## Thursday, December 31, 2015

### How did Bi-N-Bi go?

Awhile back, I promised to tell you how it went when I tried out a new game I developed while playing Bingo with Dad. Bi-N-Bi, or Decomposition Bingo, is an attempt to add a bit of strategy into the familiar game. Instead of finding a called number, you use a modified Bingo Board to try to find a pair of numbers that sum to the called number. At least that was the plan when I began testing it out with a couple of classes of sixth graders. But they had some other ideas. And some of their ideas were quite good.

The first game went pretty quickly. While the Bi-N-Bi rules allow for choice, a lot of the players used the same addends to make up the sums. I had given all of the sixth graders the same board, to test out my "choice" hypothesis (that the players would create different results) but they were unsatisfied with the ties, and many asked for a different board. Having anticipated this, I had several other boards available. There weren't enough for everyone to have a different board, but they seemed satisfied with the variety.

We played another game using the different boards and the players were happier with the results. Several sixth graders called "Bi-N-Bi" at the same time but they each had different numbers covered. After claiming their prize, a Bragging Rights Trophy, I asked if they had any suggestions for improving the game. They had a few:
• Use two or three addends;
• Use pairs (to stay with the "bi" theme) but allow for addition or subtraction; this would allow for using traditional Bingo Cards;
• Make the "Free" space a "Wild Card" that can be used to make a pair; I might use X to reinforce the idea of variable; and
• Perhaps the most ambitious idea was to use all four operations and parentheses to reinforce order of operations.
We tried the three addends version. For some of the sixth graders, this was a struggle. So I tried to model some strategies for them as I walked around. For example, I would say, "46. I could use 40+1+5 or 30+11+5 or 20+11+15." These weren't necessarily numbers on their cards but simply different ways they could think about decomposing 46.

The sixth graders also wanted to try using something more than addition, so we played a version that used any combination of addition, multiplication, or parentheses. But only if they wanted, because a few of the students seemed overwhelmed by this change. A couple of winners are shown below.

At the end of the last game, I handed out Bragging Rights Trophies to everyone as a way to thank them for their help testing Bi-N-Bi. I told them that each had demonstrated that they were mathematicians. And if they ever found themselves in one of my math education classes at GVSU, they could turn the trophy in for 1,000 Bonus Points. I do what I can to encourage the next generation of Lakers and possible MTBoS participants.