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chARTer~TECH High School for the Performing Arts2012-2013 Course SyllabusDepartment:MathematicsCourse:GeometryInstructor/s:J. Kaplan (jkaplan@) Course Description: This course introduces the foundations for the study of geometry by establishing key terms and concepts. Students study logic in order to prepare them to write formal proofs. During this course, students are expected to complete proofs on a variety of topics such as triangles, quadrilaterals, trigonometry, transformations, and circles. Students will also expand on previous course study in Algebra by applying it to the geometry concepts.Required Materials: Covered textbook, Pencils, Loose-leaf paper, Binder with dividers, & Separate composition notebook or at least a 1 subject notebook for Problems of the DayCourse Objectives: Graph ordered pairs on a coordinate plane. Identify collinear points.Identify and model points, lines, and planes. Identify coplanar points and intersecting lines and planes. Find the distance between two points on a number line and between two points in a coordinate plane. Use the Pythagorean Theorem to find the length of the hypotenuse.Find the midpoint of a segment. Complete proofs involving segment theorems.Identify angles and classify angles. Use the angle addition postulate to find the measures of angles. Identify and use congruent angles and the bisector of an angle.Identify and use adjacent, vertical, complementary, supplementary, and linear pairs of angles, and perpendicular lines. Name the five categories of angles and the triangles distinguished by their sides and by their angles.Make conjectures based on inductive reasoning.Write statement in if-then form. Write the converse of an if-then statement. Identify and use basic postulates about points, lines, and planes.Test the validity of conditional statements that involve mathematical sentences in one variable.Use the Law of Detachment and the Law of Syllogism in deductive reasoning. Solve problems by looking for a pattern.Use properties of equality in algebraic and geometric plete proofs involving segment plete proofs involving angle theorems.Solve problems by drawing a diagram. Identify the relationships between two lines or two planes. Name angles formed by a pair of lines and a transversal.Find the measures of the angles formed by two parallel lines and a transversal.Use the properties of parallel lines to determine angle measures.Find the slopes of lines. Use slope to identify parallel and perpendicular lines.Recognize angle conditions that produce parallel lines. Prove two lines are parallel based on given angle relationships.Recognize and use distance relationships amongst pints, lines, and planes.Find the distance between a point and a line.Identify the parts of triangles and classify triangles by their parts.Investigate the relationship of the angles of a triangle.Apply the Angle Sum Theorem. Apply the Exterior Angle Theorem.Name and label corresponding parts of congruent triangles.Draw congruent triangles.Use SSS, SAS, and ASA postulates to test for triangle congruence.Use the MS Theorem to test triangle congruence. Solve problems by eliminating the possibilities.Use properties of isosceles and equilateral triangles.Identify and use medians, altitudes, angle bisectors, and perpendicular bisectors in a triangle.Recognize and use tests for congruence of right triangles.Use indirect reasoning and indirect proof to reach a conclusion. Recognize and apply properties of inequalities to the measures of segments and angles. Solve problems by working backward.Recognize and apply relationships between sides and angles in a triangle.Use a graphing calculator to investigate the relationship among the measures of the sides of a triangle.Apply the Triangle Inequality Theorem.Apply the SAS Inequality and the SSS Inequality.Use the Cabri Geometry to draw parallelograms.Recognize and apply the properties of a parallelogram. Recognize and apply the conditions that ensure a quadrilateral is a parallelogram. Recognize and apply the properties of rectangles.Recognize and apply the properties of squares and rhombi.Construct quadrilaterals with exactly two distinct pairs of adjacent congruent sides.Recognize and apply the properties of trapezoid.Recognize and use ratios and proportions. Apply the properties of proportions.Identify similar figures. Solve problems involving similar figures.Identify similar triangles. Use similar triangles to solve problems.Use proportional parts of triangles to solve problems. Divide a segment into congruent parts.Recognize and use the proportional relationships of corresponding perimeters altitudes, angle bisectors, and medians of similar triangles.Recognize and describe characteristics of fractals. Solve problems by solving a simpler problem.Create fractal designs by using random numbers.Use paper folding to develop the Pythagorean Theorem.Find the geometric mean between two numbers. Solve problems involving