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ORC Resource Number #394
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Paper Pool: Analyzing Numeric and Geometric Patterns
Best Practice
PROFESSIONAL COMMENTARY

Paper Pool is played with an imaginary ball being hit from the lower left-hand corner of a rectangular grid (pool table) at a 45° angle. A ball hit at this angle will bounce off the side rails of the table at a 45° angle and will traverse the diagonals of the squares in the grid. In these lessons, students experiment with tables of different dimensions to predict the pocket into which the ball will fall and the number of hits as the ball bounces back and forth across the table. They also investigate the number of squares crossed and the total distance travelled. All of these relations depend upon the lengths of the sides of the pool table. Finally, they analyze the paths of the ball for line and rotational symmetry. Students may use a pool table applet to collect data and look for patterns. Activity sheets, questions for students, assessment options, and ideas for teacher reflection are included. Paper Pool is an application involving factors, multiples, similar rectangles, and the relation of being relatively prime. Paper Pool is based on the Comparing and Scaling unit of the Connected Mathematics Project. (author/sw)

OHIO STANDARDS
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Mathematics Academic Content Standards
Number, Number Sense and Operations Standard
Geometry and Spatial Sense Standard
Patterns, Functions and Algebra Standard
Mathematical Processes Standard
NATIONAL STANDARDS
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Principles and Standards for School Mathematics
Number and Operations Standard
Algebra Standard
Geometry Standard
Connections Standard
RESOURCE TYPE
Instructional Resource
PRACTICE LEVEL
Best Practice
STANDARDS ALIGNMENT
Grades 6–8
TOPICS
Mathematics --
Numbers and Operations;
Number theory;
Algebra;
Patterns, sequences;
Geometry;
Symmetry, transformations;
Congruence, similarity;
Connections, applications;
Technology;
KEYWORDS
angle of incidence;
angle of reflection;
similar rectangles;
applet
Publisher: National Council of Teachers of Mathematics
Author: Brian Keller