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Geometry – Scope and Sequence (Honors, College Prep, and General Studies)2016 – 2017Marking Period 1 (Sept. 1 – Nov. 17) Quarterly 1 Chapters 1, 2, 3.1 – 3.2Section TopicObjective/Goal: what the student will know and be able to doStandardHonors PaceCollege Prep PaceGeneral Studies Pace1.1Points, Lines, and PlanesIdentify and model points lines and planes.Identify intersecting lines and planes. Use correct mathematical terminology to describe geometric figures. (Extend)G. CO. 1, G.MG.121.2Linear MeasureMeasure Segments.Calculate with measures. Determine precision of measurements. (Extend)Determine accuracy of measurements. (Extend)G. CO. 1, G.CO.1221.3 Distance and MidpointsFind the distance between two points.Find the midpoint of a segment.G. CO. 1, G.CO.1211.4Angle MeasureMeasure and classify angles.Identify and use congruent angles and the bisector of an angle.G. CO. 1, G.CO.1211.5Angle RelationshipsIdentify and use special pairs of anglesIdentify perpendicular lines.Construct perpendiculars. (Extend)21.6Two-Dimensional FiguresIdentify and name polygons.Find perimeter, circumference, and area of two-dimensional figures.Use the Geometer’s sketchpad to draw and find side lengths, angle measures, and perimeter. (Extend)G.GPE.7, G.CO.1221.7Three-Dimensional FiguresIdentify and name three dimensional figuresFind surface area and volume.G.GMD.31Review and Assess 4----11 Days Lessons4 Review / Assess15 Total Days--2.1Inductive Reasoning and ConjectureMake conjectures based on inductive reasoning.Find Counterexamples12.2LogicDetermine truth values of negations, conjectures, and disjunctions.Represent conjunctions and disjunctions using Venn diagrams12.3Conditional StatementsAnalyze statements in if-then formWrite converses, inverses, and contrapositives.22.4Deductive ReasoningUse the Law of Detachment.Use the Law of Syllogism.12.5Postulates and Paragraph ProofsIdentify and use basic postulates about points, lines, and plane.Write paragraph proofs.22.6Algebraic ProofUse Algebra to write two-column proofs.Use properties of equality to write geometric proofs.12.7Proving Segment RelationshipsWrite proofs involving segment addition.Write proofs involving congruence.G.CO.9G.CO.1222.8Proving Angle RelationshipsWrite proofs involving supplementary and complementary angles.Write proofs involving congruent and right angles.G.CO.92Review and Assess4----12 Days Lessons4 Review/Assess16 Total Days--3.1Parallel Lines and TransversalsIdentify the relationship between two lines or two planes.Name angle pairs formed by parallel lines and transversals.G.CO.113.2Angles and Parallel LinesUse Geometer’s sketchpad to investigate angles formed by two parallel lines and a transversal. (Explore)Use theorems to determine the relationships between specific pairs of angles.Use algebra to find angle measures.G.CO.12G.CO. 1G.CO.92----3 teaching days--Quarterly 1Review for Quarterly ExamChapter 1Chapter 2Chapter 3.1 – 3.234 days of Lessons1 day2 days2 daysMarking Period 2 (Nov. 18 – Jan. 31) Quarterly 2 Chapters 3.3 – 3.6, 4, 53.3Slopes of LinesFind slopes of lines.Use slope to identify parallel and perpendicular lines.G.GPE.513.4Equations of LinesWrite an equation of a line given information about the graph.Solve problems by writing equations.Write equations of perpendicular bisectors on the coordinate plane. (Extend)G.GPE.523.5Proving Lines ParallelRecognize angle pairs that occur with parallel lines.Prove that two lines are parallel.G.CO.12G.CO.913.6Perpendiculars and DistanceFind the distance between a point and a line.Find the distance between two parallel lines.G.CO.12G.MG.31Review and Assess4----5 Days Lessons4 Review/Assess9 Total Days--4.1Classifying TrianglesIdentify and classify triangles by angle measures and side measuresG.CO.1214.2Angles of TrianglesFind the relationships among the measures of the interior angles of a triangle. (Explore)Apply the triangle Angle-Sum Theorem.Apply the Exterior Angle Theorem. G. CO.12, G.CO.1024.3Congruent TrianglesName and use corresponding parts of congruent polygons.Prove triangles congruent using the definition of congruence.G.CO.7G.SRT.514.4Proving Triangles CongruentUse the SSS and SAS Postulates to test for triangle congruence.Construct an angle bisector. (Extend)Prove constructions using congruent measures. (Extend)G.CO.10, G.CO.12,G.SRT.524.5Proving Triangles CongruentUse the ASA and AAS Postulates to test for triangle congruenceG.CO.10G.SRT.524.6Isosceles and Equilateral TrianglesUse properties of isosceles and equilateral