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Geometry – Scope and Sequence (Honors, College Prep, and General Studies) 2016 – 2017 Marking Period 1 (Sept. 1 – Nov. 17) Quarterly 1 Chapters 1, 2, 3.1 – 3.2 Section Topic 1.1 Points, Lines, and Planes Objective/Goal: what the student will know and be able to do 1.2 Linear Measure 1.3 Distance and Midpoints 1.4 Angle Measure 1.5 Angle Relationships Standard Honors Pace Identify 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.1 2 Measure Segments. Calculate with measures. Determine precision of measurements. (Extend) Determine accuracy of measurements. (Extend) G. CO. 1, G.CO.12 2 Find the distance between two points. Find the midpoint of a segment. Measure and classify angles. Identify and use congruent angles and the bisector of an angle. Identify and use special pairs of angles Identify perpendicular lines. Construct perpendiculars. G. CO. 1, G.CO.12 1 G. CO. 1, G.CO.12 1 2 College Prep Pace General Studies Pace 1.6 Two-Dimensional Figures 1.7 Three-Dimensional Figures Review and Assess - G.GPE.7, G.CO.12 2 G.GMD.3 1 4 - 2.1 Inductive Reasoning and Conjecture 2.2 Logic 2.3 (Extend) Identify 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) Identify and name three dimensional figures Find surface area and volume. Conditional Statements 2.4 Deductive Reasoning 2.5 Postulates and Paragraph Proofs Make conjectures based on inductive reasoning. Find Counterexamples Determine truth values of negations, conjectures, and disjunctions. Represent conjunctions and disjunctions using Venn diagrams Analyze statements in ifthen form Write converses, inverses, and contrapositives. Use the Law of Detachment. Use the Law of Syllogism. Identify and use basic postulates about points, lines, and plane. - 11 Days Lessons 4 Review / Assess 15 Total Days 1 1 2 1 2 - - 2.6 Algebraic Proof 2.7 Proving Segment Relationships 2.8 Proving Angle Relationships Review and Assess - 3.1 - G.CO.9 G.CO.12 2 G.CO.9 2 Angles and Parallel Lines - 1 4 Parallel Lines and Transversals 3.2 Write paragraph proofs. Use Algebra to write twocolumn proofs. Use properties of equality to write geometric proofs. Write proofs involving segment addition. Write proofs involving congruence. Write proofs involving supplementary and complementary angles. Write proofs involving congruent and right angles. - - Identify the relationship between two lines or two planes. Name angle pairs formed by parallel lines and transversals. G.CO.1 Use 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.12 G.CO. 1 G.CO.9 - 12 Days Lessons 4 Review/Assess 16 Total Days 1 - - - - 2 - 3 teaching days Quarterly 1 Chapter 1 Chapter 2 Chapter 3.1 – 3.2 Review for Quarterly Exam 34 days of Lessons 1 day 2 days 2 days - - Marking Period 2 (Nov. 18 – Jan. 31) Quarterly 2 Chapters 3.3 – 3.6, 4, 5 3.3 Slopes of Lines 3.4 Equations of Lines 3.5 Proving Lines Parallel 3.6 Perpendiculars and Distance Review and Assess - Find slopes of lines. Use slope to identify parallel and perpendicular lines. Write 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) Recognize angle pairs that occur with parallel lines. Prove that two lines are parallel. Find the distance between a point and a line. Find the distance between two parallel lines. G.GPE.5 1 G.GPE.5 2 G.CO.12 G.CO.9 1 G.CO.12 G.MG.3 1 4 - - 4.1 Classifying Triangles 4.2 Angles of Triangles Identify and classify triangles by angle measures and side measures Find the relationships among the measures of the interior angles of a triangle. - G.CO.12 G. CO.12, G.CO.10 5 Days Lessons 4 Review/Assess 9 Total Days 1 2 4.3 Congruent Triangles 4.4 Proving Triangles Congruent 4.5 Proving Triangles Congruent 4.6 Isosceles and Equilateral Triangles Congruence Transformations 4.7 4.8 Triangles and Coordinate Proof Review and Assess - 5.1 (Explore) Apply the triangle AngleSum Theorem. Apply the Exterior Angle Theorem. Name and use corresponding parts of congruent polygons. Prove triangles congruent using the definition of congruence. Use the SSS and SAS Postulates to test for triangle congruence. Construct an angle bisector. (Extend) Prove constructions using congruent measures. (Extend) Use the ASA and AAS Postulates to test for triangle congruence Use properties of isosceles and equilateral triangles. Identify reflections, translations, and rotations. Verify congruence after a congruence transformation. Position and label triangles for use in coordinate proofs. Write coordinate proofs. G.CO.7 