## Look for Patterns

6-8
1

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.

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 2 3 4 5 6 7 8 9 10 11 B 4 x 2 C 4 x 4 D 6 x 4

### Reference

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.

• Computer and Internet connection
• Handouts

Assessment Option

Look at Sample Record Sheet in the Handouts

Extension

Move on to the last lesson, Going the Distance.

Questions for Students

1. 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?
2. 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?

### Paper Pool Game

6-8
The paper pool game provides an opportunity for students to develop their understanding of ratio, proportion, greatest common divisor, and least common multiple.

### Analyzing Numeric and Geometric Patterns- 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.

### Going the Distance

6-8
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.

### NCTM Standards and Expectations

• 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.

### Common Core State Standards – Mathematics

• CCSS.Math.Content.6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, ''The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.'' ''For every vote candidate A received, candidate C received nearly three votes.''