I started noodling with this concept in Pre Cal, and thought I'd try a version in Algebra II. We were talking about linear functions. A review unit of sorts because they've seen how to graph a line a million times once they get to me (especially if they're coming up through an Alg I->Geometry->Math Models route). One part is determining the equation of a given line. In the past I did this in a very bland fashion. Lines on preset grids, all the points easily identifiable. This year, I gave them something like this:
There were four pictures like this, a set of axes in arbitrary locations on all of them. Were this Pre AP, I would not have provided the axes. The goal is to determine an equation for the three streets indicated. But, how do we do that? Can I really decide where the tick marks go? It doesn't matter? Really? So, there's no right answer? By the time they get to the 11th grade, they're so scared of taking a risk and being wrong it's really upsetting. Once we jumped through the initial hurdles, this went well. On some of the other map sections I had streets that you would consider to be undefined just for fun. The only problem is they were given black and white versions, and the yellow streets didn't translate well to the copies, so a few had a hard time figuring out what the heck I wanted them to use.
I give it a B+/A- as an activity, ruined mostly by the copier. Probably needs a couple tweaks.