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Euclid's Enigma

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A Mathematics/ Technology base WebQuest for highschool students

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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!