G.SRT.5 1 G.CO.10, G.CO.12, G.SRT.5 2 G.CO.10 G.SRT.5 2 G.CO.10 G.CO.12 G.CO.6 G.CO.7 1 G.CO.10 G.GPE.4 2 2 4 - Bisectors of Triangle Construct perpendicular - G.CO.10 13 Days Lessons 4 Review/Assess 17 Total Days 2 - - 5.2 Medians and Altitudes of Triangles 5.3 Inequalities in One Triangle 5.4 Indirect Proof 5.5 The Triangle Inequality 5.6 Review and Assess Inequalities in Two Triangles bisectors and angle bisectors of triangles. (Explore) Identify and use perpendicular bisectors in triangles. Identify and use angle bisectors in triangles. Identify and use medians and altitudes in triangles. Identify and use altitudes in triangles. Recognize 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. Write indirect algebraic proofs. Write indirect geometric proofs. Use the Triangle Inequality Theorem to identify possible triangles. Prove triangle relationships using the Triangle Inequality Theorem. Apply the Hinge Theorem or its converse to make comparisons in two triangles. G.MG.3 G.CO.10 G.MG.3 2 G.CO.10 1 G.CO.10 1 G.CO.10 G.MG.3 2 G.CO.10 2 4 - Quarterly 2 - - - Review for Quarterly Exam Chapter 3.3 – 3.6 Chapter 4 Chapter 5 40 days of Lessons 10 Days Lessons 4 Review/Assess 14 Total Days 1 day - - 2 days 2 days Marking Period 3 (Feb. 1 – April 5) Quarterly 3 Chapters 7, 8, 9.1 – 9.3 Section Topic 7-1 Ratios & Proportions 7-2 Similar Polygons Objective/Goal: what the student will know and be able to do 7-3 Similar Triangles 7-4 Parallel Lines & Proportional Parts 7-5 Parts of Similar Triangles Write ratios Write and solve proportions Use proportions to identify similar polygons Solve problems using the properties of similar polygons Identify similar triangles using AA Similarity Postulate, SSS and SAS Similarity Theorems Use similar triangles to solve problems Use proportional parts within triangles to find missing lengths Use proportional parts with parallel lines to find missing lengths Recognize and use proportional relationships of corresponding segments of similar triangles Use the Triangle Angle Bisector Theorem Standard Honors Pace G.MG.3 1 G.SRT.2 1 G.SRT.3, G.SRT.4, G.SRT.5 1 G.SRT.4, G.SRT.5 1 G.SRT.4, G.SRT.5 1 College Prep Pace General Studies Pace 7-6 Similarity Transformations 7-7 Scale Drawings & Models Review & Assess - 8-1 - Geometric Mean The Pythagorean Theorem and Its Converse Special Right Triangles 8-4 Trigonometry 8-5 1 G.MG.3 1 - 8-3 G.SRT.2, G.SRT.5 4 8-2 Given two figures, determine using transformations if they are similar Verify similarity after a similarity transformation Interpret scale models to find actual lengths Use scale factors to solve design problems Angles of Elevation and Find the geometric mean between two numbers Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse Use the Pythagorean Theorem to find side lengths in right triangles Use the Converse of the Pythagorean Theorem to determine if a triangle is a right triangle Use the properties of 4545-90 triangles to find side lengths Use properties of 30-60-90 triangles to find side lengths Find trigonometric ratios using right triangles Use trigonometric ratios to find angle measures in right triangles Solve problems involving - G.SRT.4, G.SRT.5 7 Days Lessons 4 Review/Assess 11 Total Days 1 G.SRT.8, G.MG.3 2 G.SRT.6 1 G.SRT.6, G.SRT.7 1 G.SRT.8 1 - - Depression 8-6 The Law of Sines and Law of Cosines 8-7 Vectors Review and Assess - 9-1 - Reflections Translations 9-3 G.SRT.9, G.SRT.10 2 G.GPE.6 2 optional optional - - 4 9-2 angles of elevation and depression Use angles of elevation and depression to find the distance between two objects Use the Law of Sines to solve triangles Use the Law of Cosines to solve triangles Find the magnitudes and directions of vectors Add and subtract vectors Use scale drawings and direct measurement to find the resultant of two vectors (Extend) Rotations Develop formal mathematical definition of reflection Draw reflections Draw reflections in the coordinate plane Develop formal mathematical definition of translation Draw translations Draw translations in the coordinate plane Explore the properties of rotations (Explore) Develop formal mathematical definition of rotation - G.CO.4, G.CO.5 10 Days Lessons 4 Review / Assess 14 Total Days 1 G.CO.4, G.CO.5 1 (G.CO.2), G.CO.4, G.CO.5, (G.GMD.4) 2 - - Quarterly 3 Review for Quarterly Exam Draw rotations Draw rotations in the coordinate plane Identify and sketch solids formed by revolving twodimensional figures about lines (Extend) Chapter 7 Chapter 8 