relationships between parts of a triangle and the altitude to its hypotenuse. Use the Pythagorean Theorem and its converse.Use the properties of 45-50-90 and 30-60-90 triangles.Find trigonometric ratios using right triangles. Solve problems using trigonometric ratios.Use trigonometry to solve problems involving angles of elevation or depression.Identify and use parts of circles. Solve problems involving the circumference of a circle.Recognize major arcs, minor arcs, semicircles, and central angles. Find measures of arcs and central angles. Solve problems by making circle graphs.Recognize and use relationships among arcs, chords, and diameters.Recognize and find measures of inscribed angles. Apply properties of inscribed figures.Use the graphing calculator and Cabri Geometry software to explore characteristics of tangents.Recognize tangents and use properties of tangents.Identify and name polygons. Find the sum of the measures of interior and exterior angles of convex polygons and measures of interior and exterior angles of regular polygons. Solve problems involving angle measures of polygons.Create tessellations using translations and rotations.Identify regular and uniform (semi-regular) tessellations. Create tessellations with specific attributes. Solve problems by using guess and checkCompare the area of a rectangle with the area of a parallelogram having the same base length and the same parallel lines.Find areas of parallelograms.Find areas of triangles, rhombi, and trapezoids.Create a regular n-gon.Find areas of regular polygons. Find areas of circles.Recognize nodes and edges as used in graph theory. Determine if a network is traceable. Determine if a network is complete.Create cross sections and other slices of solids.Use top, front, side, and comer views of three-dimensional solids to make models. Describe and draw cross sections and other slices of three-dimensional figures.Construct a tetrahedron kit.Draw three-dimensional figures on isometric dot paper. Make two-dimensional nets for three-dimensional folds. Find surface areas.Investigate Plateau's problem sing soap film.Find the lateral area and surface area of a right prism. Find the lateral area and surface area of a right cylinder.Find the lateral area and surface area of a regular pyramid. Find the lateral area and surface area of a right circular cone.Find the volume of a right prism. Find the volume of a right pare the volumes of prisms and pyramids and the volumes of cylinders and cones.Find the volume of a pyramid.Find the volume of a circular cone.Recognize and define basic properties of spheres. Find the surface area and the volume of a sphere.Graph linear equations using the intercepts method and the slope-intercept method.Use a graphing calculator to determine an equation of the line that passes through plotted points.Write an equation of a line given information about its graph. Solve problems by using equations.Solve problems involving transformations.Use graphing calculators to perform transformations.Assessment: Students will receive homework on a daily basis as well as pop quizzes based upon the homework.? Announced tests and quizzes will also be given regularly.?? Students will receive a variety of class work such as but not limited to: review games, practice worksheets, problems of the day, labs, and journals.Grading Policy:Tests (30%)Quizzes (25%)Homework (20%)Class work (25%)TESTS:Tests are always announced in advance.There will be a minimum of 2 tests per marking period including projects.Any projects count as a test grade.No extra time will be given to complete the Test unless special arrangements have been made.You may retake any Test for a maximum score of 70 using the following guidelines.Test retake must occur after schoolMust spend at least one after school help session reviewing and correcting mistakes on the test.Retake needs to occur within one week of test being returned.QUIZZES:Quizzes can be announced or unannounced.There will be a minimum of 3 announced quizzes and an undetermined number of pop quizzes.Quizzes are not eligible for retakes.CLASSWORK:There are two types of classwork:Type 1: Collected and graded for accuracyType 2: Graded for effort and completenessHOMEWORK: All homework must contain date, assigned problems, work, and answers.There are two possible types of homework:Type 1: Graded based on a homework quizType 2: Graded for effort and completenessHomework will be graded as followsOn Time = Maximum grade of 10 out of 10 points1 Class Late = Maximum grade of 5 out of 10 pointsMore than 1 Class Late = No CreditFor absences, you have the same number of days to make up the homework as you were absent. Refer to the Student Handbook. JOURNAL ENTRIES:All Journal Entries will count as 2 Homework Assignments.They are graded on the following scale:4- Completely and neatly answers the question with appropriate information. 