Pythagorean Theorem Differentiated Instruction for Use in an ...

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

Materials and Equipment Scissors (class set) glue sticks (class set) copies of Pythagorean Theorem worksheets puzzle proof one and puzzle proof two transparency of proof puzzle one right triangle tray and green and blue tiles (ETA Cuisenaire, The Proof of Pythagoras, proof 1) copies of notes for Days 2 transparency of notes page 3 calculators transparencies of questions from the textbook 8 pp 362, 19 and 20 pp 363, and 20 pp 367 copies of directions for the activity for Day 3 several rectangular boxes and triangles cut from construction paper which fit diagonally inside the box string tape copies of practice 8-6 from workbook computer The Geometer’s Sketchpad internet connection copies of activity sheets for each of the 6 additional activities 4
Overview Introduction I developed this unit in response my student teaching experience with an inclusion class. I had students who worked on many different levels. Some students could complete the lesson with minimal direct instruction while other students needed careful step by step instruction. I wanted to develop related activities for mathematically precocious students to explore while I worked with the rest of the class. I hoped that this would keep them interested in the mathematics and decrease classroom disruptions. The alternative activities can be assigned to students based on your experience with your students. I would require students to complete the class work before moving on but you may have a gifted student for which this is not necessary. The activities are not necessarily associated with one particular day and can be used at each teacher’s discretion. The additional activities are included after Day 4 in the unit plan. Day 1 Use activities to help all students discover the relationship between the areas of squares built on the sides of right triangles. Students will complete two ‘puzzle’ proofs by inspection of the Pythagorean Theorem. Each puzzle is based on a different right triangle and a different proof. Day 2 Review right triangles and the area of a square. Introduce right triangle vocabulary, leg and hypotenuse. Discuss the activities of day one and use what was learned to develop the Pythagorean Theorem. Review how to use the calculator to estimate square roots. Introduce using the Pythagorean Theorem as a way to solve problems finding the side lengths of right triangles. Day 3 Review formula for the Pythagorean Theorem and how to use a calculator to estimate square roots. Use the Pythagorean Theorem to solve problems in context. End this day with an activity that allows the students to apply what they have learned. Students will work cooperatively to find the longest rod that will fit inside a box. Day 4 Review leg, hypotenuse, and formula for the Pythagorean Theorem. In Egyptian Surveying Activity students create a right triangle with a piece of string that has been partitioned into 12 equal pieces. This activity will reinforce using the Pythagorean Theorem with right triangles only. Students will practice determining whether or not a triangle is a right triangle. 5
Page 1 and 2: Pythagorean Theorem Differentiated
Page 3: Resources Textbook Prentice Hall Mi
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 and 34: Name:_____________________________
Page 35 and 36: Answer key for the activities. Acti

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