Unit 2 WebQuest - Internet Project

The Spirit of the Games

Introduction | Task | Process | Guidance | Conclusion | Questions

Introduction
The first Olympic Games featured only one event–a foot race. In 2004, the Olympic Games featured thousands of competitors in about 300 events. The 2004 summer games were held in Athens, Greece. Did you know that a swimmer from California, Natalie Coughlin, won five medals? No woman from the U.S. has won more medals. The table below shows her events and times in Athens.

     In this project, you will explore how linear functions can be used to represent times in Olympic events.

The Task
In your new job as a sports writer for a local newspaper, you have been assigned to write an article comparing men's and women's times in a timed Olympic event. Your article needs to contain the following information:

• a brief history of the event including the names of participants that were well-known or in some way unique, and anything unusual that may have happened over the years;
• the winning times for men and women in the same timed event, such as a swimming or a running event;
• graphs of the times over the years for the event;
• a prediction for whether the men's and women's time will ever be approximately the same.

• Find data about timed Olympic events. For help, try these Web sites.
  www.hickoksports.com/history.shtml
  www.usolympicteam.com
  www.infoplease.com
  www.olympic-usa.org
  http://www.la84foundation.org/
  www.usatoday.com/sports/olympics/athens/team-usa.htm
• Make a table of the years and winning times for men and women in the same event.
• Make appropriate graphs to display the winning times.
• Research the history of the event to find any famous or unique people who have won the event over the years.
• Devise a method for determining whether the men's and women's times will ever be approximately the same in the event you chose. Include an explanation of your method in your article.
• Be creative. Add some additional data, information, or even pictures to your newspaper article.

1. How have the winning times for the event you chose changed over the years?
2. When do you think the times will be at the lowest? Is there a limit to the length of time needed to complete the event?
3. How do timed events differ from other Olympic events?
4. Have the Olympics always been held every four years? Why or why not?

• Present your article to your school newspaper for publication, if possible.
• Present the information on a Web page. Have other students critique your project and help you to make improvements to your project.
• Compile all of the articles from your class into a newspaper. Publish it using desktop publishing software.

Lesson 3–2
The table shows the winning times, in seconds, for the women's Olympic 400–meter freestyle swimming event.

1. To make graphing easier, change the year to Years Since 1924. So, 1924 will be 0, 1928 will be 4, and so on. Write the ordered pairs (years since 1924, winning time).
2. Graph the ordered pairs.
3. Is the relation you graphed in Question 1 a function? Explain why or why not.

1. Draw a line of fit for the scatter plot of the data, where x represents the years since 1924 and y represents the winning times in seconds.
2. Write an equation for a line of fit.

1. To make graphing easier, change the year to Years Since 1924. So, 1924 will be 0, 1928 will be 4, and so on. Make a scatter plot of the ordered pairs (years since 1924, winning time). Draw a line of best–fit for the data.
2. On the same coordinate plane draw the line of best–fit for the women's winning times you graphed in the Exercise in Lesson 4–6.
3. Will the winning times for the men's and women's events ever be approximately the same? Why or why not?
4. If the times will be about the same, in what year would that be?

The graph shows the winning times for the women's Olympic 200–meter butterfly. An equation for the best–fit line is y = -0.4x + 139.

1. Write an inequality for all points that lie below the best–fit line. What does this inequality represent?
2. Write an inequality for all points that lie above the best–fit line. What does this inequality represent?

TEACHER NOTES

In this project, students will research winning times in Olympic events over the years. Students will need to use events that are timed for this project, as that is the only type of event that can be approximated by a linear function. You may want to have students compare several events, say a 100-meter event and a 400-meter event, to see how the speed of the racers changes over the course of longer events. Students may want to use a graphing calculator or graphing software to analyze the winning times.

The Guidance section of the Cross Curricular Project contains questions that would be good for a whole-class discussion and for providing interdisciplinary connections. If you prefer, have each student research one of the questions and add the information they find to the final presentation of their Cross Curricular Project.

Several Web sites are included in the project to help students in completing this Cross Curricular Project. Encourage students to find additional sites and to share those sites with other students.

Students will work on this project in Unit 2.

Lesson	3–2	4–6	5–1	6–7
Page	153	231	257	337

ANSWERS
Lesson 3–2

1. (0, 362.2), (4, 342.8), (8, 328.5), (12, 326.4), (24, 317.8), (28, 312.1), (32, 294.6), (36, 290.6), (40, 283.3), (44, 271.8), (48, 259.44), (52, 249.89), (56, 248.76), (60, 247.10), (64, 243.85), (68, 247.18), (72, 247.25), (76, 245.80), (80, 245.34)
2. 
   
3. Yes; for any given value of x, there is only one value for y on the graph.

1. 
   
2. Sample answer using the graph in Question 1: y = –1.4963x + 345.67

1. (0, 304.2), (4, 301.6), (8, 288.4), (12, 284.5), (24, 281.0), (28, 270.7), (32, 267.3), (36, 258.3), (40, 252.2), (44, 249.0), (48, 240.27), (52, 231.93), (56, 231.31), (60, 231.23), (64, 226.95), (68, 225), (72, 227.97), (76, 220.59), (80, 223.10)

2. 
   
3. Yes; it appears that the lines would cross if extended past 76 years since 1924.
4. Sample answer: The times will be the same in about 106 years, or the year 1924 + 106 = 2030. However, if the pattern of years continues for the Olympic Games, there will not be games in 2030, but there will be games in 2032.

1. y < -0.4x + 139; These points are times that are less than the winning time as given by the best-fit line.
2. y > -0.4x + 139; These points are times that are greater than the winning time as given by the best-fit line.