Blogging has been a lot of fun, especially right when I got started, and also the parts where I say “this is what I’m going to do.” The hard part for me has been writing about what I actually did. You know, the part where actual reflection on my practice is supposed to happen. Yeah, that part. I realize I’ve been launching off diatribes about student relationships, tutorials about technology, and other stuff because I’m side stepping the hard part. Well no longer. Here is a write up of the final project I used with my Equations and Patterns class, which I talked about earlier.

#### What I Planned

My original plan was to teach the same ~~casino~~ carnival project that I have been doing for the past few years. Here is a brief description:

Role: The kids in this project are the ~~owners of a casino~~ planners of a school carnival and they have to plan games that make a profit while appearing to provide a fair chance for players to win (1 winner for every 3 players).

Content: For each game students will find the probability of winning, as well as the expected value of winning each of the prizes they chose from a provided list. The students were then supposed take the expected value of the overall game and predict the expected profit they would make off of 1000 visitors. The three games are all related to ~~casinos~~ carnivals:

- Dice Game – Players roll a pair of 6, 8, or 10 sided die and win a prize based on the result
- Three Spins
~~Slot Machine~~– Players spin three wheels and win a prize based on the result - Card pull – Players pull 2 cards from a standard deck and win a prize based on the result.

Each game had successively more expensive prizes that needed to be won.

Products: Students produce these 3 crazy long grids that detail all of the calculations. For each prize they would win they would fill out one row of a table that asked for number of ways to win, the price of the game, the cost of the prize. Next they have to do a little calculating to find the of the profit or value they make from that prize, and the probability of that prize winning, as well as the expected value of that prize (Profit times Probability). Each game would have 4-9 prizes, including the “losers.” Here’s an example of row of a grid from the 2nd game poster which would be won if you spun a wheel with six slices and landed on either the A, B, or C slice on all 3 wheels:

Type of slices | #of slices | #of slices | #of slices | Price of games | Cost | Profit | Probability | Expected value |

Poster | 3 | 3 | 3 | $7 | $5 | $2 | 27/216=0.125 | 0.25 |

Additionally, for students who need to include this in their graduation portfolio, students have to write a written description of what they did, and what they learned in the class. Students who just need credit can draw posters about each of their games that they think would convince players to play the game.

#### What I liked

Well, after doing this for the 4th or 5th time, I’ve gone from liking to hating and back to liking a lot of things about this project.

- One thing that never gets old is when kids do all of the math correctly, and make no profit at all, and have to go back and have to think about how to fix it.
- To help students with the games I had a series of Do Nows and pre-activities that really got students into the context.
- I always like the way students really engage with the context and the project while still having genuine interest in figuring out how to make a profit.

#### What I would change

For this, I would figure out a way to let the students have fun while they use math to make a profit. Usually what happens is that a few kids figure out the “trick,” that having cheaper prizes occur more often is how you win, and once they finish they go around and help everyone else. The “helper” role could be more formalized to encourage more students to do it. I also don’t like the card game, there are so many probabilities with a deck of cards, the kids have to work through an onerous number of situations to come up with 1/3 of the people winning. Maybe I’ll make the deck smaller, and have kids think more about the conditional probabilities that could arise when drawing cards out of the deck.

#### What I’m wondering

My big question about this project, is if it has enough math in it. Kids spend so much time doing these basic calculations of profit and probability that they are missing out on thinking through the high school level content. Is this not enough mathematical thinking for a high school algebra class?

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