## Saturday, February 9, 2008

### Lesson Idea: Probability using Deal or No Deal

No matter what I'm doing or where I am, I'm constantly making literal and mental notes of ideas I can use to improve my teaching. Sometime last year, while wandering around an educational toy store in the mall for just this reason, I mentioned to my friend Dave (a fellow teacher) how I thought the game show Deal or No Deal would be a great way to teach probability. At its heart, the show is about figuring out your chances of getting a better deal by playing on or taking the bank's offer--in other words, your probability of getting the better deal. Dave thought this was a great idea, and we returned to our perusing.

Several weeks later, Dave told me he had shared the idea with math teachers at his school, who used it in class to great success. It was apparently a huge hit. While I'm all about sharing my ideas and helping students beyond my classroom, I was a little miffed, because I hadn't actually used the idea with my students! I had forgotten all about it until Dave's reminder, and so I made a resolution to reap the benefits of my own idea this year.

Building Background

The first thing I did was introduce probability the day before the game. I started with a question: "Every time I flip a coin, I have a 50/50 chance of landing on heads or tails. So if I flip it 50 times, I should get 25 heads and 25 tails, right?" This kicks off a discussion about theoretical probability, which we then tested. Small groups flipped a coin 50 times and tallied heads and tails. Then we came back together and compared their data (experimental probability) to our theoretical probability. I also used a deck of cards to show several examples of probability (especially the idea of replacement) as well as compound probability. This would provide a foundation for our game the next day.

I already had an idea of how to adapt the game for my purposes, but I thought I would buy the Deal or No Deal card game that I had seen severely discounted at local Target stores (about \$7). I thought it would give me some ideas and at the very least neat prop (the briefcase) to use, but basically everything I needed was there in the game. The only thing I needed to add was a graphic organizer where we would calculate the probability of getting a better deal by saying "no deal" after each bank offer.

The card game has a 4 decks:
1. Briefcase cards are numbered 1-26
2. Round cards show how many briefcases to open each round (why they couldn't just write it down as a list is a mystery)
3. Bank offer cards to provide a random offer each round
4. Cash cards to hide under the Briefcase cards
The game play is simple:
1. Take one briefcase to hold onto which could be yours at the end of the game.
2. Each round, players open a diminishing number of briefcases, starting with six in Round One and ending with one in Round Nine.
3. After the briefcases are opened, the bank makes an offer, and the player can accept it (deal) and the game is over, or reject it (no deal) and keep playing.
4. If the player rejects all bank offers, they will be left with their briefcase and one other, and choose which they will open. Whatever they choose is the amount they win.
As I said, I only needed to add students finding the probability of getting a better deal if they rejected the bank offer. So I created a simple graphic organizer combining the enclosed game sheets and a table that looked like this:

Students would write in the results of each round, like so:

RoundBank Offer# of briefcases left with more money than Bank OfferProbability of winning more than Bank OfferDeal or No Deal?
1\$100,00055/20 = .25 = 25%No Deal

I used magnets to hold the briefcase cards and cash cards underneath on the board (you could also use a hanging pocket display with clear pockets, the kind you often see in elementary classrooms). I would play Howie (I considered, but did not purchase, a bald cap), there wouldn't be any models to open the cases, and the class would play as a whole group.

Playing the Game

After picking a student to start us off by claiming "our" case, I had students pick each other "popcorn style" to choose the briefcases to open each round. When it came time for the bank offer, I pretended to get calls and text messages from the bank on my cell phone. We would figure out the probability, fill in the graphic organizer like the example above, and decide whether to take the deal. Most classes wanted to play at least a few rounds no matter what before they started to argue over taking the deal or not (especially once the million dollars came off the board). In those cases, we voted.

The game took about 40 minutes to play through, and in a couple of classes we had enough time for an extremely rushed second game. Students only needed their graphic organizers and a calculator to help convert fractions to decimals and percents (since probability is shown in all three ways).

It was exciting to see the kids really get into it--the roars of disappointment when the big money came off the board, or the huge cheers when \$0.01 or \$25 came off. They laughed at my phony conversation with the bankers, and nearly everyone was engaged all day. It was a rousing success.