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# Euclid's Enigma

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A Mathematics/ Technology base WebQuest for highschool students

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### Transcript of "Euclid's Enigma"

1. 1. Euclid’s Enigma Student Pages Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] A WebQuest for 10th Grade Mathematics Designed by Tyler Bradshaw [email_address] Image courtesy of Murilo Flickr.com
2. 2. Introduction Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] There are few ideas in life that will be useful forever. Concepts that change the way people view the world, change the way people approach challenges. Nowhere do more of these brilliant notions exist than in the field of mathematics. Today you will explore one of these ideas for the purpose of understanding it’s vast impact not just within the field of mathematics, but also within your everyday life. You will become historians, engineers and fortune tellers, and in the end it will be clear that one little thought can have a lasting impact on the world as you know it. In the following you will explore one of three concepts you know in math from three different angles. You will choose either the Pythagorean Theorem, The Quadratic Equation, or the number Pi and put together a presentation on where it came from/ the historical perspective, how its useful today/ the present perspective, and how it will continue to be useful/ the future perspective. Continue to the task page for details!
3. 3. The Task Student Page Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] <ul><li>In groups of four you will construct a Power Point presentation to be given in front of the class on one of the three topics mentioned above. Your presentation will consist of : </li></ul><ul><ul><li>An introduction to your presentation telling us what it is on and what we can expect in your following slides. </li></ul></ul><ul><ul><li>A main body that is broken down into four sections: </li></ul></ul><ul><ul><ul><li>Past, the history of your topic, who came up with it? When? What did people think of it at the time? What has it been used for in the past? </li></ul></ul></ul><ul><ul><ul><li>Present, how is it applied today? Is it used in physics? Math? Engineering? Where can you find an application of it in your life? </li></ul></ul></ul><ul><ul><ul><li>Future, use what you have learned to speculate on how people will use it in the future. Will it be the same as today? Will it become obsolete? </li></ul></ul></ul><ul><ul><ul><li>Example, I want to see your topic in a worked example in a real world application. Don’t just give me a 2 + b 2 = c 2 , I want some thought into these. </li></ul></ul></ul><ul><ul><li>A conclusion summing up what you’ve told us, and what you learned from this project. </li></ul></ul>Title
4. 4. The Process Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] <ul><li>You will be assigned to groups of 4 </li></ul><ul><li>Choose your team’s topic. You can choose on of the following three topics </li></ul><ul><ul><li>Pythagorean Theorem </li></ul></ul><ul><ul><li>Quadratic Equation </li></ul></ul><ul><ul><li>PI </li></ul></ul>
6. 6. The Pythagorean Past Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] So you’re researching the past of the Pythagorean Theorem. As the historian of the group you will gather information on the history of the theorem. You should touch on Pythagoras, and his followers. Why was it so important back then? What was the inspiration for the theorem? How did he prove it? You could present information in a timeline, but anyway you can get the information across is fine. As you will find out the history of the Pythagorean theorem is a history riddled with mystery. You can use the following links to complete your research. The theorem The man More on the man The proofs A bit more You may also conduct interviews with somebody you feel is knowledgeable on the subject. If you choose to do this you must present to me who you are planning to interview and why they are qualified along with a list of questions before conducting the interview.
7. 7. The Pythagorean Present Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] So why is the good old Pythagorean Theorem important? Check out some of current applications and see how its is used today. Look for current uses and jobs that use the Theorem. You will also need to find an application or two of the Theorem in your life, (not including this class.) This has a good list of current applications, there is also some past apps so share them with your history researcher. Click here! A list of jobs that use the theorem can be found here You may also conduct interviews with somebody you feel is knowledgeable on the subject. If you choose to do this you must present to me who you are planning to interview and why they are qualified along with a list of questions before conducting the interview.
