Paper Pool

Williams, Barbara Cook Elementary School

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.
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