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The purpose of this curriculum project was to align our local Geometry curriculum with the
latest New York State Learning Standards. These standards go into effect September 2008,
with the first Geometry Regents exam being administered in June 2009.
Six high school teachers from worked together on this project. First, we combed through the
new standards thoroughly to determine similarities and differences between these standards
and our current local curriculum. We collectively decided on additional topics F-M would
include in its local curriculum, even if those topics were not part of the state mandates. Next,
we determined which standards were adequately covered in our Geometry textbooks and
which topics needed to be supplemented with other resources or teacher-made materials.
Calendars for the Regents and Honors level Geometry courses were created for each unit
and chapter, outlining daily objectives and suggested homework assignments. The daily
objectives outlined in the unit calendars encompass all of the NY State content standards, as
well as the additional topics we decided to add to our local curriculum. After creating these
unit calendars, the teachers decided which units/objectives would be included in our local
“Topics in Geometry” course. A table is included which indicates the units/objectives to be
taught, along with a suggested number of instructional days.
Once the curriculum was mapped out, we discussed use of the graphing calculator in each
unit of study. We came to consensus on when/how the calculators could be used on various
assessments, and when they should be used as instructional tools. A summary of calculator
guidelines is included on the pages entitled Graphing Calculator Guidelines Unit by Unit.
The contents of this curriculum include…






Overview of “Geometry Regents” and “Geometry Honors” courses
Overview of “Topics in Geometry” course
Graphing Calculator Guidelines, Unit by Unit
Geometry Unit Calendars for Regents/Honors
A copy of the Geometry performance indicators published by NYSED
A copy of the Geometry Crosswalk, published by NYSED.
Respectfully Submitted,
Chris Alvarez
Katie Cook
Kathy Gilbert
Dina Kushnir
Nick Lore
Kate Nowak
January 2008
Course Overview for
Geometry Regents and Geometry Honors
The unit calendars that follow have been created for the Regents level of Geometry.
Honors-level topics and optional enrichment topics are also included on the calendars.
Below is a summary of the number of days dedicated to each unit of study:
Unit of Study
# Days
Intro to Geometry
Logic
Beginning Geometry Proofs
9
9
18
Parallel and Perpendicular Lines, Angle Relationships in
Polygons
Relationships Within Triangles
Quadrilaterals
Coordinate Geometry
Similar Triangles
Right Triangles and Trigonometry
Transformational Geometry
12
Area, Surface Area, Volume
Circle Geometry
Locus
Constructions
Quadratics Unit (Optional for Regents, Mandatory for Honors)
Total
Use remaining days for projects, quiz days, quarterly exams, and
review.
9
15
10
11
8
11 for Regents
13 for Honors
14
13
8 for Regents;
11 for Honors
6
10
153 days for
Regents; 168 days
for Honors
Overview of “Topics in Geometry” Course
Topics in Geometry is a course designed for students who need an additional math credit but
struggle to succeed in a regular Regents level course. Students in this course will take a local
final exam, and will have the option of taking the Geometry regents exam based on teacher
recommendation.
Modifications to the Regents curriculum are indicated under each unit heading. The extra
days afforded by omitting topics can be used for review, practice, or projects.
Unit 1: Intro to Geometry
Omit solving 2 equations with 2 variables
Omit Algebra Proofs (Day 7)
Unit 2:Logic
Omit Logic Proofs (Day 7)
Unit 3: Beginning Geometry Proofs
Omit Days 12 – 15
Unit 4: Parallel and Perpendicular Lines, Angle Relationships
Include all content but add some extra practice days.
Unit 5: Relationships Within Triangles
Omit Indirect Proofs (Day 5)
Omit Inequality Proofs (Day 7)
Unit 6: Quadrilaterals:
Students should know all the properties of the various quadrilaterals and use them to solve
algebraic problems. No proofs will be done in this unit, unless time and the skill level of the
students allows it. Time gained by omitting proofs can be dedicated to explorations (e.g. –
Geometer Sketchpad) .