triangles.G.CO.10G.CO.1214.7Congruence TransformationsIdentify reflections, translations, and rotations.Verify congruence after a congruence transformation.G.CO.6G.CO.724.8Triangles and Coordinate ProofPosition and label triangles for use in coordinate proofs.Write coordinate proofs.G.CO.10G.GPE.42Review and Assess4----13 Days Lessons4 Review/Assess17 Total Days--5.1Bisectors of TriangleConstruct perpendicular bisectors and angle bisectors of triangles. (Explore)Identify and use perpendicular bisectors in triangles.Identify and use angle bisectors in triangles.G.CO.10G.MG.325.2Medians and Altitudes of TrianglesIdentify and use medians and altitudes in triangles.Identify and use altitudes in triangles.G.CO.10G.MG.325.3Inequalities in One TriangleRecognize and apply properties of inequalities to the measures of the angles of a triangle.Recognize and apply properties of inequalities to the relationships between the angles and the sides of a triangle.G.CO.1015.4Indirect ProofWrite indirect algebraic proofs.Write indirect geometric proofs.G.CO.1015.5The Triangle InequalityUse the Triangle Inequality Theorem to identify possible triangles.Prove triangle relationships using the Triangle Inequality Theorem.G.CO.10G.MG.325.6Inequalities in Two TrianglesApply the Hinge Theorem or its converse to make comparisons in two triangles.G.CO.102Review and Assess4----10 Days Lessons4 Review/Assess14 Total Days--Quarterly 2Review for Quarterly ExamChapter 3.3 – 3.6Chapter 4Chapter 540 days of Lessons1 day2 days2 daysMarking Period 3 (Feb. 1 – April 5) Quarterly 3 Chapters 7, 8, 9.1 – 9.3Section TopicObjective/Goal: what the student will know and be able to doStandardHonors PaceCollege Prep PaceGeneral Studies Pace7-1Ratios & ProportionsWrite ratiosWrite and solve proportionsG.MG.317-2Similar PolygonsUse proportions to identify similar polygonsSolve problems using the properties of similar polygonsG.SRT.217-3Similar TrianglesIdentify similar triangles using AA Similarity Postulate, SSS and SAS Similarity TheoremsUse similar triangles to solve problemsG.SRT.3, G.SRT.4, G.SRT.517-4Parallel Lines & Proportional PartsUse proportional parts within triangles to find missing lengthsUse proportional parts with parallel lines to find missing lengthsG.SRT.4, G.SRT.517-5Parts of Similar TrianglesRecognize and use proportional relationships of corresponding segments of similar trianglesUse the Triangle Angle Bisector TheoremG.SRT.4, G.SRT.517-6Similarity TransformationsGiven two figures, determine using transformations if they are similarVerify similarity after a similarity transformationG.SRT.2, G.SRT.517-7Scale Drawings & ModelsInterpret scale models to find actual lengthsUse scale factors to solve design problemsG.MG.31Review & Assess4----7 Days Lessons4 Review/Assess11 Total Days--8-1Geometric MeanFind the geometric mean between two numbersSolve problems involving relationships between parts of a right triangle and the altitude to its hypotenuseG.SRT.4, G.SRT.518-2The Pythagorean Theorem and Its ConverseUse the Pythagorean Theorem to find side lengths in right trianglesUse the Converse of the Pythagorean Theorem to determine if a triangle is a right triangleG.SRT.8, G.MG.328-3Special Right TrianglesUse the properties of 45-45-90 triangles to find side lengthsUse properties of 30-60-90 triangles to find side lengthsG.SRT.618-4TrigonometryFind trigonometric ratios using right trianglesUse trigonometric ratios to find angle measures in right trianglesG.SRT.6, G.SRT.718-5Angles of Elevation and DepressionSolve problems involving angles of elevation and depressionUse angles of elevation and depression to find the distance between two objectsG.SRT.818-6The Law of Sines and Law of CosinesUse the Law of Sines to solve trianglesUse the Law of Cosines to solve trianglesG.SRT.9, G.SRT.102optionaloptional8-7VectorsFind the magnitudes and directions of vectorsAdd and subtract vectorsUse scale drawings and direct measurement to find the resultant of two vectors (Extend)G.GPE.62Review and Assess4----10 Days Lessons4 Review / Assess14 Total Days --9-1ReflectionsDevelop formal mathematical definition of reflectionDraw reflectionsDraw reflections in the coordinate planeG.CO.4, G.CO.519-2TranslationsDevelop formal mathematical definition of translationDraw translationsDraw translations in the coordinate planeG.CO.4, G.CO.519-3RotationsExplore the properties of rotations (Explore)Develop formal mathematical definition of rotationDraw rotationsDraw rotations in the coordinate planeIdentify and sketch solids formed by revolving two-dimensional figures