Activity: Billiard Paths Student Page
Below is an unusual billiard table. The dimensions are determined by the lengths of the sides. When you click on the green flag a yellow ball will start to roll at a 45 degree heading and bounce off the opposite sides until it ends up in a corner. The computer will then tell you how many bounces the ball made and in what corner it wound up in.

Your Challenge: See if you can come up with a way to predict 
(1) what the number of touches will be for any given size billiard table and (2) which corner the ball will end up in.

An example (4x7 table) is done for you (above). Try the others using the Scratch tool* and see what you get.

 
W
L
Touches
Final Corner
4
7
 9
 Upper Right
8
3
    
5
4
    
10
13
    
 5
 10
    
       
       

Try other number combinations.
See what conjectures or conclusions you come with.
(Use the data sheets to help you collect more data.)

*The NCTM Illuminations paper pool app currently has a problem. Until it is fixed use this Scratch tool instead.