## Paper Pool

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

### How it Works

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.

### How to Play

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.

### Options

**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.

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?