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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 – 3.2

Section Topic Objective/Goal: what the student will know and be able to do

Standard Honors Pace College Prep Pace

General Studies Pace

1.1 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 Lessons4 Review / Assess15 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.9G.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 Lessons4 Review/Assess16 Total Days

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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.12G.CO. 1G.CO.9

2

- - - - 3 teaching days - -

Chapter 1

Quarterly 1 Review for Quarterly Exam Chapter 2Chapter 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.12G.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.12G.MG.3

1

Review and Assess

4


- -

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)

G. CO.12, G.CO.10

2

Apply the triangle Angle-Sum Theorem.

Apply the Exterior Angle Theorem.

4.3 Congruent Triangles Name and use corresponding parts of congruent polygons.

Prove triangles congruent using the definition of congruence.

G.CO.7G.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.10G.SRT.5

2

4.6 Isosceles and Equilateral Triangles

Use properties of isosceles and equilateral triangles.

G.CO.10G.CO.12

1

4.7 Congruence Transformations Identify reflections, translations, and rotations.

Verify congruence after a congruence transformation.

G.CO.6G.CO.7

2

4.8 Triangles and Coordinate Proof

Position and label triangles for use in coordinate proofs.

Write coordinate proofs.

G.CO.10G.GPE.4

2

Review and Assess

4


- -

5.1 Bisectors of Triangle Construct perpendicular bisectors and angle

G.CO.10G.MG.3

2

bisectors of triangles. (Explore)

Identify and use perpendicular bisectors in triangles.

Identify and use angle bisectors in triangles.

5.2 Medians and Altitudes of Triangles

Identify and use medians and altitudes in triangles.

Identify and use altitudes in triangles.

G.CO.10G.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.10G.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/Assess14 Total Days

Quarterly 2 Review for Quarterly ExamChapter 3.3 – 3.6

Chapter 4Chapter 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 Pace

7-1 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

G.SRT.2, G.SRT.5 1

transformations if they are similar

Verify similarity after a similarity transformation

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


- -

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

G.SRT.8 1

Use angles of elevation and depression to find the distance between two objects

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 Lessons4 Review / Assess14 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

(G.CO.2), G.CO.4, G.CO.5, (G.GMD.4)

2

coordinate plane Identify and sketch solids

formed by revolving two-dimensional figures about lines (Extend)

- - - - 4 Days Lessons - -

Quarterly 3 Review for Quarterly ExamChapter 7Chapter 8

Chapter 9.1 – 9.329 days of

Lessons1 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 lessons4 Review/Assess9 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

10-7 Special Segments in a Circle Find measures of segments that intersect in the interior of a circle

Find measures of segments

G.C.4 1

that intersect in the exterior of a circle

10-8 Equations of Circles Write the equation of a circle

Graph a circle on the coordinate plane

G.GPE.1, G.GPE.6 1

Review and Assess

4


- -

6.1 Angles of Polygons 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.

G.MG.1 1

6.2 Parallelograms Recognize and apply the properties of the sides and angles of parallelograms

Recognize and apply the properties of the diagonals of parallelograms.

G.CO.11G.GPE.4

1

6.3 Tests 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.

G.CO.11G.GPE.4

2

6.4 Rectangles Recognize and apply properties of rectangles.

Determine whether parallelograms are rectangles.

G.CO.11G.GPE.4

1

6.5 Rhombi and Squares Recognize and apply properties of rhombi and squares.

Determine whether quadrilaterals are

G.CO.11G.GPE.4

1

rectangles, rhombi, or squares.

6.6 Trapezoids and Kites Recognize and apply the properties of trapezoids, including the medians of trapezoids.

Recognize and apply the properties of kites.

G.GPE.4G.MG.3

2

Review and Assess

4


- -

12-1 Representations of Three-Dimensional Figures

Draw isometric views of three-dimensional figures

Investigate cross sections of three-dimensional figures

G.GMD.4 1 Optional Optional

12-2 Surface Areas of Prisms and Cylinders

Find lateral areas and surface areas of prisms

Find lateral areas and surface areas of cylinders

G.MG.3 1

12-3 Surface Areas of Pyramids and Cones

Find lateral areas and surface areas of pyramids

Find lateral areas and surface areas of cones

G.MG.1 1 Optional Optional

12-4 Volumes of Prisms and Cylinders

Find volumes of prisms Find volumes of cylinders

G.GMD.1, G.GMD.3

1 Optional Optional

12-5 Volumes of Pyramids and Cones

Find volumes of pyramids Find volumes of cones

G.GMD.1, G.GMD.3

1 Optional Optional

12-6 Surface Areas and Volumes of Spheres

Find surface areas of spheres

Find volumes of spheres

G.GMD.1, G.GMD.3

1 Optional Optional

12-7 Spherical Geometry Describe sets of points on a sphere

Compare and contrast Euclidean and spherical geometries

1 Optional Optional

12-8 Congruent and Similar Solids Identify congruent or similar solids

1 Optional Optional

Use properties of similar solids

Review and Assess

2


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Quarterly 4 Review for Quarterly ExamChapter 9.4 – 9.6

Chapter 10Chapter 12.2 – 12.3

44 days of Lessons

1 day 2 days 2 days

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