report: nearly nothing. I have no idea what the students do here.

I mean, it’s far from worthless. If a student can get past level ten, then she clearly has some understanding of angle and velocity and the dialog between the two. She might even ask herself some interesting questions, like, which angle gives you the longest range? But I won’t drag the laptop cart across school for those small potatoes, for that two-step lesson plan of 1) guess and 2) check.

Here is the most rigorous, reasonable question this game can ask, a question which it is fundamentally incapable of answering: can you develop a method for hitting any target in one shot? This is a question either a) Discovery didn’t think of or b) Discovery thought of but, for whatever reason, didn’t make accessible to students.

Either way, it’s frustrating. It’s frustrating that:

• there isn’t a grid for determining coordinates;
• the units aren’t defined;
• there isn’t a timer for determining parametrized equations;
• banner advertising reloads in the middle of the projectile’s flight, making a mess of my makeshift timer.
• you’re firing from the tip of the cannon, not the base of it, which adds mathematical noise;
• the layouts change at random (ie. my level three isn’t the same as your level three) which crushes my one workaround here, copying level screenshots into Geogebra.
• I think, though I can’t be sure, that you’re blowing up huts and tents in some levels, which, gross. Seriously.

All of which is frustrating. The game uses mathematical notation for angle and initial velocity. It comes packaged with its own assessment systemYou get 100 points for each unused shell. The student with the most points (likely) has the best algorithm and calculations.. This thing is so close to being useful.

Which makes it an interesting answer to Scott McLeod’s question, where are the Internet resources for your subject area? Because this game isn’t from some arcade site which I’m hopelessly trying to bang into a lesson plan. It’s from Discovery, which isn’t exactly apathetic to the needs of educators. Why didn’t the thing come with a lesson plan?

My takeaway here is that the people who know the Internet and the people who know instructional design aren’t the same people and they aren’t talking to each other enough. We are left to our own devices.

BTW: Just a little over a year later and Colleen King comes through for the team: Tactical Rescue Missions for Intergalactic Good. Great work.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

1. #### Tim

April 20, 2009 - 5:27 am -

While I’ve used various incarnations of this activity (going back to the Apple II), I’ve always had the same questions as Dan: what’s the point? What value does this bring to the students? We can certainly talk about conics and physics but without the necessary tools, it winds up being an effort in trial and error.

However, stuck in the back of my head has always been a nagging little buzz about the negative message being sent. After all, the overall goal of the game is to find the fastest and most effecient to destroy something. But maybe in the age of photo-realistic full-on war games, that buzz is overwhelmed by the sounds of AK-47s and explosions.

2. #### Michael

April 20, 2009 - 6:15 am -

Perhaps you could invite either an Army or Marine Tank or Artillery soldier(s) to talk about the math used to fire such long range shots to accurately hit their target which sometimes can exist over the horizon. (granted they have computers to speed up such calculations, but should the computer fail, they need to be able to quickly do the math themselves. What information do they need to quickly collect to input into their equation(s)?)

These would be experts in the field drawing in the reality of math that is used, therefore make the game perhaps that much more fun (or boring).

Perhaps you could have students create their own maps on grid paper to experiment with different parabolic equations.

How can a graphing calculator help in this project?

In some of these “canon” games, the tank can move. How does moving the tank affect your equations.

What if you created your own real life game with sling shots and tennis balls or a ping pong ball gun trying to make it into a trash can? If it was safe and possible, start or finish from different heights.

3. #### Scott

April 20, 2009 - 12:13 pm -

http://en.wikipedia.org/wiki/Gorillas_(computer_game)

Gorillas gives a better background for this type of thing. Why encourage kids to jump in a tank and blow eachother up when we can have them be gorillas and throw (albeit explosive) bananas at eachother.

I used to play the Qbasic version many moons ago, but the wikipedia page looks like it has links to some updated versions.

