ideas

IDEASAuthor(s): Sharon L. YoungSource: The Arithmetic Teacher, Vol. 38, No. 4 (DECEMBER 1990), pp. 23-33Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41195034 .

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IDEAS

IDEAS section for this month focuses on gathering, using, and

interpreting data about bicycling as a basis for integrating mathematics, sports, and science. Measurement, ra- tios, and other relationships are ex- plored through making graphs and finding bicycling speeds and in a par- ent-involvement activity sheet. This month the reproducible sheets for the IDEAS section are designed to be used by multiple grade levels. In- cluded are an activity sheet for parents to use with their children, three class-activity sheets, and a data sheet. A teacher may want to reproduce and use several sheets.

IDEAS

LEVELS 1-8 BICYCLING DATA SHEET

This data sheet should be duplicated and used when indicated for class-activity sheets. The following information will help you and your students interpret the bicycling data.

1. The data for adults participating in leisure sports was gathered by the Gallup Or- ganization of Princeton, New Jersey. In- person interviews were conducted with 2053 adults, who were asked, "Which of these [50 listed] sports and activities, if any, have you, yourself, participated in within the last 12 months?" The top fifteen

Edited and prepared by Sharon L. Young Mathematics Education Consultant Palm Harbor, FL 34683

This section is designed for teachers who wish to give students new insights into familiar top- ics in grades K-8. This material can be repro- duced by classroom teachers for use in their own classes without requesting permission from the National Council of Teachers of Math- ematics.

DECEMBER 1990

choices are included on the data sheet. 2. The bicycle sprint-speed records for the United States and Canada were computed from results of 200-m sprint races. These speeds could not be maintained for long periods of time.

Extension

1. Send home a copy of "Bicycling at Home." Ask students to record the results of the suggested activities and then to share their results with the class. The following references for the various methods of determining the fit of a bicycle may be helpful: • Frame size, method A: Fink's Things to Know Before Buying a Bicycle (1985) • Frame size, method B: Adapted from van der Pias 's The Bicycle Commuting Book (1989, 119) • Bicycle-seat height: van der Pias 's The Bicycle Commuting Book (1989, 57) • Handlebar height and distance: Knight's Bicycling for Fitness and Fun (1976, 73) 2. Students could conduct their own li- brary research to find out more about bicycling. See the Bibliography for suggested resources.

Bibliography Fink, Joanne. Things to Know Before Buying a

Bicycle. Morristown, N.J.: Silver Burdett Co., 1985.

Knight, Frank T. Bicycling for Fitness and Fun. Toronto: Coles Publishing Co., 1976.

McPhee Gribble Publishers. Bicycles: All about Them. Melbourne: Penguin Books Australia, 1976.

Sloane, Eugene A. The Complete Book of Bicy- cling. 4th ed. New York: Simon & Schuster, 1988.

van der Pias, Rob. The Bicycle Commuting Book. Mill Valley, Calif.: Bicycle Books, 1989.

Wilcockson, John. Bicycle. New York: Butter- ick Publishing, 1980.

Wilhelm, Tim, and Glenda Wilhelm. Bicycling Basics. Englewood Cliffs, N.J.: Prentice Hall, 1982.

IDEAS

LEVELS 1-6 COLORS OF BICYCLES

Objective Students make a guess about the most popular color for bicycles. They then plan and conduct an investigation to check the guess. Data collected in the investigation are tallied in a table, and students then write a story describing their methods and their results.

Materials

1. Copy of "Colors of Bicycles" for each student 2. Copy of "Bicycling Data Sheet" for each student in levels 3-6

Directions

1. Ask students questions like these, discussing their responses as a class:

• How many different colors do you think bicycles come in? • What are some of the colors? • What do you think is the most popular color for bicycles? • What are some ways you think you could find out what the most popular color of bicycles is? (Possible answers include the following: check with stores that sell bicycles, look at bicycles parked at school, look at bicycles in the neighborhood, ask people the color of their bicycles.) • Do you think the most popular bicycle colors for adult bicycles are the same as or different from students' bicycles? 2. Place students in groups of four to six students. Discuss group behaviors: help one another, disagree in an agreeable way, listen to others in your group, take turns.

