Illuminations: Paper Pool

# Paper Pool

This applet allows you to investigate the game of Paper Pool.

### Instructions

 The game of Paper Pool is played by hitting a ball from a corner. The ball then bounces around the table until it lands in a pocket. The lower-left corner is always corner A, and the labeling continues counterclockwise with B, C, and D. The ball always starts in corner A. The ball is hit with an imaginary cue (a stick for hitting a pool ball) so that it travels at a 45° diagonal across the grid. If the ball hits a side of the table, it bounces off at a 45° angle and continues its travel. The ball continues to travel until it hits a pocket. To put the ball in motion, click anywhere on the table. Click anywhere on the table again to reset. The sliders for Length and Width adjust the size of the table. The slider for Speed indicates how fast the ball will travel. The other options work as follows: Show Trace - Shows the path of the ball. Show Grid - Divides the table into square units. Pool Table - Shows a pool table background. Count Hits - Counts the number of hits a ball makes before landing in a pocket. Sound - Turns the sound on/off.

### Exploration

 Explore tables of various size. How many hits occur before the ball reaches a pocket? And how is the number of hits related to the size of the table? When the applet first opens, a 5 × 3 table is shown. Click anywhere on the table to see how many hits occur and the pocket in which the ball lands. Adjust the Width to create a 5 × 4 table. For this table, how many hits occur and in which pocket does the ball land? Make a prediction: How many hits will occur and in which pocket will the ball land on a 5 × 5 table? Adjust the dimensions and test your prediction. Were you correct? Continue to adjust the Length and Width to explore tables of other sizes. What happens if the Length and Width are equal? What happens if the dimensions are reversed? For example, how does a 5 × 3 table compare to a 3 × 5 table? Can you find a general rule that will allow you to predict the number of hits and the pocket in which the ball will land for any size table?

### Lessons

 More and Better Mathematics for All Students
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