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.

How do you play Bi-N-Bi?

I spent a lot of last winter playing Bingo with Dad - sometimes, three days each week; it was a bit much. Don't get me wrong, Bingo is a fine game. However, it isn't very challenging. 

"Find this number. And, by the way, it's in this column."

I understand the point (and keeping track of multiple cards with an "auctioneer" calling the numbers can be a struggle) but I wanted more. So I began to wonder what it would be like if I could cover a pair of numbers that summed to the number that was called. For example, 46 is called and I cover 30 and 16 instead. I tried this during a few games and found that most of the times when I could decompose a number into two addends, I was using the B and I columns. This lead me to create my own card.

I liked the simplicity of this design. It would be easy to create, and players would have to decompose numbers greater than 45. Also, because the game included the element of choice, everyone didn't need a different card. Hilary could cover 43, John could cover 22 and 21, and Andrew could cover 13 and 30. (I planned to only call the number, not the accompanying letter; this would allow players to pick numbers in any column.) Finally, I liked the name, Bi-N-Bi, because it could reinforce decomposing numbers into two (bi) addends.

Today, I tested the game out in the classroom of a teacher I've been working with this semester. For the first game, I gave everyone a copy of the card shown to the right to see if the element of choice was enough to keep it interesting. The B and I columns were repeated to make it easier for players to know what numbers were available. I started out making sure that everyone was familiar with the goal of Bingo - getting five in a row or the four corners. The sixth-graders agreed that this wasn't very challenging, and they were excited to explore the changes I was suggesting.

The last issue to address was checking to see if a winning card is accurately covered. A player cannot simply call out the numbers, as happens in the original game, since many covered numbers are the result of decomposition and not because they are directly called. I toyed with idea of players marking the number called on the two chips used to cover the addends but I found that confusing when I tried it (and it meant cleaning the chips or throwing them away afterwards - not very sustainable). So I had players write their number sentences out on scrap paper. For example, if I called 34, 8, and 22, players might write:

• 34 = 8 + 26
• 8 = 3 + 5
• 22 = 0 +22

And then they'd call, "Bi-N-Bi," provide each of the number sentences, and tell which of the addends they had use in their five in a row: "On the diagonal, I covered 8, 26, free space, 3, and 22."

With the instructions out of the way, I explained to the sixth-graders that I was looking for their feedback. I wanted to know what worked, what didn't, and what we might try differently. They were eager to be a part of the testing of this prototype and said so. 

A bit more nervous than I thought I'd be, I picked the first number. How'd it go? I'll tell you - in the next post.

Who you gonna call?

Please excuse me for sharing another story about my father. I promise to return to writing about teaching and learning soon. But as I process Dad's passing and what comes next, it's hard to concentrate on anything else. Besides, this story seems appropriate for Teacher Appreciation Week.

Dad and Kathy at the house

The other day I was agonizing about cleaning out the family home. Dad did nearly all of the work last year. I just needed to finish the job. Some of the furniture was coming to live with us, and a few other pieces were going up to our cabin. The rest was either going to charity or to the dump. I had talked to a local charity about stopping by to pick up a few of the gently-used items, but I was struggling with making a decision about how to dispose of the remaining pieces.

There were too many choices. I could try taking it to the dump myself, or hire a dumpster, or call a hauling company to pick it up. Paralysis crept in and nothing was getting done. Then I remembered a receipt in my dad's papers for "Acme" Hauling. He had done some business with them during the initial clean-up - twice. Dad obviously trusted this company, so I decided to call.

It was the right call. The owner answered and he agreed to give me an estimate. As I was getting ready to say good bye, ...

Owner: I was sad to read about your dad's passing.

Me: Thanks. [I was getting good at this - keep it short and end the conversation]

Owner: I went to MSHS. My name is "John Doe" and your dad was one of my math teachers.

Me: Oh, hi "John". [Can I hang up now?]

John: I wasn't the best student in school. I got into a lot of trouble. But I liked your Dad. He always gave me a fair chance. No matter what happened the day before, each class was a fresh start. I never had a teacher like that before. It's probably not surprising that math was my best class in high school.

Me: [silence - I bet you can guess why]

John: Anyways, call me when you want me to stop by and give you an estimate.

Me: Okay. Thanks.

Later, I told Kathy that I had learned a valuable lesson that day: Trust Dad. Who would Dad call? When possible, one of his former students. Someone he had built a positive relationship with and prepared for future success.

Dad and the MSHS Science Olympiad Team

Thanks, Dad, for another life lesson.