23



3. Distribute a copy of "Colors of Bicy- cles" to each student. Discuss the directions with them. 4. For item 1 , each student could make an individual guess or each group can make a group guess of the most popular color of bicycle. 5. Have each group decide on a method to collect data to check their guesses. Some suggestions for conducting the various in- vestigations are given here.

• Examination of school bicycle racks: Students could record the colors of the bicycles found in the bicycle racks at the school. This task can be accomplished by looking at the bicycles one at a time and recording each color or by having different people in each group or different groups record only certain colors. • Survey of students: Students could ask other students the color of their bicycle or the colors of their family members' bicycles. This latter method would increase the number of bicycles in the sample. • Neighborhood survey: Students could individually record the colors of bicycles found in their neighborhood. However, if a group of students compiles these data, they should be assigned sections of the neighborhood to survey so as to avoid du- plication in recording bicycles. • Telephone survey: Students could call different stores (including bicycle, depart- ment, discount, and toy stores) to find out what colors of bicycles seem to sell most readily. 6. Students will have to decide how to categorize multicolored bicycles or those of predominantly one color but with many colorful decals. They could perhaps fit in a category "other." 7. After the data are collected, encourage each group to discuss the results. Then students can individually write about their methods and their results. In particular, students should write how their results compare with their initial guess in item 1. 8. Give groups an opportunity to report their methods and findings to the class. Compare the findings of various groups to determine whether they came to the same conclusions. 9. For younger students: Write the bicycle-color data from the "Bicycling Data Sheet" on the chalkboard, listing the colors in order with the most popular color first. Explain the data to the students and ask them to compare their own results of popular bicycle colors with these new data.

M

For older students: Distribute copies of the "Bicycling Data Sheet" and discuss the data on bicycle sales by color so that item 4 can be answered. Note that students who have not been introduced to the concept of percentage can still benefit from looking at and discussing the data. A simple notion of percentage could briefly be mentioned to help students see that more blue bicycles were sold than black or red bicycles but that about the same number of those three colors sold. Since nei- ther pink nor purple (popular colors for young children's bicycles) are indicated as color choices in this table, it is important to mention that they could be included in the category "other" or that since this table does not include twelve-inch and six- teen-inch bicycles, only a small number of larger bicycles may be manufactured in those colors.

Extensions

Levels 1-4

1. Make a bar graph of the results of the bicycle-color investigation. 2. Collect data about other features of bicycles: • types of handlebars • colors of handlebar grips • sizes of wheels • brands • colors of pedals Data can be displayed using graphs or ta- bles.

Levels 5-6

1. Find the percentage of each color of bicycle. Then make a bar graph using the percentage data. 2. Discuss the terms domestic and imported with students. Ask students questions such as these:

• Is your bicycle imported or domestic?

How could you find out? (Answers will vary.) • Do you think that more domestic bicycles or more imported ones can be found at your school? In your neighborhood? (Answers will vary.) Collect the following data about bicycles at school or in the neighborhood. The data can be collected through observation or by asking students and other people about their bicycles.

• Is the bicycle domestic or imported? • Is the bicycle a twenty-inch bicycle, a lightweight ten-speed bicycle, or other type, such as a three-speed, five-speed, or all-terrain bicycle or a cruiser?

Display the data in a table, perhaps similar to the one on the "Bicycling Data Sheet" that shows U.S. bicycle sales for 1980 and 1989. Ask students to write a report about their investigation. They can compare their results with those given on the data sheet to see if their school or neighborhood follows the same trends, such as that more twenty-inch bicycles are domestic but more lightweight bicycles are imported. 3. Make a double bar graph for the data found in item 2 or for the U.S. bicycle- sales data from the "Bicycling Data Sheet." 4. Conduct a survey of students to find the fifteen most popular sports activities in which they have participated within the past year. Students could first brainstorm a comprehensive list of activities that could be shown to the people they survey.

