Paper Pool

Williams, Barbara                      Cook Elementary School
                                       962-2915
                           
Objectives:

Students will:  recognize rectangles whose sides have the same ratio; 
use the concept of common factor to find rectangles with the smallest 
area having a given ratio of sides; practice organizing data and 
looking for patterns; use the concept of common factor and a parity 
check to predict the behavior of a ball on a pool table; final corner; 
number of hits. 

Apparatus Needed:  

Students will need a ruler or straight edge and a pencil for this 
activity.  Worksheets used in this activity are taken from the Middle 
School Math Project, "The Mouse and the Elephant" book, published by 
Addison-Wesley Publishing Company, 1986.  Paper Pool is an application 
of many concepts: factors, multiples, rectangles and the relationship 
of being relatively prime.  Before seeing how to apply these concepts, 
students must gather and organize data, then search for patterns.  

Recommended Strategy:

Paper Pool is played with an imaginary ball being hit from the lower 
left-hand corner marked A, at a 45 degree angle.  A ball hit in this 
way will bounce off the sides at a 45 degree angle.  Also, if a grid is 
placed on the table, the ball always traverses on diagonals of the 
squares of the grid.  Students first learn how to predict the pocket 
into which a ball will fall and the number of hits as the ball crosses 
the table.  Students further develop their analytical skills by 
investigating the number of squares crossed.  All three relations 
depend upon the lengths of the sides of the pool tables.