Pythagorean Theorem Adventure Nancy Keck

1. Pythagorean Theorem Adventure Nancy Keck

2. The Pythagorean Theorem Student Page [Teacher Page] Title A WebQuest for 8th Grade (Connected Math 3) Introduction Task Process Evaluation Conclusion Credits Based on a template from The WebQuest Page

3. Introduction Student Page [Teacher Page] The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his students. The Pythagorean Theorem is Pythagoras' most famous mathematical contribution. According to legend, Pythagoras was so happy when he discovered the theorem that he offered a sacrifice of oxen. Pythagoras needs your help in showing disbelievers that his theorem works for all right triangles. He has the problem that some people do not believe him because they do not understand how he explains it. Your job as a group is to find ways to make everyone believers and show them that the theorem exists in real world examples. Be prepared to work hard on this project. The people you need to convince are stuck in their ways and not easily swayed. Title Introduction Task Process Evaluation Conclusion Credits

4. The Task Student Page [Teacher Page] • You will be traveling all the way back to ancient times in Greece to work as a team studying under the great Pythagoras. But be careful, the Pythagoreans had many rituals, and they approached mathematics with an almost religious intensity. Their power and influence became so strong that some people feared that they threatened the local political structure, so they were forced to disband. However, many Pythagoreans continued to meet in secret and to teach Pythagoras’s ideas. This will be your quest, and during it you will be able to: • build a table of values showing the relation between the sides of a right triangle • apply the Pythagorean Theorem to any triangle • discover the Pythagorean Theorem • show that the Pythagorean Theorem holds true for small right triangles • show that the Pythagorean Theorem does not hold true for any triangle that is not a right triangle • show to the disbelievers that the Pythagorean Theorem works • apply the Pythagorean Theorem to modern, real world problems • Once you return from your journey, you will use Xcel to build a table that you can present to any disbeliever to show them the pattern and relationship between the sides of a right triangle. You will put together a PowerPoint presentation that includes you table and different triangles, and the solutions to two real world problems that use the Pythagorean Theorem. Remember, you have to show that the Pythagorean Theorem works only for right triangles, not all triangles. Title Introduction Task Process Evaluation Conclusion Credits

5. The Process Student Page [Teacher Page] We’ve traveled way back to the time of Pythagoras. In your assigned group, you will navigate your way to proving the Pythagorean Theorem and building a table of values that will show the pattern of the relationship between the sides of a right triangle. When you get back, your last step will be to put together a presentation including real world examples of how to solve them. Meet your fellow travelers. You will be learning together and helping one another understand the Pythagorean Theorem. Open up a good line of communication. Gather some background information on where you are going and learn a little more about Pythagoras. Start by discovering the proof of the Pythagorean Theorem. Is this method any different? What does it say about the triangles it applies to? How can you write down this proof so that anyone can understand it? (Actually write it down, you need it for later) Build a table of values for the lengths of the sides of a right triangle. Write all different lengths, but keep it simple. It will be easier to see the pattern if you use small numbers. Here are some columns you might consider having in your table: length of side 1, square of side 1, length of side 2, square of side 2, length of hypotenuse, and square of hypotenuse. How does this apply to real world problems?? Check it out, here are some good problems to solve. Put this all together in one presentation. Make sure to use Xcel to build your table of values. Make this presentation look professional, you may need to use it at any time. Title Introduction Task Process Evaluation Conclusion Credits

6. Evaluation: Student Page [Teacher Page] Title Introduction Task Process Evaluation Conclusion Credits

7. Conclusion Student Page [Teacher Page] GOOD JOB!!! You have successfully convinced the disbelievers of the Pythagorean Theorem that is does in fact hold true for right triangles. Now you can begin to apply the theorem to right triangles in mathematics and in life. Because of your great work on the journey, Pythagoras can once again get back to the study of mathematics instead of having to worry about proving to everyone that his theorem holds true. You have done a great service to Pythagoras and all his students and colleagues. Your journey may be over, but you now have a presentation you can give to anyone in modern times that does not believe in the Pythagorean Theorem. Title Introduction Task Process Evaluation Conclusion Credits

