Math Connection
Who has more of a chance of winning?
If you and your friend are placing bets on this game than you should probably have a good idea of who, the bunny or the redneck, has a better chance of winning. Now, seeing that the outcome has to do with the sum of the dice rolled, you should probably understand which one you should choose based on the probability of the rolling the correct sum of the dice. If you roll a two through five or a ten, eleven, or twelve then the redneck gets to move forward one space, but if you roll a six through nine then the bunny hops one space. If you think about it, it would seem that the redneck would win because he has more sums you can roll to move him, but the sums are harder to achieve with the two dice. The bunny moves on less sums, but there are many more ways to reach the sums; therefore the bunny wins the majority of the time.
Normal Distribution
All of this has to do with a thing called Normal Distribution. Normal distribution is a pattern for which a set of data falls into called a bell curve. Normal distribution applies to dice, and it shows why the bunny has a better chance of winning. A bell curve is a general curve of a set of data that starts of low at one end and grows exponentially until an apex in the middle, then is decreases exponentially until it finally peters out at a low point on the other end. Therefore, giving the pattern a shape of a bell, hence bell curve. This a applies to dice because when you look at the sums of the two dice from low to high the pattern is that of normal distribution. For example, twos and twelves are the numbers you are least likely to get because there is only one way to achieve them. Six through nine are the sums you are most likely to get, the top of the bell curve, because they have the most possible ways to reach the sums. Seeing that the bunny has the apex of the curve under his belt he will win the majority of the time. That's not to say that the redneck will never win, it will just be less often.
Personal Connection
The main reason that I chose to do this for my project is I like to play games. When I started thinking about this project I was trying to figure out how I could incorporate math into a game and still teach some information. I did not have any idea about the game I wanted to choose, so I just started looking. I looked at puzzles, mazes, and riddles, but none of them had any real mathematical value. Finally, I was looking at games that had to deal with probability and I found that this was a very good option. This game has to deal with the probability of rolling a certain number to win the game. It was perfect for me.
While looking at the mathematics in probability, with the help of Mrs. Eagen, I came across a term called Normal Distribution. Normal Distribution explains the probability of dice. It identifies the pattern that dice follow when it comes to probability. Dice follow a pattern that falls under Normal Distribution known as the bell curve (better explained in the paragraph titled Normal Distribution). I was very interested in learning about the probability of winning games involving dice. I was really thinking about gambling and playing craps when I was learning about Normal Distribution. I have always had a dream of going to Vegas and winning a million dollars in a game of craps with Bill Gates. Now I know what chance I have of winning that game.
Composition Book Reflection
As I look back at the many topics that we have covered in math I find myself enjoying graphing equations. Now, graphing equations is a big part of Algebra. It is important to not only be able to solve algebraic equations, but it is important to be able to translate them into graphs. I enjoy graphing equations because I enjoy seeing what a bundle of numbers translates to visually. Just looking at an equation does not tell me much, but when you put it in a graph that represents a set of data then I understand a lot more about the meaning of the numbers. I also enjoy seeing how the different components of the equation shift the graph. I like to see how adding a number can move the line into a different quadrant or stretch it or shrink it. In all, I like to see the numerical values of equations represented visually in a way I can better understand.
If I had to choose one concept in math that has been an up-hill struggle, I would have to choose fractions. As a whole fractions just have not been my friends, despite how many times Miss Eagen says they are, and I have had some trouble working with them. I especially have trouble adding and subtracting them. I find it is hard to locate common denominators and transfer them to the fraction. It is especially hard when the fractions have algebraic equations in the numerator or the denominator. I have worked a lot with fractions, and the practice has really helped. I feel that with just a bit more practice I will be able to work with fractions. Now, I have not completely mastered fractions, but for the most part I understand how they work and how to carry out simple functions with them. I am coming to find that fractions can be a handy alternative to decimals, and that sometimes they are my friends.
