## Design a Track © February 2000

Susan Boone
GirlTECH '95 Participant, Master Teacher '96, '97, 99
Subject:  Algebra 1

Topic:  Multiplication of Polynomials (Geometry Integration) Proportions (scale models)

Purpose:Students will investigate track and field dimensions. Using the information gathered from this information, they will determine a general rule for marking the starting points for the 220 yard (or 200 meter) and the 440 yard or (400 meter) race. Using this general rule, they will then measure an actual track, compare their general rule to the actual dimensions and construct a scale model.

Materials:  Internet connection, yard (meter) sticks, surveyors' wheel, poster board, rulers. An AAU (Amateur Athletic Union) handbook would be beneficial.

Prior knowledge:  Students should be proficient with measuring to the nearest inch using a yard stick, or centimeter using a meter stick. Students should have a basic understanding of dimensional analysis and a command of the distributive property applied to variables.

Description:  The runners in a 220-yard dash race around the curved part of a track. If the runners start and finish at the same line, the runner on the outside lane would run father than the other runners. To compensate for this situation, the starting points of the runners are staggered. If the radius of the curve of the inside of lane 1 is x , and each lane is 1.22-1.25 meters or 4 feet wide, determine the starting point for the runners in the two inside lanes of the track. Students should collect their own data to determine the other dimensions of a track. Options include actually measuring a track on campus, or visit a Track Construction Diagram. Using this information, they will construct a scale model (1cm/1yd (or meter) ) on a poster board.

Time:  Two class periods (one for data collection and one to determine regression), plus time to construct scale model. (This is a home assignment for my students.)

Procedure: Students will collect data to determine the dimensions of the track used in track and field events. This can be accomplished by taking students to an actual track, or by searching http://www.ustctba.com/diagram_track.html. Students should be encouraged to search other web sites that may contain data on related track and field events. If students are going to actually measure a track, assign groups of four equipped with yard/meter stick.
Groups should be assigned to measure the distance:
1. around the track using the inside of lane one
2. the distance of the straight part of the track on each side
3. the distance across the straight parts of the track
4. the width of each lane
5. the distance between the starting points for the 220yd/200m dash.
Use these measurements to determine the appropriate measurements of the track using the scale 1cm/1yd/(meter). Draw a model of the track on a poster board. (The model should fit nicely on one/half of a poster board).

Activity:  Work in groups of four. Spend about five minutes investigating the measurements needed to construct a scale drawing of the track.  Measure the assigned part of the track, record data and collect measurements from other groups. (OR)
Research the following site http://www.ustctba.com/diagram_track.html and record the measurement for each of the following.

1. Distance in feet/meters around the track using lane one.
2. Distance of the "home straight".
3. Width between the straight parts of the track.
4. Width of each lane.
5. Distance between staring points for the 200m/220yard dash.
Make a scale drawing using these measurements. Your track should be made to the scale of 1cm/1yd(meter). Use the dimensions recorded on your data sheet to calculate the appropriate measures. Be sure to show the work for your calculations. (this is a nice place to use dimensional analysis).

Reference:  Glencoe, Algebra 1 Chapter 9, Section 6
These pages were developed through GirlTECH , a teacher training and student technology council program sponsored by the Center for Research on Parallel Computation (CRPC), a National Science Foundation Science and Technology Center.
Copyright February 2000 by Susan Boone

Thanks to the RGK Foundation for its generous support of GirlTECH.