8. 8. The Pythagorean Future Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] <ul><li>So you want to predict the future. Here’s what you need to do. </li></ul><ul><li>Get with your teammates to see how the theorem has been used in the past, and how it is used today. </li></ul><ul><li>Once you have a good handle on it brainstorm some ideas on how it will be used in the future. If you don’t think it will be then tell me why it will be obsolete. </li></ul><ul><li>Here are some links to help you on your quest </li></ul><ul><ul><li>Some current uses </li></ul></ul><ul><ul><li>The theorem </li></ul></ul><ul><ul><li>The proofs </li></ul></ul><ul><ul><li>A bit more </li></ul></ul><ul><li>You may also conduct interviews with somebody you feel is knowledgeable on the subject. If you choose to do this you must present to me who you are planning to interview and why they are qualified along with a list of questions before conducting the interview. </li></ul>
9. 9. Pythagorean Example Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] Examples need to be realistic and interesting. You should look at the resources in the past , present , and future sections. You will use this information to come up with an original real world example problem that applies what you know about the Pythagorean Theorem. You should use the slides of your presentation as steps in your example be able to explain what you are doing and how the theorem applies.
11. 11. The Quadratic Past Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] So you’re researching the past of the Quadratic Equation. As the historian of the group you will gather information on the history and background of this formula. You should touch on who first discovered it and what did they use it for. Why was it so important back then? What was the inspiration? You could present information in a timeline, but anyway you can get the information across is fine. As you will find out the history of the Quadratic Equation is as interesting as it is useful. You can use the following links to complete your research. The History Babylonian Mathematics More You may also conduct interviews with somebody you feel is knowledgeable on the subject. If you choose to do this you must present to me who you are planning to interview and why they are qualified along with a list of questions before conducting the interview.
12. 12. The Quadratic Present Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] So why is the good old Quadratic Equation important? Check out some of current applications and see how its is used today. Look for current uses and jobs that use the equation. You will also need to find an application or two of the equation in your life, (not including this class.) This has a good list of current applications, there is also some past apps so share them with your history researcher. Click here! A list of jobs that use the theorem can be found here Here is some more information and uses You may also conduct interviews with somebody you feel is knowledgeable on the subject. If you choose to do this you must present to me who you are planning to interview and why they are qualified along with a list of questions before conducting the interview.
13. 13. The Quadratic Future Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] <ul><li>So you want to predict the future. Here’s what you need to do. </li></ul><ul><li>Get with your teammates to see how the Equation has been used in the past, and how it is used today. </li></ul><ul><li>Once you have a good handle on it brainstorm some ideas on how it will be used in the future. If you don’t think it will be then tell me why it will be obsolete. </li></ul><ul><li>Here are some links to help you on your quest </li></ul><ul><ul><li>Some current uses </li></ul></ul><ul><ul><li>The Equation </li></ul></ul><ul><ul><li>A bit more </li></ul></ul><ul><li>You may also conduct interviews with somebody you feel is knowledgeable on the subject. If you choose to do this you must present to me who you are planning to interview and why they are qualified along with a list of questions before conducting the interview. </li></ul>
14. 14. Quadratic Example Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] Examples need to be realistic and interesting. You should look at the resources in the past , present , and future sections. You will use this information to come up with an original real world example problem that applies what you know about the Quadratic equation. You should use the slides of your presentation as steps in your example be able to explain what you are doing and how the Equation applies.
16. 16. The Pi Past Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] So you’re researching the past of the Pi. As the historian of the group you will gather information on the history of pi. You should touch on what Pi represents and where Pi came from. Why was it so important back then? How has it been useful throughout history? Contributing scientists. You could present information in a timeline, but anyway you can get the information across is fine. As you will find out the history of Pi is a fascinating one. You can use the following links to complete your research. A brief history Little more history A good explanation You may also conduct interviews with somebody you feel is knowledgeable on the subject. If you choose to do this you must present to me who you are planning to interview and why they are qualified along with a list of questions before conducting the interview.
17. 17. The Pi Present Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] So why is Pi important? It’s just a number right? Oh but there is so much more Check out some of current applications and see how its is used today. Look for current uses and jobs that utilize Pi. You will also need to find an application or two of how Pi plays a role in your life, (not including this class.) This has a good explanation of pi and also some uses in scientific fields. Follow the links on this page to find a number of formulas using Pi! Just a little Pi fun! You may also conduct interviews with somebody you feel is knowledgeable on the subject. If you choose to do this you must present to me who you are planning to interview and why they are qualified along with a list of questions before conducting the interview.
