Where's Math The Math?
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The project examines the math involved in a mini U.E.F.A. Champions League soccer ball, focusing on calculating its surface area based on hexagons and pentagons using specific formulas. The student also estimates the number of touches they will have on the ball throughout the year by analyzing their practice and game schedules along with future tournaments and futsal sessions. The calculations culminate in a total of 107,100 estimated touches for the year, integrating personal experiences with mathematical concepts.
Where's Math The Math?
- 1. Where is the Math? By 7 th Grade Student
- 2. The artifact that I chose to do my where’s the Math? Project on is a mini U.E.F.A. Champions League soccer ball. Most soccer balls are made from hexagons and pentagons and this one has designs over the hexagons and pentagons. There is a red star on each pentagon and there is a white, rounded, equilateral triangle. I chose this artifact because I play a lot of soccer and I think that you can see a lot of math in soccer balls.
- 3. The problem that I solved was to find the surface area of the ball by just doing one measurement. Since the hexagons and the pentagons share the same sides I found the formula to find the area of hexagons and pentagons by knowing the measurement of only one side. Then I multiplied the area of each by the number of hexagons or pentagons there are. Then I added them together to get roughly the surface area of the ball. The formula for the area of a hexagon is 2.60 x side squared. The measurement of one side is 1.25 inches and then I multiplied it by itself which equals 1.56 inches squared. With that measurement I made the equation: 2.60 x 1.56 = 4.0594 inches squared. Then I multiplied that by 20, that’s how many hexagons there are, which equals 82.188 inches squared. Next I found the formula for the area of a pentagon, which is 1.72 x side squared. Since I already knew what the side squared was I just plugged that into the equation, which is 1.72 x 1.56 = 2.6882 inches squared. Then I multiplied that by 12, which is 32.2584. Next I added 81.188 and 32.2584 which equals 113.4464 inches squared, which is roughly the surface area. To check my answer, I found out the formula for the surface area of a sphere. The formula is 4 x π x radius squared. I found the radius, 2.94 inches, and multiplied it by itself, which is 8.64 inches squared. Then I put that into the equation: 4 x π x 8.64 = 108.94 inches squared. This answer is so close to 113.4464 that I feel that my way of calculating the surface area of the ball is correct.
- 4. My Fermi Question is how many touches on a soccer ball will I get this year? First I looked at soccer and figured out how many touches I get in 1 minute for practices and for games. For practices I put 10 touches per minute and for games I put 5 touches per minute. Then since my practices are 90 minutes I said that I got 900 touches every soccer practice and since my games are 70 minutes long I said that I got 350 touches per game. Then I multiplied 900 by 24 because that was how many practices we had in the fall season, which is 21,600 touches. I multiplied 350 by 10, the number of games we had, which equals 3,500. Then for the practices I multiplied 21,600 by 2 to get 43,200 touches in practice for both the fall and the spring seasons. After that I multiplied 3,500 by 2 to get 7,000 touches in games for both the fall and the spring seasons. Next I found out the number of touches during tournaments by doing 350 touches a game multiplied by 4, the number of games in a tournament, which equals 1,400 touches for 1 tournament. I am guessing that we are going to have 6 tournaments in the year (3 of them already happened). I did 1,400 x 6 = 8,400 touches for tournaments for the whole year. Next I Figured out the number of touches I will have in futsal (indoor soccer) by figuring out the number of touches I will get in 1 minute for both practices and games. For practices I figured I got 15 touches in 1 minute on average and for games I figured I got 10 touches per minute on average. Then, for practices, since they are 90 minutes long I multiplied 15 and 90 and I got 1,350 touches on the ball for 1 futsal practice. For games since the games are 40 minutes in a game I multiplied 40 by 10 to get 400 touches in 1 futsal game. Then for the practices I multiplied 1,350 by 18, which is how many practices there will be, to get 24,300 touches in all the futsal practices. For the games I multiplied 400 and 8, which equals 3,200 touches for all of the futsal games. Next I found out the number of touches I will get in the summer at Two Rivers (soccer camp). I figure I will get around 10 touches per every minute I spend playing soccer at the camp. I will spend 5 hours a day for a week playing soccer at Two Rivers, so I multiplied 300 minutes by 10 touches a minute which is 3,000 touches a day. Since I will go there for a week, I multiplied 3,000 by 7, which equals 21,000 touches that I will get at Two Rivers. Finally I added up 43,200 + 7,000 + 8,400 + 24,300 + 3,200 + 21,000 = 107,100 touches in the whole year.
- 5. I was able to connect math with my artifact very well. The most challenging thing in this problem for me was understanding all the formulas. One thing that was new and really fascinating was being able to find roughly the surface area of the ball by just making one measurement. Something different I would do if I were to do this project again would be to also do something with the design of the stars and the rounded triangles as well as finding the surface area of the ball with the hexagons and pentagons.