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A WebQuest for Algebra II

Designed by

Joe Boernerboernerj@gmail.com

Based on a template from The WebQuest Page

George Steinbrenner is a Mathematician

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You just got a job as assistant to the general manager of a major

league baseball team. Last season your team was awful. Your manager informs

you that he is very irritated by the team’s lack of success and he wants a solution to

the problem.

There are numerous baseball statistics that are kept in order to

compare how players do around the league. There are also many ways that we

can relate these stats to concepts we have learned in this class and that is what you

will learn to do in this Web Quest.

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In order to impress your boss you decide to figure out and present which player(s) would

be best for the team to acquire so your team will be successful next year.

Argue your decision with a linear regression model for each statistic made in Excel or an

application of you choice.

Try your best, make this assignment your own, and don’t be afraid to ask questions.

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The Task

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To accomplish this job, this procedure might help you correctly find the right player for your team.

1.Pick at least ten teams to research (Winning Percentage, Runs Batted In, Home Runs, Stolen Bases, Earned Run Average, and Batting Average.)2.Find the relationship of each of the other five statistics with winning percentage. Obtain the regression equation where winning percentage is the y or dependent variable, and the other variables are the x or independent variable. 3.Identify the variable that is most strongly related to winning percentage. 4.Use internet resources to determine which player led the league in this statistic. 5.Use the regression equation obtained in #2 to predict the winning percentage, given that your team obtains this player. (That is, his stat becomes the x variable in the equation, and you are obtaining y. Don’t forget to add in your teams statistics from last year.) 6.Prepare an oral argument for the owner, explaining your reasoning and convince her that your team needs this player.

Here are some websites that list various baseball teams and their statistics for previous years.http://sports-ak.espn.go.com/mlb/indexhttp://www.sportsline.com/mlbhttp://www.baseball1.com/http://mlb.mlb.com/index.jsphttp://www.mlb-teams.com/stats/stats_index.phphttp://www.baseball-statistics.com/http://www.thebaseballcube.com/http://www.ncaa.org/stats/baseball/baseballMenu.htmlhttp://www.baseball-almanac.com/bstatmen.shtmlhttp://en.wikipedia.org/wiki/Baseball_statistics

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Beginning0-3

Developing3-6

Accomplished6-9

Exemplary10

Score

Research As far as anyone can tell, research was not done or is inaccurate.

Required number of teams researched was less than half the required number and there is not enough information to conclude anything.

Statistics are questionable.

Required number of teams researched was not met or their winning percentage s were in the same ranges.

Statistics are mostly accurate.

10 teams were researched and they were from a broad range of winning percentage.

Statistics are extremely accurate by confirming multiple sources

Graphing As far as anyone can tell, graphing was not completed for any statistic.

Most of the information on the graphs are inaccurate and the required number of graphs is not met.

5 graphs are included for each statistic, however either plots are missing from the graph or a line of best fit is inaccurate.

5 graphs are included for each statistic. Each graph has ten plots with a line of best fit. Equation for the line of best fit is also included.

Mathematical Reasoning

Student didn’t make a decision and failed to show any work for their project.

Student has failed to comprehend the information and did not back up their decision with mathematics. Little work is shown or it is inaccurate.

Student didn’t make the right decision, however was able to back up their augment with mathematics. Most of the work is shown and is accurate.

Student is able to accurately depict the information in order to make a decision. Work is shown for how they acquired equations and their reasoning.

Presentation Presentation was not given or no effort was taken for the presentation part of the project.

Student shows little effort in how they presented their information and visual aids were not made or improperly used.

Student simply presents the information and their decision. Visual aids are used but not utilized.

Student presents the information according to the role. Use of visual aids is outstanding and a description of them is also given.

Participation As far as anyone can tell, this student was off task for most of the project and disturbed adjacent classmates.

Student was sidetracked at most of the time by not focusing attention to the project. Consistent socializing was observed.

Student was sidetracked at times by not focusing full attention to the project. Occasional socializing was observed.

Student was on task the entire time while working on the project. Was not afraid to ask questions or help fellow students by answering question.

EvaluationExample:

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From this activity you have learned a way to compare which independent

variables most correlate to a dependent variable. There are other ways we can use this

method. Can you think of any others?

