The Zipper would be cool as a follow-up to the Ferris Wheel. (a) It’s oblong instead of circular, so that’s a bit of an interesting curve ball from the usual stuff. (b) The individual cars also rotate, so you have to account for two motions at once. DESMOSIFY IT!

On the upper end of the scale might be tea cups (circular motion-ception) and a pendulum ride, like those pirate ships that take a while to build momentum before whirling you 360º.

All good ideas so far. I’d like to see a roller coaster for both height vs time and speed vs time. It’s another one that the coaster would strongly suggest a wrong answer for height vs time, but the speed is quite challenging to graph.

On Jason’s idea I’d love to see one of those drop towers that goes asymptotic to the ground at the end.

@Mike S: Agreed.

It’d be great if one of these was an actual video, Dan Meyer style. Any reasoning behind the flash animations?

Oh, so many options! The first few that I’ve thought of in no particular order:

1) Something with a jump discontinuity. The easiest way I see to do this is to add a velocity option for some of the existing rides. Unfortunately a macro-scale position graph cannot achieve this, unless we allow for telelportation (as in “Height Off Ground” in graphingstories.com).

Rationale: Students may be under the assumption that all graphs can be drawn by putting a pen down, moving it, then lifting it back up someplace else.

2) Parametric. The bumper cars offer a fantastic opportunity to be converted to a parametric equations exercise (as does the Ferris wheel, actually, but I prefer bumper cars).

Rationale: While the audience is different here, I know I initially struggled (as I believe did many other students), in getting an intuitive sense of what was going on witTh parametric. We need some good exploratory opportunities for students to develop an intuition here.

3) Step function. In addition to a jump continuity as explained above, a step function might be nice. My initial thought was someone waiting in line, with the y axis as the number of people ahead of them, but reflection reveals this is fraught with certain difficulties. Instead I suggest graphing the amount of ice cream on your cone: Get three scoops, one at a time, then lick the remainder until it is gone.

Rationale: Such a graph could help illustrate the difference between step graphs and say, linear functions.

4) I agree with John about a coaster, and I think this would be especially true if it goes through a loop.

Rationale: This is touched on by bumper cars already in that backwards motion does not mean the graph needs to go backwards, but unlike bumper cars, this one is self intersecting which doesn’t mean the result needs to be self-intersecting.

5) Something where you graph multiple curves representing distinct objects interacting with one another on the same graph (in different colors perhaps). Go-Karts might be a good option for this one.

Rationale: The graph would allow students to interpret things like “Who is in the lead?” and “What does it mean when the graphs intersect?”

Basically any of the kinds of graphs from graphingstories.com would make good entries.

How about a water flume?

Maybe a roller coaster if you are graphing speed over time (rather than height, so it doesn’t conform to the shape of the ride)

What about the tilt-a-whirl, since body motion is needed to have it twirl in a certain direction, to complete the circle and possible make it twirl faster? I hope I am not showing my age here.

“It’s unclear to me what we do if a student just scribbles away on the grapher.”

True enough. I shifted from suggesting “standing in line” to “scoops of ice cream” because the second is a quantity that can be thought of as either continuous or discrete. However this doesn’t solve the problem of multiple values. Same goes for graphing velocity of a ride.

Here’s my revised attempt: I’ve been to amusement parks where the price of some of the specialty rides is adjusted based on attendance. So early in the morning going up the bungee swing might be $10, then later it is $15 or $20, and say $35 in the middle of the day when there are crowds and long lines. If the price were displayed via a vertical number line with a big arrow on it to show the price then multiple arrows could pop up at a time to represent multiple prices.

A few more ideas for which I can’t immediately think of a context I like: Inequalities? Relations that aren’t functions? Graphs containing single points? Something polar?

I had to google a bunch of these rides. I guess I haven’t been to enough carnivals. Also, don’t search for these rides on youtube — you’ll never want to go to a carnival again. I’ve got a bunch of questions back, specifically about three clusters of suggestions.

(1) Velocity vs time graphs (@Jason, @Jim, @Chuck, @John).

Velocity v. time graphs bring up some extra fun/challenges on our side for interpreting what the student drew. Multiple values — do we split the path of the person? If there’s a gap, does the little guy pick up where he left off? What does it mean to travel with an undefined velocity for 1 second? Also, for the speed folks, are you picturing the graph is “speed” (magnitude of velocity), or something like vertical-component of velocity? In particular, do we want to allow for a negative “speed” on speed graphs?

(2) Graphs with discontinuities (@Jim)

Cannon Man would have a jump discontinuity at the moment the parachute pops if we’re graphing velocity — would that fit the bill?

For discontinuous graphs in general, how do you think we should treat the connected version (with vertical lines) vs the discontinuous, disconnected version? In the case of cannon-man popping a chute, I’m not even sure which would be technically “correct.” What do you think the distinction is between connected step graphs and disconnected ones / and what type of question could we ask to try to tease that distinction out?

(3) inception graphs seem potentially “frightening” — maybe in a good way if there’s an intuitive place to start… (two motions super-imposed) (@Lusto, @Jonathan, @Megan, @Liz, @Dan).

