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Williams, Barbara Cook Elementary School
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.
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.
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.