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.
Assessment Option
Look at Sample Record Sheet in the Handouts
Extension
Move on to the last lesson, 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.
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
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.