Answers

Answers will vary.

Extension answers

Answers will vary. Some possible double bar graphs for item 3 showing U.S. bicycle sales are shown in figure 1.

ARITHMETIC TEACHER

^^^^^^^^^H U.S. Domestic and Imported Bicycle Soles, 1 989

in . __^^M__ __^^^b_ _^^H__ g« . ,

Twenty inch Lightweight Other

Types of Bicycles



IDEAS

LEVELS 3-8 PEDALS AND WHEELS

Objective Students informally explore relationships among the wheel circumference, pedal revolutions, and distance a tricycle or bicycle goes. Using different tricycles and bicycles, students first measure the distance around the wheel (circumference). Next, they find the distance each cycle goes for one, two, three, four, and five revolutions of the pedal. The data are collected and displayed in a table. Students then write about their investigation.

Materials

1. A small standard tricycle 2. A Big Wheel™ (preferably 16" wheel size) 3. A twenty-inch bicycle 4. A twenty-six-inch bicycle (preferably with a single gear) 5. Measuring tapes or sticks (metric or customary) 6. Calculators (optional but helpful) 7. A copy of "Pedals and Wheels" for each student 8. A copy of "Bicycling Data Sheet" for each student

Directions

1. Ask students questions like these to discuss similarities and differences among and between tricycles and bicycles:

• How are standard tricycles and Big Wheels alike? (3 wheels, pedal connected to the front wheel) • How are they different? (Seat of the Big Wheel is lower; pedals are in different positions) • How is a tricycle different from a bicycle? (3 wheels vs. 2 wheels; pedal on bicycle connected to gear between the wheels rather than to the wheel, as on a tricycle) • How are small bicycles different from large bicycles? (Wheel size, multiple gears) • In a twenty-inch bike, what does "twenty-inch" refer to? (Wheel diameter)

DECEMBER 1990

^^^^^^^J Distance Traveled by Tricycles and Bicycles*

Number of pedal turns 12 3 4 5

Small tricycle 38 OQ. inches . 38 76 114 152 190 38 OQ. inches .

(Distance around wheel)

Big Wheel™ 50 inches 50 10° 150 200 25°


Twenty-inch bicycle ZQ. . 158 316 474 632 790 6J ZQ. inches


Twenty-six-inch bicycle 82 inches 225 450 675 900 1125


•Distances are given in inches for purposes of the example; other units are possible.

2. Distribute copies of the "Bicycling Data Sheet" to each student and discuss the information about wheel sizes of tricycles and bicycles. Ask students these questions: • Why do bicycles and tricycles come in so many different wheel sizes? (Smaller wheels for shorter people) • Does the size of the wheel have any- thing to do with how far the tricycle or bicycle can go? (Answers will vary.) Tell students that they are going to explore this question to find an answer.

3. Distribute a copy of "Pedals and Wheels" to each student and discuss the directions with them, as appropriate. Make sure students understand that they will first measure the front-wheel circumference of each tricycle and bicycle. Met- ric or customary units can be used, as appropriate for your class. Ask students for various methods they could use to measure the distance each tricycle and bicycle moves for one pedal revolution. One possible method is to place the front wheel directly over a starting line with one pedal in the up position and then move the pedal one complete revolution so that the front wheel moves beyond the starting line. Mark on the floor the stopping point where the tire touches the floor, measure the distance traveled, and record. 4. Ask students for various methods to find the distance traveled for two, then three, then four, and finally five complete pedal revolutions. An obvious method would be to use the same method de-

scribed in item 3, but move the pedals through two, three, four, and five revolutions, measuring the distance traveled from the starting line each time. Another method would be to use the distance for one revolution and add that amount each time for other numbers of revolutions, for example, if a bicycle goes 150 inches in one revolution, then add 150 inches for each new revolution.


