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Mathematics and Sports WebQuests |
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Introduction:
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Most people are familiar with sports rules and terminology; however, they are not always aware of the important role that math plays in
sports. A myriad of data on players, teams, divisions and leagues is provided by the media and the sports world. You have been
selected to explore how math is used to compute, summarize and analyze this
data.
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The Tasks:
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You are probably familiar with professional sports and stay abreast of scores
and standing for your favorite teams. In each webquest below, you will
engage in web-based inquiry to answer the questions presented and to perform the tasks required. Links are included in each
webquest to
help you explore. In some cases, you may also need to browse the sports and the math resources
listed at the bottom of this page. As you embark on your web explorations, keep
in mind that most of the links on this page target a new browser window. You
might not be able to do all four webquests at once. These tasks will require a computer, access
to the web, graph paper (see the math resources below), paper, pencil and a
ruler. Access to a printer is helpful, but not required.
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WebQuest 1: Baseball Stats
Part I: Batting Average
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The following tasks may require some of the sports resources listed near the
bottom of this page.
Try our Lessons on Decimals, then do
the following: |
- What is a batting average?
- How is a batting average calculated?
- Calculate the batting averages for the following players.
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PLAYER |
AT-BATS |
HITS |
BATTING AVERAGE |
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Ken Griffey, Jr |
600 |
173 |
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Sammy Sosa |
625 |
180 |
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Tony Gwynn |
411 |
139 |
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- Order the batting
averages in tem 3 from least to greatest.
- Compute the batting averages for 25 players in the 2008
season.
- Find historical player stats for 20 baseball players from the 2009 season.
- Compute the batting average for each player.
- Create a table for your results.
- How does a batting average measure a player's performance?
Part II: Earned Run Average
- What is an Earned Run Average?
- How is an ERA calculated?
- Gather pitching stats for Earned Runs (ER) and Number of Innings Pitched
(IP).
- Calculate the ERA for each pitcher.
- Create a table for your results.
- How does an earned run average measure a pitcher's performance?
WebQuest 2: Win-Loss Percentage
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Win-Loss Percentage is important data for any team. For example, WL% can
be computed for a baseball
team. However, WL% is also used in other sports.
Try our Lessons on Understanding Percent,
then do the following: |
- Look at win and loss data for teams in football. For example, the
NFL.
- Compute the WL% for five teams in a league, five in a conference and five in a
division.
- Create a table for your results.
- Look at win and loss data for teams in basketball, for example, the
NBA.
- Compute the WL% for ten teams of your choice.
- Create a table for your results.
- What other sports use WL%?
- Is WL% always expressed as a percentage? Explain your answer.
WebQuest 3: The NBA Draft Lottery
- What is the formula for the number of possible combinations of r objects
from a set of n objects?
- How many different committees of 5 people can be chosen from a group of 11?
- How many non-playoff teams participate in the Draft Lottery?
- What kind of balls are used?
- How many numbered balls are placed the lottery machine?
- How many balls are randomly drawn from the lottery machine?
- Does the order in which the balls are drawn matter?
- How many combinations are there when the balls are randomly selected from
the lot of numbered balls?
- How many combinations are actually used in the NBA Draft?
- What is wrong with the numbered balls shown in this
image taken from this
page?
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In the draft lottery, numbered balls are drawn to the top of the machine to determine a
combination. The team that has been assigned that combination will receive the number one pick.
Non-playoff teams are then ranked in reverse order of their regular season record,
and are assigned chances, as shown here.
The largest number of outcomes is assigned to the team with the worst record.
The team with the second worst record gets the second largest number of
outcomes, and so on for each of the 14 teams in the lottery. The experiment is
conducted, and the team to which the winning outcome was assigned receives the
first pick in the NBA Draft. Therefore, the NBA Draft is weighted in favor of the worst lottery teams based on their season record. |
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- One outcome is disregarded: it is given to no team and ignored. How many
outcomes are then distributed among the non-playoff teams?