18. 18. The Pi Future Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] <ul><li>So you want to predict the future. Here’s what you need to do. </li></ul><ul><li>Get with your teammates to see how Pi has been used in the past, and how it is used today. </li></ul><ul><li>Once you have a good handle on it brainstorm some ideas on how it will be used in the future. If you don’t think it will be then tell me why it will be obsolete. </li></ul><ul><li>Here are some links to help you on your quest </li></ul><ul><ul><li>Explanation and current uses </li></ul></ul><ul><ul><li>Pi facts </li></ul></ul><ul><li>You may also conduct interviews with somebody you feel is knowledgeable on the subject. If you choose to do this you must present to me who you are planning to interview and why they are qualified along with a list of questions before conducting the interview. </li></ul>
19. 19. Pi Example Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] Examples need to be realistic and interesting. You should look at the resources in the past , present , and future sections. You will use this information to come up with an original real world example problem that applies what you know about Pi. You should use the slides of your presentation as steps in your example be able to explain what you are doing and how Pi applies to your example.
20. 20. Evaluation Page 1 Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] Evaluation Page 2 Content Section Score CATEGORY 10 7 4 2 Introduction Introduction grabs attention of class, accurately introduces topic, and previews presentation. Introduction accuratley introduces topic and previews presentation, but is presented in a monotone fashion Introduction off topic and does a poor job of previewing presentation. No introduction/ I have no idea what you are talking about or how it relates. Past Facts are historically accurate, presented in a logical way. Good examples of past applications. Facts are accurate, but difficult to follow at times. Good examples of past applications. Some inaccuracies, presented in unclear fashion. No or poor examples of past applications. Many inaccuracies, no logical order, no examples of past applications Present Multiple accurate representations of present applications. Original thoughts on use in everyday life. A couple present applications. Original thought on use in everyday life. A couple present applications. Little original thought, mostly regurgitated information. One or no present applications. No original thought. Future Good outside the box thinking of future applications with supporting evidence. Clever ideas but with little support may be a bit of a stretch to see where you are coming from. Not much thought put into, no supporting evidence for ideas. Difficult to follow thought. No reasonable thought, or clearly unserious ideas.
21. 21. Evaluation Page 2 Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ]
22. 22. Conclusion Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] It is easy to get frustrated with math when all you see are numbers and symbols on a page in your text book. It is my hope that when you complete this lesson that you will see how fun math can be! Or at least that what you are learning has some real world applications. Everything here has a fantastic history and future and if you so choose you can be a part of that future, and possibly change the way people think about math, the world, or the universe!
24. 24. Euclid’s Enigma(Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page A WebQuest for 10th Grade Mathematics Designed by Tyler Bradshaw [email_address] Evaluation Teacher Script Conclusion
25. 25. Introduction (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page This lesson was developed for the educator licensing course titled Educational Technology and Assessment (EDUC331) at Colorado State University. This lesson is a mathematical WebQuest intended as an end of course group project for 10 th grade mathematics or technology. It utilizes lessons on Pythagorean Theorem, The Quadratic Equation, and Pi. It requires research on the subjects, use of PowerPoint technology, and critical thinking. Evaluation Teacher Script Conclusion
26. 26. Learners (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page This lesson primarily involves 10 th grade level mathematics, and technology skills, but also encourages public speaking and critical thinking. This is a moderately advanced lesson and could be used in higher grade levels as well. Prior to this lesson students must have experience with web based research, PowerPoint, and at least an introduction to the mechanics of public speaking. Mathematics involved require knowledge of the Pythagorean Theorem, the Quadratic Equation, and Pi. Evaluation Teacher Script Conclusion
