In math class, we have been working on different scenarios that involve probability. About every week, we are given a new problem to work out that involves probability whether it is a game or a word problem. Our class used two approaches to deal with probability: simulations & experiments and theoretical analysis. We only used the approach of experimenting when it came to dice games or the counters game. Theoretical analysis is used for problems that involve calculations and tables, such as Paula’s Pizza and Pointed Rugs.
In total, we completed ten different problems and games that involved probability. We learned different ways to deal with probability by doing many different problems. To start off, the class participated in a game called Waiting For A Double. To play the game, students had to roll a pair of dice until they got a double number. They would have to record the number of times before they get a double to see the probability of getting a double out of so many rolls. A few other games we played were Spinner Give and Take (Al vs Betty), The Gamblers Fallacy, Expecting the Unexpected (Coin Flip Experiment), and The Counters Game (Two Dice Sum Experiment). All of these games involved the method of simulations and experiments. By experimenting, I learned that it will never be an accurate representation of probability because each turn is different.
In total, we completed ten different problems and games that involved probability. We learned different ways to deal with probability by doing many different problems. To start off, the class participated in a game called Waiting For A Double. To play the game, students had to roll a pair of dice until they got a double number. They would have to record the number of times before they get a double to see the probability of getting a double out of so many rolls. A few other games we played were Spinner Give and Take (Al vs Betty), The Gamblers Fallacy, Expecting the Unexpected (Coin Flip Experiment), and The Counters Game (Two Dice Sum Experiment). All of these games involved the method of simulations and experiments. By experimenting, I learned that it will never be an accurate representation of probability because each turn is different.
The theoretical analysis method was used in the rest of problems: Paula’s Pizza, Rug Games, Create Your Own Rug Game, Pointed Rugs and Mia’s Cards. These problems involved working out a solution using calculations and tables. I learned that calculations and tables have to be double checked while using probability to make sure it is the right number. It also is way easier to find probability when it’s written on the paper since part of it is already given. I think the ideas from the two methods affect my behavior in situations that involve probability because I know how to look at it logically. I know what I need to do whenever probability is involved just because of the two methods I learned while doing these problems. I am most proud of The Counters Game because I was able to quickly figure out what number the dice would add up to, so I could maximize my chance of winning. The object of The Counters Game is to remove all counters from the game board. The game board has 11 labeled boxes from 2-12 and each player puts 11 counters on their board. Players are allowed to place the counters anywhere they choose, including putting more than one in a box. During the game, a pair of dice is rolled and the numbers on the dice are added up creating one of the 11 numbers. If a counter is placed in the box that has the same number as the sum of the dice, the counter is then removed. If there are no counters in the box, then the players do nothing and their turn ends. My initial strategy was to put one on each square except 2 and 12, then I would put the extra ones on square 7 and 8. After completing one round of the game using this strategy, I ended up winning and learned how often the dice fall on certain numbers. The next round, I changed my strategy to see if I would win again. This time, I put one counter on square 6, three counters on square 7, three on 8, two on 9 and two on 10. While playing the round, I noticed that I wasn’t able to get the numbers I wanted, causing me to lose the game. The third time around, I changed my strategy again, putting one on square 4, one on square 5, two on 6, two on 7, three on 8 and two on 9. It was strange, but this time I ended up winning the game. I am proud of this probability game because I feel I executed it well and got different results that added up in the end. My results showed me that the best area to put the counters is on square 6, 7, and 8.
Throughout these probability problems, I used Habits of a Mathematician to help me complete the problem, but two of them really helped me out in the end. When it came to the theoretical analysis problems, the habit “Stay Organized” because it is very important to have all the information sorted out to not get confused in the future. I stayed organized by keeping all the information I needed in one area and my work in another area. I feel I have grown in staying organized because I used to have all my work all over the page with no order, but now I am more organized in my work in where I separate from info. For example, for Paula's Pizza I kept all my work organized in tables to keep track of what my options were, and I kept my work separate from the tables
When I dealt with the simulations and experiments, I used the habit “Be Confident, Patient, and Persistent” because the games did tend to go on for a very long time and I would become a little impatient. I would tell myself that I will keep myself together and keep on going even if it started to annoy me a little by how slow it was going. I have grown with this habit because I’m not a very patient person, but while doing these problems, I was since I knew it is essential to my learning. For example, Waiting For A Double was a really difficult game for me to stay patient. I was getting annoyed by how long it was taking to get through the game about halfway. I then told myself it will be over soon and I can continue on with other things, so I will be patient and wait.
It was very interesting to deal with probability and do many different problems that dealt with the same thing. Overall, I learned so much about probabilities that I didn’t know before, and I feel it has strengthened my learning experience in math.
It was very interesting to deal with probability and do many different problems that dealt with the same thing. Overall, I learned so much about probabilities that I didn’t know before, and I feel it has strengthened my learning experience in math.