Also — you can put it on your iphone :)

4. #### Rich

April 20, 2009 - 4:39 pm -

Coming in with probably the oddest entry of all, there’s always Hillbilly Pig Toss. It has pretty much similar shortcomings (especially with items 1, 2, 3 and 5 from Dan’s list) (fortunately, no pigs are killed in the making of this game), but it does vary a few things like the height of the launcher relative to the catcher, etc.

p.s. Be sure to turn your volume down before the first time the catcher succeeds, or you’ll get an extremely loud “Yee haw!”

p.p.s This is part of a larger set of FunBrain math games which are riddled with distracting ads, but somehow by searching for this specific game, the page that I found has ZERO ads showing!

5. #### Tom Hoffman

April 20, 2009 - 8:08 pm -

What you really want to do is have the kids write the program. The fact that in 2009 this still sounds like a pie in the sky idea to most people should make you fear for our future.

6. #### Jason Dyer

April 21, 2009 - 8:08 am -

Since I’ve done this over the summer with real life bottle rockets, a launcher that could be set at any angle, and a vertical target, I’m not finding the computerized version nearly as interesting.

I’ve also run a simpler version of this in my classroom with wads of paper. Why must everything be digital?

7. #### Dan Meyer

April 21, 2009 - 9:00 am -

Digital objects are useful to me only when the real, tangible objects are too inconvenient or too expensive to bring into the classroom. I don’t know where anyone in these pages has insisted that everything run digitally.

Aside: you make your launcher and the lab that accompanies it sound like the easiest, most obvious things in the world to acquire and use. I’d enjoy reading more about this because none of it sounds easy or especially obvious to me. I’m interested.

8. #### Rich

April 21, 2009 - 11:02 am -

Dan, you should pick up one of the most basic Estes kits (the Alpha III is plastic, already assembled, and part of a launching kit) for only a few bucks. It’s a tradition with my brothers and me that we try to launch a few rockets every year after Thanksgiving dinner, as long as the weather allows. You can adjust the launch angle within a pretty decently wide range. No sense in spending many hours building a rocket from a kit if you’re not really into that aspect of it.

It sounds like Jason’s using an even simpler bottle rocket setup, probably with some sort of pipe like PVC as the launch tube?

9. #### colleenk

April 21, 2009 - 11:09 am -

@TomHoffman Fear not – there are some people out there teaching math through programming. At my learning center, we have K-3 students exploring geometry, measurement, and number sense with a reincarnation of the old LOGO turtle. Students in grades 4-8 are developing pre-algebra skills via Scratch and Alice. Our high school students are learning functions and geometry by programming Flash applications. This is all taking place at a private math center, though, not a school. I think there’s also a Python movement headed by Kirby Urner: http://www.grunch.net/4dsolutions/kirby.html

@Dan In defense of the Cannon Challenge, it really wasn’t intended to be used by math teachers but I understand your frustration. Imagine this (fictional) scenario: You find the Cannon Challenge, play the game, see the potential. You decide it needs a grid, a timer, defined units, and a little less destruction. Ok, here it comes….you download the source code, images, and sound effects that Discovery makes available to educators who want to make derivitive works. You change a few parameters or have your students do it (as Tom suggests). I think it’s unlikely that programmers will create activities that suit everyone. However, going open source would enable anyone to tailor those activities to fit their needs. If we are forced to use pre-designed apps, we’ll never be content. In the absense of open source, designers need to create activities rich with features that can be controlled by the user. However, that would significantly increase development time and, therefore, the overall cost. There are no easy answers.

10. #### Dan Meyer

April 21, 2009 - 12:13 pm -

@colleenk, that sounds amazing, but unlikely, given the formidable pay wall Discovery has built around much of its content. Fella can dream, I guess.

@Rich, are you able to hold the initial velocity constant with rocket kits?

And then I wonder about wind resistance, especially with projectiles as light as rockets. In my ideal simulation, students would calculate how to hit a target a football field away. The digital simulation reduces some of that noise, which appeals to me.

11. #### Nancy Bosch

April 21, 2009 - 3:20 pm -

…after raising three sons the idea of a bunch of high schoolers with PVC pipes and bottle rockets makes me shutter. Stay with virtual….or make sure your liability insurance is paid up!

