Inspired by the general enthusiasm for the process in the MtBOS, I tried my first 3 Act Math Lesson(s) today.
If this is somehow the first place you’ve heard that term, Dan Meyer has been the main force and originator of this structure, and I’ve also seen good explanations of the structure from Dane Ehler, Geoff Kraal, and many other. I think this series of blog posts by Dan Meyer is maybe the best place to really start understanding the structure.
We just finished basic triangle trigonometry and word problems, and are about to start applying trigonometry to area, so I was looking for problems to help us hone in on those, and I found a couple: Boat on the River by Andrew Stadel and the Big Nickel task by Kyle Pearce and others.
I had never done this before, so I decided to try something new and NOT overprepare. Didn’t make a handout, or a structure, or a OneNote page, or a powerpoint, or anything. Just watched the videos myself, made sure I understood the basics of what happened, and wing it.
It kind of worked.
Boat on the River
I told the students “We will watch a short video. Ask whatever questions you can about what you see.”
We watched the act 1 video three or four times and I elicited and wrote down questions.
Result from one class:
Some of the questions were silly (9), some were answerable by watching the video we had more carefully (1, 2, 12, 13ish, 10ish), some were ineffable (16), some required outside knowledge (11, from a student who sails), and MANY were math. I was going for #3, so that’s good. To solve!
I showed them the pictures on the PDF provided by the task.
(There is another image that establishes a scale for these pictures of 1 in = 10 ft). Since we already knew how to work with sine ratios, this was easy for the girls to work with, and they found that the boat will make it… barely. I let them work on this in partnerships for 5 minutes, explain their work, and then…
We watched the Act 3 Video and clapped when the boat [spoilers!] made it through.
A success. I don’t feel like the students were hugely more invested in this than in more “normal” word problems, but if I increase the enthusiasm of my presentation I think we can get there. I do like the basic structure, and calling for questions brings me back to the first steps of the Engineering Design Process from my science teaching days; a useful way to get ideas.
Since we had never done area problems that required trig, this was a harder, longer task for my students, but that wasn’t the only stumbling block I ran into here.
After watching the short video at the top of the task, my students thought the monument was funny, but their questions were silly, snarky, and didn’t really go where I was hoping. I eventually had to straight up give them the question I was hoping for, the last one.
I don’t know how to inspire the sort of sideways silliness needed to find that question; a perfectly designed 3 act may do a better job of getting them there simply from the video, and maybe this one isn’t perfect. Or maybe I just need a sillier group of students to get there.
“What do we need to know?” was actually more interesting here. We needed to know dimensions of the big nickel and the real nickel (height and thickness) and my students pointed out that we also needed to know if it were hollow or solid – basically is this a problem about surface area or volume! This part was fun, as we scoured the wikipedia entry for the information we needed:
- It is 9.1 m tall, 0.61 m thick.
- It is made of steel plates attached to a skeleton – basically hollow!
- A real nickel is 2.12 cm tall, 1.27 mm thick
I told them this was all they needed and let them loose. We have studied the area and angles of regular polygons before; I told them they may want to remind themselves of those formulas and techniques, as well as look for right triangles to use trig. I would say about 2/3 of each class got very close to finding the area of both the big nickel (in square meters) and the little nickel (in square cm). Some needed more hints and guidance than others. This part was slow, and frustrating, but went well. We got to the end of class and I asked how many nickels it would take to tile the front of the big nickel, and then we had to remember that square meters and square cm are not the same unit – so we got to review square unit conversions again, which we tackled earlier in the year. The math of this was good.
… there isn’t really one. We can find other people’s solutions, but unfortunately there is no way to get the kind of satisfactory resolution from this problem that we got from the boat. I think this may actually disqualify this as a true 3-act problem. It is a GOOD problem, but, frankly, nobody has ever built the Big Nickel out of nickels, so we don’t have an answer to the question outside the theoretical.
How do you create the resolution of Act 3 when the problem at hand can’t actually be done?
My first attempt at 3 act problems was fun, and led to good math, but needs work. I think I need to add some structure, and I need to think more about some of the components, specifically how to get the resolution of Act 3 when the problem does not allow for it and how to get the “right” question out of Act 1 when it’s not necessarily obvious (but IS creative and interesting).