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FOUNDATIONS OF GEOMETRY CURRICULUM COMPETENCY GOALS I. OBJECTIVES Review Radical 2 days Solving Equations Circle Equations 2 days 1 day Distance/Midpoint Slope/Slope Intercept Parallel and Perpendicular Lines MBC.G.5.1 2.03(d) 2 days 1 day 1 day Explain the relationships among angles formed by perpendicular lines and transversal of parallel lines 9 days of instruction; 1 review day; 1 test day; total of 11 days Basics of Geometry Definitions, Notations, Angle Pairs MBC.G.1.4 2.02 4 days Parallel Lines and Transversal MBC.G.2.3 2.02 Constructions MBC.G.1.5 Summarize the structure and relationship between undefined terms, defined terms, axioms/postulates, methods of reasoning and theorems. Explain the relationships among angles formed by perpendicular lines and transversals of parallel lines. Use paper-folding techniques, compasses and straight edges and dynamic geometric software to make connections among geometric relationships. 6 days of instruction; 1 review day; 1 test day; total of 8 days Construct arguments that prove conjectures and theorems or disprove conjectures related to (c) isosceles triangles Use the Pythagorean Theorem to solve problems in two-and three-dimensional settings. 1 day Totals for Unit 2 III. Represent circles as equations based on the center and the radius, the center and a point on the circle and the endpoints of the diameter. MBC.G.2.3 Total for Unit 1 II. Timeframe Triangles Isosceles Triangles Pythagorean Theorem MBC.G.6.1 2.03 (a) MBC.G.8.1 2.03(a) 2 days Incorporate within units 1 day Special Right Triangle Trigonometric Ratios Angle of Elevation and Angle of Depression Geometric Mean MBC.G.8.3 2.03(a) MBC.G.8.2 1.01 2.03(a) Use properties of special right triangles to solve problems. Use sines, cosines, and tangents to determine side lengths and angle measures in right triangles. 3 days MBC.G.6.1(f) 2.03(a) Construct arguments that prove conjectures and theorems or disprove conjectures related to (f) geometric mean 9 days of instruction; 1 review day; 1 test day; 11 total days 1 day MBC.G.6.3 2.03(b) Construct arguments to prove properties of special quadrilaterals. 4 days of instruction; 1 review day; 1 test day; 6 total days Calculate the measure of central angles, inscribed angles and circumscribed angles. Calculate arc measure and arc length within a circle. 9 days of instruction; 1 review day; 1 test day; 11 total days Use matrix operations to model translations, reflections, origin-centered dilations and origin–centered rotations (90 degrees, 180 degrees, and 270 degrees). Understand the relationship of rigidity to congruence and dilations of similarity. 4 days of instruction; 1 review day; 1 test day; 6 total days 4 days Use formulas and strategies to solve problems involving volume and surface area of cones, spheres, and composite figures, Use the 3:2:1 relationship among volumes of circular cylinders, hemispheres and cones with the same height and circular base and 3:1 relationship between the volume of a prism and pyramid with the same base area and height. See Above 19 days Totals for Unit 3 IV. Quadrilaterals Special Properties Totals for Unit 4 V. Circles All Information MBC.G.7.1 2.03(d) MBC.G.7.2 2.03(d) Totals for Unit 5 VI. Transformations All Information MBC.G.4.1 MBC.G.4.2 3.01 3.02 Total for Unit 6 VII. Formulas Area, Surface Area, Volume Area of Shaded Regions Composite Figures MBC.G.9.1/9.2 1.02 2.04 MBC.G.9.1/9.2 1.02 2.04 MBC.G.9.1/9.2 1.02 2.04 See Above 3 days 9 days 4 days Geometric Probability Similarity Ratios: Area, Surface Area, Volume, and Side Length Totals for Unit 7 Exam Review MBC.G.9.1/9.2 1.02 2.04 MBC.G.9.1/9.2 1.02 2.04 See Above See Above 19 days of instruction; 1 review day; 1 test day; 21 total days Teacher Discretion