Then Kate Nowack of f(t) fame tweeted a link to a video:
There is genius in this video. Maybe not original math genius, but genius all the same. The connection was obvious. Pythagorean theorem and maybe some trig. Best of all students would need to think about lines, angles and triangles. Perfect.
I didn't really like the way the question was framed, felt like he gave away a bit too much (even in the original video, the one above presents the solution), but it does make for a good video. Before class I drew a series of 4 dots on all of the whiteboards, providing spaces for the students to present their results with some semblance of order. Each time an improved result was written up the class was drawn to it and they madly checked each other's math.
I heard things like, "that side is a hypotenuse and the other side is 1, so that side (the hypotenuse) is more than 1!" Or, "you used 0.333 instead of 1 over 3 that's why it didn't work!" Freaking awesome.
30 minutes in, I stopped class and asked how many wanted more time? Almost unanimously they wanted more time. I gave them the option of seeing the answer, but they didn't want it. What more can a teacher ask for? Finally, I ended the 65 minute period with the video and a brief discussion. During which one student asked, "Do mathematicians really play with soap bubbles?" With a twinkle in my eye, I replied, "Yep."
Math is real. Soap bubbles are real. The learning was real. No pseudo-context needed.