Proving the Point: A Perigon of Geometry
Tuesdays at 3:00 pm and Thursdays at 4:30 pm Eastern for 16 weeks
Instructor: Lisa Fontaine-Rainen
What happens when you make that point? What if you draw this line in the sand? Geometry may sound a lot like arguing, but the deductive logic behind it makes those arguments, well, pointless.
Proving the Point: A Perigon of Geometry is an advanced, fast-paced high-school level geometry course that encourages deep understanding of geometric concepts, with an emphasis on Euclidean geometry, and deductive reasoning to construct proofs. We will be working on completing a full Geometry curriculum in 16 weeks.
The course is designed to meet the needs of gifted and twice exceptional students ready to tackle high school geometry. In response to the needs of these students, the course is designed to be flexible and responsive – thinking, learning, and engagement take precedence over all else. With this in mind, the syllabus may change based on the needs of the students.
This course will weave Geometry: Seeing, Doing, Understanding by Harold Jacobs with Art of Problem Solving’s Introduction to Geometry. Students are encouraged to have access to both texts – please contact the instructor directly if this is a financial hardship.
Students will need to do homework outside of class to ensure we can keep up the pace. This will include in-depth problems, simple exercises, proofs, quizzes and tests, and projects. Work will be modified based on the learning needs of each student, and opportunities for further exploration will usually be provided. Grades are optional – learning is constant.
Syllabus:
Week 1: Introduction to Geometry
Week 2: Introduction to Deductive Reasoning
Week 3: Lines and Angles – an introduction to construction
Week 4: Congruence – Triangles and Constructions
Week 5: Inequalities in Geometry
Week 6: Parallel Lines and Proofs
Week 7: Quadrilaterals
Week 8: Transformations
Week 9: Area
Week 10: Similarity
Week 11: The Right Triangle – an introduction to Trigonometry
Week 12: Circles
Week 13: Concurrence Theorems
Week 14: Regular Polygons
Week 15: Geometric Solids
Week 16: Non-Euclidean Geometries