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 / Objective/Goal: what the student will know and be able to do / Standard / Honors Pace / College Prep Pace / General Studies Pace1.1 / Points, Lines, and Planes / · 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
1.2 / Linear Measure / · Measure Segments.
· Calculate with measures. Determine precision of measurements. (Extend)
· Determine accuracy of measurements. (Extend) / G. CO. 1, G.CO.12 / 2
1.3 / Distance and Midpoints / · Find the distance between two points.
· Find the midpoint of a segment. / G. CO. 1, G.CO.12 / 1
1.4 / Angle Measure / · Measure and classify angles.
· Identify and use congruent angles and the bisector of an angle. / G. CO. 1, G.CO.12 / 1
1.5 / Angle Relationships / · Identify and use special pairs of angles
· Identify perpendicular lines.
· Construct perpendiculars. (Extend) / 2
1.6 / Two-Dimensional Figures / · 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) / G.GPE.7, G.CO.12 / 2
1.7 / Three-Dimensional Figures / · Identify and name three dimensional figures
· Find surface area and volume. / G.GMD.3 / 1
Review and Assess / 4
- / - / - / - / 11 Days Lessons
4 Review / Assess
15 Total Days / - / -
2.1 / Inductive Reasoning and Conjecture / · Make conjectures based on inductive reasoning.
· Find Counterexamples / 1
2.2 / Logic / · Determine truth values of negations, conjectures, and disjunctions.
· Represent conjunctions and disjunctions using Venn diagrams / 1
2.3 / Conditional Statements / · Analyze statements in if-then form
· Write converses, inverses, and contrapositives. / 2
2.4 / Deductive Reasoning / · Use the Law of Detachment.
· Use the Law of Syllogism. / 1
2.5 / Postulates and Paragraph Proofs / · Identify and use basic postulates about points, lines, and plane.
· Write paragraph proofs. / 2
2.6 / Algebraic Proof / · Use Algebra to write two-column proofs.
· Use properties of equality to write geometric proofs. / 1
2.7 / Proving Segment Relationships / · Write proofs involving segment addition.
· Write proofs involving congruence. / G.CO.9
G.CO.12 / 2
2.8 / Proving Angle Relationships / · Write proofs involving supplementary and complementary angles.
· Write proofs involving congruent and right angles. / G.CO.9 / 2
Review and Assess / 4
- / - / - / - / 12 Days Lessons
4 Review/Assess
16 Total Days / - / -
3.1 / Parallel Lines and Transversals / · Identify the relationship between two lines or two planes.
· Name angle pairs formed by parallel lines and transversals. / G.CO.1 / 1
3.2 / Angles and Parallel Lines / · 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 / 2
- / - / - / - / 3 teaching days / - / -
Quarterly 1 / Review for Quarterly Exam / Chapter 1
Chapter 2
Chapter 3.1 – 3.2 / 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 / · Find slopes of lines.· Use slope to identify parallel and perpendicular lines. / G.GPE.5 / 1
3.4 / Equations of 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) / G.GPE.5 / 2
3.5 / Proving Lines Parallel / · Recognize angle pairs that occur with parallel lines.
· Prove that two lines are parallel. / G.CO.12
G.CO.9 / 1
3.6 / Perpendiculars and Distance / · Find the distance between a point and a line.
· Find the distance between two parallel lines. / G.CO.12
G.MG.3 / 1
Review and Assess / 4
- / - / - / - / 5 Days Lessons
4 Review/Assess
9 Total Days / - / -
4.1 / Classifying Triangles / · Identify and classify triangles by angle measures and side measures / G.CO.12 / 1
4.2 / Angles of Triangles / · Find 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.10 / 2
4.3 / Congruent Triangles / · Name and use corresponding parts of congruent polygons.
· Prove triangles congruent using the definition of congruence. / G.CO.7
G.SRT.5 / 1
4.4 / Proving Triangles Congruent / · Use 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.5 / 2
4.5 / Proving Triangles Congruent / · Use the ASA and AAS Postulates to test for triangle congruence / G.CO.10
G.SRT.5 / 2
4.6 / Isosceles and Equilateral Triangles / · Use properties of isosceles and equilateral triangles. / G.CO.10
G.CO.12 / 1
4.7 / Congruence Transformations / · Identify reflections, translations, and rotations.
· Verify congruence after a congruence transformation. / G.CO.6
G.CO.7 / 2
4.8 / Triangles and Coordinate Proof / · Position and label triangles for use in coordinate proofs.
· Write coordinate proofs. / G.CO.10
G.GPE.4 / 2
Review and Assess / 4
- / - / - / - / 13 Days Lessons
4 Review/Assess
17 Total Days / - / -
5.1 / Bisectors of Triangle / · Construct perpendicular bisectors and angle bisectors of triangles. (Explore)
· Identify and use perpendicular bisectors in triangles.
· Identify and use angle bisectors in triangles. / G.CO.10
G.MG.3 / 2
5.2 / Medians and Altitudes of Triangles / · Identify and use medians and altitudes in triangles.
· Identify and use altitudes in triangles. / G.CO.10
G.MG.3 / 2
5.3 / Inequalities in One Triangle / · 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. / G.CO.10 / 1
5.4 / Indirect Proof / · Write indirect algebraic proofs.
· Write indirect geometric proofs. / G.CO.10 / 1
5.5 / The Triangle Inequality / · Use the Triangle Inequality Theorem to identify possible triangles.
