Part I Lesson Plan Format - Denver Public Schools
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Oscar Trono
ET/IL Final Project
March 2, 2004
Mini-Unit: Analyzing Real-World Data
Specific Lesson Title: The Super Bowl: Exciting or Boring, Can Mathematics Tell the Story?
Subject Areas: Math, Computer Technology
Grade Level: 8
Mini-Unit: Analyzing Real-World Data
Analysis of real-world data involves the use of basic algebra including percentages, mean, median and mode. Typical graphs used to represent this kind of statistical analysis include pie charts and stem-leaf plots. To analyze and report data, students must be proficient in the following topics, covered in the mini-unit:
• Working with Variables and Data
• Order of operations
• Mean, Median, Mode
• Variable Expressions
• Organizing and Graphing Data
In this mini-unit, students investigate several sets of real world data, ranging from speeds of animals, elevations of mountains, heat transfer data (from Science lab class) to Super Bowl scores. Students learn methods of data retrieval & collection, organization, analysis and synthesis.
Within each lesson, the skills practiced are computer-oriented, including organizational, computational and graphical. A variety of critical thinking skills are also required (e.g., differentiating fact and opinion, analyzing, evaluating, defending).
“The Super Bowl…” Lesson Summary
Purpose: Use statistical analysis to find answers to essential questions
Objectives:
Students will:
• Collect Super Bowl data via the Internet
• Organize data from past Super Bowls in Microsoft Excel spreadsheet
• Calculate the point spreads of final scores using formulas in Excel
• Calculate the Mean, Median and Mode using Excel
• Construct stem-leaf plots with help of Sort function in Excel
• Group data into point spread ranges
• Calculate the percentages in each range
• Construct a pie chart using Excel
• Answer questions relating to essential questions
• E-mail results to teacher
Materials
Handouts (Worksheet examples, instructions and questions)
Computers with Microsoft Word, Excel and Internet Access
Procedure
1. Initiate a class discussion based on some introductory essential questions, e.g., “Each year the Super Bowl is one of the most watched TV events. What makes the event so exciting? Has the Super Bowl always been exciting? How can we use math to answer these questions?” Explain that point spread is the difference between the winning and losing teams. Determine relationship between point spread and game’s excitement (e.g., a point spread of one touchdown might indicate an exciting game, or a point spread of three touchdowns might indicate a boring game)
2. Gather past Super Bowl scores via Internet research. Make spreadsheets that calculate point differences. Use sorter to help generate a stem-leaf plot. Calculate mean, median and mode.
3. Analyze data by grouping point spreads in following ranges: 1-7 points, 8-14, 15-21 and more than 22. Calculate percentage for each group and make a pie chart.
4. Report findings and answer questions centered around introductory essential questions.
5. E-mail results to teacher.
Assessment
• Classroom discussion of essential questions
• Completed worksheet and questions (typed with Microsoft Word)
• E-copy of Spreadsheet and pie chart
• Students graded per 100 point rubric
Expected Student Outcomes
Student can:
• Initiate Internet Search
• Use Excel to make spreadsheets, do calculations, sort and graph
• Make a stem-leaf plot
• Calculate Mean, Median (using Excel) and find Mode
• Use Excel to make pie chart
• Use E-mail to correspond with teacher
Math, IL and ET Standards
The Lesson meets all 6 Durango School District Math Standards as follows:
1. Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems
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.
3. Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.
4. Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.
5. Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning used in solving these problems.
6. Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving situations and communicate the reasoning used in solving these problems.
The Lesson Meets IL Standards 1-6 as follows
1. The information literate student accesses information efficiently and effectively.
2. The information literate student evaluates information critically and competently.
3. The information literate student uses information accurately and creatively.
4. The information literate student is an independent learner who pursues information related to personal interests.
5. The information literate student is an independent learner who appreciates literature and other creative expressions of information.
6. The information literate student is an independent learner who strives for excellence in information seeking and knowledge generation.
The lesson meets the following Durango 9-R Technology Ends Assessments for 8th Grade:
• Increase computer access skills and file management skills.
