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Geometry Honors (High School) Course 1206320 Year at a Glance Holt McDougal Larson Geometry Throughout the year, students will relate new vocabulary to familiar words, listen to, read, and discuss familiar and conceptually challenging text and will use new vocabulary that is introduced and taught directly. (LA.910.1.6.1, 6.2, 6.5 and LA.1112.1.6.1, 6.2, 6.5) Students will also use a variety of problem solving strategies and will apply these skills using axioms and theorems in writing proofs. (MA.912.G.8.1 through 8.6) First Quarter Chapter 1 Body of Knowledge: Geometry Standard 1: Points, Lines, Angles, and Planes MA.912.G.1.1 MA.912.G.2.1, 2.7 Building Blocks of Geometry A. Defining point, line, angle, ray, plane B. Segments and their measures C. Angles and their measures D. Segment and angle bisectors E. Introduction to perimeter, circumference and area Chapter 2 Body of Knowledge: Discrete Mathematics Standard 6: Logic MA.912.D.6.1, 6.2, 6.4 Body of Knowledge: Geometry Standard 4: Triangles MA.912.G.4.5 Reasoning and Proof In Geometry A. Inductive reasoning B. Deductive reasoning C. Conditional statements D. Reasoning with properties of Algebra E. Proving theorems F. Planning a proof Chapter 3 Body of Knowledge: Geometry Standard 1: Points, Lines, Angles, and Planes MA.912.G.1.2, 1.3 Perpendicular and Parallel Lines A. Lines and angles B. Parallel and transversals C. Proving lines and parallel D. Lines in the coordinate plane Second Quarter Chapter 4 Body of Knowledge: Geometry Standard 2: Polygons MA.912.G.2.2, 2.6 Standard 4: Triangles MA.912.G.4.1, 4.3 Congruent Triangles A. Triangles and angles B. Triangle inequality C. Proving triangles are congruent D. Applications in the real-world Similarity A. Use properties of similar triangles B. Apply segment divided proportionally theorems C. Prove triangles are similar Body of Knowledge: Geometry Chapters 5 and 6 Body of Knowledge: Discrete Mathematics Standard 6: Logic MA.912.D.6.3, 6.4 Body of Knowledge: Geometry Standard 1: Points, Lines, Angles, and Planes MA.912.G.1.2 Standard 8: Mathematical Reasoning and Problem Solving MA.912.G.8.1 through 8.6 (on-going) Page 1 Course description: http://www.floridastandards.org/Courses/PublicPreviewCourse37.aspx REV 11/08/12 Standard 4: Triangles MA.912.G.2.3,4.2,4.3, 4.4, 4.6, 4.7 Properties of triangles A. Medians, altitudes midsegment B. Perpendiculars and bisectors C. Inequalities in triangles D. Construction of angles E. Inequality theorems NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx Standard 2: Polygons MA.912.G.2.4, 2.6 Transformations A. Transformations B. Reflections C. Rotations D. Translations Geometry Honors (High School) Course 1206320 Third Quarter Chapter 7 Body of Knowledge: Geometry Standard 5: Right Triangle MA.912.G.5.1 through 5.4 Body of Knowledge: Trigonometry Standard 2: Trigonometry of Triangles MA.912.T.2.1 Right Triangles & Trigonometry A. Pythagorean theorem and converse B. Special right triangles C. Similarity in right triangles D. Right triangle trig ratios E. Law of sines and cosines F. Solve real-world problems using trigonometry Quadrilaterals A. Polygons B. Properties of parallelograms C. Proving quadrilaterals are parallelograms D. Rhombuses, rectangles and squares E. Trapezoids and kites F. Proving theorems about quadrilaterals G. Special quadrilaterals H. Fibonacci sequence and golden ratio (Ch 6.3) I. Similarity (Ch 6.3) Chapters 10 and 11 Body of Knowledge: Geometry Chapter 8 Body of Knowledge: Discrete Mathematics Standard 6: Logic MA.912.D.6.2, 6.4 Standard 11: Sequences and Series MA.912D.11.5 Body of Knowledge: Geometry Standard 2: Polygons MA.912.G.2.3, 2.5 Standard 3: Quadrilaterals MA.912.G.3.1 through 3.4 Standard 7: Polyhedra and Other Solids MA.912.G.7.4 Holt McDougal Larson Geometry Fourth Quarter Chapters 11 and 12 Chapter 9 Body of Knowledge: Geometry Body of Knowledge: Geometry Standard 2: Polygons MA.912.G.2.5 Standard 2: Polygons MA.912.G.2.6 Standard 7: Polyhedra and other Solids MA.912.G.7.1, 7.2, 7.3, 7.5, 7.6, 7.7 Area and Volume A. Area of polygons B. Prisms and cylinders C. Pyramids and cones D. Displacement and density E. Spheres F. Polyhedrons G. Cross sections H. Total surface area I. Similar solids (Ch11.3) Standard 4: Triangles MA.912.G.4.8 . Standard 6: Circles MA.912.G.6.1 through 6. 