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Understanding and Applying the Pythagorean Theorem
Carol Szatko
Mathematics




Unit created on 6/21/1999 EST.
Last modified 3/7/2000 10:29:23 AM EST.


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Fundamental Understandings (help)


1. To understand the background pertaining to the proof of the Pythagorean Theorem. 2. Applying the Pythagorean Theorem to calulate lengths of sides in right triangles and other figures. 3. Applying the Pythagorean Theorem in solving problems involving real life situations. 4. Applying the converse of the Pythagorean Theorem to determine if the triangle is a right triangle.


Technology ISTE Standards (info) 


Basic operations and concepts Technology productivity tools Technology communication tools Research tools Technology problem-solving and decision-making tools

Information Literacy Standards (info) 




Relevance (help)


Reside at the heart of the discipline The Pythagorean Theorem and its converse is used in solving problems involving boundaries, packing, construction, real life situations. In order to solve these problems, the student will have to identify a right triangle and its parts, use the formula a2 + b2 = c2, and plug into this formula the correct lengths of a right triangle. Represents a big idea having enduring value beyond the classroom: With the understanding of the Pythagorean Theorem and its converse, students will apply the concepts in solving real life situations. Require uncoverage, meaning that misconceptions need to be identified and clarified: With the study of Pythagoras and the proof of the Pythagorean Theorem, it will enable the student to make the connection between the areas and the lengths of the sides of a right triangle.

Assessment (help)


a. Checks on understanding throughout the unit with the use of worksheets, oral discussions, quizzes. b. Students will be given a "problem of the day" to be solve within a group. c. Students will be given a "problem of the day" to be solve by themselves. d. End of a unit project which will determine the students understanding and use of the Pythagorean theorem and its converse.

Components (help)


1. Students will use the computer to study the background to the Pythagorean Theorem. Who was Pythagoras? How was the relationship between area and lengths proven? 2. In groups, students will discover the Pythagorean Theorem for themselves through a problem solving activity. 3. How to apply the Pythagorean Theorem to a right triangle? Students, working with a partner, will do problems finding the missing side of a right triangle. 4. In groups, students will discover the relationship between right, acute, and obtuse triangles and the solution to a2 + b2 = c2. What type of ` triangle is formed if a2 + b2 = c2? (Converse of the Pythagorean Theorem) What type of triangle is formed if a2 + b2 > c2? What type of triangle is formed if a2 + b2 < c2? 5. How does the Pythagorean Theorem relate to real life situations? With partners, students will be given situations in which the Pythagorean Theorem will have to be applied.

URLs (help)


http://www.ops.org/north/tc/lessons/math/geometry/index.htm


Workforce Competencies (info) (help)



Lessons


Pythagorean Theorem #2
Pythagorean Theorem #3
Pythagorean Theorem #1
Who is Pythagoras?





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Career Connection to Teaching with Technology
USDOE Technology Innovation Challenge Grant
Marshall Ransom, Project Manager
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