In PreCalculus, I tend to be application heavy whenever possible. This unit, which has focused on analytic trigonometry, has been pretty high on the abstraction ladder. I try to emphasize right triangle trigonometry in nearly everything we do so that students have a way in, but that's still pretty abstract. I decided it was time to do something more on the application side.
Enter Dan Meyer's Boat Dock, a makeover concept he put together a year ago on his blog.
After collecting the data, I asked students to clarify what they meant by 'best' and 'worst'. Student comments were focused on safety, cost, and limiting the movement of the ramp.
I shared that the maximum safe angle for the ramp was 18˚, and then called upon PearDeck to use one of its best features to see what the class was thinking visually. I asked students to draw the best ramp.
After having them draw it, I had them calculate the length of the best ramp. This is where some of the best conflict arose. Not everyone responded, for a number of reasons, but the spread was pretty awesome in terms of stoking conversation. Check it out:
The source of some of the conflict was this commonly drawn triangle, which prompted lots of productive discussion.
When students built their safest ramp using the Boat Dock simulator, it prompted the modelling cycle to return to the start, which is always great to have the ability to do.
I then asked students to create a tool using a spreadsheet, program, or algorithm by hand for finding the safest ramp of least cost for every random length of the ramp in the simulator. This open-ended request led to a lot of students nodding their heads about concepts learned in their programming classes being applied in a new context. It also lead to a lot of confusion, but productive confusion.
This was a lot of fun - I need to do this more often. I say that a lot about things like this though, so I also hope I follow my own advice.