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Grade: Middle
Subject: Mathematics

#3667. Baseball Relationships - Using Scatter Plots

Mathematics, level: Middle
Posted Sun Feb 12 17:05:05 PST 2006 by Lance Curry (curryls@pickens.k12.sc.us).
Easley High School, Easley, SC, USA
Materials Required: Paper, Pencil, Graphing Calculator
Activity Time: 50 - 60 mins
Concepts Taught: scatter plots, slope, intercept, linear equation, regression

1) Algebra I CP
2) Baseball Relationships – Using Scatter plots
3) Goal(s)
Having a grasp on the concept of slope as rate of change and determining slope and intercepts from graphs, tables, and algebraic representations are big ideas for Algebra 1. Also, interpreting the meaning of slope and intercepts in different situations including real-life situations is key to a student’s total understanding of those concepts. Using real-life situations can help the students enjoy mathematics more which is an affective goal for my class.

4) Objectives
Students will improve in their knowledge and skills in the following:
• Use data sets to determine functional (systematic) relationships between quantities. (IA2)
• Represent relationships among quantities using tables, graphs, and equations including representations involving spreadsheets and graphing calculators. (IA4)
• Represent, display, and interpret data using scatterplots including representations on graphing calculators and computers. (IB4)
• Write a linear equation that fits a data set, check the model for “goodness of fit,” and make predictions using the model. (IB5)
• Develop the concept of slope as rate of change and determine slope from graphs, tables, and algebraic representations. (IIB1)
• Interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs. (IIB2)
5) Materials Required
Students need to bring:
Paper
Pencil
I, the teacher, will provide graphing calculators for the students, use the computer with projection screen, and the dry erase board.
6) Procedures
• Focus (approx. 5 mins.)
I will first start off the class talking about the recent events in the baseball playoffs (i.e. a homerun to win the game). Then I will pose the question: Does the number of homeruns hit during the regular season affect a team’s winning percentage?
• Exploration (approx. 10-15 mins)
I will first let the class speculate on the question, receiving their feedback and discussion of the problem, and then I will show in Excel the data that I have collected for the students to analyze and ask them to construct a scatter plot with a graphing calculator (data can be found at http://www.espn.com/ or http://www.baseball-reference.com/ ). I will lead the class in setting up the calculators to graph the data and find a line of best fit. Have someone use the overhead calculator to draw the graph and regression line and outline it on the dry erase board.
• Discuss (approx. 25 mins)
Lead a classroom discussion in which the following topics are addressed:
• Talk about the term winning “percentage” and lead the class to refine the term to winning ratio.
• Discuss the equation of the line
• Determine the slope and what it means
• Determine the y-intercept and what it means
• Show other graphs and talk about their slopes and intercepts
• Reflect (approx. 20 mins.)
Ask the following:
• The Chicago Cubs faltered at the end of the season this past year. Let’s rewrite a little history. At the beginning of September the Cubs had a winning percentage of 54.5%. In the 30 games they have left they want to increase to a winning percentage of 60.0%. How many homeruns do they need to hit for the entire year to end with a winning percentage of 60.0%? (246 homeruns)
(Cubs are in the NL)
• MLB is again expanding. The new expansion team, the [insert your city’s “new” team i.e. “Clemson Fury”], has high aspirations in their first year of existence as they want to win 50% of their games. According to our 2004 graphs, how many homeruns do they have to hit in each league in order to achieve their goal?

• Extend (approx. 10 mins.)
Why do you think the graphs are different between NL and AL? (designated hitter, etc.)
The 1982 Cardinals hit a whopping 67 homeruns during the regular season; according to the equation we found for NL 2004 what would be their predicted winning ratio? (33.5%) Compare to actual. (The 1982 Cardinals won the World Series that year with a winning percentage of 56.8%. They were dead last in homeruns, but were known for their speed by leading the league in stolen bases.)
Is this equation a good representation of the data to use?
What other aspects of the game could you analyze?

7) Assessment (on an upcoming test)
Provide a scatter plot that uses real world data. Ask them to interpret the data.
For example: Look at the following scatter plot (data on free throw % vs. winning % in the NBA). In your own words, describe what the slope and intercept in this context mean, according to the equation of the line of best fit.