The interactive Paper Pool game provides an opportunity for students to develop their understanding of ratio, proportion, greatest common denominator and least common multiple.
In this investigation, students are asked to play a game called Paper Pool. The game is played on rectangular grids made of congruent squares, such as the one shown here.
An imaginary ball is hit from the lower left-hand corner (labeled A) at a 45° angle. A ball hit in this way will bounce off each side it hits at a 45° angle. The ball continues to roll until it reaches a pocket located at one of the corners.
Students will predict the pocket at which the ball will stop and how many hits will occur.
The Paper Pool unit was adapted with
permission and guidance from the Connected Mathematics Project.
Individual Lessons
Lesson 1 - Learn the Game
In the following lessons of this unit, students will have an opportunity to fully explore the patterns that result from the Paper Pool game. In this lesson, however, students will only spend time learning the rules, playing the game, and collecting data.
Lesson 2 - How Many Hits?
Students will continue their investigation of the Paper Pool game by exploring more tables and organizing the results. Using the data that they collect, they will attempt to find a relationship between the size of the table, the number of hits that occur, and the pocket in which the ball lands.
Lesson 3 - Graphical Representations for the Number of Hits
Finding a rule for the number of hits is only the first step in exploring the Paper Pool game. Students can gain a deeper understanding of the patterns by considering graphical representations of the results.
Lesson 4 - Which Pocket?
In this lesson, students continue their investigation by discovering a rule to predict the pocket in which the ball will land. As an extension, students can also consider the number of squares that a ball crosses while traversing its path.
Lesson 5 - Wrapping It Up
In the first four lessons of this unit, students investigated the Paper Pool game, collected data, identified patterns, and made predictions about the number of hits, the pocket in which the ball lands, and the path of travel. In this lesson, students finalize their work and write a report that summarizes all of their findings.
