Illuminations: Paper Pool: Analyzing Numeric and Geometric Patterns

Paper Pool: Analyzing Numeric and Geometric Patterns

Unit Overview

Lesson 1

Lesson 2

Lesson 3

Lesson 4

Look for Patterns

The interactive paper pool game in this i-Math investigation provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple.

Learning Objectives

Students will

gather and organize data
search for patterns
recognize rectangles with sides in the same ratio (similar rectangles)
use the simplest ratio to predict the stopping pocket and the number of hits

Materials

Computer and Internet connection
Handouts

Instructional Plan

When you think you can predict the outcomes, write rules that you could use to determine what will happen to the ball as it travels on a table of any size. Your rules should tell you, without drawing the path, the number of hits and the ending corner for the ball.

Reorganizing the data is sometimes a useful technique to see patterns in the data. Sort or regroup the data first by the corner (pocket) where the ball stops and then by the number of hits.

If you are using a spreadsheet tool, frequently, this can be done by sorting columns. Sort the data first by the corner in which the ball lands and then by the number of hits.

If you are working with the data by hand, you may want to create a new table such as the one below. A few entries have been added. Remember to record the dimensions of the pool table in the form bottom edge x side edge.

Results for Paper Pool Tables of Different Sizes

Corner where ball stops.	Total Number of Hits Including Start and Finish
Corner where ball stops.	2	3	4	5	6	7	8	9	10	11
B		4 x 2
C	4 x 4
D				6 x 4

Questions for Students

What patterns do you observe in the table? Which of these patterns may be useful in predicting the outcome for a Paper Pool table of any size?
Examine the dimensions for all pool tables where the ball lands in the same corner with the same number of hits. What do you observe?

Click here to for additional questions to explore

Assessment Options

Answers

NCTM Standards and Expectations

Data Analysis & Probability 6-8

Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit.
Use conjectures to formulate new questions and plan new studies to answer them.

This Paper Pool Table Investigation adapted with permission and guidance from:

Comparing and Scaling: Ratio, Proportion, and Percent, Connected Mathematics Project, G. Lappan, J. Fey, W Fitzgerald, S. Friel and E. Phillips, Dale Seymour Publications, (1998), Paper Pool Project, pp.106-111.