We started class with a recap of the challenge from yesterday. I recorded the legs and estimated areas from a selection of students, and then solicited ideas for how to relate the three quantities. Because of the estimation with partial box counting, very few triangles worked perfectly, but they worked.
Of course, most students were stumped after trying addition, seeing that it didn't work, and not knowing what to do next. A couple remembered the correct equation before we even got to this point, but a select few actually stumbled across the connection and didn't make the A=1/2 b*h connection until we were done.
It's fun getting to see that light bulb go off; even more so when it's something "simple" that they saw in middle school and didn't recognize. It's as if most students don't even realize that there IS a back story to where the content comes from. They're so used to being spoon fed a bunch of stuff that they're expected to memorize and regurgitate, that they never stopped to think about what's "behind the curtain" so to speak.
And that's kinda my whole point in doing this, so I'm calling today a win.