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An ancient theorem with modern applications. a 2 + b 2 = c 2 Pythagorean Theorem Special Needs Accommodations Click to Listen

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Special Needs Accommodations: Requires help from Special Education since the mathematic concepts are difficult to process and reason. The needs listed below require help as well. For hearing needs: Students may read the text and notes on the bottom of the slides. YouTube audio and narration may be a problem. For vision needs: Students that can’t see well may need help with interactive slides. They may listen to the narrative. A screen reader may be used as well. For motor coordination: Require help to use the interactive slides. Click to Return To Presentation

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Pythagoras Greek credited for theorem. Lived about five hundred years B.C. 569 – 475 B.C. Click here for more images.here

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Pythagoras saw a relationship between the areas of squares and the sides of a right triangle. x side leg hypotenuse

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Proof + = 3 2 + 4 2 = 5 2 9 units + 16 units = 25 units

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Proof + = a = 3 b = 4 c = 5

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http://www.myastrologybook.com/PythagoreanTheorem16c.gif Proof right triangle

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Pythagorean Theorem Defined In a right triangle,right triangle the sum of the square of the two legssquare a 2 + b 2 is equal to the square of the hypotenuse.hypotenuse = c 2

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x a = 3 c = 5 b = 4 3 2 + 4 2 = 5 2 Right Angle Triangle right angle hypotenuse leg a 2 + leg b 2 = hypotenuse c 2

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To find Square Root, Use Inverse Operations Adding and subtracting are inverse operations: 3 + 4 = 7 and 7 – 4 = 3 Square and square root are inverse operations: 3 x 3 = 9 or 3 2 = 9 and 3 2 = 3

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Find the square of 3: type “3 x 3 = 9” Click on calculator image to calculate. Find the square root of 9: first type 9, then (radical) symbol, answer = 3. Solve by using a calculator:

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Use mental math to find the square of a number: For more review of squares, click here.here If you like games and are fast with squares, click here.here

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Use calculations to find the square root of a number: http://www.youtube.com/watch?v=rHyaXYtjqvY

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Real-life solutions: A baseball diamond measures 90 feet on each side. Find the distance from home plate to second base. Give your answer in both in decimals and square root. For answer, click here.here http://www.statemaster.com/wikimir/images/upload.wikimedia.org/ wikipedia/en/1/17/Baseball_field_overview_thumbnail.png

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Answer to baseball diamond: The distance from home plate to second base is 127.3 feet. If using mental math the answer is 90 2 feet. Question: Why are some answers better in decimals and not in square root? Click to Return To Presentation http://www.statemaster.com/wikimir/images/upload.wikimedia.org/ wikipedia/en/1/17/Baseball_field_overview_thumbnail.png

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Real-life solutions, continued: Microsoft clip art You are moving. If the height of the truck is 5 feet, and the distance from the truck to the bottom of the ramp is 8 feet, how long is the ramp? For answer, click here.here

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Moving ramp length: The length of the ramp is 9.4 feet. Click to Return To Presentation 5 ft. 8 ft.

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Assignment: Rubric on slide 20. Cooperative partners: make a web search of real- life examples using the Pythagorean Theorem. The next slide gives three examples you may use instead. Make a two page PowerPoint: Page 1, your own real-life word problem adapted from the web, include an image with the URL to document it. Page 2, answer and how you solved it. All slides will be put into a class PowerPoint. You will solve them for a class assignment. See sample on slides 21 and 22.

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Assignment: Examples of real-life problems from the web: The Pythagorean Theorem and Ladders The Pythagorean Theorem and Pyramids Pole in a Box Microsoft clip art Click to Return To Presentation

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PowerPoint Rubric __ / 10 2 slides (2 pts.) Clear explanation of real-life example, with good sentence structure and spelling (4 pts.) Uses a clip art or picture (1 pt.) Uses URL of picture or indicates it is Microsoft clip art (1 pt.) Answer is correct and shows how to solve (2 pts.) Totals 10 points.

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Sample Assignment: A handicapped couple need a ramp. The landing measures two feet from the ground. Building code requires it to Building code be at least 16 feet long. How far from the landing do you start the ramp? Answer Answer http://www.vadeck.com/images/ramps/modular-aluminum-handicap-ramp.jpg

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The ramp needs to start 15.8 feet from the porch landing. a 2 + b 2 = c 2 2 2 + b 2 = 16 2 4 + b 2 = 256 b 2 = 251 b 2 = 251 b = 15.8 feet 16 2 b2b2 2 Click to Return To Presentation

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Jobs that use Pythagorean Theorem Management Professional Farming Construction Installation Production Click here for job links…here Microsoft clip art

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Exercise Solve x 2 = 4. x = ± 2. Solve x 2 = – 4. no real solution Exercise.

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