8. Credits & References Student Page [Teacher Page] www.creativecommmons.org http://www.pbs.org/wgbh/nova/proof/puzzle/ http://www.arcytech.org/java/pythagoras/history.html http://rubistar.4teachers.org/index.php http://jwilson.coe.uga.edu/EMT669/Student.Folders/Morris.Stephanie/EMT.669/Essay.1/Pythagorean.html Books Fitzgerald, William M., Susan N. Friel, Glenda Lappan, and Elizabeth D. Phillips. Looking for Pythagoras, the Pythagorean Theorem. Ed. James T. Fey. Glenview: Prentice Hall, 2004. Nuzzo, M. (2008, June 20). Life Lessons - A Book Review of "The Ultimate Gift". Retrieved March 1, 2009, from http://ezinearticles.com/?Life-Lessons---A-Book-Review-of-The-Ultimate-Gift&id=1265081 Lesson Plan Marfitano, L (2007). Pythagorean Theorem Webquest. Retrieved February 28, 2009 from http://www.slideshare.net/lmarfita/pythagorean-theorem-webquest WebQwest http://www.webquest.org/index.php Title Introduction Task Process Evaluation Conclusion Credits

9. The Pythagorean Theorem(Teacher) [Student Page] Teacher Page Title A WebQuest for 8th Grade (Connected Math 3) Introduction Learners Standards Process Resources Evaluation Teacher Script Conclusion Credits Based on a template from The WebQuest Page

10. Introduction (Teacher) [Student Page] Teacher Page Title Introduction Learners This lesson stems from the book, Looking for Pythagoras used by Poudre School District in Fort Collins, Colorado. It has been designed to make the lesson more interactive and for students to use experimental techniques in their learning. Some students may need additional help and resources from the teacher, and that is perfectly fine. Other students may begin to want to learn everything using a WebQuest. While participating in this WebQwest, students will learn background information on Pythagoras and ancient times in mathematics, along with how to prove the Pythagorean Theorem and apply it to modern problem solving. Standards Process Resources Evaluation Teacher Script Conclusion Credits

11. Learners (Teacher) [Student Page] Teacher Page Title Introduction Learners This lesson is specifically made for eighth grade mathematics students. It can be extended to either seventh grade students or ninth grade students, based on their knowledge and abilities. Students will continue to use the Pythagorean Theorem in later geometry classes, so it may be useful to modify this lesson for higher level students studying the benefits of the Pythagorean Theorem. Standards Process Resources Evaluation Teacher Script Conclusion Credits

12. Curriculum Standards (Teacher) [Student Page] Teacher Page Title Introduction Learners • Essential Math Standards leading to the outcomes of this activity: • 1.1a Understand the characteristics of irrational numbers. • 1.1b Understand the relative magnitude of square roots (for example, √72 lies between 8 and 9). • 1.6a Estimate solutions with irrational numbers. • 4.5b Apply the Pythagorean theorem to solve real-world problems. • 5.4a Use the Pythagorean theorem. • 6.2a Apply order of operations to evaluate simple expressions with integers. • This activity will also teach teamwork and compromise as the students work closely with their group. Students must use good communication skills to help each other to discover the Pythagorean Theorem and put together a presentation covering their discovery. Students may also need to employ creative problem-solving techniques and critical thinking. Standards Process Resources Evaluation Teacher Script Conclusion Credits

