I did it for meatballs, might as well try it again.
This is a link to a page that I would give to students to work their way through Robert Kaplinsky’s Guatemalan Sinkhole task.
It goes like this:
Students get a series of images and a quick video showing the 2010 Guatemalan sinkhole.
They’re asked what they wonder, and to estimate what it might cost to fill the hole with concrete.
Then, they move on to the mathematics. They read a brief CNN excerpt about the sinkhole:
And use that information to find its size and the cost of filling it with concrete.
This is where things get exciting. They have to dig the dimensions out of the article above, and find the cost of concrete on the internet. There are several directions they can go, and they’re all fine with me as long as they can justify their model and their answer. However, I anticipate needing to push some partner work and peer help to get everyone through this step. That said, this is real modeling, and is (I think) the most important part of the task.
There’s no resolution for this question — I couldn’t find a cost or explanation on the internet. I extend it in several ways for act three, but students will have to live with not knowing. I do try to leave the task with several perplexing questions, including:
Anyway, that’s my digital take on this task. It adds some interesting value to the problem. I ask students to do brief research on the web (and there are several other opportunities I passed on, in the name of focus on the mathematics). Students own watching the video, and can click back to the pictures if they need. They also need to read two excerpts and reference many pieces of information to form their model, and putting students on computers opens up more possibilities in terms of extension.
I do like this lesson in its digital format, but I liked the pencil-and-paper version I did last year as well. I’m still not sold on digital, but I’ve enjoyed making two lessons and will probably experiment a bit more. This lesson only took about 40 minutes to build, and I will hopefully get faster as I put more and more together. If you’d like to click through and try it out, link is here — I’d love to hear feedback!
Five Twelve Thirteen 
This is really interesting to see. I liked how you use technology as a means to get richer feedback from your students, especially with the questions that require students to articulate themselves. How did it work when you actually use it with students? Are you able to actively track who is not participating or is it too challenging to do that while class is going on?
I liked your extension and the extra info you have in terms of actual cost. It is worth considering the value of extending the problem with extra rich mathematics versus straying from whatever the original mathematics goal was (perhaps cylindrical or conical volume) to other topics such as proportions and cost.
Thanks for sharing.
Thanks Robert. I haven’t done this with a class yet, but I’m curious to see how well I can monitor the feedback. One disadvantage of this system compared to some others is that it isn’t actually instant feedback — I don’t see the students’ answers until after they finish the section they’re on and hit “submit”. I will be able to see how quickly students are working based on the time it takes them to submit, which I think will be the most valuable piece before I gain experience with this system.
hey, this is great! i appreciate so much all the wonderful work you’ve done putting this together.
i’ve gone through and done the entire activity making comments and suggestions throughout. i’m going to use this for sure. if you didn’t get my comments on the google forms, let me know.
one additional question — is this all done in class? one class, two? do the students already know the volume formula or not? thanks! 🙂
Thanks Kate, glad you enjoyed it — got the comments, definitely appreciate the feedback.
I think this would be one class. I wrote it with the intent of getting everyone through the posing of the problem, the calculation, and the analysis, and put the extension questions in for students who finished early.
I’m not sure exactly where this would fall in a unit on volume. Last year I introduced cylindrical volume with this task: http://threeacts.mrmeyer.com/youpourichoose/ which is more straightforward and motivated the formula for volume of a cylinder. Then taught a stripped-down version of this lesson the next day to have students apply the formula in a rich context. This is much more ambitious than what I did last year, and I’m not totally sure how it fits with the rest of my materials in 3-D geometry. Will have to keep thinking on that one!