• Use technology to achieve process writing, i.e., draft, edit, revise, format, review, and independently publish a document using word processing including graphics, editing tools, proofing tools, etc.
• Use global communication networks, i.e., world wide web
• Use spreadsheets or databases to create documents using the data (graphs, charts, or reports)
Technology Application
Collecting, tabulating, analyzing and reporting data can be a tedious, time-consuming task. In the traditional math classroom many math skills are learned and practiced when working with data, especially for a statistical analysis. For the sake of learning computation/graphing skills and number sense, most statistical problems ask students to crank out numbers without technology. Tedious arithmetic and slow graphing process can sometimes impede the true learning goals of a statistics problem, especially for kinesthetic learners.
Using technology (hand calculators, spreadsheets and graphing programs), affords students who struggle with arithmetic and traditional pencil/paper techniques, an alternative problem solving process. In most cases, technology speeds up the problem-solving, more accurately simulating the “real world”. However, therein lies a dilemma for the math teacher: How much skill practice is sacrificed with technology?
My lesson on Super Bowl statistics comes after students have had ample skill practice using traditional pencil and paper. By using spreadsheets to construct databases and perform statistical calculations, students now learn the “real world” methods for tabulating and analyzing data. In the real world, efficiency is often the bottom line, and Microsoft Excel is completely efficient. Finally, in today’s business world, a neat, graphical summary of a problem is simply necessary. Using Excel’s graphing features to present their analysis, students will get a sense of how a real problem might be evaluated by the client (in this case, the teacher).
Essential and Higher Level Questions
The Web diagram shows some of the essential questions discussed and critical thinking skills used. The critical thinking skills, shown by green clouds, are situated near the activity or question. This lesson covers most of the critical thinking skills outlined in ET/IL “look-fors.”
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Research Process
Definitions of McKenzie’s Research Cycle steps are given in the table below. Also included are research skills that are important to teach. A description of how my final project incorporates these steps follows the table.
McKenzie’s Research Cycle
|Step |Definition |Some Research Skills taught or reviewed |
|Questioning |Questioning involves brainstorming an essential |Laying out a web diagram, e.g., using Inspiration to put forth |
| |question(s), and mapping out the extent of the work |the appropriate questions and subsidiary questions, and to map |
| |that lies ahead. |out a research plan. Using the Internet for some cursory |
| | |exploration to gain some understanding of essential question. |
|Planning |Planning asks the question, “What is the best way to |Using the Internet, investigating possible primary resources, and|
| |find good information that will help answer the |setting up database files for information storage. |
| |subsidiary questions?” In addition, finding ways to | |
| |store retrieved information can be planned in this | |
| |step. | |
|Gathering |While using the plans from the above steps, students |Learning the technicalities of Internet searches such as logical |
| |gather useful and pertinent information in a |operators, truncation, the Thesaurus, and developing an |
| |structured, organized and well-thought manner. |exploratory mentality. |
|Sorting/sifting |Sorting/Sifting is an important precursor to |Combining, editing, prioritizing, eliminating, tabulating, |
| |synthesizing. Much of the sorting and sifting can be |outlining, organizing…these are all key strategies that students |
| |done during the previous gathering step, but should |must practice and learn to become efficient at sorting and |
| |now be done methodically and systematically. This is |sifting. |
| |the foundation for the final steps. | |
|Synthesizing. |Arranging information, the research product begins to |Same skills as needed in the sorting, sifting steps. “Inventing |
| |take form in this important step The problem is |and Visualizing” are also key to this step because the researches|
| |brought into a much clearer focus. |must make some sense of all the data collected. |
|Evaluating |This is the time to step back and ask, “Is more |Critical thinking and evaluating skills must be stressed. |
| |research needed?” Students revisit the essential |Students must be taught to critically evaluate their own work. |
| |questions before moving on to the final step. | |
|Reporting |Alas, findings are reported and recommendations made |Using multimedia presentation software is a key skill that |
| |in a manner best suited to the audience, e.g., a |students should be taught in order to present in a neat, coherent|
| |PowerPoint presentations might suit a large audience |and cogent manner. |
| |of visual learners. | |
The McKenzie Research Cycle, on the surface, presents a method for finding information that helps solve a problem. In my final project, I ask students to solve a “real world” statistics problem that initially involves looking for some specific information. The research portion (information gathering) of my final project is small, but when I look deeper at the problem solving methodology of McKenzie, all the steps are certainly appropriate.
