Illuminations: Paper Pool: Analyzing Numeric and Geometric Patterns

# Paper Pool: Analyzing Numeric and Geometric Patterns

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.

### NCTM Resources

Principles and Standards for School Mathematics

 More and Better Mathematics for All Students
 © 2000 National Council of Teachers of Mathematics Use of this Web site constitutes acceptance of the Terms of Use The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. The views expressed or implied, unless otherwise noted, should not be interpreted as official positions of the Council.