Trip Planning Activity

For an (imaginary) locally developed math class, we did an interesting open-ended activity. We were given a choice between going bowling or going to a movie, and had to predict how much money we'd need for the evening. This included transportation costs, food, admission, and anything else that may apply. It was a very real application of math. There is sometimes a tension between the exactness of math and the practicality of estimation. I often think estimation and guesswork is crammed into problems where it doesn't belong, so it was nice to see a perfectly appropriate and realistic use of estimation. As the students, we were required to figure out bus fare or approximate the cost of gas. We needed to research the cost of a movie ticket and and try to anticipate what food we'd want and how much it would cost. All in all it was a very useful, dare I say fun, activity. The natural danger of course is that students will not use their phones or computers for the task at hand, and some classroom management will be needed to meet that challenge. However, if you can keep your students on task, I think if would be a very rewarding lesson for them.

"Deal or No Deal" Probability Game

A very fun game was played in the math class during a sample lesson on probability. We played "Deal or No Deal", based on the game show. We were divided into groups of two. In each pair, one person was the banker and the other was the contestant. We had a chart covered in cards, each of which having a dollar value on the underside of the card. The contestant picked a card at random, and the banker and contestant then haggle over how much the banker will pay for the card. During each round, the values on the remaining cards are gradually revealed, giving the contestant and banker information with which they can try and figure out how much the contestant's card might be worth. The trick is that the banker wants to buy the card for less than it's worth and the contestant wants to sell it for more than its worth. To take an extreme case, suppose all the cards have been revealed and we know that the contestant's card is either worth $1 or $500,000. If the banker offers $250,000, each player has a 1/2 chance of making or losing $250,000. Would that be a good offer from the banker? Perhaps. The interesting part of this game is that while the probability is important, there is also a lot of room for judgement. If I was the contestant, I would take the $250,000. If I was the banker, I would probably offer a lot less than $250,000 since I would rather earn $500,000 or nothing than make or lose $250,000. However, since the contestant only stands to gain, there may be a "bird in the hand" type of reasoning that would make the guarenteed $250,000 more attractive than the $500,000 or nothing. In short, there's a lot of higher-level thinking that can go into strategy for this game, and could have interesting applications in financial math and economics as well. If I ever get to teach data, it's definitely a game I would try to incorporate.