7 Geometry of Circles A. Arc lengths and area of sectors B. Ratio of areas C. Chord properties D. Tangent properties E. Arc and angle properties F. Circumference / diameter ratio G. Inscribed angles H. Area and circumference Page 2 Course description: http://www.floridastandards.org/Courses/PublicPreviewCourse37.aspx REV 11/08/12 Year at a Glance NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx Body of Knowledge: Discrete Mathematics Standard 6: Logic MA.912.D.6.4 Standard 9: Vectors MA.912.D.9.3 Coordinate Geometry A. Vectors B. Midpoint formula(Ch 8) Geometry Honors (High School) Course 1206320 Qtr 1 Qtr 2 Qtr 3 YEAR LONG Qtr 4 MA.912.G.8.1 High Analyze the structure of Euclidean geometry as an axiomatic system. Distinguish between undefined terms, definitions, postulates, and theorems. MA.912.G.8.2 Moderate Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards. MA.912.G.8.3 Moderate Determine whether a solution is reasonable in the context of the original situation. MA.912.G.8.4 High Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture. MA.912.G.8.5 High Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs. MA.912.G.8.6 High Perform basic constructions using straightedge and compass, and/or drawing programs describing and justifying the procedures used. Distinguish between sketching, constructing, and drawing geometric figures. Week of Explicit Instruction Quarter 1 MA.912.G.1.1 Moderate Find the lengths and midpoints of line segments in two-dimensional coordinate systems. MA.912.G.1.2 Moderate Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass or a drawing program, explaining and justifying the process used. MA.912.G.1.3 Moderate Identify and use the relationships between special pairs of angles formed by parallel lines and transversals. MA.912.G.2.1 High Identify and describe convex, concave, regular, and irregular polygons. MA.912.G.2.7 Moderate Determine how changes in dimensions affect the perimeter and area of common geometric figures. MA.912.D.6.1 Moderate Use truth tables to determine truth values of propositional statements. MA.912.D.6.2 Moderate Find the converse, inverse, and contrapositive of a statement MA.912.D.6.4 Moderate Use methods of direct and indirect proof and determine whether a short proof is logically valid. MA.912.G.4.5 Moderate Apply theorems involving segments divided proportionally. Page 3 Course description: http://www.floridastandards.org/Courses/PublicPreviewCourse37.aspx REV 11/08/12 NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx Year at a Glance Holt McDougal Larson Geometry Text Alignment Text Alignment Geometry Honors (High School) Course 1206320 Week of Explicit Instruction Quarter 2 MA.912.G.2.2 Moderate Determine the measures of interior and exterior angles of polygons, justifying the method used. MA.912.G.2.6 High Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane. MA.912.G.4.1 Moderate Classify, construct, and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular. MA.912.G.4.3 High Construct triangles congruent to given triangles. MA.912.D.6.3 Moderate Determine whether two propositions are logically equivalent. MA.912.D.6.4 Moderate Use methods of direct and indirect proof and determine whether a short proof is logically valid. MA.912.G.1.2 Moderate Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass or a drawing program, explaining and justifying the process used. MA.912.G.2.3 High Use properties of congruent and similar polygons to solve mathematical or real-world problems. MA.912.G.4.2 Moderate Define, identify, and construct altitudes, medians, angle bisectors, perpendicular bisectors,orthocenter, centroid, incenter, and circumcenter. MA.912.G.4.3 High Construct triangles congruent to given triangles. MA.912.G.4.4 Moderate Use properties of congruent and similar triangles to solve problems involving lengths and areas. MA.912.G.4.6 High Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles. MA.912.G.4.7 Moderate Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge theorem. MA.912.G.2.4 High Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons. to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent to the original shape. Create and verify tessellations of the plane using polygons. MA.912.G.2.6 High Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane. Page 4 Course description: