The Math 8b course is designed to teach the fundamentals of logic and geometric proofs, including similar and similar triangles, quadrilaterals, and polygons, circles, power of a point, three-dimensional geometry, as well as intermediate notions of counting and probability including casework counting, inclusion-exclusion, Pascal's triangle, Fibonacci and Catalan numbers, combinatorial identities, the Binomial Theorem. A few algebraic proofs will be also attempted. Overall the course is structured to develop problem-solving skills and logical reasoning, through geometric and algebraic proofs. Olympiad-level geometric proof problems and geometric constructions will also be discussed. While this class shares a number of topics with the Geometry Honors school classes, it focuses on a number of topics and explores them in-depth instead of taking a thin-spread approach. The class is appropriate for students who are interested in STEM subjects and want to develop an ability to reach proof-based conclusions about the world surrounding them. Homework Policies: As a parent, I know that time-consuming homework is a concern for both students and parents. During semester-exam weeks we will have math battles or no homework activities. On regular weeks, the homework will be divided into two sections. One section has mandatory exercises that students need to be able to solve independently while showing their work. Successful completion of weekly mandatory exercises is required not only to successfully pass the class but also to build up the knowledge one needs to further advance through the class. Solving the exercises of this section should not require more than 2-4h per week depending on the student’s ability. The other section will contain challenging problems which might take more time and which will be discussed together in the subsequent class as well.

Homeworks

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