Teacher's CyberGuide Pythagorean TheoremBy John KaucherApple Valley Middle SchoolJohn_Kaucher@avsd.k12.ca.us Content Summary: This unit of study provides math resources for students in an 8th grade Geometry course to study the Pythagorean Theorem. Introduction: In this unit, students, working individually, with partners or small groups, will use various Web sites to investigate the Pythagorean Theorem. They will learn the history of Pythagoras and the Pythagorean Theorem and will see a variety of proofs of the Pythagorean Theorem. They will then choose one proof and demonstrate it to the class, individually or in small groups. The student activities are independent of one other and do not have to be completed in any order or by all students. Each activity culminates in a student-created product. Disclaimer: The links in this guide have been scrutinized for their grade and age appropriateness; however, content of links on the World Wide Web change continuously. Teachers should review all links before introducing CyberGuides to students. Student Activity 1 http://www.geom.umn.edu/~demo5337/Group3/hist.html Students will knot a rope in 12 evenly spaces. They will then use this rope to test for right angles in the room by forming the rope into a 3-4-5 right triangle, giving an angle of 90 degrees. Students will visualize a proof from an oriental design using isosceles right triangles. (Links to the Chinese Proof are no longer there) (Euclid's Proof takes a very long time to download--2 minutes and just shows the scroll in Greek that he actually wrote) The time for the rope activity will take one or two class periods to make the rope and test right angles. The other activity could be done at home for homework or the text day in small groups using square tiles or isosceles right triangles. Materials: 1. An 18 inch piece of rope for each child. 2. At least 32 isosceles right triangles of identical size per group. 3. Access to a computer at school or at home. Activity / Objective: 1. Learn a brief history of Pythagoras. 2. Compare right angles with a 3-4-5 right triangle. Assessment Suggestions: 1. Teacher observation of students comparing their knotted right triangles with right angles in the room. 2. Check students' written work describing how and why one can prove the Pythagorean Theorem using the tile pattern. Student Activity 2: http://www.cut-the-knot.com/pythagoras/#uni Materials: 1. Access to a computer 2. Paper and Pencil 3. Graph Paper. Activity / Objective: 1. Students see many different proofs of the Pythagorean Theorem. 2. Students will demonstrate competency at proving the Pythagorean Theorem using one of the methods. Assessment Suggestions: 1. Teacher check of students written proof. 2. Teacher observation of proof demonstrated orally to the class individually or in small groups. Websites / Links: 1.Pythagoras, biography 2.Ask Dr. Math § Another incarnation of #4 § They try and try and try § President Garfield's 3.A proof of the Pythagorean Theorem by Liu Hui (third century AD) California Content Standards addressed: Math Geometry Standards 14.0 and 15.0 http://www.cde.ca.gov/board/pdf/math.pdf 14.0 Students prove the Pythagorean theorem 15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides or right triangles. 1.W.Dunham, The Mathematical Universe, John Wiley & Sons, NY, 1994. 2.W.Dunham, Journey through Genius, Penguin Books, 1991 3.H.Eves, Great Moments in Mathematics Before 1650, MAA, 1983 4.R.B.Nelsen, Proofs Without Words, MAA, 1993 5.R.B.Nelsen, Proofs Without Words II, MAA, 2000 6.J.A.Paulos, Beyond Numeracy, Vintage Books, 1992 7.T.Pappas, The Joy of Mathematics, Wide World Publishing, 1989 8.F.J.Swetz, From Five Fingers to Infinity, Open Court, 1996, third printing * The format for this CyberGuide was based on the template which was part of Project TEC, a grant funded by the California Technology Literacy Challenge Grant. |