Pythagorean Theorem Differentiated Instruction for Use in an ...

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

Additional Activities: Activity 1: Investigate the area of squares proof using The Geometer’s Sketchpad Set up this activity on a PC with GSP. Students will be able to alter the size of the right triangle to investigate whether the area of squares proof works with any right triangle. Activity 2: Area proof using half circles This activity allows students to investigate whether an area proof will work if the shapes built on the sides of the right triangle are not squares. Activity 3: Algebraic proof This activity is for students who have superior algebraic skills. Follow the directions from The Proofs of Pythagoras page 6. Activity 4: Internet search for President Garfield’s Proof Use this activity to make a Social Studies connection. Have students search the internet to learn more about more about Garfield and find his proof. Activity 5: Finding the length of a line segment. This activity encourages students to use the Pythagorean Theorem to determine the length of line segments drawn on a grid. Activity 6: Theodosian Spiral This activity provides an interesting application for the Pythagorean Theorem. 6
Day 1 Lesson – Puzzle Proofs of the Pythagorean Theorem Objectives: Students will be able to: state that the area of squares built on the legs of a right triangle is equal to the area of the square built on the hypotenuse. conjecture that the same relationship applies to all right triangles. Materials: Scissors, glue sticks, copies of Pythagorean Theorem worksheets puzzle proof one (page 7), puzzle proof two (page 8) and puzzle pieces (page 9), transparency of proof puzzle one (page 7), right triangle tray and green and blue tiles Outline of Activities: 1. Review right triangles. Students should define right angle and find examples in the classroom. Students should define right triangle. Create a right triangle in corner of the blackboard using a yard stick. 2. Students should begin puzzle proof one. Their task is to cover the largest square with pieces of the smaller squares and look for the relationships between the areas of the squares. Read through the directions with the students. Have then cut out the pieces and cover the two small squares. Then use the same pieces to cover the largest square. There may be students who can work ahead and begin puzzle 2 on their own. Demonstrate the solution to the puzzle using the transparency. 3. Students should begin puzzle two. Their task is to cover the largest square with pieces of the smaller squares and look for the relationships between the areas of the squares. Read through the directions with the students. Have then cut out the pieces. They should cover the two small squares and then use the same pieces to cover the largest square. Students who finish the puzzle proofs quickly and identify the relationship can begin work on an alternate activity. Demonstrate the solution to the puzzle proof using the right triangle tray and green and blue tiles. 4. Class discussion. Can the pieces of the two smaller squares be used to cover the larger square? Invite students to form conjectures about whether they think this will work for all right triangles. We did two proofs of the Pythagorean Theorem, point out that there are many different proofs including one by President Garfield. Assign students additional activities as needed. 7
Page 1 and 2: Pythagorean Theorem Differentiated
Page 3 and 4: Resources Textbook Prentice Hall Mi
Page 5: Overview Introduction I developed t
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
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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
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Page 29 and 30: Name: ________________________ Acti
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Page 35 and 36: Answer key for the activities. Acti

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