Math Buddies

Today in grade 12 we invited the grade 11s from across the hall to join us to solve a problem. We worked together in random groups of 3, decided by drawing playing cards. The question we were working on was determining how many ways there were to “win” a game of 3D tic tac toe.

The representations used were pretty neat to see. We have been working on 3D vectors lately, and talking about the x,y,z axis and various planes, so grade 12s were jumping in to represent in pictures, and have good conversations with grade 11s to understand the problem and come up with a plan to represent their thinking.

Having blocks to hold and manipulate helped ground the conversations, and were useful when justifying conclusions. Groups saw and organized the “wins” in several different ways, which was neat to see. Some groups after doing a 3x3x3 case, were asked about a 4x4x4 or 5x5x5, and one group dove in and tried to model a general case of a cube of length w.

After coming up with models, they were asked to graph them, look for features of the graph, explore the domain, and talk about what set of numbers made sense for this task. One group even wrote a piecewise function as a model.

Grade 12s were great collaborators, bringing some additional knowledge from advanced functions, and vectors, while grade 11s had some knowledge about functions, domain and range at the top of their minds. It was a successful collaboration and the room was buzzing for the last period on a Friday before a long weekend. Way to end the week on a high note. Thanks to all for participating. Thanks to Al Overwijk for the inspiration of this problem.