Distance traveled (in inches) 150 300 450 600 750

5. Place students in four groups. Discuss group behaviors: help one another, disagree in an agreeable way, listen to others in your group, take turns. 6. Give each group one of the tricycles or bicycles and some measuring tapes or rul- ers. After the groups complete a measurement, the tricycles and bicycles can be ro- tated to the other groups. Note: If a multigeared twenty-six-inch bicycle is used, have students conduct the investigation with just one gear. 7. After the table is completed, have each group discuss the results and make conjectures as to why the small tricycle went the shortest distance and the twenty-six- inch bicycle went the greatest distance. Elicit from students the idea that the distance a tricycle moves for one pedal revolution is the same as the wheel circumference but the distance a bicycle moves for one pedal revolution is much greater

25



^^^^^^^^^^B -Tape

^^^^^^^3 Numbers of Pedal and

Tire Revolutions

'revalut.ons 4 8 12 16 20

evolutions 11 22 33 44 55

than the wheel circumference because of the chain-and-gear system. Each student can then write a summary paragraph for question 3 on the worksheet. 8. Encourage each group to make a report to the class about its findings. Compare results from different groups. Measure- ments will likely vary slightly from group to group. Ask students why this discrep- ancy might occur. Discuss with students possible reasons that the twenty-inch bicycle goes so much farther than the Big Wheel. Elicit two reasons from students, as appropriate to the grade level: (1) The wheels are of different sizes, and (2) the bicycle has a gear mechanism that allows the wheel to revolve more than one time for each pedal revolution.

Answers

1 . Answers will vary depending on the actual tricycles and bicycles used. A sample table is shown in figure 2.

Extensions

1. Students can informally explore the gear ratio of bicycles. Place a tape or chalk mark on the back of an upside-down bicycle so that the tape or mark is at the highest point of the tire and the pedal is in an up-down position, as in figure 3. Two students will need to be counters: one to count the number of pedal revolutions and one to count the number of tire revolu-

26

tions. Pedal the bicycle until the tire and the pedal are again in the same position. Record the number of revolutions. Then complete a table to show the relationship between the number of pedal revolutions and the number of tire revolutions, as in figure 4. Note: Other methods for explor- ing gear ratio are included in the following activity.

IDEAS

LEVELS 5-8 WHAT IS YOUR BICYCLING SPEED?

Objective Students explore informal and formal ways to gather data for use in determining their individual bicycling speeds. They write about their data-gathering methods.

Materials

1. A bicycle for each group of students. Use multigeared bicycles if possible, making sure that the gear housing is not covered. 2. Calculators (optional but very helpful) 3. Measuring tapes and sticks (in customary units or metric units) 4. A copy of "What Is Your Bicycling Speed?" for each student. 5. A copy of "Bicycling Data Sheet" for each student. 6. A clock or watch that measures time in seconds

Directions

1. Ask students these questions, discussing their responses as a class:

• How fast do you think a dog can run? A horse? (Answers will vary.) • Do you think you can ride a bicycle faster than a dog can run? A horse? (An- swers will vary.) • How fast do you think you can go on your bicycle? (Answers will vary.) • How fast do you think racers can go on their bicycles? (Answers will vary.) 2. Distribute copies of the "Bicycling Data Sheet." Discuss with students the various speeds of world-class bicyclists and animals. Compare the data with the guesses students made in item 1 . Note that the data for the sprint speeds is based on a sprint distance of 200 meters. It would not be possible to continue these speeds for a significantly longer time. 3. Ask questions like these to generate ideas on what affects a bicycle's speed and how bicycle speed can be determined.