- From a mathematical standpoint, why do you think is this done?
- What is 14C4? How would you
compute this?
- Can a team's win-loss record affect their chances of getting the first draft
pick?
WebQuest 4: Graphing Historical Data for a Sport or Event
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Tables and graphs are commonly used to summarize sports statistics. Standings for teams and leagues are often summarized in tables, and historical data
about a sport or event is often summarized in graphs.
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The 2010 Winter Olympics in Vancouver, British Columbia, Canada
ended on February 28, and the accompanying Paralympics are being held March
12-21. The first of the modern Summer Games opened on Sunday, March 24, 1896, in Athens, Greece.
The first IOC Games was hosted in the Panathenaic stadium in Athens in 1896.
The Winter Games were added in 1924. Historical
data about this event has been tracked for years! For example, view
a bar graph of Winter Olympic medals by country. |
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The Super Bowl
is the championship game of the National Football League (NFL), the premier
association of professional American
football. It was first played on January 15, 1967. The Super Bowl is a
very popular football event. A great deal of historical
data about the Super Bowl is available, including Super
Bowl Standings. |
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The following tasks may require some of the math and sports resources listed near the
bottom of this page.
Try our Lessons on Data and Graphs,
then do the following. |
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- Gather historical data from the Olympics. For example, choose
a country and look at the data. If you chose the United
States, then you would see a table for number of
participants, men, women, sport, and medal.
- Print the Olympic data you gathered, or save it to your computer.
- Decide which type of graph is appropriate
for summarizing
your data.
- Graph your Olympic data.
- Gather historical data from the Super Bowl. For example, Super Bowl Game-Time Temperatures
can be summarized in a line graph.
- Print the Super Bowl data you gathered, or save it to your computer.
- Decide which type of graph is appropriate
for summarizing
your data.
- Graph your Super Bowl data.
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Other Topics for Further Exploration
- Percent change in number of home runs scored by a
baseball player.
- Field goal percentage
(FG%) in basketball.
- Pythagorean Expectation [ 1
] [ 2
] [ 3
]
[ 4
]
- Win Probability (WP)
in Football.
- Win Expectancy (WE)
in baseball.
- Advanced NFL Stats including:
- Sabermetrics, the study of baseball statistics [ 1
] [ 2
] [ 3
]
- Simpson's Paradox - correlation does imply causation [ 1
] [ 2
] [ 3
] [ 4
] [ 5
]
Topics for Lower Grades:
- Students can look at the basics of football
scoring and add whole numbers.
- The Super
Bowl uses Roman Numerals to identify each game. Write these Roman
Numerals as numbers in standard form.
- Have students compare and
order decimals by looking at batting averages of their favorite baseball players.
They can find real data for players at websites such as ESPN.com.
They should be reminded that a batting average is stated as a three-digit number; however,
it is actually a decimal rounded to the nearest thousandth.
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Topics for High School and College:
- Mathematics in Sports
- Mathematics and Sport Theme Articles
Sports Resources:
Math Lessons: Try these Units of Instruction
- Decimal Part I
- Understanding Percent
- Percent Applications
- Probability
- Data and
Line Graphs
Math Resources: Try these Printables
- Bar graph paper (PDF)
- Line graph paper (PDF)
- Paper for circle graphs (PDF)
- Create
a graph
- Comparing Graphs
Other Resources:
- Links to selected websites in each webquest above.
- Search engines
such as Bing, Google,
Yahoo!
Evaluation:
- Print or save tables, graphs and other data you gathered in these webquests.
- Discuss your findings with a classmate or family member, and a teacher or a
sports aficionado.
- Name three formulas you learned in these webquests.
- Create five original problems from math and sports.
- Share your problems on
Facebook.
- Add the graphs you created to our
Facebook
page.
Conclusion:
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Congratulations! You have explored the important role that math plays in the world
of sports. These explorations should give you a better understanding of
sports, probability and statistics.
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Interactive Math Goodies Software
