RATIO AND PROPORTION
Wheels in Motion
Activity 3: Finding Distance
Students will measure distances traveled by revolutions of a bicycle tire and make predictions based on their measurements. Also use the student copy.
To understand the relationship between wheel circumference and distance traveled for bicycles. Introduction: Have you ever noticed that when you are bicycling, the distance you travel is related to the number of revolutions the wheels make?
Answers will vary. Sample answers are based on a 21-speed, 26-inch (tire size) mountain bike.
One way to predict the number of revolutions of the bicycle wheel in 20 meters is to divide the number of centimeters (e.g., 2000 for 20 m) by the number of centimeters traveled in one revolution. Another method is to first divide the number of centimeters per revolution (obtained from the table in Part A) by 1000 to get the number of meters per revolution and then divide 20 meters by the number just calculated for meters per revolution.
Discuss the following situation as a class or in small groups: "Once while riding on my bicycle along a path, I crossed a strip of wet paint about 6 inches wide. After riding a short time in a straight line, I looked back at the marks on the pavement left by the wet paint picked up on my tires. What did I see?" There will be a series of six-inch marks, with half made by the front wheel and half made by the rear wheel. The distance between the "front wheel" marks will be the circumference of the front wheel. The distance between the "rear wheel" marks will be the same. Distance between front and rear wheel marks will depend on the frame size of the bicycle.
Activity 4: Comparing Distances
Students will graph the relationship between distance traveled and number of bicycle wheel revolutions, and calculate the relationship between diameter and distance traveled.
To make accurate predictions of distance traveled from tire size and number of wheel revolutions on a bicycle.
Remind students of the relationship they found between circumference and diameter (Activity 2). Do you think the relationship between distance traveled and bicycle wheel revolutions is linear (i.e., plotted points lie on a line)? Yes. Does the relationship depend on how fast you go? No. Would you rather have large or small wheels on your bicycle? Speed is dependent on gears and pedaling speed, rather than wheel size.
Activity 5: Pedaling Distances
Students will make predictions about distances traveled and measure actual distances based on revolutions of the bicycle pedals.
To understand the relationships between gear size and distance traveled for various gears on a bicycle.
Have you every thought about how much you have to pedal to get where you are going? Have ever realized that the gear you are in determines how much you have to pedal? In this activity, we will look at the relationship between the number of times you pedal and how far you travel.
Sample answers are based on a 26-inch tire.
100 meters » 50 revolutions
1000 meters » 500 revolutions
Activity 6: Gear Ratios
Students will calculate gear ratios and relative bicycle speed. Also use pages S6 and R2.
To understand the relationships between gear size and speed for various gears on a bicycle.
Have you ever realized that the more you pedal, the more your wheels turn, and the farther you go? [Discuss how the gears on a bicycle are arranged, lowest to highest (see the Reference Sheet).] In this activity, you will look at the relationship between the number of times you pedal and how far you travel.
Sample answers are based on a 21-speed, 26-inch (tire size) mountain bike.
Rear Sprockets: 14 16 18 21 24 28
Front Sprockets: 28
2. The back gear must have exactly half as many teeth as the front gear.
3. No, because the rear sprocket would need 25 1/2 teeth.
Area 10 Mathematics and Technology Professional Development Center
Permission is granted to duplicate these materials for classroom use.
Last updated on 1/30/1999