Analyzing Rich Eisen’s 40 Yard Dash

Posted: November 19, 2010 in Uncategorized

Since state testing is going on this week, my Algebra 2 first block class was ahead of the other class.  I decided to take on one of Dan Meyer’s WCYDWT problems and see what the students came up with.  To set the stage, we first looked at a Jacoby Ford video where he takes it 94 yards for a touchdown.  We talked about a common football player benchmark, the 40 yard dash. 

Video:

We paused it at about 1:37 and the students came up with questions that they had towards the video. 

They came up with a list very fast.  We decided  to analyze the speed at Rich Eisen was running.  The question we started with was

“How fast is Rich moving?”

Sub-Questions:

“How can we measure speed if it is changing?”

“How long should the distance intervals be?”

“How can we minimize error in our calculations?”

Students decided we would need stopwatches.  Luckily I had a box of them =)  Students got into groups and we decided to give each of them different 10 yard intervals to analyze.   We replayed the video and about 20 stopwatches went to work.

Our data:

Students got 4 times for each interval and decided taking an average of these was a good idea.  Next they needed to figure out how to change it to miles per hour which we decided before would be our units.  They went through the unit conversions and put their answers on the board. 

We also put up a distance vs. time graph from our data:

 

Questions:

“What do you think the graph will look like”  (asked before we graphed it obv)

“How would the graph continue if it were 100 yards? 200 yards? ”

“How long does it take for a typical athlete to reach top speed?”

“What would it look like if Rich truly ran like our graph?”

“How is the slope changing?”

“How would this graph compare to Jacoby Ford’s graph?”

“Sources of error?”, “How can we improve?”

“If given a 5 yard head start, where would Rich and Jacoby’s graph cross?”

“What type of function best reprents the start and end of his run?”

Conclusion:

As we watched the ending part of the video, students became very interested to see the reults.  We noticed that when we stopped the video after the 10 yard mark the speed was higher than our interval speed so we got to have a discussion on average vs. instant speed.  How could we get our average speed closer to the instant speed?  Little did they know, the students started thinking about a Calculus topic.  The students and our discussion came up with more questions than we could handle, which was a good thing.  Props to Dan Meyer for the idea.

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Comments
  1. Dan Meyer says:

    Thanks for posting the results of your investigation. It’s always useful for me to see how other teachers use these things. I’m subscribing to your work here and I hope to find you blogging more.

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