• How do you think you could determine your speed on a bicycle? (Use a cyclome- ter or an odometer or use a stopwatch to determine the time required to cover a premeasured distance and calculate the speed.) • How do you think you could determine your own bicycling speed without actually riding a bicycle? (Answers will vary.) • What do you know about gears on bicycles? How do they affect the speed of a bicycle? (For each pedal revolution, the wheels go through more than one revolution, allowing the cyclist to go faster than if the wheel revolved only one time for each pedal revolution.) 4. Distribute copies of "What Is Your Bi- cycling Speed?" to each student and discuss its contents. In particular, note that in items 3 and 4, students will be comput- ing two different distances and that the distance for item 4 is based on the distance calculated for item 3. 5. Place students in groups of three to five students. Discuss group behaviors: help one another, disagree in an agreeable way, listen to others in your group, take turns. 6. Direct each group first to discuss various methods for finding the data needed for A, B, and C. Some possible methods for each are given here: A. Gear ratio (number of wheel revolutions for each pedal revolution). Three methods are included here. • Method Al: With the bicycle upside down and the pedals in a vertical position (one under the other), place a piece of tape or a chalk mark on the outer edge of the

ARITHMETIC TEACHER



27

rear tire at its highest point (see fig. 3). Students then use their hands to make one complete revolution of the pedals, simul- taneously noting how many times the back wheel revolves by watching the position of the tape or chalk mark. Students can estimate the fractional part of a revolution if needed.

• Method A2: Use method Al but count the pedal revolutions and the wheel revolutions until the pedal and the wheel both end up in the position they were in at the start. The number of wheel revolutions can be divided by the number of pedal revolutions to determine the gear advantage (or gear ratio). For example, if the wheel made five revolutions for two revolutions of the pedal, then the gear advantage is 2.5, found by dividing 5 by 2.

Number of wheel revolutions Number of pedal revolutions

• Method A3: Divide the number of pedal-gear teeth by the number of wheel-gear teeth:

Number of pedal-gear teeth Number of wheel-gear teeth

B. Circumference: Here are some methods students might use:

• Method Bl: Younger students can measure the distance directly with a tape measure or use a piece of string to match the distance around the tire and then measure the string. • Method B2: Older students can use the wheel size (its diameter) and multiply by pi (it) to find the circumference (d x tt = Q.

C. Number of revolutions per minute

• Method Cl (indoor method): Students estimate the number of revolutions they can pedal with their legs and feet in one minute by using their hands to pedal an upside-down bicycle, as shown in figure 4. When doing so, stress with students that they should not attempt to pedal as fast as possible but rather at a continuous rate that they think they could maintain for one hour with their legs and feet. This rate is called the cadence. • Method C2 (outdoor method): Time students for fifteen seconds as they ride a bicycle outdoors while pedaling constantly. Have them count the number of revolutions they pedal during this time, which can then be multiplied by 4 to find the number of revolutions for one minute. 7. To answer item 3, students will need to

DECEMBER 1990

^^^^^^^9

^^^^^^^^H

ijfjim^n U.S. Female Sprint-Speed Records

Age 1 6-1 7 l^^^^^^^^^^^^^^l

0 20 40 60 80 100

Speed (km/h)



find the product that results from multiply- ing the data obtained for A, B, and C. Ask why they think this product gives them the distance for one minute. Note that if customary units are used, this answer is likely to be computed in inches. It can be changed to feet by dividing the number of inches by 12. If metric units are used, this answer could be in centimeters or in decimal parts of a meter. 8. To answer item 4, students should be encouraged to work as a group, discussing procedures that could be used. Using a calculator, students first need to multiply by 60 to find the distance for one hour (60 minutes). If this distance is in inches, students can divide by 12 to find the number of feet traveled in one hour and then divide by 5 280 to find the number of miles traveled in one hour. If this distance is in centimeters, students can divide by 100 000 to find the number of kilometers traveled in one hour. You may need to work with students to interpret the quo- tients resulting from these division calcu- lations, as they are likely to have many decimal places. Students could round to the nearest whole unit or tenth of a unit.

9. Have students compare their speeds with the bicycle sprint-speed records for the United States and Canada given on the "Bicycling Data Sheet."

Extensions

1. Use a multiple-speed bicycle. Have students compute their bicycling speeds in three different gears and compare them. 2. Students can make a bar graph to display bicycle-sprint-speed-record data from the "Bicycling Data Sheet." They will need to select speeds in kilometers per hour or in miles per hour and then round the speeds to the nearest whole number. 3. Read the following situation aloud to students and have them make conjectures about the answer.