Are you picturing these as parametric graphs? If not (or if so), what grade level / subject matter do you think this would be targeting? Can you guys elaborate on an effective, low-floor way to get into that kind of task? Seems like it could be frighteningly.

@Michael — what did you mean by double-ferris wheel? Separate x-y coordinates graphs?

@Jim — just wanted to quickly second @Dan: the rationales in your list are great. I find it so much easier to think about / tweak an interaction on the foundation of a specific pedagogical purpose.

Graph height, speed, velocity, and distance travelled of a baseball during, say, this play: http://www.youtube.com/watch?v=EdepjcbE3bU. The ball is pitched (horizontally), hit (way up), caught, held, and thrown back to the pitcher (leisurely). I think it’s important (whether using this example or another) to realize one scenario has multiple variables to graph, answering multiple questions, and that a graph is not a picture.

An extension: allow students to control the Cannon Man or a ragdoll character inside the left window, creating a new loop:
1. Create your own animation puzzle.
2. Can you graph the height over time? The speed? The velocity?
3. See how well you tracked your own animation puzzle.
4. Challenge your classmates…
5. Class discussion: whose puzzle was the toughest? Why?

@Eil

I mean something like this.

@Jason @Mike I like the ideas of the drop tower and the pendulum rides. I had also thought of these.

At our local amusement park, the drop tower, called Dragon’s Descent, starts near the ground, travels up to the top (220 feet) in a few seconds, then pauses at the top before dropping. It includes a couple of bounces before slowly lowering the riders safely to the starting level. A velocity vs time graph would be pretty interesting. Constant upward velocity at the beginning – zero velocity at the top – downward velocity for the drop followed by some brief oscillation and then constant downward velocity as the carriage is lowered gently toward the ground.

The pendulum ride, called the Sea Dragon, uses a motorized wheel to get it up to speed, to maintain full speed, and then again to slow it down. (It doesn’t do a 360.) It would be interesting to graph both the height vs time and velocity vs time graphs. I wonder if students would realize that the maximum velocity happens at the bottom of the ride.

By the way, our amusement park has Physics Fun Days in May. I’ll be sharing this application with my colleagues. It would be great to have our students think about these rides and motions before we go to the park.

Thanks for continuing to do this great work, Dan (& friends)

Looking at the same “story” through different “lenses” (i.e. height from ground, distance traveled, speed) is always a rich learning experience for students. I was thinking about the use of “speed” as the dependent variable in some of your stories. It is harder to match exactly unless you have units because it’s hard to say how fast or slow something is moving on a graph with no unit labels. For example with your bumper car, “How high should I start the speed on the y-axis?”. One thought on addressing this would be to use a simple icon (like a star) on the y-axis to let the students know where the speed graph will begin. With your bumper cars, they could draw a horizontal line indicating constant speed as the car curved along the path, but then quickly drop to the x-axis and ride it at 0 after the crash. For some speed graphs, there will still be some subjectivity in how much to go up or down, but you could still get a pretty good match of the overall shape. Just a thought.

I agree with Adam–this is a great opportunity to show why functions are different from relations. You kind of see that with the bumper cars, and the animation does nicely show multiple cars appearing at once, but it’s less clear to a novice what’s going on.

Eric – I like! Very fun to play with different speed curves and see what happens. Also, it’s impressive that your team was able to add this new feature so quickly.

As promised, we’ve built a couple more scenarios based on your ideas. We built Adam’s recommendation of a roller-coaster with a loop in it to demonstrate that although the track has a loop, the graph of height vs time doesn’t:

https://labs.desmos.com/carnival/scenario/rollercoaster#rollercoaster

We also followed Chuck and John’s advice to try graphing velocity vs time on a roller-coaster to provide a more challenging scenario, and to show that the graph isn’t shaped like the track:

https://labs.desmos.com/carnival/scenario/rollercoastervelocity

Do these look like what you were envisioning? Do they inspire any more ideas?

A couple of pieces of feedback:

1) Awesome! Thanks for putting this together! I think you worked out a good way of doing velocity.

2) On the zipper, it goes up too high and too low… The correct height goes off the graph when I try to draw it. Not sure what’s going on with that.

3) I presume y’all will come up with more tailored “misconception” graphs for the second slide (for example, have students respond to feedback about a student who draws a graph with a loop for the roller coaster.

4) What about both position and velocity graphs at the same time? Perhaps one is editable and the other is just shown? Or perhaps both are editable? Obviously there are multiple ways to present the position graph based on the velocity, but something akin to whatever formula you currently use to display the roller coaster car could be used.

@Kevin — bumper car “distance travelled” isn’t showing multiple values? Or the bumper “velocity along path”?

Latter one’s here:
https://labs.desmos.com/carnival/scenario/bumpervelocity#bumpercars

There is some great stuff around the winter Olympics at the moment…..ski jumping, slopestyle snowboarding as they zip up those curves and do acrobatics…..distance and speed is interesting.

We were discussing this earlier….it seems easier to ask them to graph the horizontal speed and vertical speed….velocity is a vector and asking for speed is hard as it is the length of this vector…