I think I’d do it in the form of a series of emails. The president of the company wants to start a new product: bungee jumping! He wants it to be amazing, but safe. He attaches a video to show what he means.

The marketing gal sez yeah, hey, I know! Let’s guarantee the customer gets no further than 1 foot from the ground!

Company lawyer says whoa who whoa, we have to be safe or we’ll be sued! We need to test this. Send everyone to all the popular jumps and let them check it out.

Accounting VP says uh, I don’t think so. The budget won’t stand for it. We’ll need to test it first. Simulations would be much better–less risk, less insurance, less cost.

Crazy Al, the Engineer: you know, my sister used to throw her Barbies over the porch on a string. No bounce, though. Maybe we could use rubber bands or something.

I’d have that be the first handout, and see what happened.

MPG:

Would you give any of the above versions of this task to students on the first day or in the first week of class, all things being equal?

The only comment I’ll add to this interesting conversation (and specifically to your question) is that there is a lot of interesting work we can do before passing any of these versions out.

The worksheet, and whatever is on it, can help a student structure her work and thinking. But tables, blanks for questions, empty equations, gridded graphs — those are all too heavy a structure for the initial development of the Barbie Bungee question.

For #1, I first show a bungee jump video and then get the students to ask questions. Eventually someone will wonder how they know how much bungee to use. Bingo. I then talk about using math to model a situation. So how do they model this? Some kids will say they can use trial and error with some masses on the bungee cord. Some kids will say they do experiments with smaller cords to see how they behave. Bingo again. I then present barbie and her bungees, and what was essentially the same as activity #1. Not ideal, but it was ok.

Thinking back to when I tried bringing TI data collection devices into my classrooms in the late 1990s/early 2000s, I have to say that on some level that fear is well-justified (and even worse things can occur). But at that point, it really didn’t occur to me to create more open-ended tasks with less scaffolding. I wanted to see how the technology worked, give them a chance to see that you can collect data from a physical (is that the simpler way of getting at “real-world”) situation, and then apply the math they’d learned or were learning to that data. That process seemed “sufficient” in principle, but frankly it didn’t play out so well in practice for a lot of reasons.

I don’t imagine it would have gone dramatically worse if I’d done these tasks with them in a manner closer to the third choice here. And today, I can readily see creating much more open and flexible investigations. I think the drive for group data shouldn’t trump the goal of getting students to think divergently and creatively. Let the class come to the conclusion (at some point in the term) that it wants data from everyone that can be combined and examined statistically or in some other way.

How to create such classroom cultures starting on Day 1 seems to me to be harder and more vital than how to take a given task and open it up (that’s not meant as a put-down of the latter process; it’s certainly very important, and for some teachers daunting enough in itself). Would you give any of the above versions of this task to students on the first day or in the first week of class, all things being equal? Or is there a process that you’ve used successfully that builds to a point where you can give something closer to Version 3 than either of the others, and then continue to build student confidence in dealing with less scaffolded, less directed investigations?

Act 1: Present video of scenario. I notice / I wonder. Present question “how many elastics to bungee as close as possible w/o hitting the floor?”. Estimate; too low, too high, best guess.
Act 2: Hand out Barbies & elastics. Groups collect data. Solve (predict) in any way they like.
Act 3: Test our predictions. Consolidate w/ Desmos activity builder to ensure all groups can see how to determine a line of best fit for the data & use the equation or graph to make predictions.

I can’t wait!!!

In Version 1, students are asked to do three trials for each length. Do they know why? (The teacher would find this out in step 7, I guess.) Why rubber band lengths of {0, 1, 2, 3, 4, 5, 6, 7}? Why not collect data that is a little more “spaced out,” like every 2, 3, or 2 or 3? I notice that there’s no mention of an equation in this version. Maybe that (step 9) is where it’s the students who begin to do the math? (I mean, I can’t imagine that the graph will extend far enough to the right to reach the number of rubber bands to use for the long height.)

I wanted to like Version 2 more. In part 2, the independent and dependent variables are labelled. I’m not sure if that’s a big deal. But the author giving away that the rate of change is constant / the model is linear in the first question of part 3 is. I am making the assumption that the Barbie Bungee activity isn’t the students’ introduction to linear relations. (There are tasks that better suit this purpose – Mathalicious’ Domino Effect, for one.) Then again, maybe it is. If students have been learning about linear relations and slopes and y-intercepts, I can’t explain the author’s wording of questions 1 to 3 in part 3 (or speculate on what this says about the teacher’s beliefs).

Yes, Version 3 is wordy, but I don’t think that the intent is to simply hand it out and sit back while kids struggle to read it; I see it as supporting a classroom conversation. Tough to say without a lesson plan.