A pebble was picked up in the tire tread of a moving bicycle whose tire has a circumference of 86.5 inches (220 cm). Is the distance the pebble travels between the two successive points at which the pebble touches the ground more than, less than, or the same distance as the circumference? {Note: This tire is for a 26" bicycle.)

After discussing possible answers and their reasons for them, have students conduct an investigation to determine the answer. Place students in groups, each with a bicycle. (Note: The investigation can use bicycles of any size. Have each group

28

place tape or a chalk mark on the edge of one of the bicycle's tires to represent the pebble. Have students find some method for drawing a path that shows the move- ment of the pebble, starting at ground level and returning to its original position. One method is to place the bicycle near a wall covered with a large sheet of butcher paper, with the "pebble" mark at ground level. Then move the bicycle slowly, pause after it is moved every five inches or so, and mark the new position of the "pebble" on the paper until the "pebble" re- turns to the original position. In this way a number of positions of the "pebble" can be represented on the paper as shown in figure 5. The position points can be connected, making a curved line to indicate the path of the pebble as in figure 6. This path is called a cycloid. A cycloid is the curved path of a point on the circumference of a rolling circle.

Students can measure the distance from A to B on the ground and then along the cycloid. Ask students to find the relationship between the cycloid's length and the tire's diameter.

See Bennett and Nelson (1979, 154) and Williams and Shuard (1970) for activities regarding cycloids. 4. Many excellent activities for extension

can be found in Ames (1977) and Mold (1973).

Answers

Answers will vary.

Extension answers

2. Answers will vary depending on the data selected. One possible graph is shown in figure 7. 3. The pebble would travel a greater distance than the tire's circumference. Note that the cycloid's length for any rolling circle is greater than the circle's circumference, regardless of its size. The cycloid's length is 4 times the length of the circle's diameter.

Bibliography Ames, Pamela. "Bring a Bike to Class." Arith-

metic Teacher 25 (November 1977):50-53. Bennet, Albert B., Jr., and Leonard T. Nelson.

Mathematics, an Activity Approach. Boston: Allyn & Bacon, 1979.

Mold, Josephine. Rolling. Cambridge: Cam- bridge University Press, 1973.

Williams, Elizabeth, and Hilary Shuard. Ele- mentary Mathematics Today: A Resource for Teachers Grades 1-8. Menlo Park, Calif.: Addison-Wesley Publishing Co., 1970.

In-Service Meetings

I^^HHI lementary Teachers- ^^^^^H You are Special m^^l to NCTM!

As a teacher at an elementary school that is a member of the NCTM you are entitled to a special individual member registration fee at our conferences. Group discounts may also apply. Con- sult your school administration regarding the Dwight D. Eisenhower (formerly Title II) funds earmarked for teacher training. Join us at any of the upcom- ing meetings! For further information, a program booklet, or a listing of local and regional meetings, contact the National Council of Teachers of Mathematics, Dept. PD. 1906 Association Dr.. Reston.VA 22091; Telephone: (703) 620-9840; Fax:(703)476-2970; CompuServe: 75445,1161.

