This is a quick one that I wanted to record here to remember, and to share. Before we made our playing card Platonic Solids, I asked students to do a little number exercise with their cards, that I adapted from Sarah’s First Day Activity.
Their ticket to begin building the solids was the completion of this challenge: Create a 5 x 5 grid of cards, in which every row and column adds to 31. We decided as a group that J, Q, and K were worth 10, Aces were worth 1, and all of the other cards were worth their face value. The groups who began with some ideas of symmetry got to the answer much more quickly, but I had one group who just bulldozed their way through until they made it by sheer force of will. We debriefed as a whole group, shared our different problem solving (…or bulldozing) methods. The kids were totally surprised to find that their solutions were not unique. A nice extension would be to count the solutions. How many ways are there to solve this array?