Counters GameIn this unit, as the name implies, we learned about probability. We had to think a lot about the occurrence and percentage of a certain item. For example, an experiment that we did, the Counters Game. We found that when rolling two dice, you have a higher chance of rolling a 6, 7, or 8 because there are multiple ways to get that number while numbers like 2, 11, and 12 have the lowest chance of being rolled because there is only one way to obtain those numbers. The game was played by the players getting 11 counters, and we had to place all of them on any number we liked, and spread the counters out however we liked. Then, we rolled the dice and if we got a number with a counter on it, we removed the counter and our turn was over after one roll. We started with an initial strategy that was most of the time, ineffective because we spread out all 11 counters on each number 2-12. After a few games, students figured out that numbers towards the middle had a higher chance of being rolled and put multiple counters on those numbers, which proved to be the most effective way to win. This experiment taught us that the more ways the are to get a certain number, the better chances there are of getting it, its just a matter of finding that number. In this activity, I am most proud of how fast I realized that the numbers 6, 7, and 8 had the most probability of occurring.
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Rug Games
Another experiment that we did was the Rug Games activity. In this experiment, we were given a a problem sheet with illustrations of rugs with different designs and colors on them. We had to determine what part of the rug would an object land on if it was dropped at random. The process of doing this was to look at the design of each rug, then section off different parts of the rug until we had a certain number of small pieces of the rug, for example, a rug would have 21 parts after it was sectioned off. 15 of those sections were gray and 6 were white. Then, we calculated the percentage of the fractions 15/21 and 6/21 to give us a percentage of how much space that part of the rug took up. After completing 5 different rugs, we were tasked with making our own rug with our own design, and then had to solve the one we made.
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Unit Reflection
In this unit, we did a lot more activities involving theoretical probability besides these three like Waiting for a Double, the Gambler's Fallacy, Paula's Pizza and many more. The activity that I am most proud of is the Counters Game because of how I used Habits of a Mathematician to find the best strategy for getting rid of all of my counters. The Habits of a Mathematician that I think that the two Habits of a Mathematician that I grew with were Looking for Patterns and Being Systematic. I grew in being systematic because I experimented with a ton of different methods and made changes to things that I already had. I grew on looking for patterns because in probability, there are a lot of patterns involved in finding the chance of something occurring.
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