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Introduction ( Task ( Process ( Resources ( Evaluation ( Conclusion ( Credits
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Introduction
This web-quest was created as an extension to the CMP unit: Looking for Pythagoras. The focus of this quest is to provide background information in which you, the student, can build upon prior knowledge to solve real world problems using the Pythagorean Theorem.
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Introduction ( Task ( Process ( Resources ( Evaluation ( Conclusion ( Credits
Task
This unit was developed to support a proficient understanding of the Pythagorean Theorem. You will first explore and write about Pythagoras. You will investigate his important contributions, his biographical information and provide interesting facts in part one of this quest.
In the second part of this quest you will explore the theorem as explained by Pythagoras. You will investigate sites and fill out a questionnaire to show proficient understanding and learning of the theorem.
In the third and last part of this quest you will apply what you have learned about the Pythagorean Theorem to solve real world problems.
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Introduction ( Task ( Process ( Resources ( Evaluation ( Conclusion ( Credits
Process
QUEST #1 Who was Pythagoras?
In Quest #1 you will be gathering information on the life and contributions of the Mathematician Pythagoras. Visit the sites below and take notes on a 3X5 index card for each site. Pay attention to his biographical information and any interesting facts and contributions. You will turn in these note cards along with your essay. Please refer to the scoring rubric located in the evaluation section before you explore these sites. You should have six note cards when you are finished with this part of the quest.
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Pythagoras Biographical Links
History of Pythagoras and His Theorem
Pythagoras
Pythagoras - The Man
Pythagoras - All Aspects of His Life
Pythagoras - History for Kids
History of Pythagoras
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QUEST#2 What is the Pythagorean Theorem?
Now, you will explore the Pythagorean Theorem. As you explore this section you will need to document your findings from each website on the "EXPLORE IT" Questionnaire located below. Print this questionnaire and hand in.
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Pythagorean Theorem Links
1) An Interactive Proof of Pythagoras' Theorem
2) Animated proof of the Pythagorean Theorem
3) Davide P. Cervone ~ The Pythagorean Theorem
4) Pythagorean Theore0m with Tile Patterns
5) Annotated Proof of the Pythagorean Theorem
6) Pythagorean Puzzle
7) Pythagorean Theorem Main Page
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EXPLORE IT! Questionnaire
Name: _____________________ Date: ________________
Group: _____________________ Teacher: _______________
DIRECTIONS: Print out this form, complete this questionnaire as you explore each of the seven websites. Be careful to read each question and answer it completely before moving on to the next question. If need more space use a separate sheet of lined paper, label questions appropriately and attach to questionnaire. Turn in, when completed, to your teacher.
1) An Interactive Proof of Pythagoras’ Theorem
A. At this website you will see the Pythagorean proof in action. As you progress through the proof it shows you a different way to prove the theorem. Instead of showing that the areas of the smaller squares add up to the area of the big one, what does it show instead? Be sure to give an example and explain your reasoning.
B. Also at this website it discusses what a shear is. Explain what a shear is and provide an example.
2)Animated Proof of the Pythagorean Theorem
A. At this website it shows you an animated proof of the theorem. What does the animation start with and then what finally happens to the quadrilaterals?
B. This website mentioned congruent quadrilaterals. What is a congruent quadrilateral?
3) Davide P. Cervone ~ The Pythagorean Theorem
A. At this site it provides a visual proof of the Pythagorean Theorem. Copy this figure and write the brief explanation.
4) Pythagorean Theorem with Tile Patterns
A. At this site it provides historical information about the theorem. What does it specifically say about what Pythagoras found?
B. This site also shows a tile pattern. Copy the tile pattern and provide the information
that proves the theorem.
5) Annotated proof of the Pythagorean Theorem
A. Describe what you observe at this site. Be specific. Provide examples if you would like.
6) Pythagorean Puzzle
A. At this site it tells you to check it out – click on “Shockwave version” and follow instructions for the interactive proof. Demonstrate the proof below using the same diagram and showing how you moved the squares.
