Math = Love: Probability Bingo

## Tuesday, January 28, 2014

### Probability Bingo

 Foam Counting Blocks to Make Dice (From Dollar Tree)

Over Thanksgiving Break, I picked up some foam counting blocks from Dollar Tree for \$1.  I don't remember where I saw the idea originally, but someone had suggested that these be purchased and used to make your own dice.  They've been sitting under my podium, just waiting to be used.

I'm not positive if I ever actually blogged about it, but I attended an AP Summer Institute for AP Statistics this summer at The University of Tulsa (my alma mater) with Dave Ferris.  Dave is an AP Stats teacher in Noblesville, IN.  He has a website that is chock full of stats resources.  This is my first time to ever teach statistics, so I have referenced it frequently.

My statistics students have been working really hard since we came back from Christmas Break.  We've been dealing with the probability of random variables.  I was in the mood to postpone the next section in our textbooks by doing a fun, thought-provoking activity.  (Don't worry.  This is a non-AP stats class.)

On Dave's probability resource page, I found a file called "Probability Bingo."  I opened the file, and I was instantly intrigued.  (By the way, the file gives credit to Brian Mehmed, 2011 WV APSI.)

Here are the instructions at the top of the bingo card:

Each of two die has colored faces, 3 green, 2 blue and 1 red. The two dice will be rolled. The outcome will be considered to be one “bingo call.” If you have this outcome on your bingo card, mark it off. The winner will be the student who gets a bingo card completely marked off (all 25 squares). Mark each square on your bingo card (use BG for “blue green,” BB for “blue blue,” etc.) so that you have the best chance of winning.

 Probability Bingo Dice

Two of my students volunteered to make the necessary dice for this activity.  At first, they colored the sides of the foam cubes.  But, the colors were hard to differentiate since the foam was orange underneath.  I suggested that they take a sharpie and write the first letter of the name of the color on each face of the die.  They decided we should have just done that in the first place.

After the dice were made, I handed out blank bingo cards (two-sided) to my students.  We discussed how the dice were made, and they got to work filling out their bingo cards.  I decided I wanted to play along.  I quickly calculated the probability of each combination of colors.  I multiplied each probability by the 25 bingo squares to determine how many squares I should label with each color.  I had one square left at the end, so I went ahead and labeled it RR even though the probability of rolling a RR is approximately 0.03.

The students took turns rolling the two dice.  With each roll, we marked off the combination once.  This is not your typical bingo game.  You're not looking for five in a row.  You're looking to be the first to fill up your entire bingo card.  At first, I was off to a good start.  With every roll, I got to mark off a square.

 Probability Bingo Card - Game 1 (Beginning)

Then, the dark time began.  I quickly ran out of Blue/Green squares.  So, did my students.  We all agreed that we should have put more Blue/Green squares on our bingo cards.  The GG combination was not rolled as much as I would have liked.

 Probability Bingo Card - Game 1 (Middle)

I didn't take a picture of it, but I sat for a long time with only my RR square unmarked.  I wasn't the only person waiting for an RR.  Eventually, an RR was rolled, and I won!

 Probability Bingo Card - Game 1 (End)

My students instantly wanted to play again.  I had anticipated this, hence the double-sided bingo cards.  Based on our first round of bingo, my students set out to create a better bingo card.  One of my students decided to calculate the probability like I had.  She accidentally left the BB combination off of her card.  She was not happy about this!

Just for fun, I decided to leave my card exactly the same since I had won the first round.  Here's the start of Round 2.

 Probability Bingo Card - Game 2 (Beginning)

Pretty soon, history repeated itself.  Once again, I found myself waiting and waiting and waiting for RR.

 Probability Bingo Card - Game 2 (End)

That Red/Red combination never came because another student filled up her card first.  The moral of the story?  If there's only a 3% chance that something will be rolled, don't put it on your bingo card.

In order to give my students a grade for the day, I asked them to calculate the probability of rolling each color combination.  Then, they had to critique the strategy of designing your card to reflect these probabilities.

 Colored Dice Probabilities

I would definitely recommend this activity!  It was thought-provoking and fun.  If time allows, I would love to play this with my Algebra 1 students when we review probability for the EOI.

1. I can't wait to use this with my Pre-Algebra 2 and Algebra 1 classes. They will have so much fun and it will give them a much better understanding of probability. I am addicted to Dollar Tree for teaching supplies and always trying to figure out ways to use the items they have. Thanks for sharing :)

1. You'll have to let us know how it goes on your blog! I just love teaching probability through games!

And, I think I'm addicted to Dollar Tree, too. I justify it by telling myself that there are worse things I could be addicted to! :)

2. I love lessons where I want to play along and figure stuff out (Though, admittedly, my students don't *always* share my enthusiasm). In this case, my gut says you'd do better by filling the whole bingo card with GG than by trying to use a balanced distribution.

The awesome ting is that being wrong would be part of the learning.

1. Agreed!

And, I think your GG strategy would work quite well! We were all quite sad when we had marked out all of our GG squares.

3. Where you get the 36 in your calculations of probability?

1. 6 ways to roll first die x 6 ways to roll second die

4. I love lessons where I want to play along and figure stuff out (Though, admittedly, my students don't *always* share my enthusiasm). In this case, my gut says you'd do better by filling the whole bingo card with GG than by trying to use a balanced distribution.
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