27. 27. Curriculum Standards (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page <ul><li>Colorado Model Content Mathematics Standards adressed </li></ul><ul><li>Standard 1 </li></ul><ul><li>Students develop number sense and use numbers and number relationships in problem-solving </li></ul><ul><li>situations and communicate the reasoning used in solving these problems. </li></ul><ul><li>Standard 2 </li></ul><ul><li>Students use algebraic methods to explore, model, and describe patterns and functions involving </li></ul><ul><li>numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning </li></ul><ul><li>used in solving these problems. </li></ul><ul><li>Standard 4 </li></ul><ul><li>Students use geometric concepts, properties, and relationships in problem-solving situations and </li></ul><ul><li>communicate the reasoning used in solving these problems. </li></ul><ul><li>Standard 5 </li></ul><ul><li>Students use a variety of tools and techniques to measure, apply the results in problem-solving </li></ul><ul><li>situations, and communicate the reasoning used in solving these problems. </li></ul><ul><li>Standard 6 </li></ul><ul><li>Students link concepts and procedures as they develop and use computational techniques, </li></ul><ul><li>including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem solving situations and communicate the reasoning used in solving these problems. </li></ul><ul><ul><li>. </li></ul></ul><ul><li>Thinking and communications skills were encouraged: </li></ul><ul><li>Inference-making, critical thinking, creative production, creative problem-solving, observation and categorization, comparison, teamwork, public speaking. </li></ul>Evaluation Teacher Script Conclusion
28. 28. The Process (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page <ul><li>In groups of four students will construct a Power Point presentation to be given in front of the class on one of the three topics mentioned above. The presentation will consist of : </li></ul><ul><ul><li>An introduction to the presentation telling what it is on and what we can expect in the following slides. </li></ul></ul><ul><ul><li>A main body that is broken down into four sections: </li></ul></ul><ul><ul><ul><li>Past, the history of the topic, who came up with it? When? What did people think of it at the time? What has it been used for in the past? </li></ul></ul></ul><ul><ul><ul><li>Present, how is it applied today? Is it used in physics? Math? Engineering? Where can students find an application of it in their life? </li></ul></ul></ul><ul><ul><ul><li>Future, students use what they have learned to speculate on how people will use the topic in the future. Will it be the same as today? Will it become obsolete? </li></ul></ul></ul><ul><ul><ul><li>Example, students will present their topic in a worked example in a real world application. </li></ul></ul></ul><ul><ul><li>A conclusion summing up the presentation, and what was learned from this project. </li></ul></ul><ul><ul><li>See the student process page for a step by step. </li></ul></ul><ul><li>This lesson is intended to be comprehensive in nature accomplishing bits and pieces as the term progresses a minimum of three weeks assignment to presentation is recommended for completion. This lesson will require some outside of class work on the part of the students. </li></ul><ul><li>It is recommended that groups are selected by the instructor to ensure quality and cohesive work. Elaboration may be required on some of the critical thinking aspects of the project, and should be tailored to the instructors desired goals for the project. </li></ul><ul><li>It is recommended that computer lab time is set aside for this project at various stages of the term as the instructor sees fit. </li></ul>Evaluation Teacher Script Conclusion
29. 29. Resources (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page <ul><li>You will need: </li></ul><ul><ul><li>Access to a computer lab with internet connection </li></ul></ul><ul><ul><li>Microsoft Office PowerPoint on as many computers as there are groups </li></ul></ul><ul><ul><li>Computer with projector screen for presentations </li></ul></ul><ul><ul><li>Access to YouTube </li></ul></ul><ul><ul><li>A working knowledge of all of the above </li></ul></ul><ul><ul><li>This lesson can be accomplished with one tech knowledgeable instructor </li></ul></ul>Evaluation Teacher Script Conclusion
30. 30. Evaluation (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page The main objective of this lesson is to get student to make the connection between the lesson and their life. If it is clear that they have put some thought into this and were able to make that connection then this lesson was a successful one. Secondary objectives include use of web and technology, research skills, critical thinking skills, and speaking skills. If student display some or all of these the fore mentioned standards as well as the objective of the lesson will be met . See the rubric for detailed expectations. Evaluation Teacher Script Conclusion
