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**Department of Mathematics Education**

Indianapolis 500

The average speeds at the Indianapolis 500 auto race
over the years can be modeled by a linear equation. Students are asked to make a scatter plot of
the speeds for selected years and approximate a line of best fit. Then they research a different set of data
and find a linear equation that models it.

To motivate the students, discuss the data for the Indy 500
race. Ask students what accounts for the
obvious increase in speed over the years.
Encourage students who are familiar with automobile racing to share some
of their technical knowledge.

Ask students what they envision for the future. Do they think the speeds will increase
steadily? Do they think there will come
a time when the speeds will level off?
Do they think some technological advance will cause a dramatic increase
in speeds?

## Directions

You can have students can work in pairs. For questions 1-4, each student should draw
the scatter plot and determine a line of best fit. The partners can then compare lines of best
fit to see how closely they match. Why
is theirs different from their partners? Stress the
fact that when using this technique, the lines of best fit are
approximations. There is no one right
answer. They can use the Internet
to find the actual speed of the 2000 race.

Using the calculator
is optional. In higher classes, the
students should be familiar with the graphing calculator. In lower classes, this would be a good way to
introduce it. For
question 5, the students can work together to determine the correct calculator
procedure for finding the regression equation.
Be sure the students understand that the calculator uses a well-defined
algorithm, so this time, there will be only one right answer.

This problem has many aspects you can go into, slope,
y-intercept, equation of a line, and use of technology. It also has many entry and exit points.

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