Download Geometry Scope and Sequence

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