My lesson, “Super Bowl…Exciting or Boring? Can Math Tell the Story?” is based on a statement, followed by 2 essential questions, “Each year the Super Bowl is one of the most watched TV events…1) What makes a Super Bowl exciting and 2) Can math help us determine if Super has been exciting?” This falls in line with the first step, questioning. From these essential questions, students should follow with subsidiary questions that lead to a statistical analysis of scores of all past 37 Super Bowls. Typical questions that come up…Can you analyze the scores to determine what percent of Super Bowls have been exciting?…Can you use Math (Statistics) in your analysis?…Can you predict if the next Super Bowl will be exciting? What point spread indicates that the game was exciting? Students generate many questions (beyond what I’ve listed) during initial planning.
Students must plan a strategy for answering the essential question. Using the plan, students research past game scores (gathering), organize and synthesize the data using statistical analysis. Finally, students evaluate the data and report their findings in a tabulated and graphical summary.
My final project math problem is not research intensive in the traditional sense of research projects, so there is not much chance for plagiarism. We are simply using the Internet to find historical data and using Microsoft Excel to analyze the gathered data.
The project is “real life” in the sense that using analytical skills (in this case statistical analysis) are typical problem solving tools. This is another strategy for a student’s toolkit. I chose the Super Bowl scores because I thought 8th graders might find this a fun, challenging and interesting problem on the eve of Super Bowl XXXVIII. The problem is based on an event that many students are likely to watch.
Collaboration Plan
My plan was discussed with and documented by Corky Stahn the week of Feb 2. Our discussion included how to improve the lesson’s essential questions, and how the IL standards were met. Amy Kendziorski, Asst. Principal, observed the lesson on 2/26/04.
Lesson Introduction
My lesson, “The Super Bowl…Exciting or Boring? Can Math Tell the Story?”, is introduced by a statement, followed by 2 essential questions. The statement: “Each year the Super Bowl is one of the most watched TV events. The questions: 1) What makes a Super Bowl exciting and 2) Is the Super Bowl always exciting?” I will pose these questions to my students and facilitate the discussion that follows. From these essential questions, students should follow with subsidiary questions. (Students generate many questions during initial planning, that will be answered in the course of the project)
At this point, during the discussion I ask students to hypothesize about the game, solely based on what they know. They will keep that hypothesis in mind as we do the mathematical analysis.
Computer Activities
|Computer Activity |When / Where |Student Role |Software |
| | | | |
|Essential Question Discussion |Math Classroom |Group Discussion |N/A |
|Clarifying Problem and Overview of |Math Classroom |Group Discussion & |N/A |
|Work & look at Inspiration Web Diagram| | | |
|Review of Excel Commands |In Computer Lab |Group Discussion |Microsoft Excel |
| | |(teacher uses projector) | |
|Internet Search for Super Bowl Data |In Computer Lab |Individual/and Collaborative |Search Engines |
| | |(students help neighbors) | |
|Create Spreadsheet to calculate point |In Computer |Individual/and Collaborative |Microsoft Excel |
|spreads |Lab | | |
|Statistical Analysis (Mean Median |In Computer |Individual/and Collaborative |Microsoft Excel |
|Mode) |Lab | | |
|And data grouping | | | |
|Answer data questions |In Computer Lab |Individual/and Collaborative |Microsoft Excel |
|Calculate percentages and Generate pie|Computer Lab |Individual/and Collaborative |Microsoft Excel |
|chart | | | |
|Present findings and send to Teacher |Computer Lab |Individual |Microsoft Word and Student |
| | | |E-mail |
|Problem Debrief |Classroom |Class Discussion |N/A |
Supporting Activities
Students construct (pencil and paper) a Stem and Leaf plot from the Excel Spreadsheet data. Although this seems antiquated next to their more sophisticated, computer-based analysis, CSAP testing requires an understanding of these plots. A lesson on these plots will have been presented earlier (using other data), so they will have prior knowledge. Students often collaborate while constructing the plots.
