This is the first part of a four-part project. We recommend that students work on this project with a partner. One class period will be needed for pairs to collect their data. They can continue to investigate the task and draft their reports outside of class. Part of a second class period could be used for comparing results and finalizing reports. You may want to have pairs or individuals share their results in a class summary of the
project.
Introduce the Paper Pool game to your class with the following description:
Marisa created a game called Paper Pool. Her pool tables were rectangles drawn on grid paper. The pockets at each corner were labeled A (lower left), B (lower right), C (upper right), and D (upper left). Marisa described each table by its size, giving the horizontal length first and the vertical height second. The figure below shows a 6 × 4 table.
How to Play Paper Pool
- 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 ensure that all students understand how the game is played, launch the Paper Pool game. (This particular version of the game will show only a 5 × 3 table.) Alternatively, you can use a transparency of the Introduction to Paper Pool to discuss the rules with your students.
Try It!
Allow students to play the Paper Pool game with 4 × 2 and 4 × 4 tables. Ask students, "In which pocket does the ball land on each table?"
On each of these tables, allow students to explore the applet by adjusting the controls to the right. Have students change the speed and check or uncheck some of the boxes. Although you do not want to devote a large amount of time to teaching students how to use this tool, it is important that they understand the features. The better students understand this tool, the more efficient they will be when exploring later in this unit. In particular, they will be able to perform more investigations if they increase the speed.
Set up the rest of this unit by saying the following to students:
After designing Paper Pool and playing several games on tables of various sizes, Marisa wondered about two things.
- Is there a way to predict the pocket at which the ball will stop?
- Is there a way to figure out how many hits will occur?
In the rest of this unit, you will perform investigations and try to answer her questions.
Students can continue their investigations of other Paper Pool tables by proceeding to the next lesson, Explore More Tables, or by completing the Paper Pool Tables activity sheet.
