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# Comparing and Scaling: Paper Pool Students investigate the pattern of bounces for a pool ball as it makes its way around pool tables of various dimensions. As you might expect, ratio and scaling are involved in this Project. For a pool table with given dimensions students predict the number of times the ball “hits” the sides of the table and which of the four pockets it will fall.

## Students Goals

• Gather and organize data
• Search for patterns
• Recognize rectangles whose sides have the same ratio
• Use the simplest ratio to predict the stopping pocket and number of hits

## Materials Needed to do the experimentation with paper & pencil

• This project is a good summary of the proportional reasoning that students have been working on throughout Grade 6 and Grade 7.

## Possible CCSS

#### Ratios and Proportional relationships 6.RP

Understand ratio concepts and use ratio reasoning to solve problems.

1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

a. Make tables of equivalent ratios relating quantities with whole- number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

b. Solve unit rate problems including those involving unit pricing and constant speed.

#### Statistics and Probability 6.SP

Develop understanding of statistical variability.

#### Ratios and Proportional relationships 7.RP

Analyze proportional relationships and use them to solve real-world and mathematical problems.

1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

2. Recognize and represent proportional relationships between quantities.

a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

c. Represent proportional relationships by equations.

3. Use proportional relationships to solve multistep ratio and percent problems.