The interactive paper pool game provides an opportunity for students to develop their understanding of ratio, proportion, greatest common denominator and least common multiple. This investigation includes student resources for the Paper Pool project, preparation notes, answers, and a holistic-by-category scoring rubric with guidelines for how it can be used to assess the project. Samples of two students' work and a teacher's comments accompany the suggested rubric.
In this investigation, students are asked to play a game called Paper Pool. The game is played on rectangular square-grid tables, 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 encounters a pocket. Pockets are located at each corner.
Students are asked to predict at which pocket the ball will stop and how many hits will occur by the time the ball comes to a stop. To do this, students will need to investigate several Paper Pool table sizes. Finding a solution will require them to recognize relationships between rectangles whose sides have the same ratio.
Math Content
- Gather and organize data
- Search for patterns
- Recognize similar rectangles; that is, realize that side lengths are in the same ratio
- Use the simplest ratio to predict the stopping pocket and the number of hits
Individual Lessons
Lesson 1 - Paper Pool Game The paper pool game provides an opportunity for students to develop their understanding of ratio, proportion, greatest common divisor, and least common multiple. Lesson 2 - Explore More Tables The interactive paper pool game in this i-Math investigation provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. Lesson 3 - Look for Patterns The interactive paper pool game in this i-Math investigation provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. Lesson 4 - Going the Distance The interactive paper pool game in this i-Math investigation provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple.
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