Regional Conference8 1990-91 Sacramento, California 7-9 February 1991

South Bend, Indiana 14-16 March 1991

1991-92 Louisville, Kentucky 10-12 October 1991

Baltimore, Maryland 31 October-2 November 1991

Albuquerque, New Mexico 7-9 November 1991

San Juan, Puerto Rico 1K-20 November 1991

Nashua, New Hampshire 21-23 November 1991

Long Island, New York 4-6 December 1991

Des Moines, Iowa 30 January- 1 February 1992

Eugene, Oregon 18-20 March 1992

Montreal, Quebec 23-25 August 1992

NCTM Annual Meetings

69th Annual Meeting New Orleans. Louisiana 17-20 April 1991

70th Annual Meeting Nashville. Tennessee 1-4 April 1992

71st Annual Meeting Seattle. Washington 31 March -3 April 1993

72nd Annual Meeting Indianapolis. Indiana 13-16 April 1994

73rd Annual Meeting Boston, Massachusetts 6-9 April 1995

74th Annual Meeting San Diego. California 25-28 April 1996

HcibH

ARITHMETIC TEACHER



ideas ̂v» ^ül Name

Bicycling at Home Dear Parents,

Your child has been using mathematics in class while collecting and investigating data about bicycles and bicycling. Two additional activities are suggested on this sheet. You and your child may want to do one or both of them together. The results can be recorded and shared with classmates. ilT^K

How Far Can You Coast on Your Bike? W!p*5 '*# 1. Find a level place for bicycling and mark a start line and VW^¿ftL^ /^^rntffl^v

a "coast" line, as shown. [^âLY^*' / • ' 2. Pedal your bike as fast as you can from the start line until / a It I ' I) ' *'

you cross the coast line, then coast on your bike (no / ^Jj <; A jk y-'s ' ■ JL

pedaling) as far as you can go. / J ^ * .¿r'. ¿^ /j-A^rr^^N 3. Measure the distance you coasted after crossing the ( ^j i*1"

"^ ( â^' 6/jT Â_ t

coast line. You can measure with a ruler or a tape or with / ^^"-V -j^ fc/ ( '-', • | "^ j the length of your stride. I '. " / | Í J^Z-t^/jl^

Does Your Bike Fit You? Handlebar 1. Use one of these two methods to find the size of frame p

- - Hap

that fits you. l

^^7 '^ Method A: Find your height and divide by 3. ji v ' Method B: For a racing bike, subtract 10 in., or 25.5 cm, g1 31 ^-- -y/ '' yvvW~~^'

from your leg length. For a mountain bike, ^ | /^- ^-- -

^'' -y/

'' ///AV - ^s'

subtract 11 in., or 28 cm, from your leg |; |- // // '' Vv /Y ( ('k ''

Measure the size of your bicycle's frame and compare it 'V^ d^ZZL^W 'V yj with your results. ■* ^C^- ^s< -m x^ - -^y

2. The bicycle seat height should be 1 09 percent of your leg Measuring frame size, seat height, length. and handlebar distance

3. The handlebar height should be about the same as the . seat height (except for high risers). / A

4. The distance from the handlebar to the seat should be , the same as that from your elbow to your fingertips. I - Jl - '

' ' ' - I to

( S w W *

Measuring leg length

Caution: If you make adjustments to the seat or the handlebars so they fit you better, make sure that you leave at least 2.5 in., or 6 cm, of the seat post inside the seat tube and the same amount of the stem in the head tube.

From the Arithmetic Teacher, December 1990



IDEAS ^

V»

Colors of Bicycles Jía 1. Make a guess. Which color do you think is the most v*€*-** /

popular for bicycles? ^"^^-^ ixfcifí* 2. Find a way to check your guess. Use tally marks to jft ^>0!v V^i

record your results in the table below. J^^lT^yjcW ^ ̂ ^£^rv*& ***u.

^ Number of Bicycles of Each Color Colors Tally marks Number

3. Write a story. Tell what you did and what you found out about your guess.

(Titlü

4. Are the most popular colors listed on the ''Bicycling Data Sheet" the same as the ones you found?




IDEAS -^yj ^dl Name

Pedals and Wheels Work in a group.

1. Measure the circumference (distance around wheel) of the front wheel for each tricycle and bicycle. Record the measurements in the table below.

2. Turn the pedal one complete turn and measure the distance each type of tricycle and bicycle moves. Finish the table to find how far each one moves for one to five turns of the pedal.

