Pool Pockets Case Study

Pool Pockets POW BY: Khushi Patel & Natalie Wolschlager.

Problem Statement:
You are launching a ball from the lower-left corner of a pool table at a 45 degree angle. Both the height and the width of the table are whole number dimensions and the pool table is always a rectangle. The only pockets are those in the four corners. Which pocket does the ball hit? How many times does it bounce before it hits the pocket?
Process:
We made rectangles on the graph paper to find the number of rebounds of the dimensions. Then we started doing 1 by X graphs and finding the rebounds for that. Then the 2 by X graphs, and the 3 by X graphs. After that, we found patterns for each by X graph. After figuring out patterns, we sent out spies to other groups to help get the overall formula. The formula that we found was: L+(H-2). We tried them on different rectangles, but the formula didn’t work for all of them. So then we tried fixing it by tweaking it. We then noticed that the rectangles with the same scale factor had the same number of rebounds. After noticing this, we added this to our formula, creating:Let X/Y=L/H,where X/Y is the reduced ratio. The rule is (X + Y ) - 2. We tried that on multiple rectangles with different number dimensions. Then we found out that it did work on all of them and that we had found the super formula!

The rule is (X+Y)-2. Here are some examples of the generalization being used:

SElf Assessment:
Rubric:
Problem Statement
Process
Solution
Self Assessment
LA
Includes all necessary information.(2 points)
3 pieces of evidence and explanation, showing what you did to solve the problem.
(3 points)
Correct answer, proof and generalizations. (3 points)
Rubric, percent grade using the rubric, and math learned
(3points)
Contains no grammatical or spelling errors.
(1 points)

PS 2/2
Process 3/3
Solution
3/3
SE 3/3
LA