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Honors Geometry Geometry Theorem In-Class Assignment (40 points) For this assignment, you will research a theorem, problem or topic that we have not studied this semester. In a group of two or three, you and your partners will find a topic on the internet, in another geometry book, or even in our own book and research it. You will then create a presentation on your topic and discuss it in class on Friday. Your presentation should include a Geometer’s Sketchpad design illustrating the theorem. You should turn in a short, one- or two-page typed summary of the topic and any interesting history behind it (including the history of the creator), in addition to a printout of your GSP or TI-Nspire sketch. You must cite at least two sources (Wikipeadia cannot be used as a source.) Remember to follow copyright law and provide appropriate documentation of sources. Some ideas for possible theorems/ projects for study: (Note: In a class, no two groups may study the same theorem/problem/project) Aubel’s Theorem Blashke’s Theorem Jung’s Theorem Johnson’s Theorem Kepler-Poinsat polyhedra Koch’s snowflake vs Sierpinski’s Lebesque’s minimal problem Limacon of Pascal Malfatti’s Problem Poincare’s model of hyperbolic geometry Plateau’s problem (use soap bubbles) Seven circles Theorem Steiner’s Theorem Philo’s Line Peaucellier’s cell (linkage strips) Monge’s Theorem Miquel’s Theorem Penrose tilings Blanche Descarte’s Division of a Square Holditch’s Theorem Cycloid by Mersenne “Flatland” by Edwin A Abbott taxicab geometry spherical geometry A theorem of your own choice, with instructor approval. Guidelines for presentations: Your presentation should be aimed at another geometry student who knows nothing about the topic. Define unfamiliar terms, for example, do not assume everyone knows what a “medial triangle” is. Begin your group presentation with a brief summary of your work on the investigation. (What is it about? What is the main point of the theorem?) Your GSP sketch should be a “good” sketch that if moved around, still shows the theorem is true. Be sure that each member of the group participates in the presentation. Individual students in the group will receive a grade for the individual parts of the presentation. Honors Geometry Geometry Theorem In-Class Assignment (40 points) Grading Standards: Organization Is the presentation organized? Did you make the group familiar with the topic? Content Was the information correct? Did the speaker include clear diagrams as needed? Did the speaker answer questions (if any) correctly? Clarity Did the audience understand what the speaker was talking about? Did the speaker add explanations and examples when necessary? Delivery Was the presentation interesting? Each component will receive a score of 5-0 for a total of 20 points for the presentation. 5: Exemplary response (Did a great job) 4: Competent response (Did a good job) 3: Emerging (Almost; a fair job) 2: Not effective (Not quite, but they tried) 1: Minimal attempt (Not much effort given to topic) 0: No attempt (Did not even try) Your summary report and sketchpad printout will be worth 20 points each and will be graded based upon: The information is correctly illustrated. (6 points each) The information is organized and labeled in a clear manner. (6 points each) Printout of Geometer’s Sketchpad or Ti-Nspire sketches are included. (4 points) There are no spelling or grammar errors. (4 points maximum deduction) Honors Geometry Geometry Theorem In-Class Assignment (40 points) Honors Geometry Theorem Presentation Names: Theorem: Organization Content Clarity Delivery Total: /20 Grading Standards: Organization Is the presentation organized? Did you make the group familiar with the topic? Content Was the information correct? Did the speaker include clear diagrams as needed? Did the speaker answer questions (if any) correctly? Clarity Did the audience understand what the speaker was talking about? Did the speaker add explanations and examples when necessary? Delivery Was the presentation interesting? Each component will receive a score of 5-0 for a total of 20 points for the presentation. 5: Exemplary response (Did a great job) 4: Competent response (Did a good job) 3: Emerging (Almost; a fair job) 2: Not effective (Not quite, but they tried) 1: Minimal attempt (Not much effort given to topic) 0: No attempt (Did not even try)