## 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.

I would have liked to give them maybe five probability word problems for homework as an informal assessment. We are working on the measurement project I posted earlier this week, and their focus should be on that. Instead, we will have an alternative assessment on Monday. In keeping with my no-multiple-choice-test policy, I am thinking we will create mini-posters (Idea #1 in my book Ten Cheap Lessons) for this and the rest of this unit.

If we had more time, I would like have students create their own probability game, or adapt an existing game to include probability calculations. This would encourage higher order thinking and make it more memorable for the long term, as well as provide a game they could later play for review.

As I look to next year, I'm also looking for ways to incorporate compound probability into our game or post-game follow up, since those questions often pop up on standardized tests.

If you like this idea and the others posted here on I Want to Teach Forever, please check out my new book, Ten Cheap Lessons: Easy, Engaging Ideas for Every Secondary Classroom. It's available now at Lulu.com and coming soon to bookstores everywhere. As always, please contact me with your feedback and questions. Thank you!

Shannon said...

I love this lesson plan. It's funny I am writing a lesson plan right now and wanted to use Deal or No Deal also so I started looking on the web for some good ideas and I found yours. Thanks

Anonymous said...

I am a student studying to be a teacher. During one of my preclinical experiences I am required to teach two math lessons. As I sat watching Deal or No Deal tonight on t.v. I wanted to see if anyone had created a math lesson with it. I found this and it is fantastic! I plan to use it next week!

Anonymous said...

hello...i was reading over your post for the Deal or No deal lesson and I have a question...why did you have 5/20 under that one category...what does the 20 represent? if u could write me back I would appreciate it.
righteousguidance481@hotmail.com

Mr. D said...

The idea of the game is that after each offer from the bank, we calculate our chances of getting a better deal by continuing to play. In that example, 6 out of 26 total briefcases are opened in the first round, leaving 20 unopened. If there were only 5 unopened cases containing more than \$100,000, the chances of getting a better deal was 5 out of 20, which can be written as 5/20, .40, or 40%. I hope this helps!

Anonymous said...

If you only have a 40% chance of winning, why would you say no deal? You have less the a 50% chance of getting more money, so wouldn't you say Deal?

Mr. D said...

Anonymous: That makes sense mathematically, but not in the context of playing the game. First, if it's only the first round of the game, you can't expect anyone to say "deal" no matter the odds. Secondly, players usually make their decisions based on their chances of getting the million dollar briefcase, even if those chances are slim. Finally, I think most people would still go on with a 40% chance, because 40 is still a psychologically satisfying number, big enough to take a chance on. Probability helps us see our odds more objectively, but you just can't eliminate the risk-taking aspects in this game.

Anonymous said...

Isn't 5/20 = 1/4 which means that there is a 25% chance that the player will win more than the \$100,000 offer?

Mr. D said...

Anonymous: You are right--I can't believe I missed that even after so many people have left comments about it! Of course, it makes it much riskier to not take the deal when you have such a small chance of getting more money, but as I wrote previously, who's going to take the deal so early in the game? The way this game works, your probability of getting a better deal by playing can actually increase as the game goes on, because the offers are random (and thus may decrease). I'll fix the post. Thanks!

Ky Turner said...

I kept your same worksheet, however I didn't buy the game. I had my lap top projected on the screen, and went to the online Deal or No Deal game on nbc.com. I split the class into two groups, let them decide on a number (or I chose for them if they couldnt agree) and then 1 by 1 they would give me their suitcase numbers. I made it competitive by seeing which team could get the most money. Just another way to make this game even cheaper!

Anonymous said...

I love the idea and your willingness to share it! Thanks!

What do you consider an appopriate grade level for this activity?

Mr. D said...

Ky: I had considered using the online version of the game, but the equipment wasn't always available and our Internet access was not reliable enough to plan a lesson like this around. It's a good idea if you have access to technology, but not all districts provide it. That's why I went with the analog version of the game--which by the way was not at all expensive. In fact, I recall it being on sale for about \$8.

Anonymous: I used this game with 9th grade Algebra I students, but I think it's simple enough for middle school students who might be seeing challenging probability for the first time... maybe 7th grade and up. If anyone reading has tried it with younger students with any success, please let us know!

Anonymous said...

I am also in my student teaching and was going to use this game in fifth grade. Do you think this is too difficult for fifth grade gifted class? Are fifth graders able to understand the relationship between fractions, decimals and percentages?

I love the idea. I bought the game on Target.com. Thanks for sharing.

Mr. D said...

Well, now having worked with more students around the 5th grade level recently, I can tell you two things:

1) At that level, they should absolutely be learning (or have learned) converting between fractions, decimals and percents, regardless of the probability aspect. You may want to give them some problems before then to gauge their ability, and if they don't seem ready, you can downplay the conversion part of it. You might just ask them to consider if each fraction is more or less than half, which is an easier way to conceptualize it and to help them decide to take the deal or not.

2) I think that the game is straightforward enough between the play and the simple graphic organizer that a gifted group of 5th graders should be able to handle it.

Good luck and let us know how it goes.

Clive Townsend said...

Surely the different prizes' values come into play too..?
Imagine your three options were \$1, \$2, and \$99, and the banker offered you \$3.
Your system would suggest only a 1/3 chance of winning more than the banker's offer, so you'd accept the deal.
The way I see it, \$34 would be a fair offer...