http://www.floridastandards.org/Courses/PublicPreviewCourse37.aspx REV 11/08/12 NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx Year at a Glance Holt McDougal Larson Geometry Text Alignment Geometry Honors (High School) Course 1206320 Week of Explicit Instruction Quarter 3 MA.912.G.5.1 High Prove and apply the Pythagorean theorem and its converse. MA.912.G.5.2 Moderate State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle. MA.912.G.5.3 Moderate Use special right triangles (30° - 60° - 90° and 45° - 45° - 90°) to solve problems. MA.912.G.5.4 High Solve real-world problems involving right triangles. MA.912.T.2.1 Moderate Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right triangles. MA.912.D.6.3 Moderate Determine whether two propositions are logically equivalent. MA.912.D.6.4 Moderate Use methods of direct and indirect proof and determine whether a short proof is logically valid. MA.912.D.11.5 High Explore and use other sequences found in nature such as the fibonacci sequence and the golden ratio. MA.912.G.2.3 High Use properties of congruent and similar polygons to solve mathematical or real-world problems. MA.912.G.2.5 Moderate Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons, etc.). MA.912.G.3.1 Moderate Describe, classify, and compare relationships among quadrilaterals including the square, rectangle, rhombus, parallelogram, trapezoid, and kite. MA.912.G.3.2 Moderate Compare and contrast special quadrilaterals on the basis of their properties. MA.912.G.3.3 High Use coordinate geometry to prove properties of congruent, regular, and similar quadrilaterals. MA.912.G.3.4 High Prove theorems involving quadrilaterals. MA.912.G.7.4 Low Identify chords, tangents, radii, and great circles of spheres MA.912.G.6.1 High Determine the center of a given circle. Given three points not on a line, construct the circle that passes through them. Construct tangents to circles. Circumscribe and inscribe circles about and within triangles and regular polygons. MA.912.G.6.2 Low Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles. Page 5 Course description: http://www.floridastandards.org/Courses/PublicPreviewCourse37.aspx REV 11/08/12 NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx Year at a Glance Holt McDougal Larson Geometry Text Alignment Geometry Honors (High School) Course 1206320 MA.912.G.6.4 Moderate Determine and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents). MA.912.G.6.5 High Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. MA.912.G.6.6 Moderate Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle. MA.912.G.6.7 Moderate Given the equation of a circle in center-radius form or given the center and the radius of a circle, sketch the graph of the circle. Page 6 Course description: http://www.floridastandards.org/Courses/PublicPreviewCourse37.aspx REV 11/08/12 NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx Year at a Glance Holt McDougal Larson Geometry Geometry Honors (High School) Course 1206320 Week of Explicit Instruction Quarter 4 MA.912.G.2.5 Moderate Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons, etc.). MA.912.G.7.1 Moderate Describe and make regular, non-regular, and oblique polyhedra, and sketch the net for a given polyhedron and vice versa. MA.912.G.7.2 Moderate Describe the relationships between the faces, edges, and vertices of polyhedra. MA.912.G.7.3 Moderate Identify, sketch, find areas and/or perimeters of cross sections of solid objects. MA.912.G.7.5 Moderate Explain and use formulas for lateral area, surface area, and volume of solids. MA.912.G.7.6 Moderate Identify and use properties of congruent and similar solids. MA.912.G.7.7 Moderate Determine how changes in dimensions affect the surface area and volume of common geometric solids. MA.912.G.2.6 High Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane. MA.912.G.4.8 High Use coordinate geometry to prove properties of congruent, regular, and similar triangles. MA.912.D.6.4 Moderate MA.912.D.9.3 High Use methods of direct and indirect proof and determine whether a short proof is logically valid. Use vectors to model and solve application problems. Page 7 Course description: http://www.floridastandards.org/Courses/PublicPreviewCourse37.aspx REV 11/08/12 NGSSS: http://www.floridastandards.org/Standards/FLStandardSearch.aspx Year at a Glance Holt McDougal Larson Geometry Text Alignment