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Activity I: Will Women Athletes Ever Catch and Surpass Their Male Counterparts? (Grade Level 5-8)

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Standards

Standard 2: Patterns, Functions, and Algebra
Standard 5: Data Analysis, Statistics, and Probability
Standard 9: Connections

Objectives

  • read, interpret, and reason from graphic representations
  • fit straight lines to data
  • determine the equation of a line
  • determine the point of intersection of two straight lines
  • find the y-value of an equation for a given x-value.

adobe acrobat Student Activity (PDF File)
Answers (PDF File)

Activity I

The following graphs are the simultaneous plots of the Olympic records for men and women in the same event over the same years.

sport

sport

  1. Explain why the plots for the 100-meter freestyle decrease while the plots in the high jump graph increase.
  2. Judging from the graph, does it appear that the women will ever jump as high as the men jump in the same year? Explain.
  3. Judging from the graph, does it appear the women and men will ever swim the 100-meter freestyle in the same record time in the same year?
  4. Draw straight lines on the high jump scatter plots, find their equations, and use that information to support your arguments from problem 2.

     

    1. Draw straight lines on the freestyle scatter plots, find their equations, and use that information to support your arguments from problem 3.

    2. Use the equations of the lines created in problem 5 to determine the year when the women will swim the 100-meter freestyle in the same time as the men. What is that predicted time?
    3. Do you think that the solution to problem 5 is a possible achievement? Explain your reasoning.

     

    *This activity could be modified for an elementary level by eliminating problems 4-7. This activity could also be modified for upper level students. Have students determine if they find the "best" fit lines in problems 4 - 7 to be least squares linear regression lines. Then have them determine a model with a "better" fit and write a supporting argument for their choice.