12. #### Rich

April 21, 2009 - 4:09 pm -

Yeah, you’re right Dan, anything with a propellant (like a model rocket or even a water rocket) would be accelerating until burnout which definitely complicates matters. That’s a good argument in favor of the paper wads. What about making some sort of rubber band slingshot deal, but mounted to a base (instead of being handheld)…. You could even measure the tension before launch; create some sort of rough scale for the stretch in the bands vs. the amount of tension to calibrate it. Then when you launch you’ll only officially have acceleration while the projectile is still in contact with the rubber bands…. On the other hand, an argument against the paper wads is that you’d have moderate air resistance pretty quickly, which is negative acceleration, which is just as complicating as the rocket engine stuff above.

I think a model rocket launch would be very cool to students, but then stepping it down to something you could do (safely) in the classroom would give you better, more measurable, results.

I’m not a rocket scientist but there are times when I wish that had given that a thought.

13. #### Jason Dyer

April 22, 2009 - 4:27 pm -

Apologies: the last comment was more of a reply to general webosphere attitudes than this particular blog.

I know 4 ways of doing the real-life launcher (3, predictably enough, are from other people). Let me contemplate which one would be best to write up and report back.

14. #### Jason Dyer

April 22, 2009 - 5:20 pm -

(This is one of the “borrowed” lessons, with a few tweaks from myself.)

Supplies: marbles, cardboard and construction paper, cups, stopwatches.

Studies build slopes leading down to ramps with cardboard and construction paper. The launch at the end should be built so that it can be adjusted freely as to angle.

The marbles aren’t flung down the slope, they should put up at particular heights on the slope and let go. To change velocity students should pick a higher or lower point on their ramp to let go.

Students experiment with stopwatches, variable heights, variable angles, get a sense of their ramp, come up with equations.

For the finale, a cup is set at some distance (only revealed when the time for the challenge comes up) and the students try to get the marble in the cup in as few tries as possible.

A very careful group can do it on the first try.

15. #### Jason Dyer

April 22, 2009 - 5:26 pm -

(Also, from experience, acceleration with a bottle rocket happens very quickly and for the purpose of high school equations can be considered negligible.)

16. #### Clint H

April 24, 2009 - 12:59 am -

Since the weather is heating up, why not buy a water balloon slingshot or make a funnelator.

I did this with my AP Calc students years ago after their exam:

1. Give them 10 balloons so they can gather data on how changing the parameters (angle of elevation, amount of pull in the slingshot) changes the distance of their projectile.
2. Give them time to work out the calculations and maybe give them a few more shots after they have their initial guess.
3. On day of the contest, come dressed in your swim trunks and sit yourself somewhere on the football field. See who can hit you…

17. #### Tom Hoffman

April 24, 2009 - 6:10 am -

It seems to me that a key part of Dan’s approach is being engaging while avoiding time consuming hands-on experiments and activities. That is, maybe it is best if the kids do the whole rocket/slingshot whatever project and do all the measurements and theorizing themselves, but if you can get 80% of the benefit and engagement of that with some well designed graphics, in 20% of the class time (or less), then the graphic is the way to go.

18. #### Dan Meyer

April 24, 2009 - 1:18 pm -

Nobody here seems particularly self-righteous about his own lesson plan. I hope we can all acknowledge the importance of a cost-benefit analysis of every plan, every day, an analysis that, even for the same lesson plan, will be different for different teachers.

Me, I know I need to bank as much time as possible for WCYDWT?, miscellaneous questions, and daily show and tell, so if you’re going to have me a) setting up a lab or b) leaving the classroom or c) both at the same time, I need an especially compelling reason.

Firing water balloons at a teacher and launching bottle rockets from a cannon sounds like more fun than this (hypothetical) NLOS activity, but:

a) the NLOS simulation allows for some pretty serious mathematical analysis, with quadratic equations and everything, whereas water balloons are more of the same guess-and-check-and-adjust, and Jason didn’t mention whether or not wind resistance messes with the bottle rockets.

b) I can get every other student her own NLOS simulator but I can’t get every other student her own water balloon slingshot or bottle rocket launcher. That means a lot of students won’t engage.

