Some middle school and high school students complete math projects as part of their curriculum or their involvement in math fairs. Math projects often involve experimentation, so you can use these types of projects to study and examine factors that affect outcomes. Topics are typically divided into categories, such as estimation, geometry, probability or finance. Teachers and judges will likely require you to present your hypothesis, data and conclusions on a poster board or a tri-fold board and may want you to write a research paper to accompany your project.

## Geometry: Angles and Shapes

Examine how varying angles affect your ability to make baskets in a basketball goal. Measure a consistent distance from the goal and record how many baskets you make at different angles, such as making 50 shots at 30-, 45- and 90-degree angles to the hoop. Show your results with a bar graph and use your conclusion to explain whether the results supported or disproved your hypothesis. Or, build models of various parallelograms, using wood, pipe cleaners or plastic straws, and then show how those with the same base and height have the same area. Use your data and conclusions to prove the validity of the Pythagorean theorem.

## Probability: Birthdays and Candy

Demonstrate how the laws of probability don't always align with human reasoning or intuition. Take four polls -- 23 people in each poll -- and record each person's birthday. Select a different group of people for each poll. Even though there are 356 days in a year, a 50 percent chance exists that two people in each of your polls will have the same birthday. Or, show how the laws of probability accurately predict outcomes. Empty a bag of colored candies, count them and record the number of each color. Determine the ratio of each color compared to the total number, such as 25 red pieces out of 100 total candies, which is a one to four ratio. Test the accuracy of the ratio by randomly selecting individual pieces -- replacing them each time you draw -- and then record your findings. Perform the experiment with each color.

## Finance: Bank Accounts and Groceries

Determine the benefits of saving money in various types of bank accounts that offer different interest rates. Don't actually put the money in any bank accounts, as interest takes time to accrue. Instead, calculate, record and report as if you made the deposits. Use the same starting amount, such as 1,000 dollars, to ensure that your comparisons are credible. Visit banking websites or local banks to determine current interest rates and available options for savings or investment plans. Or, visit a local grocery store and calculate your family's savings if you bought generic-brand school lunch items, rather than brand-name items for your school lunches for a month. Compare similar items, such as generic and brand-name juice boxes, not brand-name juice boxes and generic soda pop, which will add credibility to your project. Record and report your savings.

## Estimation: Beans and Rolls

Show how it's more difficult to accurately estimate amounts when you're working with larger numbers. Select three jars -- pint-size, quart-size and gallon-size, and fill each with dry Lima beans. Estimate how many beans are in each jar and record your guesses. Count the total number of beans in each jar and report your findings. Or, estimate how texture affects surface tension by rolling a ball on different materials. Measure a distance, such as 25 feet, and guess how long it will take a plastic ball to roll that distance on carpet, grass, tile, linoleum, hardwood flooring, cement, black top pavement or ice at an ice skating rink. Use a stopwatch to compare the actual times with your guesses. Start the ball rolling by using a low-tension poker or sling shot to ensure that the initial ball speed is the same each time.

#### References

- American Mathematical Society: Research Projects for Students
- Stony Brook University: Possible Science Fair Mathematics Projects; Afton H. Cayford at the University of British Columbia
- Illinois Institute of Technology: Science Fair Project Ideas
- Science Buddies: Pure Mathematics Project Ideas
- Science Fair Adventure: Statistics and M&M's

#### Photo Credits

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