Spiralling in MDM 4U continues and we've reached the end of the second spiral. With a great focus on probability and counting techniques, students have had the opportunity to experience and demonstrate in these two spirals knowledge of permutations, combinations, factorials, binomial and geometric distributions, probability and odds.
Most students chose to revolve their games around dice and cards. These were manipulatives that we had used repeatedly in class and they were comfortable determining probability with.
Some examples included:
Game #1:
A player pays 3 tickets for the dealer to roll a 20-sided die on a flat table.
- If the die lands on an even number (red) excluding 20, the player loses the 3 tickets they bet withA player pays 3 tickets for the dealer to roll a 20-sided die on a flat table.
- If the die lands on an odd number (black) excluding 1, the player loses 1 ticket they bet with and 2 tickets are given back to them
- If the die lands on either a 1 or 20 (green), the player wins 10 tickets, but paid 3 to play so overall gains 7 tickets
Game #2:
The name of the game is Cross the River, this is because the pathway takes the students across a beautiful river. It costs the student 2 tickets each time they play this game. It guarantees that the student wins every time! He or she will start on the start sign and will start off by rolling the two dice once. If he/she rolls an odd sum then he/she will move up two spaces, but if he/she rolls an even sum then he/she will move up one space. They will get four rolls in total. This game guarantees that they win because if they roll four even sums, which is the minimum, they will at least get to the fourth space, and this will give them one ticket back. Technically they are winning, but in reality they are losing one ticket in the sense that they pay 2 tickets to play, but only get 1 ticket back.
Game #3:
The name of my game is “The Role Of Fortune”. I choose this name because I was hoped that the familiarity of the name, derived from “The Wheel Of Fortune” would grab the students attention and draw them towards my game. My game is a very simple game which will captivate and interest younger students because of its ease to play and enjoyment from playing. My game costs 3 tickets and involves rolling 2 die. The rules are simple, your objective is to roll a sum of 2, 3, 4, 7, 10, 11, or 12. Any other role will result in the loss of your 3 tickets. A sum of 2 or 12 results in the grand prize of 3 tickets. A roll of 3 or 11 results in a prize of 2 tickets and finally a roll of 4 or 10 results in the prize of 1 ticket.
We then had the opportunity to host the grade 8 math class for a Games Day. Students used the opportunity to collect experimental data for their games. Following the Games Day, students were asked to analyze their experimental data and compare it with their theoretical calculations.
When students began planning their game, they focused primarily on making it unfair - as stated in the expectations of the project. After the Games Day, students were then contemplating how to make their games more "interesting" and more fair. As part of their final reflection about the project, students commented on improving their game by making it straight forward (not too many steps) but also fun and not too obvious.
Finally, students were asked to create a sign for their game so that players knew the rules of the game, the cost of the game, and the probability of winning the game. They struggled with how to state the probability of winning their game without giving away that it was unfair. It was another example of a reassuring theme in the course that we must be analytical with data to ensure we have the whole picture and do not simply believe all that we read.
