2) Groups share with the whole class the patterns or relations they have found. The teacher then introduces the terms hypotenuse (long side) and legs (shorter sides). Students investigate and discuss relations between the long side of each triangle and the two shorter sides. Each group measures the three sides of their triangles and enters the measurements into a spreadsheet. Description of Project or Narrativeġ) Working in groups of three or four, students create a variety of right-angled triangles by cutting corners from rectangular sheets of paper or cardboard using a straight edge. They investigate the possible generalization of the theorem to other similar shapes drawn on the sides of right triangles using dynamic geometry software. They search the Web for information on Pythagoras and many different visual proofs. Once the Pythagorean relation has been established, students generate visual proofs using duplicate cutouts of right triangles and the dynamic software. They also use the spreadsheet to square the values of each measurement and look for possible relations among squared values. Students use the spreadsheet to look for possible patterns in the measurements. They measure the sides of these various right triangles and record measurements in a spreadsheet. Task - Students construct a variety of right triangles using a right-angled set square, cutting corners from pieces of paper or cardboard, or using dynamic geometry software. In the middle grades, an investigation of the lengths of the sides of right triangles and the area of squares drawn on those sides introduces students to irrational numbers, - Pythagorean triples (derived from right triangles with integer sides), and methods of indirect measurement used for solving real-life problems. Purpose - The Pythagorean Theorem is one of the most useful relations in mathematics. Grade Level: 6 - 8 Subject Area: Geometry Topics Addressed: Triangles Aim: To define and discover the Pythagorean Theorem Objective(s): Students will be able to: - Identify the right angle, hypotenuse, and legs of a right triangle - Explore the relationship between the lengths of the three sides of a right triangle to develop the Pythagorean Theorem - Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle - Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator Technology used: Student Technology: Geometer’s Sketchpad, Google Spreadsheets & any technology tool of their choice to present a proof developed by the student Teacher Technology: Geometer’s Sketchpad, Google Spreadsheets & projector Length of Lesson: 5 days about 40 minutes each day Investigating and Understanding the Pythagorean Theorem
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