Here's a project that will teach you about math as you follow some of your favorite players or teams. You'll be comparing day-to-day performance with long-term averages, and trying to determine if the "streaks" and "slumps" over shorter time periods are due to random chance or something else. When you've finished, you'll have a better understanding of some important concepts in statistical analysis and baseball.
If a player goes 0-for-20, does that mean anything? Using probability theory,…
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Here's a project that combines sports and math. You'll learn how to use correlation analysis to choose the best team batting statistic for predicting run-scoring ability (Albert, 2003). You'll also learn how to use a spreadsheet to measure correlations between two variables.
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Almost all of the games we play are based on math in some way or another. Card games, board games, and computer games are designed using statistics, probabilities, and algorithms. Begin by reading about games and game theory. Then you can choose your favorite game and investigate the mathematical principles behind how it works. Can combinatorial game theory help you to win two-player games of perfect knowledge such as go, chess, or checkers? (Weisstein, 2006; Watkins, 2004) In a multi-player…
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Take shots at a set distance from the basket, but systematically vary the angle to the backboard. For a basic project: How do you think your success rate will vary with angle? Draw a conclusion from your experimental results. A bar graph showing success rate at different angles can help to illustrate your conclusion. For a more advanced project: Use your knowledge of geometry and basketball to come up with a mathematical expression to predict your success rate as a function of angle…
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Block off one-third of a soccer net with a cone, 5-gallon bucket or some other suitable object. Shoot into the smaller side from a set distance, but systematically varying the angle to the goal line. Take enough shots at each angle to get a reliable sample. How does success vary with angle? For a basic project: How do you think your success rate will vary with angle? Draw a conclusion from your experimental results. A bar graph showing success rate at different angles can help to…
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A fractal is, "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced/size copy of the whole" (Mandelbrot, 1982). There are many different fractal patterns, each with unique properties and typically named after the mathematician who discovered it. A fractal increases in complexity as it is generated through repeated sets of numbers called iterations. There are many interesting projects exploring fractal geometry that go beyond…
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Soils are made of particles of different types and sizes. The space between particles is called pore space. Pore space determines the amount of water that a given volume of soil can hold. Porosity is the percentage of the total volume of soil that consists of pore space. Compare the porosity of different types of soil. Which types of soil hold the most water? Can you see this under a microscope?
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Animals come in all shapes and sizes, even humans. You can look up different statistics about different kinds of animals using the Internet: average body size, brain size, life expectancy and generation time are some examples. Is there a correlation between body size and life span? Is there a correlation between body size and brain size? Is there a correlation between body size and generation time? Is there a correlation between body size and the size of your footprint? (Comparative Mammalian…
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What causes the most stress for teenagers? Is it school? family relationships? peer pressure? worries about the future? Design a survey to find out what contributes to teens' stress levels. Possible variations include: How do teenagers deal with stress? Are today's teens more or less stressed than their parents were as teenagers? Were the sources of stress the same for your parent's generation or different? (Idea from De Biasi, 2003)
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Math can make you money! If you understand some basic math, you can make good decisions about how to keep, spend, and use your hard earned dollars. Try an experiment comparing the same balance in different types of bank accounts. How much better is a savings account than a checking account? What difference does the interest rate make? Which is better, an account that earns compound or simple interest? Can you compare the short and long term costs of borrowing money compared to saving the cash…
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