3- Complete answer but work isn’t neat. Work is neat but the entry may be missing one concept.2- Work isn’t neat and a concept is missing. Work is neat but several concepts are missing.1- The student attempted to answer the question.0- The student didn’t complete the journal entry.PROBLEMS OF THE DAY:Each day students will have a problem to complete when they enter the classroom.Problems are to be completed in a composition notebook or subject notebook.Please note that problems of the day will sometimes be collected unannounced and be counted as a pop quiz, so it is important that the students get to work immediately when they come in as they will not have extra time to complete the problem once it has been announced that they will be collected.On the day of the end of chapter assessment, the notebooks will be collected and the problems of the day will be graded as follows:Each problem is worth a max of 1 point? point for correct work? point for correct answer? point for date of the original problem of the day and for attempting the problemAs long as the problem didn’t count as a pop quiz, we go over the problem as a class after everyone has had a chance to try the problem. Therefore, there is no reason for a student to get a question marked wrong once the problems are collected as they had a chance to correct the problem when we went over it as a class.If students are absent they are still responsible for the problem of the day. They may get them from a class mate or from my website at Policies:Be on time. Be in your seat by the time class is scheduled to start. Complete the following:Put I-pods and phones away in purse, backpack, etc (ear buds should not be in your ears)Remove backpacks and purses from desksPlace homework in the corner of your deskHave pencils already sharpenedComplete the Problem of the DayBe respectful.As per school rules there are no cell phones in class.Show respect toward fellow classmates and the teacher.Raise hand and wait to be called on by the teacher before you speak.Please be advised that cursing will not be tolerated in any form and will result in an automatic teacher detention and possible referral to the office.No listening to IPOD during class without permission!No lavatory or locker passes during a lesson, with an exception of emergencies for lavatory. Go before or after class or wait until classwork time.Be attentive.Try to come to class everyday! If you are absent, it is YOUR responsibility to get the notes and assignments missed while you were absent from a classmate, which means, the teacher will not remind you of the missed assignment. Assignments will be posted on my website daily at and copies of handouts can also be found in the proper folder. Course Outline:DISCOVERING POINTS, LINES, PLANES AND ANGLESIntegration: AlgebraPoints, Lines and PlanesMeasuring SegmentsMidpoint and Segment CongruenceExploring AnglesUsing TechnologyAngle RelationshipsCONNECTING REASONING AND PROOFInductive Reasoning and ConjecturingIf-Then Statements and PostulatesUsing TechnologyDeductive ReasoningVerifying Segment RelationshipsVerifying Angle RelationshipsUSING PERPENDICULAR AND PARALLEL LINESParallel Lines and TransversalsUsing TechnologyAngles and Parallel LinesIntegration: AlgebraProving Lines ParallelParallel lines and DistanceUsing TechnologyIntegration: Non-Euclidean GeometryIDENTIFYING CONGRUENT TRIANGLESClassifying TrianglesModeling MathematicsMeasuring Angles in TrianglesExploring Congruent TrianglesModeling MathematicsProving Triangles CongruentAnalyzing Isosceles TrianglesAPPLYING CONGRUENT TRIANGLESSpecial Segments in TrianglesRight TrianglesIndirect Proof and InequalitiesInequalities for Sides and Angles of a TriangleUsing TechnologyThe Triangle Inequality TheoremInequalities Involving Two TrianglesEXPLORING QUADRILATERALSUsing TechnologyParallelogramsTests for ParallelogramsUsing TechnologyRectanglesSquares and RhombiModeling Mathematics: KitesTrapezoidsCONNECTING PROPORTION AND SIMILARITYIntegration: AlgebraExploring Similar PolygonsIdentifying Similar TrianglesParallel Lines and Proportional PartsParts of Similar TrianglesFractals and Self-SimilarityAPPLYING RIGHT TRIANGLES AND TRIGONOMETRYModeling Mathematics: Pythagorean TheoryGeometric Mean and the Pythagorean TheoremIntegration: TrigonometryAngles of Elevation and DepressionANALYZING CIRCLESa. Exploring CirclesAngles and ArcsArcs and ChordsInscribed AnglesUsing TechnologyTangentsIntegration: AlgebraPOLYGONS AND AREAPolygonsModeling Mathematics: Tessellations and TransformationsTessellationsUsing TechnologyArea of ParallelogramsArea of Triangles, Rhombi, and TrapezoidsModeling MathematicsArea of Regular Polygons and CirclesSURFACE AREA AND VOLUMEModeling MathematicsExploring Three Dimensional FiguresNets and Surface AreaSurface Area of Prisms and CylindersSurface Area of Pyramids and ConesVolume of Prisms and CylindersModeling MathematicsVolume of Pyramids and ConesSurface Area and Volume of SpheresCOORDINATE TRANSFORMATIONS Mappings Reflections Translations Rotations Dilations ................
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