The Math of Bicycles: Wheel Figure This Out (Grades 4-7)

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It often seems that kids and bicycles are permanently attached during the summer time. The mathematics and science of bicycles offers interesting questions. Bicycles have become specialized to better accommodate a range of special purposes. From the past when you were limited to a Stingray, a regular bike, or a ten-speed, today you have options including the BMX, road bikes, mountain bikes, and hybrid bikes, which are a cross between a mountain bike and a road bike.

To develop the mathematics, we will look at the differences among bikes. Have students bring in a range of different types of pedal-powered vehicles. Try to include as many different types as possible. Some suggestions include a tricycle, a standard single-speed bike, an old three-speed bike, a BMX bike, a road bike, a mountain bike, and a hybrid bike.

First, we want to compare how far each bike travels when the pedals make one complete revolution or, in bicycle terms, "one crank of the pedal." You will need some space to do this, and this should be done with teams walking next to the bike turning the pedal, not riding it. You do not want to let the bike coast.

1. Do all the bikes travel the same distance?

2. Why do the bikes travel different distances when each was given the same single revolution or "crank" of the pedal?

3. Look at the wheels. For each bike, measure and record the height of each wheel. The height of the wheel can be measured from the ground, through the center of the wheel, to the top. This is also called the diameter of the wheel.

4. Now measure and record how far the wheel roles if it makes one complete revolution. Start with the valve stem at the bottom and roll the bike forward until the valve stem is back at the bottom. Measure how far the bike traveled. This measure is also called the circumference of the wheel.

5. Compare the height of the wheel to the distance around. If you had to pick a number to multiply the height by to get the distance around, what number would you chose?

6. The distance around the wheel is a little more than 3 times the height of the wheel. Or in math terms, the circumference is a little more than 3 times the diameter. The actual number is pi, which is approximately 3.14. Check and see if this relationship is true for your tires.

7. If you increase the height of the tire by 1 inch, describe any changes to the distance around the tire.