This class begins at the intersection of Algebra and Geometry - graphing. The introductory concepts include ordered pairs, the Cartesian coordinate system, and plotting points. The students learn to graph linear equations in two variables (including horizontal and vertical lines using x- & y-intercepts), how to calculate slope, and how to use slope in graphing a line. The class works with slope-intercept form, standard form, and point-slope form, then moves into the basic concepts of Euclidean Geometry. Specific topics covered include congruency, parallel lines and transversals, congruent, and similar triangles. If time permits, students continue working with proofs of the geometric properties of circles.
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First, the class reviews and then develops greater facility in working with fractions, signed numbers, order of operations, and the distributive property. Next, students simplify expressions and linear equations, then solve algebraic equations. Students progress into the intersection of Algebra and Geometry - graphing. The class next moves into polynomials, including their characteristics, performing operations on them, using the distributive property, the FOIL method, and special products. The class also works with exponents, positive integral exponents, and negative integral exponents. From polynomial simplification, the class proceeds to the exact opposite operation, polynomial factoring. By the end of this factoring unit, the class masters factoring out the Greatest Common Factor, factoring trinomials, and the difference of squares.
This class explores the Ancient Greek mathematical mind. Beginning each day with Pythagoras’ Golden Verses, students ask how do we know what we know? Understanding the Greek motivation to know the world through observation and thinking (rather than story and tradition) allows us to see why Euclid, the Father of Geometry, devoted his life to the systematic construction of theory after theory, based only on a handful of assumptions (postulates), definitions, and logical presuppositions. Finally, after practicing at the Great Greek Geometric Games using only compass and straightedge, the class studies Euclid’s proof of the Pythagorean Theorem.
Through observation, experimentation, measurement, and calculation, students study motion in a historical context, making observations and asking questions as they were first asked by the scientists of the Age of Reason. Students repeat some of the classic experiments of Copernicus, Kepler, Brahe, Galileo, and Newton. At the end of the course, the students understand the laws governing the motion of planets, stars, galaxies, as well as satellites, baseballs, and leaves.