Chapter 9.1 – 9.3 - 4 Days Lessons - - 29 days of Lessons 1 day 2 days 2 days Marking Period 4 (April 6 – June 16) Quarterly 4 Chapters 9.4 – 9.6, 10, 12.2 – 12.3 9-4 Compositions of Transformations 9-5 Symmetry 9-6 Dilations Draw glide reflections and other compositions of isometries in the coordinate plane Draw compositions of reflections in parallel and intersecting lines Identify line and rotational symmetries in twodimensional figures Identify plane and axis symmetries in threedimensional figures Use graphing technology to explore the properties of dilations (Explore) Draw dilations Draw dilations in the coordinate plane Explore how triangle congruence and similarity follow from an understanding of transformations (Extend) G.CO.2, G.CO.5 2 G.CO.3 1 G.SRT.1, G.CO.2, (G.CO.8, G.SRT.3) 2 Review & Assess - 10-1 4 - Circles and Circumference 10-2 10-3 Measuring Angles and Arcs Arcs and Chords 10-4 Inscribed Angles 10-5 Tangents 10-6 Secants, Tangents and Angle Measures 10-7 Special Segments in a Circle Identify and use parts of circles Solve problems involving the circumference of a circle Identify central angles, major arcs, minor arcs, and semicircles, and find their measures Find arc lengths Recognize and use relationships between arcs and chords Recognize and use relationships between arcs, chords and diameters Find measures of inscribed angles Find measures of angles of inscribed polygons Use properties of tangents Solve problems involving circumscribed polygons Construct inscribed circles and circumscribed triangles (Extend) Find measures of angles formed by lines intersecting on or inside a circle Find measures of angles formed by lines intersecting outside the circle Find measures of segments that intersect in the interior - G.CO.1, G.C.1 5 days lessons 4 Review/Assess 9 Total Days 1 G.C.2, G.C.5 1 G.C.2, G.MG.3 1 G.C.2, G.C.3 1 G.CO.12, (G.CO.13, G.C.3), G.C.4 2 G.C.4 1 G.C.4 1 - - 10-8 Equations of Circles Review and Assess - 6.1 - Angles of Polygons Parallelograms 6.3 Tests of Parallelograms 6.4 Rectangles 6.5 G.GPE.1, G.GPE.6 1 4 6.2 of a circle Find measures of segments that intersect in the exterior of a circle Write the equation of a circle Graph a circle on the coordinate plane Rhombi and Squares Find 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. Recognize and apply the properties of the sides and angles of parallelograms Recognize and apply the properties of the diagonals of parallelograms. Recognize the conditions that ensure a quadrilateral is a parallelogram. Prove that a set of points form a parallelogram in the coordinate plane. Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles. Recognize and apply properties of rhombi and squares. - G.MG.1 9 Days Lessons 4 Review/Assess 13 Total Days 1 G.CO.11 G.GPE.4 1 G.CO.11 G.GPE.4 2 G.CO.11 G.GPE.4 1 G.CO.11 G.GPE.4 1 - - 6.6 Trapezoids and Kites Review and Assess - 12-1 - Representations of ThreeDimensional Figures Surface Areas of Prisms and Cylinders 12-3 Surface Areas of Pyramids and Cones 12-4 12-5 12-6 12-7 G.GPE.4 G.MG.3 2 4 12-2 Determine whether quadrilaterals are rectangles, rhombi, or squares. Recognize and apply the properties of trapezoids, including the medians of trapezoids. Recognize and apply the properties of kites. Volumes of Prisms and Cylinders Volumes of Pyramids and Cones Surface Areas and Volumes of Spheres Spherical Geometry Draw isometric views of three-dimensional figures Investigate cross sections of three-dimensional figures Find lateral areas and surface areas of prisms Find lateral areas and surface areas of cylinders Find lateral areas and surface areas of pyramids Find lateral areas and surface areas of cones Find volumes of prisms Find volumes of cylinders Find volumes of pyramids Find volumes of cones Find surface areas of spheres Find volumes of spheres Describe sets of points on a sphere Compare and contrast Euclidean and spherical geometries - G.GMD.4 8 Days Lessons 4 Review/Assess 12 Total Days 1 - - Optional Optional G.MG.3 1 G.MG.1 1 Optional Optional G.GMD.1, G.GMD.3 G.GMD.1, G.GMD.3 G.GMD.1, G.GMD.3 1 Optional Optional 1 Optional Optional 1 Optional Optional 1 Optional Optional 12-8 Congruent and Similar Solids 1 Identify congruent or similar solids Use properties of similar solids Optional Optional Review and Assess - 2 - - - 8 Days Lessons 2 Review/Assess 10 Total Days - - Quarterly 4 Review for Quarterly Exam Chapter 9.4 – 9.6 Chapter 10 Chapter 12.2 – 12.3 44 days of Lessons 1 day 2 days 2 days