13. The Process (Teacher) [Student Page] Teacher Page Students must be split up into groups of four before the activity begins. Be aware of how they work together and the individual strengths and weaknesses of the students in the group. They will need to work very closely with each other, so make sure they will get along for the remained of the project. Multiple classes may be doing this at one time, so use each one as a learning experience. We’ve traveled way back to the time of Pythagoras. In your assigned group, you will navigate your way to proving the Pythagorean Theorem and building a table of values that will show the pattern of the relationship between the sides of a right triangle. When you get back, your last step will be to put together a presentation including real world examples of how to solve them. Meet your fellow travelers. You will be learning together and helping one another understand the Pythagorean Theorem. Open up a good line of communication. Gather some background information on where you are going and learn a little more about Pythagoras. Start by discovering the proof of the Pythagorean Theorem. Is this method any different? What does it say about the triangles it applies to? How can you write down this proof so that anyone can understand it? (Actually write it down, you need it for later) Build a table of values for the lengths of the sides of a right triangle. Write all different lengths, but keep it simple. It will be easier to see the pattern if you use small numbers. Here are some columns you might consider having in your table: length of side 1, square of side 1, length of side 2, square of side 2, length of hypotenuse, and square of hypotenuse. How does this apply to real world problems?? Check it out, here are some good problems to solve. Put this all together in one presentation. Make sure to use Xcel to build your table of values. Make this presentation look professional, you may need to use it at any time. Title Introduction Learners Standards Process Resources Evaluation Teacher Script Conclusion Credits

14. Resources (Teacher) [Student Page] Teacher Page Title • To implement this lesson, you may need: • Class sets of books (Looking for Pythagoras) • Computers for each student in the class (this could be a building computer lab or mobile laptop station) • Access to the internet • Access to Word, Xcel, and PowerPoint • Educational websites that advance the learning of the Pythagorean Theorem for students • One teacher can effectively implement this lesson, but it is easier to have additional help for the students when working on the computers Introduction Learners Standards Process Resources Evaluation Teacher Script Conclusion Credits

15. Evaluation (Teacher) [Student Page] Teacher Page • This lesson will be successful if: • students fulfill the objectives and standards • work well in groups • establish effective group communication • understand the Pythagorean Theorem and area able to use the theorem in real world problems • You will evaluate the progress and understanding of the group using the rubric in the students section of the WebQwest. You may want to add or take away from the given rubric to fit your class and students better. Title Introduction Learners Standards Process Resources Evaluation Teacher Script Conclusion Credits

16. Conclusion (Teacher) [Student Page] Teacher Page Title This lesson is a great way to let students take a hands on approach to learning. It will allow different learning styles to excel and it will help certain students comprehend the material better because of the self-exploration piece of the activity. Students may not fully comprehend the topic, but with the assistance of the teacher, the students will have the ability to learn about the Pythagorean Theorem in multiple ways. Introduction Learners Standards Process Resources Evaluation Teacher Script Conclusion Credits

17. Credits & References (Teacher) [Student Page] Teacher Page www.creativecommmons.org http://www.pbs.org/wgbh/nova/proof/puzzle/ http://www.arcytech.org/java/pythagoras/history.html http://rubistar.4teachers.org/index.php http://jwilson.coe.uga.edu/EMT669/Student.Folders/Morris.Stephanie/EMT.669/Essay.1/Pythagorean.html Books Fitzgerald, William M., Susan N. Friel, Glenda Lappan, and Elizabeth D. Phillips. Looking for Pythagoras, the Pythagorean Theorem. Ed. James T. Fey. Glenview: Prentice Hall, 2004. Nuzzo, M. (2008, June 20). Life Lessons - A Book Review of "The Ultimate Gift". Retrieved March 1, 2009, from http://ezinearticles.com/?Life-Lessons---A-Book-Review-of-The-Ultimate-Gift&id=1265081 Lesson Plan Marfitano, L (2007). Pythagorean Theorem Webquest. Retrieved February 28, 2009 from http://www.slideshare.net/lmarfita/pythagorean-theorem-webquest WebQuest http://www.webquest.org/index.php Title Introduction Learners Standards Process Resources Evaluation Teacher Script Conclusion Credits