I’d rather the real-life experience here but it’s too expensive.

19. #### Clint H

April 27, 2009 - 12:51 am -

I don’t see tackling this topic as a way to bank time for other endeavors; this is the endeavor for which I have banked time.

For any student who has aspirations of being an engineer, rocket scientist, mechanic, builder or tinkerer, they need more than a computer simulation, where everything is rosy and wind resistance doesn’t matter.

I would take my 1 or 2 weeks that I have banked elsewhere, use kinematics to determine the vertical and horizontal velocities of our projectile, use vector analysis to determine the muzzle velocity of our cannons that we built, use regression to determine a function that gives distance horizontal distance as a function of launch angle (assuming maximum muzzle velocity), make predictions and test our results, and then show up prepared to apply what we have learned with the calculations to back up our decisions. On the day, whether it works or not, we will be prepared to reflect upon our work, our results and our possible sources of error so that next time we can be more efficient.

In the cost-benefit analysis of my lessons and classroom time, creating and interpreting real life data ranks the highest of anything.

20. #### Dan Meyer

April 27, 2009 - 5:17 pm -

Fair enough with your allocation of time. Fair enough, also, with your inclusion of mathematical noise into the classroom dialogue, though I think there is a fine line between too much noise and too little as well as a fine moment to introduce that noise and a lot of lousy ones.

Assuming your lab strikes all those balances, I’m left with two questions:

1) How do they replicate the activity? The NLOS activity is replicable. Jason’s marble activity includes an adjustable chute. I don’t see how funnelators can be fired with the same reproducible accuracy.

2) Have you purchased or constructed multiple funnelators for multiple small groups of students? If not – that is, if there is only one or two funnelators – how do you challenge the whole class?

21. #### Jason Dyer

April 28, 2009 - 5:38 am -

The reason the chute manages to be fairly reproducible is a.) the launcher mechanism is gravity and b.) marbles are a consistent shape. The main is error is a.) the students measuring angles — good grief does this get error b.) the students measuring distances and c.) the students taking times.

Each student group should be making their own. Of course between devices there isn’t consistency, but that’s part of the whole appeal of the lesson — each group of students has their own unique dataset to work on. (If you’re really worried about that, there’s a variation involving flexible pipes, but that requires actual money to pull off.)

22. #### Clint H

April 29, 2009 - 1:58 am -

1. This activity is no more subject to replication than an experimental probability activity where students flip a coin 50 times: The results may or may not be exactly the same for each trial but the cumulative effect of the gathered data serves to strengthen our model. There are two, of course, two assumptions here. A) The groups are measuring the launch angle accurately, and B) the groups are applying maximum force to the catapult.

2. You know the answer to this one already: by carefully choosing groups and scaffolding support for those groups. Do you divide groups by ability? Or do you create mixed ability groups? That’s up to you to decide. I would probably create groups by ability so that support can be provided to those groups that need it. It would also allow the strong groups to extend their experimentation by varying the initial velocity of their projectile.

I have never constructed multiple funnelators, to answer your question. I don’t, however, see that as the major obstacle to this unit.

23. #### Dan Meyer

April 29, 2009 - 8:10 am -

I can’t seem to clarify this question:

What do the groups who aren’t using the funnelator do?

I realize there are calculations and measurements to perform but part of my attraction to the digital simulation is that everyone has ready access to the launcher. In every lab I have ever conducted as a teacher or participated in as a student, having only one apparatus for the entire class will result in a lot of disengaged, wasted time.

24. #### Nancy Bosch

April 29, 2009 - 5:45 pm -

Maybe different groups are doing different stuff–the funnelator, the slingshot, the trebuchet, ramps, etc–rotate then come back to the big group to report findings–which most helped to demonstrate the concept, etc. Just a thought.