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I modified this Web Quest from a sample web quest from Leah P. McCoy at Wake Forest University. http://www.wfu.edu/~mccoy/NCTM99/

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A WebQuest for 10th Grade (Algebra)

Designed by

Joe Boernerboernerj@gmail.com

Based on a template from The WebQuest Page

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George Steinbrenner is a Mathematician)

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This lesson was developed for EDUC331: Educational Technology and Assessment which is a class in the Colorado State University Education Licensure Program. It was intended to get us familiar with planning, creating and sharing a Web Quest project.

This project is an attempt to related linear graphs and linear regression to a real world problem. The students take on the role of someone who hires baseball players for a major league baseball team. Through researching statistics of successful teams they should be able to decide which statistic most correlates to winning percentage. The final result should be a presentation which argues their decision to their boss.

This lesson has not been implemented in the classroom yet and therefore I don’t know the complexity.

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I feel that this lesson would be somewhere in the Algebra curriculum. Students must know how to make scatter plots with a line of best fit, find equations for linear graphs, and be able to compare different graphs as well as know what they mean.

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Standard 2:Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.

represent functional relationships using written explanations, tables, equations, and graphs, and describing the connections among these representations;

solve problems involving functional relationships using graphing calculators and/or computers as well as appropriate paper-and-pencil techniques;

model real-world phenomena (for example, distance versus- time relationships, compound interest, amortization tables, mortality rates) using functions, equations, inequalities, and matrices; Standard 3:Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.

fit curves to scatter plots, using informal methods or appropriate technology, to determine the strength of the relationship between two data sets and to make predictions;

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To accomplish this job, this procedure might help you correctly find the right player for your team.

1.Pick at least ten teams to research (Winning Percentage, Runs Batted In, Home Runs, Stolen Bases, Earned Run Average, and Batting Average.2.Find the relationship of each of the other five statistics with winning percentage.  Obtain the regression equation where winning percentage is the y or dependent variable, and the other variables are the x or independent variable. 3.Identify the variable that is most strongly related to winning percentage. 4.Use internet resources to determine which player led the league in this statistic. 5.Use the regression equation obtained in #2 to predict the winning percentage, given that your team obtains this player.  (That is, his stat becomes the x variable in the equation, and you are obtaining y. Don’t forget to add in your teams statistics from last year.) 6.Prepare an oral argument for the owner, explaining your reasoning and convince her that your team needs this player.

What the students should do is make graphs for each stat from the ten teams they chose. After they find their line of best fit, they will determine which line has the greatest slope which would be the stat that most correlates to winning percentage.

I feel this lesson shouldn’t take more than 3 class periods including the presentations. If the students know what to do, they should have all the stats needed within one period.

VariationsStudents could work in pairs or groups or hand in a report rather than do a presentation.

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Unless the students work on this at home, it is ideal to have one computer for every student and have Microsoft Excel installed on them.

Teachers should probably supply some sort of graph paper that the students can use for visual aids during their presentation.

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I will know that this lesson is successful if the students come to a reasonable conclusion and they are able to back up their decision with mathematics. I would look to see if their charts, graphs, and lines are accurate and they successfully understood their data to come to their conclusion. When it comes to the presentation, I would not be too strict but make sure that they get their point across. I would feel that the student should be able to argue their point within a three minute presentation.

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This would be a sample graph of ten teams for how batting average correlates to winning percentage. For this example it doesn’t really correlate because the line of best fit wont have a high slope.

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At the begging of this lesson, students should research multiple teams with different winning percentages and log the statistics of Runs Batted In, Home Runs, Stolen Bases, Earned Run Average, and Batting Average. Graphs should be made for each statistic and a line of best fit must be present with the equation of it visible. Throughout this process, the work that shows how students come up with the graphs and equations must be present. After they decide what statistic their team needs most, they need to find the player who led the league last year in that category. Then they can plug in that players statistic in order to predict how much their team will benefit from this player. Students should then prepare a presentation like they were going to try to convince their boss that acquiring this player should be their biggest concern.

Timeline:First period- Students research all the teams needed and begin forming graphs and figuring out equations for lines.Second period- Students make a decision on what they feel will help their team the most and research the player they want to acquire. Presentations and visual aid graphs are also prepared.Third period- Depending on the class size or time of each period this part may take a couple of days and that is the students presenting their decision and the mathematics behind it.

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This lesson would be a quick way to give your students experience creating linear models and show them a real world example of how they can use what they learn.

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I modified this Web Quest from a sample web quest from Leah P. McCoy at Wake Forest University. http://www.wfu.edu/~mccoy/NCTM99/

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