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PYTHAGOREAN THEOREM: LEARNING SQUARED PLUS TEACHING SQUARED EQUALS UNDERSTANDING SQUARED |
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Master Teacher: Ken McCoy |
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OverviewThis lesson provides students with an in-depth understanding and appreciation for the Pythagorean Theorem through independent exploration. Students will describe, in writing and drawings, a working definition of the Theorem, various proofs of the Theorem and examples of its application. Students will communicate their findings through a team-teaching opportunity and through activities created by the teaching efforts of their peers. Learning ObjectivesStudents will be able to:
Oregon Standards Available at:http://www.ode.state.or.us/cifs Mathematics - Geometry
Media ComponentsVideo Check the link at http://www.opb.org/edmedia/trs/ to find access to the video(s) from unitedstreaming™ referenced in this lesson plan.
Web
MaterialsPer Student:
Per Class and/or Group:
Prep for TeachersSession I: Acquire materials and equipment. Download and preview the video clips, discovering helpful points to highlight for students during discussion and activities. Acquire the free Window's Media Player to view clips. Session II: Find examples of typical rubric for suggestions of class-created group evaluation rubric. Create a list of appropriate Internet sites and search methods to aid students in independent discovery, printing them out as a handout and/or bookmarking them on class computers or creating a Web site with links. Prepare each computer to be used with the necessary plug-ins for Web sites used (especially the free Flash and Shockwave Players available at http://www.macromedia.com/). When using media, provide students with a Focus for Media Interaction, a specific task to complete and/or information to identify during or after viewing of video segments, Web sites or other multimedia elements. Introductory ActivityGive the following hypothetical: "My Uncle Bob just emailed me and said he's locked himself out of his house. He left the water running in the bathtub and needs to get back in before it overflows. Walking around the house, he noticed that a window was open on the second floor, 25 feet above the ground. There is also a bush under the window, so he'll have to place the ladder 10 feet from the house. All his neighbors have different length ladders. What length of ladder does he need to borrow?" First, allow students the chance to guess the length of ladder without using math. Next, students can use graph paper to draw a representation of the hypothetical, perhaps seeing if the grid of the graph paper is of help. Students can then use their ruler to devise a scale. Free exploration is important here as students will discover the difficulty of solving the problem without the Pythagorean Theorem. (10 minutes total) Learning ActivitiesSession I Step 1: Present the hypothetical and ask students to use graph paper to present their answers. Have students use rulers to draw and measure their work, reminding them of the need to be neat and organized to aid them in arriving at an accurate answer. (10 minutes) Step 2: As students work, explain to them that they are working on a problem that is older than your Uncle Bob, maybe older than bathtubs and two-story houses, and maybe even older than ladders. Step 3: Give basic information on Pythagoras and his approach to the problem. Information gleaned from Web sites and video clips, provided in this lesson plan, can be helpful in this brief informational presentation. (3 minutes) Step 4: Provide students with a Focus for Media Interaction by having them make notes on their drawings from Step 1 while viewing clips from the video, "Project Mathematics: Theorem of Pythagoras" (22:00): 1) "The Theorem of Pythagoras: Three Questions from Real Life" (02:52) and 2) "Discovering the Theorem of Pythagoras" (01:18). Play the video clips. (5 minutes) Step 5: Upon the completion of Step 4, discuss with the
class how the algebraic exploration of the Pythagorean Theorem can
be difficult to grasp for a beginner. Ask for responses as to why
that might be. Possible answers include: "When dealing with
numbers, it can be hard to see what's happening." (5 minutes) Step 7: State to the class, " 'Rediscovered, again and again' and that's what we're going to do," in an effort to reveal the activities ahead. Explain that they will rediscover the Pythagorean Theorem on their own through independent research and exploration. Explain that your role of teacher will be as support in their efforts, as a resource if needed, as an observer and as a participant in their final activity. (2 minutes) Step 8: Before answering any questions about what's ahead, provide students with a Focus for Media Interaction by asking them, "How would you teach someone this concept of the Pythagorean Theorem?" Play the video clip, "Applying the Pythagorean Theorem" (01:15), from the video, "Project Mathematics: Theorem of Pythagoras" (22:00). (2 minutes) Step 9: Allow for a short discussion regarding some ideas as to how students would teach the concept. Explain to students that for the rest of their study of the Pythagorean Theorem they will be preparing to do just that, teach the Theorem and its various proofs to the class. (10 minutes) Session II Step 1: Restate the focus for the group: to teach the Pythagorean Theorem to the class. Explain that in order to do that, one would need to have at least some familiarity and understanding of the Theorem itself. Ask students, "How could you gain that understanding?" Wait for an answer that refers to research, using that statement to explain that students will be involved in research to prepare their lessons. (2 minutes) Step 2: Students are encouraged to work in teams of two (squared) to explore and illustrate the Pythagorean Theorem and at least two of its proofs, one of which will be taught to the class. Students are grouped, through choice, teacher selection or some other means, and now situate themselves to sit as a group. (3 minutes) Step 3: Ask students, "Have you ever tried to learn something when the lesson or teacher was boring?" Use their responses to explain that their lessons will need to be well-planned, engaging and involve some activity to explore the concept they're attempting to teach. (2 minutes) Step 4: Model two lessons, asking students to be ready to discuss positives and negatives of each lesson upon its completion.
Step 5: As students discuss in their groups, teacher passes out copies of an example assessment rubric as a guide for the next step. Step 6: Guided by the teacher, the class will design a rubric to be used in evaluation of teaching teams. Once created, a student or group will be responsible for creating the form and disseminating it to the class, one copy for each group per student. (6 minutes) Step 7: Teacher passes out the list of acceptable Web sites and search engines for use in the project. Step 8: Students will use the suggested Internet sites and search terms to independently extend their learning about the Theorem and the various proofs. Step 9: Students will have one to three workdays for exploration and preparation of their presentations, during which time groups are free to collaborate with other groups to share information and teach concepts. Early in the workday schedule, it may be helpful to publish for the class's benefit which work groups plan to cover which proofs, to help lower the chances of a proof being taught multiple times. Culminating ActivityStudents will team teach their findings and illustrations of their assigned proofs. Presentations will include lesson presentation, activity and assessment, as well as a chance for the class to evaluate the team via the class-designed rubric. Depending on class size, number of groups and time planned by each group, this activity will undoubtedly take multiple sessions to complete. Cross-Curricular ExtensionsHealth & Physical Education
Mathematics
History and Social Studies
Community Connections
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