about lines (Extend)(G.CO.2), G.CO.4, G.CO.5, (G.GMD.4)2----4 Days Lessons--Quarterly 3Review for Quarterly ExamChapter 7Chapter 8Chapter 9.1 – 9.329 days of Lessons1 day2 days2 daysMarking Period 4 (April 6 – June 16) Quarterly 4 Chapters 9.4 – 9.6, 10, 12.2 – 12.39-4Compositions of TransformationsDraw glide reflections and other compositions of isometries in the coordinate planeDraw compositions of reflections in parallel and intersecting linesG.CO.2, G.CO.529-5SymmetryIdentify line and rotational symmetries in two-dimensional figuresIdentify plane and axis symmetries in three-dimensional figuresG.CO.319-6DilationsUse graphing technology to explore the properties of dilations (Explore)Draw dilationsDraw dilations in the coordinate planeExplore how triangle congruence and similarity follow from an understanding of transformations (Extend)G.SRT.1, G.CO.2, (G.CO.8, G.SRT.3)2Review & Assess4----5 days lessons4 Review/Assess9 Total Days--10-1Circles and CircumferenceIdentify and use parts of circlesSolve problems involving the circumference of a circleG.CO.1, G.C.1110-2Measuring Angles and ArcsIdentify central angles, major arcs, minor arcs, and semicircles, and find their measuresFind arc lengthsG.C.2, G.C.5110-3Arcs and ChordsRecognize and use relationships between arcs and chordsRecognize and use relationships between arcs, chords and diametersG.C.2, G.MG.3110-4Inscribed AnglesFind measures of inscribed anglesFind measures of angles of inscribed polygonsG.C.2, G.C.3110-5TangentsUse properties of tangentsSolve problems involving circumscribed polygonsConstruct inscribed circles and circumscribed triangles (Extend)G.CO.12, (G.CO.13, G.C.3), G.C.4210-6Secants, Tangents and Angle MeasuresFind measures of angles formed by lines intersecting on or inside a circleFind measures of angles formed by lines intersecting outside the circleG.C.4110-7Special Segments in a CircleFind measures of segments that intersect in the interior of a circleFind measures of segments that intersect in the exterior of a circleG.C.4110-8Equations of CirclesWrite the equation of a circleGraph a circle on the coordinate planeG.GPE.1, G.GPE.61Review and Assess4----9 Days Lessons4 Review/Assess13 Total Days--6.1Angles of PolygonsFind and use the sum of the measures of the interior angles of a polygon.Find and use the sum of the measures of the exterior angles of a polygon.G.MG.116.2ParallelogramsRecognize and apply the properties of the sides and angles of parallelogramsRecognize and apply the properties of the diagonals of parallelograms.G.CO.11G.GPE.416.3Tests of ParallelogramsRecognize the conditions that ensure a quadrilateral is a parallelogram.Prove that a set of points form a parallelogram in the coordinate plane.G.CO.11G.GPE.426.4RectanglesRecognize and apply properties of rectangles.Determine whether parallelograms are rectangles.G.CO.11G.GPE.416.5Rhombi and SquaresRecognize and apply properties of rhombi and squares.Determine whether quadrilaterals are rectangles, rhombi, or squares.G.CO.11G.GPE.416.6Trapezoids and KitesRecognize and apply the properties of trapezoids, including the medians of trapezoids.Recognize and apply the properties of kites.G.GPE.4G.MG.32Review and Assess4----8 Days Lessons4 Review/Assess12 Total Days--12-1Representations of Three-Dimensional FiguresDraw isometric views of three-dimensional figuresInvestigate cross sections of three-dimensional figuresG.GMD.41OptionalOptional12-2Surface Areas of Prisms and CylindersFind lateral areas and surface areas of prismsFind lateral areas and surface areas of cylindersG.MG.3112-3Surface Areas of Pyramids and ConesFind lateral areas and surface areas of pyramidsFind lateral areas and surface areas of conesG.MG.11OptionalOptional12-4Volumes of Prisms and CylindersFind volumes of prismsFind volumes of cylindersG.GMD.1, G.GMD.31OptionalOptional12-5Volumes of Pyramids and ConesFind volumes of pyramidsFind volumes of conesG.GMD.1, G.GMD.31OptionalOptional12-6Surface Areas and Volumes of SpheresFind surface areas of spheresFind volumes of spheresG.GMD.1, G.GMD.31OptionalOptional12-7Spherical GeometryDescribe sets of points on a sphereCompare and contrast Euclidean and spherical geometries1OptionalOptional12-8Congruent and Similar SolidsIdentify congruent or similar solidsUse properties of similar solids1OptionalOptionalReview and Assess2----8 Days Lessons2 Review/Assess10 Total Days--Quarterly 4Review for Quarterly ExamChapter 9.4 – 9.6Chapter 10Chapter 12.2 – 12.344 days of Lessons1 day2 days2 days ................
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