Another quick post, here’s another project I’ve used in the classroom… just today actually.
We’re studying Expected Values (Probability Distributions) and I found two powerful videos from the gameshow, “Deal or No Deal” where the issue of E(X) arises quite naturally. tbh, any video of Deal or No Deal implicitly deals with Expected Values!
The videos can be found here: http://nchow.ca/DorND-DB
The first video is of a contestent who has a $200,000 case left, and the $1,000,000 case left. The banker offers her $561,000 to stop playing the game. There is tons of drama, and it’s impossible not to get invested into the outcome of her decision, (Spoiler Alert: she declines the offer, and ends up with the million dollars, for a nice heart-warming ending.)
My setup: I would play the video up until Howie asks the natural hook, “So, Deal or No Deal?” and then pause the video. After the students stop groaning, get them to put themselves in the contestant’s situation and decide if they would take the deal or not (this isn’t hard :P). Have them form groups and then debate their decisions. Teasing out some math inherent in this situation is a plus, but really you just want them to invest in the problem. I used this as a nice introduction to expected values, a topic most people are unfamiliar with unless they’ve studied finite math before (or are professional gamblers!). After your students debate, play the rest of the video and ask whether it was a good decision. This segues naturally into the topic of expected values.
The second video is of a contestent who has a $0.01 case left, and the $10,000 case left. The banker offers her $5,500. This video acts as a nice consolidation at the end of the class to drive expected values home. You can ask similar questions, if she should take the deal or not. (Spoiler Alert: She ends up balking the deal and winning a penny.)
The beautiful part about these two videos is that the math works out. When the expected value is more than the offer, the contestent goes for it and wins the million. When the expected value is less than the offer, the contestent goes for it and wins a penny. It’s prudent here to talk about taking a $361,000 chance at coin flip odds. This is a life-changing amount of money, and I definitely would have taken the deal, even though I understand that the value is lower than my expected one… and I explained and justified this hypothetical decision to my students!
Just my thoughts, use as you wish!
On that note, how would you use this in your classroom?
1. Expected values resolve the question in my previous post, “Should Derren Brown be happy it took ~9 hours?”. Proof is again left to the reader, but the quick answer is probably not. 😛
2. Apparently I’ve won the UOIT Faculty of Education Tech Award! I didn’t know it existed, but I’m ecstatic to be the recipient! The cash prize of $500 is nice too. 😉
3. On that cash note, I’m almost done my B.Ed and ready to be certified come the end of April. I’m happy to report that I have two job interviews this Thursday afternoon. They’re both for Science and/or Math positions, and I’d be over-the-moon if I got either one. Wish me luck!