SPOTSYLVANIA COUNTY PUBLIC SCHOOLS Geometry CURRICULUM PACING GUIDE Notes: Pacing: 20 blocks Pacing: 24 blocks Pacing: 16 blocks Pacing: 13 blocks Pacing: 5 blocks Units Listed in the same column can be rearranged in any order as long as they are all taught before the Division Assessment is given. For each Division Assessment consider using those questions as part of your usual assessment for the last unit immediately prior to the Division Assessment. Consider using the Division Assessment #2 as part of your Midterm Exam. Assessments # 2 – 4 will include commonly missed questions from the previous division assessment. Those questions will be discussed at the Sharing Best Practices Meetings. Division Assessments must be given in one sitting, not broken down and given at different times. Review Unit (2 blocks) Algebra Skills Vocabulary Pre-Test Unit 1 Lines (6 blocks) G.3 a Distance, Midpoint, Slope - From graph, 2 points, equation of a line - Include missing endpoint G.3 b Parallel or Perpendicular - Equation of a Line **Review/Assessment** Unit 2 Angles (6 blocks) Angle Pairs G.2 a Determine whether lines are parallel G.2 b Verify Parallel Lines G.2 c Real World Parallel Lines **Review/Assessment** Unit 3 Logic (5 blocks) G.1 a Converse, Inverse, Contrapositive G.1 b Verbal to Symbolic G.1 c Venn Diagrams G.1 d - Use deductive reasoning **Review/Assessment** Unit 4 Triangles Part I (8 blocks) G.5 a,b,c Ordering sides & angles, triangle inequality (does this form a triangle) G.5 d Range of Values for 3 rd Side G.6 Congruent Triangles - From pictures & coordinate plane - Two-Column Proofs **Review/Assessment** Unit 5 Triangles Part II (7 blocks) G.8 Right Triangles - Pythagorean Thm & Converse - Special Right Triangles - Trigonometry - Elevation/Depression **Review/Assessment** Unit 6 Transformations (3 blocks) G.3 c,d Symmetry & Transformations **Review/Assessment** Unit 7 Similar Triangles (4 blocks) G.7 Similar **Review/Assessment** Unit 8 Quadrilaterals & Polygons (8 blocks) G.9 Quadrilaterals - Verify characteristics of quadrilaterals - Use properties of quadrilaterals G.10 Polygons - Interior Angles - Exterior Angles - Tesselations **Review/Assessment** Unit 9 3D Figures (5 blocks) G.13 Surface Area & Volume G.14 Ratios of Similar Solids **Review/Assessment** Unit 10 Circles (9 blocks) G.11 Circles - Vocabulary - Central & Inscribed Angles - Other Angles - Chords, Secants, Tangents - Other Segments - Inscribed & Circumscribed Polygons - Arc Length & Sector Area G.12 Equation of Circle **Review/Assessment** Unit 11 Constructions (3 blocks) G.4 a Congruent Segment G.4 b Perpendicular Bisector G.4 c Perpendicular to point not on a line G.4 d Perpendicular to point on a line G.4 e Angle bisector G.4 f Congruent Angle G.4 g Parallel Line **Review/Assessment** R E V I E W Updated: 6/20/2016 Enrichment Topics: Geometric Mean, Special Segments, Truth Tables Division Assessment #2 (1 block) Suggested Date of Completion: January 26th Division Assessment #4 (1 block) Suggested Date of Completion: May 2nd Division Assessment #3 (1 block) Suggested Date of Completion: March 14th Division Assessment #1 (1 block) Suggested Date of Completion: November 2nd
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Notes: Pacing: Pacing: 20 blocks 24 blocks 16 blocks 13 ...€¦ · 16 blocks Pacing: 13 blocks Pacing: 5 blocks Units Listed in the same column can be rearranged in any order as
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SPOTSYLVANIA COUNTY PUBLIC SCHOOLS Geometry CURRICULUM PACING GUIDE
Notes: Pacing:
20 blocks
Pacing:
24 blocks
Pacing:
16 blocks
Pacing:
13 blocks
Pacing:
5 blocks
Units Listed in the same
column can be rearranged
in any order as long as
they are all taught before
the Division Assessment is
given.
