Measuring the height of very tall objects can be accomplished by using the concept of right triangles. Start by picking several tall objects, such as gigantic buildings in your neighborhood. Go to these locations and stand several hundred feet away from the building. Make sure you have the exact length measured. Point a yardstick at the top of the building. Have a partner measure the angle between the ground and the yard stick. Write down the angle next to the length you are standing from the object. Multiply the distance by the tangent of the angle to get the height of the object. Use the tangent button on your calculator to simplify this equation. The equation will read b * tan(angle)=height where b equals the distance.
Puzzles often take a great deal of math ability to perform. They also use a lot of logic and reasoning, two ideas that sixth graders will be starting to study in their math problems. Select a group of puzzles that require math to perform. These puzzles include Sudoku, number ordering or complex multiplication or division problems. Print these out and give them to the attendees of the math fair. Work through each puzzle with them step by step and discuss the mathematic principles at work in the puzzles. Take volunteers to help you solve the puzzles. Have a new person perform each step, if possible. Hand out new puzzles for attendees to take home.
Probability is the measurement of how likely an event is going to occur based on observable information. One of the easiest ways to illustrate probability would be to use dice throws. The probability of throwing any number on one die is one in six. The probability of throwing any one combination of two dice would be one in thirty six. Adding more dice simply multiplies the probability by six. Roll the dice multiple times while people watch. Write down the results of each roll. Roll until you roll all dice combinations. Write the number of dice rolls it took and find out how closely it matches the mathematical probability. Give people watching a chance to guess what the next dice roll will be, based on probability.
Pool is a game of carefully choosing angles and ricocheting the balls properly to knock them into the pockets. Illustrate this by bringing a small model pool table to the math fair. Place a few balls on the table and discuss the ways angles interact on the pool table. A ball shot at an angle to the table wall will ricochet off the wall at the complementary angle. Shoot the balls a few times to illustrate this point to the people watching. Let volunteers take shots of their own. Pick people who know how to play pool as well as players who don't. Let as many people get a chance to shoot as possible.