31. 31. Teacher Script (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page <ul><li>Introduce the lesson: The student pages do a pretty good job with what is expected, but you may want to add some of your own thoughts or expectations here. </li></ul><ul><li>Explain the functionality of the model. The side bar links will help students navigate between main heading pages, but there are also many links on the pages themselves that they will need to follow. </li></ul><ul><li>Let them navigate their way through the task page where you may get some questions on expectations. This is primarily up to you to instruct them on what you want as the facilitator, you can also refer them to the Evaluation page, (link is in the sidebar,) for further details. </li></ul><ul><li>The next step will take them to the process page where you can assign them to groups on step 1or have them navigate further to get the feel of the project before letting them start. Step 2 of the process page allows student to choose one of the three topic options. You can assign a topic or let them choose. I will navigate you through the Pythagorean Theorem option, The other two are typical. </li></ul><ul><li>This link will lead them to step three of the process where they are instructed to divide up the work. I would leave this to them, but you may offer some guidance. </li></ul><ul><li>The research topics for them to choose are listed see next slide </li></ul><ul><li>. </li></ul>Evaluation Teacher Script Conclusion
32. 32. Teacher Script Cont. [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page <ul><li>. </li></ul><ul><li>Each link will take them to their research topic page. These pages are embedded with web links related to there topic and research interest. There is also instructions on what is expected. It is recommended that you navigate these pages so that you are familiar with them. The following is an example of the Past page. And one of the web link pages. </li></ul><ul><li>See the next slide for continued script </li></ul>Evaluation Teacher Script Conclusion
33. 33. Teacher Script (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page . Evaluation Teacher Script Conclusion <ul><li>Also On the process page the students are instructed they would be grading each other. This is one method for tracking participation. It is recommended that you develop a way of tracking participation tailored to your expectations and classroom. </li></ul><ul><li>Step 5 of the process pages has web links to YouTube demos on Microsoft PowerPoint that may be applicable to their presentations. </li></ul><ul><li>The final steps outline expectations of the presentation. At this point you should direct them to the Evaluation pages and review the expectations. </li></ul>
34. 34. Conclusion (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page There are few ideas in life that will be useful forever. Concepts that change the way people view the world, change the way people approach challenges. It is the purpose of educators to enlighten young minds and guide them to become the ones that to come up with these notions. Use this lesson to help you on your quest. Evaluation Teacher Script Conclusion
35. 35. Credits & References (Teacher) [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Pages Title page image from Murilo on Flickr Teacher page sidebar image from Microsoft Clipart tag = teacher Links on this Web Quest http://en.wikipedia.org/wiki/Pythagorean_theorem http://en.wikipedia.org/wiki/Pythagoras http://www.arcytech.org/java/pythagoras/history.html http://www.londonderry.org/lms/lmc/curr.cfm?subjectId=7 http://xpmath.com/careers/topicsresult.php?subjectID=3&topicID=9 http://www.worsleyschool.net/science/files/pythagoras/pythagoreantheorem.html http://plus.maths.org/issue29/features/quadratic/index-gifd.html http://www-history.mcs.st-andrews.ac.uk/HistTopics/Babylonian_mathematics.html http://en.wikipedia.org/wiki/Quadratic_equation http://plus.maths.org/issue30/features/quadratic/index-gifd.html http://xpmath.com/careers/topicsresult.php?subjectID=2&topicID=10 http://mathforum.org/library/drmath/sets/select/dm_quadratic.html http://en.wikipedia.org/wiki/Quadratic_equation http://ualr.edu/lasmoller/pi.html http://library.thinkquest.org/C0110195/history/history.html http://en.wikipedia.org/wiki/Pi http://www.facade.com/legacy/amiinpi/ http://www.geocities.com/SiliconValley/Pines/5945/facts.html YouTube videos Courtesy of DemoTrainer on YouTube Webquest resources The WebQuest Page The WebQuest Slideshare Thanks to Dr. Jim Folkestad the instructor of the course this was developed for (EDUC331) Check out his blog SWITCHSPACE Evaluation Teacher Script Conclusion
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