Mr. D said...

The offers absolutely plays into decisions, because in the card game, the offer is randomly drawn from a deck. So the offers don't always make sense (as they would during the real game), which probably helps extend the game time as students rarely get a good deal.

Clive said...

Sorry - the last sentence of my post made it sound like I had issues with the banker's offer. It's actually the method of deciding whether to 'deal' or not that I don't understand.

Imagine \$1,\$5, and \$1,000,000 remain.
The random banker card offers \$999,999 (unlikely I suspect - I'm just being extreme for emphasis).

So your students would fill in their table like this...

Bank Offer: \$999,999

# of briefcases left with more money than Bank Offer: 1

Probability of winning more than Bank Offer 1/3 = 33%

Deal or No Deal?: No Deal

But surely they SHOULD deal in this case?

Clive said...

Oops - just realised my mistake in the last post! They WOULD (and should) deal.

But if the random offer was \$10, they would STILL deal, as there's only a 33% chance of winning more.

This seems to be a bad move to me.
What have I missed?

Mr. D said...

Clive: Well, if students got an offer of \$10 with \$1, \$5 and \$1,000,000 on the board, you're right, they would only have a 33 1/3% chance of getting a better deal. Mathematically speaking, it's not a great deal, but just like the earlier comments about not taking the best mathematical deal, not taking the chance that late in the game just isn't any fun in the context of the game.

Also, keep in mind that the kids are not bound by probability, it's meant to be an advisory. If they want to take the deal at any point, even with a small chance of getting the big money, they can and most likely will. The idea is to show them exactly how slim those chances are, and that games like these are rarely skewed in their favor.

In the end, the math shouldn't trump the fun of the game, of taking a chance at some point.

Sarah said...

I love this lesson plan! I already taught this concept at the 7th grade level, but this would have been a way to make it fun and relavent for my students.

kmgigot said...

Great Lesson Plan! My students LOVE LOVE LOVE Math Labs and interactive lessons. I'm teaching Probability and Stats in a few weeks and am excited to try it out.

I am so grateful that you put this lesson up online. I am a student teacher and I am about to teach this lesson on Thursday to a 7th grade math class. Wish me luck!

doug s said...

the decision the students make is based only partly on probability. the offer and decisiion should be based on mathematical expectation.

math exp = (probability)(dollar amount won)

at beginning of game math expectation = (1/26)(.01) + (1/26)(1) + (1/26)(5) + ...

it changes after each case is drawn.

Deal or no deal game said...

This is a really great lesson, it fits in very nicely with game theory, thanks for writing it.

M O'Neale said...

What a great idea. I'm working on a way to simplify it for my primary kids. I can see what Clive was trying to get at in a previous comment and I see it like this... \$1, \$2, \$99 left with an offer of \$3 you have a 2/3 chance of getting a higher offer because getting rid of either the \$1 or \$2 surely must increase the offer. Cheers

Anonymous said...

I used this lesson in my 9th grade Algebra class today. It was awesome. I used the interactive game online. The bank offers make more sense, but there is still the idea that even though the probability is low in the first round, you should still keep playing. I actually added an odds column for my students to compute the odds from knowing the probability. Thanks for a great idea!

Mr. D said...

UPDATE: A reader sent in a spreadsheet that calculates the bank offers for you. Read the post here.

- said...

So I'm a substitute who recently used this game to allow students to learn about probability and earn extra point on a test they didn't do so well on. Prior to actually playing the game, I thought this was a fantastic idea. However, once in the classroom, I noticed that I wanted students to get more out of the lesson and make it more challenging. So I guess my question is, how can I up the difficulty level?

Melissa said...

I am a new special ed. teacher who did not ever think that I would be teaching math. Thank you so much for this idea and the website. I will be using it a lot. I like to keep my students engaged.

Melissa said...

I am a brand new special education teacher who never thought that I would be teaching eighth grade math. Thank you so much for this site. I will be on here a lot. I love the engaging activities and will be using deal or no deal next week.

Scott Z said...

I am writing a lesson plan using Deal or no Deal but instead of using probability, we are going to use expected value to determine if we should keep playing or not.

I am curious if this would be a good 2 day lesson. First day using probability, second day using expected value. They could decide which works better, probability, expected value, or some combination of both.

What are your thoughts on using expected value and what are your thoughts on doing this as a 2 day lesson using both?

Mr. D said...

Scott, I don't see why not. It would certainly give your students a clear basis of comparison.

Darlena said...

Thanks for sharing! I can't wait to try out!

Lisa said...

I used the foundation of this lesson using Probability to make the decision for each round. I also included expected value as well.
I used the on-line game to play the game. We did one "practice" game as a class to begin. Then I split the class into two teams (they chose boys vs. girls) and had a competition to see which team would end their game with the most money. We are a lap-top school, so I then had each student go to the website and play the game themselves to determine the "individual" champion.
I have a block schedule so I was able to also cover Expected Value. This could be a second day of the lesson if you teach on a regular 50 minute period. We made our decision at each round based on the expected value of the remaining briefcases. I am including my handout that I used for this lesson.
We had a lot of fun playing this game. Thanks for the great ideas!