The Pythagorean Theorem and Sports.

How many times have you taught the Pythagorean Theorem using the standard triangle, drew the squares to show it all works out, or you've had them draw a standard triangle like a 3-4-5 or 12-5-13 on a piece of paper.  Next, they've drawn square off the legs, color them before cutting them out and placing them inside the drawn square for the hypotenuse?

Instead of talking about ladders stuck up against a multi story building, lets apply it to football, a topic most males in your classroom can relate to.

The National Science Foundation created a wonderful three to four minute video designed to show people how the Pythagorean Theorem is used to calculate the angle of pursuit taken by a football player who wants to tackle the guy with the ball.  Sorry, I don't watch football so I really don't know all the names of the positions.

Picture this is you will.  The receiver catches the ball and starts running in as straight a line as he can down the field.  The person who needs to tackle him is about 30 fyards to the right.  He runs in a diagonal so he can tackle the receiver at around the 40 yard mark.  Using the Pythagorean theorem, he'll have to run about 50 yards to intercept the receiver and tackle him.  The video is well done and shows students how this works.

This site provides a written explanation of the material on the video. The nice thing about a written explanation, is students have a chance to practice reading for information which meets a reading standard.

In addition,  a researcher discovered that this same theorem could be used to predict a teams expected wins based on the number of runs scored and the number of runs they allowed.  Think of it this way:
Expected wins = (Number of runs scored)^2/(number of runs scored)^2 +(number of runs allowed)^2.  This is referred to as the Pythagorean Expectation.

It works this way.  Say the Dodgers scored 720 runs while allowing 640 runs.  You square the 720 for 518,400, then square the 640 for 409,600 and add the two numbers together for 928000.  Now we have 518,400/(518,400 + 409,600)  or 518,400/928,000 = .558.  So the Dodgers should win 55.8% of their games over the season.  This means if they played 170 games, they should win 95 of their games.

Furthermore, the application of the Pythagorean Theorem in Baseball is used to determine how far the second baseman has to throw to home or third base has to throw to third.  The baseball diamond is 90 feet from base to base so that makes it easy to calculate the distances.  If you'd like to do an activity on Baseball, this site has the worksheet and answers one could easily use in the classroom.