I gave my AP Calculus BC kiddos some rough problems to deal with on HW last night. On one of the problems they were asked to consider the greatest integer function – to be called the floor function from here on – and they were to graph the relation (floor(x))^2 + (floor(y))^2 = 1. A tough problem for sure but a couple of students nailed it. Most did not, so I fired up Desmos to show them the graph thinking we’d spend some time discussing why the graph was what it was. Desmos gave a nice graph but one of my students insisted it was not quite right.
So, I told them (kind of bragging, honestly) that I had met Eli this past summer and I would tweet out our issue. My last blog post was about sharing my learning with my students and here was another great opportunity. Eli tweeted back with another go at the graph – found here
This happened while we were still in class! I got to show my students this graph and it still was not quite right. I wrote back to Eli again and his response was awesome. He tweeted back that this problem would be a lunch time conversation at Desmos World Headquarters. How fantastic is this? I get to share with my students tomorrow that a problem we shared out to the world was going to result in some brilliant guys reprogramming their fantastic tool so that it would tackle this thorny problem. Don’t know that it gets much better than this. Oh yeah, as an added bonus I was sent another take on the problem by Christopher Danielson. Here is his take
Days as a teacher don’t get much better than this. Oh yeah, I should note that I got so wrapped up in these tweets and talking to my Calc students after school about this problem unfolding that I was late to get my children from their bus. A friend had to call me to get me out of my classroom building to go grab them. For one afternoon math seemed more exciting than seeing my own children.