For each Division
Assessment consider using
those questions as part of
your usual assessment for
the last unit immediately
prior to the Division
Assessment.
Consider using the
Division Assessment #2 as
part of your Midterm
Exam.
Assessments # 2 – 4 will
include commonly missed
questions from the
previous division
assessment. Those
questions will be discussed
at the Sharing Best
Practices Meetings.
Division Assessments
must be given in one
sitting, not broken down
and given at different
times.
Review Unit (2 blocks)
Algebra Skills
Vocabulary
Pre-Test
Unit 1 Lines (6 blocks)
G.3 a Distance, Midpoint, Slope
- From graph, 2 points, equation
of a line
- Include missing endpoint
G.3 b Parallel or Perpendicular
- Equation of a Line
**Review/Assessment**
Unit 2 Angles (6 blocks)
Angle Pairs
G.2 a Determine whether lines
are parallel
G.2 b Verify Parallel Lines
G.2 c Real World Parallel Lines
**Review/Assessment**
Unit 3 Logic (5 blocks)
G.1 a Converse, Inverse,
Contrapositive
G.1 b Verbal to Symbolic
G.1 c Venn Diagrams
G.1 d - Use deductive reasoning
**Review/Assessment**
Unit 4 Triangles Part I
(8 blocks)
G.5 a,b,c Ordering sides &
angles, triangle inequality
(does this form a triangle)
G.5 d Range of Values for 3rd
Side
G.6 Congruent Triangles
- From pictures & coordinate
plane
- Two-Column Proofs
**Review/Assessment**
Unit 5 Triangles Part II
(7 blocks)
G.8 Right Triangles
- Pythagorean Thm &
Converse
- Special Right Triangles
- Trigonometry
- Elevation/Depression
**Review/Assessment**
Unit 6 Transformations
(3 blocks)
G.3 c,d Symmetry &
Transformations
**Review/Assessment**
Unit 7 Similar Triangles
(4 blocks)
G.7 Similar
**Review/Assessment**
Unit 8 Quadrilaterals &
Polygons (8 blocks)
G.9 Quadrilaterals
- Verify characteristics of
quadrilaterals
- Use properties of
quadrilaterals
G.10 Polygons
- Interior Angles
- Exterior Angles
- Tesselations
**Review/Assessment**
Unit 9 3D Figures
(5 blocks)
G.13 Surface Area &
Volume
G.14 Ratios of Similar
Solids
**Review/Assessment**
Unit 10 Circles
(9 blocks)
G.11 Circles
- Vocabulary
- Central & Inscribed Angles
- Other Angles
- Chords, Secants, Tangents
- Other Segments
- Inscribed & Circumscribed
Polygons
- Arc Length & Sector Area
G.12 Equation of Circle
**Review/Assessment**
Unit 11 Constructions
(3 blocks)
G.4 a Congruent Segment
G.4 b Perpendicular Bisector
G.4 c Perpendicular to point not
on a line
G.4 d Perpendicular to point on a
line
G.4 e Angle bisector
G.4 f Congruent Angle
G.4 g Parallel Line
**Review/Assessment**
R
E
V
I
E
W
Updated: 6/20/2016 Enrichment Topics: Geometric Mean, Special Segments, Truth Tables
Division
Assessment #2
(1 block)
Suggested Date
of Completion:
January 26th
Division
Assessment #4
(1 block)
Suggested Date
of Completion:
May 2nd
Division
Assessment #3
(1 block)
Suggested Date
of Completion:
March 14th
Division
Assessment #1
(1 block)
Suggested Date
of Completion:
November 2nd
SPOTSYLVANIA COUNTY PUBLIC SCHOOLS Geometry CURRICULUM GUIDE
G.1 The student will construct and judge the validity of a logical argument consisting of a set of premises and a
conclusion. This will include
a) identifying the converse, inverse, and contrapositive of a conditional statement;
b) translating a short verbal argument into symbolic form;
c) using Venn diagrams to represent set relationships; and
d) using deductive reasoning.