· Prove triangle relationships using the Triangle Inequality Theorem. / G.CO.10
G.MG.3 / 2
5.6 / Inequalities in Two Triangles / · Apply the Hinge Theorem or its converse to make comparisons in two triangles. / G.CO.10 / 2
Review and Assess / 4
- / - / - / - / 10 Days Lessons
4 Review/Assess
14 Total Days / - / -
Quarterly 2 / Review for Quarterly Exam / Chapter 3.3 – 3.6
Chapter 4
Chapter 5 / 40 days of Lessons / 1 day / 2 days / 2 days
Marking Period 3 (Feb. 1 – April 5) Quarterly 3 Chapters 7, 8, 9.1 – 9.3
Section / Topic / Objective/Goal: what the student will know and be able to do / Standard / Honors Pace / College Prep Pace / General Studies Pace7-1 / Ratios & Proportions / · Write ratios
· Write and solve proportions / G.MG.3 / 1
7-2 / Similar Polygons / · Use proportions to identify similar polygons
· Solve problems using the properties of similar polygons / G.SRT.2 / 1
7-3 / Similar Triangles / · Identify similar triangles using AA Similarity Postulate, SSS and SAS Similarity Theorems
· Use similar triangles to solve problems / G.SRT.3, G.SRT.4, G.SRT.5 / 1
7-4 / Parallel Lines & Proportional Parts / · Use proportional parts within triangles to find missing lengths
· Use proportional parts with parallel lines to find missing lengths / G.SRT.4, G.SRT.5 / 1
7-5 / Parts of Similar Triangles / · Recognize and use proportional relationships of corresponding segments of similar triangles
· Use the Triangle Angle Bisector Theorem / G.SRT.4, G.SRT.5 / 1
7-6 / Similarity Transformations / · Given two figures, determine using transformations if they are similar
· Verify similarity after a similarity transformation / G.SRT.2, G.SRT.5 / 1
7-7 / Scale Drawings & Models / · Interpret scale models to find actual lengths
· Use scale factors to solve design problems / G.MG.3 / 1
Review & Assess / 4
- / - / - / - / 7 Days Lessons
4 Review/Assess
11 Total Days / - / -
8-1 / Geometric Mean / · Find the geometric mean between two numbers
· Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse / G.SRT.4, G.SRT.5 / 1
8-2 / The Pythagorean Theorem and Its Converse / · 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 / G.SRT.8, G.MG.3 / 2
8-3 / Special Right Triangles / · Use the properties of 45-45-90 triangles to find side lengths
· Use properties of 30-60-90 triangles to find side lengths / G.SRT.6 / 1
8-4 / Trigonometry / · Find trigonometric ratios using right triangles
· Use trigonometric ratios to find angle measures in right triangles / G.SRT.6, G.SRT.7 / 1
8-5 / Angles of Elevation and Depression / · Solve problems involving angles of elevation and depression
· Use angles of elevation and depression to find the distance between two objects / G.SRT.8 / 1
8-6 / The Law of Sines and Law of Cosines / · Use the Law of Sines to solve triangles
· Use the Law of Cosines to solve triangles / G.SRT.9, G.SRT.10 / 2 / optional / optional
8-7 / Vectors / · 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) / G.GPE.6 / 2
Review and Assess / 4
- / - / - / - / 10 Days Lessons
4 Review / Assess
14 Total Days / - / -
9-1 / Reflections / · Develop formal mathematical definition of reflection
· Draw reflections
· Draw reflections in the coordinate plane / G.CO.4, G.CO.5 / 1
9-2 / Translations / · Develop formal mathematical definition of translation
· Draw translations
· Draw translations in the coordinate plane / G.CO.4, G.CO.5 / 1
9-3 / Rotations / · Explore the properties of rotations (Explore)
· Develop formal mathematical definition of rotation
· Draw rotations
· Draw rotations in the coordinate plane
· Identify 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 3 / Review for Quarterly Exam / Chapter 7
Chapter 8
Chapter 9.1 – 9.3 / 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 / · Draw glide reflections and other compositions of isometries in the coordinate plane· Draw compositions of reflections in parallel and intersecting lines / G.CO.2, G.CO.5 / 2
9-5 / Symmetry / · Identify line and rotational symmetries in two-dimensional figures
· Identify plane and axis symmetries in three-dimensional figures / G.CO.3 / 1
9-6 / Dilations / · 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.SRT.1, G.CO.2, (G.CO.8, G.SRT.3) / 2
Review & Assess / 4
- / - / - / - / 5 days lessons
4 Review/Assess
9 Total Days / - / -
10-1 / Circles and Circumference / · Identify and use parts of circles
· Solve problems involving the circumference of a circle / G.CO.1, G.C.1 / 1
10-2 / Measuring Angles and Arcs / · Identify central angles, major arcs, minor arcs, and semicircles, and find their measures
· Find arc lengths / G.C.2, G.C.5 / 1
10-3 / Arcs and Chords / · Recognize and use relationships between arcs and chords
· Recognize and use relationships between arcs, chords and diameters / G.C.2, G.MG.3 / 1
10-4 / Inscribed Angles / · Find measures of inscribed angles
· Find measures of angles of inscribed polygons / G.C.2, G.C.3 / 1
10-5 / Tangents / · Use properties of tangents
· Solve problems involving circumscribed polygons
· Construct inscribed circles and circumscribed triangles (Extend) / G.CO.12, (G.CO.13, G.C.3), G.C.4 / 2
10-6 / Secants, Tangents and Angle Measures / · Find measures of angles formed by lines intersecting on or inside a circle
· Find measures of angles formed by lines intersecting outside the circle / G.C.4 / 1