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

Explore More Tables

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

For now, focus on answering these two questions:

In what corner will the ball stop?
How many hits will have occurred by the time the ball stops?

Each question is asking you to find out what happens to a ball as it travels on the Paper Pool tables.

Use the interactive pool table below to explore the results for different Paper Pool tables. Record your data into a table with three columns like the one below. You may want to enter your data into a spreadsheet or other similar data tools for later analysis. Remember to record the dimensions of the pool table in the form bottom edge x side edge.

Table Dimensions	Number of Hits	Corner
6 x 4	5	D
4 x 4	2	C
4 x 2	3	B

You will need to examine more tables to test your ideas about where the ball will stop and how many hits will have occurred. When you think you can predict the outcomes, write rules that you could use to determine what will happen with different size pool tables.

Questions for Students

Are there any situations in which you know for sure the ball will land in pocket B? in pocket C? in pocket D?
You may have observed that the ball never lands in pocket A. Will this always be so? Explain your thinking.
Suppose you were to play Paper Pool on a table of size 150 by 300. Can you predict where the ball will land? How many hits will occur?

Teacher Reflection

Tailor the project to meet your needs:

Decide the extent of the project you wish students to investigate. If you wish to see how your students organize data, do not hand out the record sheet or have students go through the next page Look for Patterns which helps students to organize their data. Click here for sample data organized by pocket and number of hits.

Decide if you want students to answer the question of how far the ball travels in diagonal units. Students will need to create a new record sheet to explore this question effectively. This gives students a second chance to organize data. If so, you can have them do Part 4: Go the Distance

If students were guided through the first organization, then this question provides an opportunity for them to organize and present their data. You may want to make the presentation of the data for the dimensions and path length explicit in the assignment.

NCTM Standards and Expectations

Data Analysis & Probability 6-8

Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.
Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population.

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.