Understanding the Standard (Teacher Use Only)
Essential Understandings
Essential Knowledge and Skills
Resources, Activities and Extensions
Inductive reasoning,
deductive reasoning,
and proof are critical
in establishing general
claims.
Deductive reasoning
is the method that
uses logic to draw
conclusions based on
definitions, postulates,
and theorems.
Inductive reasoning is
the method of drawing
conclusions from a
limited set of
observations.
Proof is a justification
that is logically valid
and based on initial
assumptions,
definitions, postulates,
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to
Identify the converse, inverse,
and contrapositive of a
conditional statement.
Translate verbal arguments
into symbolic form, such as
(p q) and (~p ~q).
Determine the validity of a
logical argument.
Use valid forms of deductive
reasoning, including the law of
syllogism, the law of the
contrapositive, the law of
detachment, and
counterexamples.
Select and use various types of
reasoning and methods of
Resources for G.1
Key Vocabulary:
Valid, Invalid Inverse, Converse, Contrapositive Conditional, Bi-Conditional, If & Only If Negate Hypothesis, Conclusion Logically Equivalent Argument All, Some, None Law of Detachment, Law of
SPOTSYLVANIA COUNTY PUBLIC SCHOOLS Geometry CURRICULUM GUIDE
two sides.
Solve real-world problems
given information about the
lengths of sides and/or
measures of angles in
triangles.
Suggested Assessment(s):
Cross-Curricular Connection
SPOTSYLVANIA COUNTY PUBLIC SCHOOLS Geometry CURRICULUM GUIDE
STRAND: Triangles
Course: Geometry Suggested Pacing: 4 blocks
Prerequisite Skill(s):
Set up & solve equations; distance; plotting points; triangle sum theorem; angle pairs; deductive reasoning
Standard:
G.6 The student, given information in the form of a figure or statement, will prove two triangles are congruent, using
algebraic and coordinate methods as well as deductive proofs.
Understanding the Standard (Teacher Use Only)
Essential Understandings
Essential Knowledge and Skills
Resources and Activities
Congruence has real-
world applications in
a variety of areas,
including art,
architecture, and the
sciences.
Congruence does not
depend on the position
of the triangle.
Concepts of logic can
demonstrate
congruence or
similarity.
Congruent figures are
also similar, but
similar figures are not
necessarily congruent.
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to
Use definitions, postulates,
and theorems to prove
triangles congruent.
Use coordinate methods, such
as the distance formula and the
slope formula, to prove two
triangles are congruent.
Use algebraic methods to
prove two triangles are
congruent.
Resources for G.6
Key Vocabulary:
Congruent Angle Angle Side Angle Side Angle Side Angle Side Side Side Side Hypotenuse Leg Vertical Angles Parallel Lines Linear Pair All Angle Pairs Bisect Midpoint Altitude Reflexive Property
G.8 The student will solve real-world problems involving right triangles by using the Pythagorean Theorem and its
converse, properties of special right triangles, and right triangle trigonometry.
Understanding the Standard (Teacher Use Only)
Essential Understandings
Essential Knowledge and Skills
Resources and Activities
The Pythagorean
Theorem is essential
for solving problems
involving right
triangles.
Many historical and
algebraic proofs of the
Pythagorean Theorem
exist.
The relationships
between the sides and
angles of right
triangles are useful in
many applied fields.
Some practical
problems can be
solved by choosing an
efficient
representation of the
problem.
Another formula for
the area of a triangle
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to
Determine whether a triangle
formed with three given
lengths is a right triangle.
Solve for missing lengths in
geometric figures, using
properties of 45-45-90
triangles.
Solve for missing lengths in
geometric figures, using
properties of 30-60-90
triangles.
Solve problems involving right
triangles, using sine, cosine,
and tangent ratios.
Solve real-world problems,
using right triangle
trigonometry and properties of
Resources for G.8
Key Vocabulary:
Hypotenuse, Legs Perpendicular Short Leg, Long Leg Opposite, Adjacent Sine, cosine, tangent Ratios Trigonometry Isosceles Right Triangle Acute Triangle, Obtuse Triangle, Right Triangles 30-60-90 & 45-45-90 Special Right Triangles