7) Pythagorean Theorem Main Page
A. As you review this site visit the applications of the Pythagorean Theorem. Choose the textbook problems and solve the first problem. Be sure to show all of your work including the formula.
QUEST #3 Real World Applications
Finally, you will investigate real world applications of the Pythagorean Theorem. You will do each problem and record your work on the "Real World Applications" template located below. Explore the link below and review the Pythagorean Theorem. Answer the three problems found at this site. Remember, you must show all of your work and explain your reasoning for each problem solved.
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Real World Applications Worksheet
Name: __________________ Teacher: ______________
Group: __________________ Date: ________________
Solve each of the three problems found at the link provided in Quest #3.
Problem #1: Baseball
(Remember to show all of your work and explain your reasoning.)
Problem #2: Ladders
(Remember to show all of your work and explain your reasoning.)
Problem #3: Pyramids (Super Challenge)
(Remember to show all of your work and explain your reasoning.)
Introduction ( Task ( Process ( Resources ( Evaluation ( Conclusion ( Credits
Resources
• web sources are listed in the various sections of this web-quest
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Introduction ( Task ( Process ( Resources ( Evaluation ( Conclusion ( Credits
Evaluation
Who was Pythagoras?
Student Scoring Rubric
Use this rubric as a guide for the research paper required in Quest #1
|Category |4(proficient) |3 (almost) |2(apprentice) |1(novice) |0 |
|Organization |Information is very |Information is |Information is |The information |NO ATTEMPT |
| |organized with |organized with |organized, put |appears to be | |
| |well-constructed |well-constructed |paragraphs are not |disorganized. | |
| |paragraphs and |paragraphs. |well-constructed. | | |
| |subheadings. | | | | |
|Note Cards |Notes are recorded and|Notes are recorded |Notes were taken and |Notes are recorded |NO ATTEMPT |
| |organized in an |legibly and are |some cards were turned |only with peer | |
| |extremely neat and |somewhat organized. |in. |/teacher assistance | |
| |orderly fashion. There|Most of the cards are | |and reminders. Few | |
| |are a total of six |there. | |cards were turned in. | |
| |cards. | | | | |
|Quality of Information|Information clearly |Information clearly |Information clearly |Information has little|NO ATTEMPT |
| |relates to the main |relates to the main |relates to the main |or nothing to do with | |
| |topic. It includes |topic. It provides 1-2|topic. No details and |the main topic. | |
| |several supporting |supporting details and|/or examples are given.| | |
| |details and /or |/or examples. | | | |
| |examples. | | | | |
|Paragraph Construction|All paragraphs include|Most paragraphs |Paragraphs included |Paragraphing structure|NO ATTEMPT |
| |introductory sentence,|include introductory |related information but|was not clear and | |
| |explanations or |sentence, explanations|were typically not |sentence were not | |
| |details, and |or details, and |well constructed. |typically related | |
| |concluding sentence. |concluding sentence. | |within the paragraphs.| |
|Mechanics |No grammatical, |Almost no grammatical,|A few grammatical, |Many grammatical, |NO ATTEMPT |
| |Spelling or |Spelling or |Spelling, or |Spelling, or | |
| |punctuation errors. |punctuation errors. |punctuation errors. |punctuation errors. | |
Student:_________________________________________SCORE:_________________
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“Explore It! Questionnaire” and “Real World Applications Worksheet” will also be evaluated for total grade.
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Introduction ( Task ( Process ( Resources ( Evaluation ( Conclusion ( Credits
Conclusion
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Students have been provided with a variety of interactive experiences to support a proficient understanding of the Pythagorean Theorem as explained by Pythagoras. Students explored the life of Pythagoras, learned about the theorem he is famous for and utilized this knowledge to solve real-world problems.
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Introduction ( Task ( Process ( Resources ( Evaluation ( Conclusion ( Credits
Credits
• Kimberly Crabtree, Kennedy, MS QuestGarden
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