Culminating Activity
Students synthesize their data into a pie chart and complete a set of statistical questions (the bulk of student work). Next, they use this graphical representation to evaluate the original Essential questions. The problem will culminate with three main activities.
1. Evaluate original hypothesis and differentiate between fact and opinion. What did the statistical analysis show? Have games been exciting or boring based on point spreads? Is this an accurate assessment?
2. Report findings. Students organize their data & results and defend them in a written summary. This summary is E-mailed to the teacher.
3. Share as group. Students share their findings in a large class discussion. As a class, the project is debriefed. What did the class learn as a whole? What worked? What didn’t work? Can Mathematics tell us something about the nature of the Super Bowl.
Assessment Grading Rubric (as given to students prior to project)
Super Bowl Project Grading Rubric
You will be given points for completion of the following:
1. _____ Find historical Super Bowl data on Internet (5 points)
2. _____Tabulate data in Excel Spreadsheet (10 points)
3. _____Use formulas in Excel to tabulate Year, Super Bowl #, and Point Spread (5points)
4. _____Use Excel Mean, Median, Mode functions to perform statistical analysis(worth 5 points)
5. _____Construct a Stem and Leaf Plot for point spread data (worth 10 points)
6. _____Answer the statistical questions #1-8 in the handout (worth 20 points)
7. _____Group point spread data and create spreadsheet for making pie chart (worth 10 points)
8. _____Make a pie chart using Excel. Label each slice as a percentage. Show legend and Title (worth 10 points)
9. _____Write summary of your findings (at least 300 words). include original hypothesis and defend your current position based on statistical analysis (worth 20 points)
10. _____Send Excel spreadsheets & graph and summary via E-mail
(worth 5 points)
_____TOTAL SCORE OUT OF 100
Bibliography
Martin, Hope. The Math of Sports. 1st ed. Portland: Walch, 2000.
Billstein, Rick. Math Thematics. 1st ed. Evanston: McDougal Littell, 1999.
McKenzie,Jamie. Beyond Technology. 1st ed. Bellingham:FNO Press,2000
(Following were searched via OPAC:)
King, Andrew. Math for Fun Projects. 1st ed. Brookfield: Copper Beach Books, 1999
Farmer, Lesley. Mathematics Through Sports. 1st ed. Englewood:Teacher Idea Press, 1999
Management Plan
After the introduction (detailed above), students will receive an instructional handout that includes examples of the spreadsheet (sans data), the nine questions they will answer and the grading rubric. We will review the instructions in detail before moving to the computer lab.
I will remind students of some of the basic rules we follow whenever we are in the computer lab.
• Quietly wait in the hallway until I open the door.
• Enter single –file
• No Food, Drink or Gum in the Lab
Once in the computer lab, I will guide the students. When doing the Excel portion, students will follow this order of steps:
• Log-on
• Open Microsoft Excel
• Look at the Projector Screen (During my demonstration all students must be facing the screen or I will not speak…this works every time!)
• I open my file and show students some key operations. When I think they are ready, I let them begin. This quick demo will focus students and get them started quickly and quietly.
While working on their assignments Students may:
• Consult with students sitting on either side of them
• Ask teacher questions by raising hand.
Otherwise, I expect students to work quietly and NOT move around the room.
Students must:
• Work in the Computer Lab with Teacher supervision
• Get Teacher OK to print an Excel document
• Get Teacher OK to use Internet or Student E-mail
Students know these rules from the beginning of the school year. Having rules in place makes for an orderly learning environment.
If students finish their work, they are allowed to play Number Munchers or Green Globs.
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