Distance Traveled by Tricycles and Bicycles


Small tricycle


<^' Big Wheel™

K^J? ^^rr^^ (Distance around wheel)

^ g Twenty-inch bicycle


S^ O Twenty-six-inch bicycle

^ - ^ ^ S (Distance around wheel)

3. Which cycle went the farthest in five turns of the pedal? Tell why.




IDEAS -^ y» ^_l Name

What Is Your Bicycling Speed? Work in a group. ^^%ïsr

1. Use the animal speeds on the "Bicycling Data Sheet" to finish this sentence: t lí^S~a£ When I ride a bicycle, I think I can go as fast as a , ^^V^^7^v5C' which can run per hour.

(Name of animal) />/M3 W^^

2. Use a bicycle to collect data for A, B, and C and write how you found the data. ° - ' v// J^Cr^r- 'y¿7J You will need these data to compute your bicycling speed.

'^-.r - j^X¿_*/

Data How data were obtained

A. Number of wheel revolutions for each pedal revolution (gear advantage or gear ratio)

B. Distance around a tire (wheel circumference)

C. Number of revolutions of pedal you can make in one minute

3. How far can you pedal in one minute? (Multiply answers A x B x C.)

4. How far can you pedal in one hour? Tell how you found out.

5. What is your bicycling speed per hour? 6. How does your actual speed in problem 5 compare with the speed you guessed in problem 1 ? Are the two speeds

close?




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Bicycling Data Sheet Percentages of U.S. adults U.S. bicycle sprint-speed participating in leisure sports records (1990)

1989 1988 Male

Swimming 38 36 Age krñTh mpii

ÌZto Bowling II 22 21 21 15"16 63-26 39-28 Bowling 22 21 21 17 ™ .. .,-„

S3f Bowling

i 22 21 21

'l 17 ™ ..

I S5 .,-„

I & Pool or billiards 20 17 Fema)e Running or jogging 19 17 1 1 Weight training 16 19 _^ge

km/h mph

Bicycle touring or racing 16 11 1 3-15

53.03

32.93 Softball 16 16 16-17 60.32 37.46 Volleyball 15 13 18+ 63.78 39.61 Motorboating 15 12 - ¡ - ¡ - I ¡ - -- - I ¡ Aerobics or "dancereize" 13 14 Source: AdaPted

¡ from data ¡ provided

¡ by U.S. Cycling

¡

Golf 13 12 1 Federation

Source: Gallup Organization

i 1 Canadian bicycle sprint-speed Percentages of 1989 bicycle records (1990) sales by color for bicycles 1 1 twenty inches and larger j^ km/h mph

- ; 1 Male 68.51 42.54

Bue, 24 Female I

59.95 I

37.23 Black 23 I I Red 22 Source: Adapted from data provided by Canadian White 8 Cycling Association Silver 5 Yellow 2 A" others I 16 I Animal speeds and bicycling Source: Bicycle Market Research Institute Speeds

U.S. bicycle sales (in * millions) I - Human - - ^- 245

^ 152 -

L_ * 1_ Human bicycling 245 152 Domestic shipments Imports behind a car

Type of bicycle 1980 1989 1980 1989 Cheetah 101 63 -y -. - r 3.7 ^ ö"t 2.3

ñ 0 TI 1.5

- "ec' kangaroo 72 45 Twenty-inch 3.7 ^ 2.3 ö"t ñ 0 TI 1.5 Racehorse 69 43 ru tu on li i7 o o Greyhound 68 42

Other I 01 I 19 I °3 I 15 Giraffe 51 32 Source: Adapted from data provided by the Bicycle Human bicycling 50 31 Manufacturers Association of America 'or ̂ nour

- 1 Human running 42 26 r^ ; - : ; rr~. ; 1 ElePhant 39 24 Sizes of tricycle and bicycle Blue whale 37 23 wheels (diameters in inches) Lizard 29 is

Bee 18 11 Standard tricycles: 1 0# 1 2, 1 3f 1 6 Penguin (in water) 1 3 8 Big Wheels™: 11,11^,13,16, 1 ' Bicycles: 1 0, 1 2, 1 6, 1 8, 20, 24, 26, 27 Source: Guinness Book of Essential Facts




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