Course:



Course: Geometry – college prep level DEPARTMENT: MATHEMATICSSCHOOL YEAR: 2013-2014TEACHER: MS. rOUNSLEYTEXT:Geometry; Prentice Hall ; ? 2007COURSE REQUIREMENTS AND MATERIALS: Students must have completed an Algebra I course and have been recommended to be in this level. The teacher assumes students will be entering college after their senior year and teaches with that goal in mind. The assigned text, student i Pad, a scientific calculator, loose-leaf notebook, and pencil are needed daily. Graph paper, ruler, and protractor are needed as announced.BASIS FOR GRADING:Homework, quizzes, unit exams, cumulative exams, and projects will be assigned point values in order to determine grades. Student achievement will be assessed as stated in the course requirement section, with the letter grade determined as listed in the MPS handbook. GOALS:This course emphasizes and integrates logical reasoning and spatial visualization skills. Technology skills will be used to help students discover and study geometric relationships. Along with learning about geometric figures and relationships between and within them, students will develop their deductive reasoning skills. They will apply their skills to real-life situations. Algebraic skills will be integrated throughout. Problems from SAT and other standardized tests will be given so that students will be comfortable with such questions on college entrance exams. TOPICS BY TERM:Term 1: Point, lines, and planes; deductive reasoning; properties of Algebra/Geometry needed in proofs; parallel lines and planes; congruent trianglesTerm 2: Relationships within triangles; quadrilaterals; ratios and proportions; similar polygons; right triangles Term 3: Transformations; circles; areas and perimeters; and if time allows - surface areasMISCELLANEOUS:Cooperative learning is vital to understanding and learning geometry. Projects will be used to supplement learning experiences in the course. Students may be required to study topics in preparation for class discussions and practice.COURSE OF STUDYGEOMETRY – COLLEGE PREP LEVELTERM I:[Begin with a brief review of Algebra skills needed for the course.]UNIT 1: TOOLS OF GEOMETRY: Objectives: To learn how to make plausible conclusions based on patterns; to learn the foundation blocks of geometry; to look at ways to measure segments and angles; to use constructions and the coordinate plane to represent figuresPatterns and Inductive ReasoningPoints, lines, and planesSegments, rays, and distance1-5,6 Measuring Segments and Angles Basic ConstructionsThe Coordinate PlanePerimeter, Circumference, and Area**Unit ExamUNIT 2: DEDUCTIVE REASONING: Objectives: To recognize the hypothesis and conclusion of an if-then statement, to state a converse, inverse, and contrapositive of a statement; to use known algebra properties to introduce the use of “rules” in geometric thinking; to be introduced to proofs and thinking skills as applied to basic geometric figures.2-1 If-then statements, converse5-4 Inverse and contrapositive2-2 Biconditionals and Definitions2-3 Deductive Reasoning2-4 Reasoning in Algebra2-5 Proving Angles Congruent **Unit ExamUNIT 3: PARALLEL LINES AND PLANES: Objectives: To distinguish between intersecting lines, perpendicular lines, parallel lines, and skew lines; to state and apply the theorem about the intersection of two parallel planes by a third plane; to identify and use postulates and theorems about angles formed by parallel lines and a transversal.3-1 Properties of parallel lines3-2 Proving lines parallel3-3 Parallel and Perpendicular lines3-4 Angles of a triangle3-5 Angles of a polygon**Unit ExamUNIT 4: CONGRUENT TRIANGLES: Objectives: To identify corresponding parts of congruent figures; to prove triangles congruent by SSS, SAS, ASA, and HL; to use CPCTC in proofs 4-1 Congruent figures4-2 SSS and SAS Congruence4-3 ASA and AAS Congruence4-4 CPCTC4-5 Isosceles and Equilateral Triangles4-6 Right Triangle Congruence 4-7 Using CPCTC**Unit ExamCumulative Exam re Term ITERM II:UNIT 5: RELATIONSHIPS WITHIN TRIANGLES: To learn about geometric relationships within triangles; to learn about midsegments, bisectors of angles and sides; concurrent lines, medians, altitudes; inequalities in trianglesMidsegments of trianglesBisectors of trianglesConcurrent lines; medians and altitudes5-5 Inequalities in trianglesUNIT 6: QUADRILATERALS: Objectives: To classify quadrilaterals; to apply the definition of a parallelogram and the theorems about properties of parallelograms and special parallelograms; to prove quadrilaterals are parallelograms; and to know and use theorems about trapezoids and kites.Classifying quadrilateralsProperties of parallelogramsWays to prove quadrilaterals are parallelogramsSpecial parallelogramsTrapezoids and kites**Unit ExamUNIT 7: SIMILAR POLYGONS: Objectives: To express a ratio in simplest form; to solve for an unknown term in a proportion; to express a proportion in an equivalent form; to use proportions to find missing values of segments; to state and apply properties of similar polygons.Ratios and proportionsSimilar polygonsProving triangles are similarTheorems for similar trianglesProportional lengths in triangles – geometric means**Unit ExamUNIT 8: RIGHT TRIANGLES: Objectives: To determine a geometric mean and use is to determine lengths re a right triangle; to state and use the Pythagorean theorem; to know the relationships between sides of special triangles; to know and use trigonometric functions.8-1 The Pythagorean theorem and its converse8-2 Special right triangles8-3 The tangent ratio8-4 The sine and cosine ratios8-5 Applications of right triangle trigonometry**Unit examCumulative Exam re Term IITERM IIIUNIT 9: TRANSFORMATIONS : Objectives: To use knowledge of coordinates and spatial reference to translate, rotate, reflect, or dilate figures. Know some of the symbolism used with these transformations. 9-1 Translations9-2 Reflections9-3 Rotations9-5 Dilations 9-6 Composites of Reflections**Unit assessmentUNIT 10: CIRCLES: Objectives: To define circles and their parts, sphere, arc, inscribed and circumscribed polygon, chord, tangent, secant, and to find measures of these.12-1 Basic terms, tangent lines12-2 Chords and arcs12-3 Inscribed angles12-4 Angle measures and segment lengths12-5 The formula and circles in the coordinate plane**Unit assessmentUNIT 11: AREA: Objectives: To find the area of a rectangle, parallelogram, triangle, special quadrilateral, and regular polygon. To use the relationship between similar figures in problems. To find the measurements of parts of circles.10-1 Areas of Parallelograms and Triangles10-2 Areas of Trapezoids, Rhombi, and Kites10-3 Areas of Regular Polygons10-4 Perimeters and Areas of Similar Figures10-5 Trigonometry and Area10-6 Circles and Arcs10-7 Areas of Circles and Sectors** Unit assessmentIf time allows:Unit 12: SURFACE AREA and VOLUME: Objectives To use what information about finding perimeter and area to find surface area and volume.11-1 Space Figures and Cross Sections11-2 Surface Areas of Prisms and Cylinders11-3 Surface Areas of Pyramids and Cones**Unit assessmentCumulative Exam re Term IIIIn addition: As time permits within any given unit – SAT PRACTICE: Objective: To see geometry questions in the SAT format. A project will be assigned for students as part of the final exam grade. ................
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