Pythagorean Theorem Differentiated Instruction for Use in an ...

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$By: Melissa Hanel Math B/Grade 11 5 Day Unit Plan Technologies ...$

Name: _______________________________ Activity 6 The Theodosian Spiral begins with a triangle which has legs measuring 1 unit. Each new triangle is drawn using the hypotenuse of the previous triangle as one leg with a second leg measuring 1 unit. This creates a spiral which winds around counterclockwise. Use the Pythagorean Theorem to find the length of each hypotenuse in the Theodosian Spiral. Label the spiral below. Express the lengths using √ symbol. 1 1 1 1 1 2 1 1 1 1 Add the next two triangles to the spiral. Label the length of the sides. Describe the method you used. (Use complete sentences) 34
Answer key for the activities. Activity 1: Student’s answers will vary. Activity 2: Leg of length 3 Area = ½ π(1.5)² = 3.5 sq units Leg of length 4 Area = ½ π(2)² = 6.3 sq units Leg of length 5 Area = ½ π(2.5)² = 9.8 sq units The sum of the areas of the half circles built on the legs is equal to the area of the half circle built on the hypotenuse. Activity 3: (a + b )² = c² + 4(1/2ab) a² + ab + ab + b² = c² + 4(1/2)ab a² + 2ab + b² = c² + 2ab a² + 2ab – 2ab + b² = c² + 2ab – 2ab a² + b² = c² Activity 4: Garfield’s proof can be found: http://mathworld.wolfram.com/PythagoreanTheorem.html Garfield’s proof is based on a trapezoid. Information on Garfield can be found: http://www.americanpresident.org/history/jamesgarfield/ Activity 5: Length of segment AB 2² + 5² = 29 √29 = 5.385164807 Length of segment CD 2² + 3² = 13 √13 = 3.605551275 Length of segment EF 3² + 5² = 34 √34 = 5.830951895 Length of segment GH 1² + 5² = 26 √26 = 5.09901919514 Length of segment JK 2² + 2² = 8 √8 = 2.828427125 35
Page 1 and 2: Pythagorean Theorem Differentiated
Page 3 and 4: Resources Textbook Prentice Hall Mi
Page 5 and 6: Overview Introduction I developed t
Page 7 and 8: Day 1 Lesson - Puzzle Proofs of the
Page 9 and 10: Name ______________________________
Page 11 and 12: Day 2 Lesson - Developing the Pytha
Page 13 and 14: page 2 Count the blocks in the smal
Page 15 and 16: page 4 How can we use the Pythagore
Page 17 and 18: Name:___answer key_________________
Page 19 and 20: page 4 How can we use the Pythagore
Page 21 and 22: Day 3 Lesson - Applying the Pythago
Page 23 and 24: Name: _____________________________
Page 25 and 26: Answers 1) 22 cm 2) 51 in 3) 16 ft
Page 27 and 28: Name: _answer key__________________
Page 29 and 30: Name: ________________________ Acti
Page 31 and 32: Name:______________________________
Page 33: Name:_____________________________

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