## 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.

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 |

- Computer and Internet connection
- Handouts

**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?

### Paper Pool Game

### 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

### 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

### Common Core State Standards – Mathematics

Grade 6, Ratio & Proportion

- 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.''

Grade 8, Stats & Probability

- CCSS.Math.Content.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Grade 6, The Number System

- CCSS.Math.Content.6.NS.B.4

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

### Common Core State Standards – Practice

- CCSS.Math.Practice.MP8

Look for and express regularity in repeated reasoning.