Unit 7: Coordinate Geometry
Spend extra time writing equations of lines.
Only do coordinate geometry proofs involving triangles and parallelograms.
Proofs should be broken down into smaller steps.
When having students solve a linear-quadratic system of equations, emphasize use of the
graphing calculator.
Unit 8: Similar Triangles
Prove triangles similar using AA Theorem only. (Omit the SSS and SAS similarity theorems).
Unit 9: Right Triangles and Trigonometry
Omit Vectors
Unit 10: Transformations
Omit Isometry and preservation of properties.
Rotations should be about the origin only.
Unit 11: Area, Surface Area, Volume
Omit area and arc length of sectors.
Omit surface area of a cone or pyramid.
Unit 12: Circles
Algebraic/numeric problems only (based on Circle Theorems). No proofs.
Unit 13: Locus
Include all content in this unit. Keep the coordinate geometry problems on the simple side.
Unit 14: Constructions
Include all content in this unit.
.
Graphing Calculator Guidelines Unit by Unit
Unit 1: Intro to Geometry
Students should be tested on their ability to solve quadratic equations AND systems of
linear equations, both graphically AND algebraically WITHOUT use of a graphing
calculator. Quadratic Equations and systems of equations will be solved in the context of a
geometry problem.
Unit 2:Logic
No restrictions on calculator use.
Unit 3: Beginning Geometry Proofs
No restrictions on calculator use.
Unit 4: Parallel and Perpendicular Lines, Angle Relationships
No restrictions on calculator use.
Unit 5: Relationships Within Triangles
No restrictions on calculator use.
Unit 6: Quadrilaterals:
Students should be tested on their ability to solve quadratic equations AND systems of
linear equations, both graphically AND algebraically WITHOUT use of a graphing
calculator. Quadratic Equations and systems of equations will be solved in the context of a
geometry problem.
Unit 7: Coordinate Geometry
Students should be tested on their ability to solve a quadratic-linear system of equations
(including the equation of a circle), both graphically AND algebraically WITHOUT use of a
graphing calculator.
Unit 8: Similar Triangles
No restrictions on calculator use.
Unit 9: Right Triangles and Trigonometry
No restrictions on calculator use.
Unit 10: Transformations
No restrictions on calculator use.
Unit 11: Area, Surface Area, Volume
No restrictions on calculator use.
Unit 12: Circles
Students should be tested on their ability to solve quadratic equations AND systems of
linear equations, both graphically AND algebraically WITHOUT use of a graphing
calculator. Quadratic Equations and systems of equations will be solved in the context of a
geometry problem.
Unit 13: Locus
No restrictions on calculator use.
Unit 14: Constructions
No restrictions on calculator use.
Unit 15: Quadratics Unit
The graphing calculator should be used as a tool for discovering the properties of a
quadratic function in various forms (standard form, vertex form, factored form). Students
should then be able to achieve all the objectives in the unit without use of a graphing
calculator.
Sections and page numbers refer to
Geometry (New York Version),
Prentice Hall Mathematics, 2007
Integrated Geometry
Unit 1: Intro to Geometry
Day Topic(s)/Objectives Covered
Suggested Assignment
1
2
Points, Lines, and Planes
Segments, Rays, Parallel Lines and
Planes
Definition of Midpoint
Types of Angles and Angle Pairs
Classifying Triangles
Triangle Congruence
SSS and SAS
Section 1-3
Section 1-4
Section 1-5
Section 1-6
Supplement classifications
Section 4-1
Section 4-2
None (Review)
G.G.28, 29
5
ASA and AAS
Section 4-3
G.G.28
6
More Problem Solving
p. 234 (systems of linear)
Review of solving quadratics and
Supplement quadratics
2 equations with 2 unknowns
Properties of Equality and Algebraic Section 2-4
Proofs
Review
Test
3
4
7
8
9
Standards
Addressed
G.G.1 – G.G.11
None (Review)
None (Review)
None
Integrated Geometry
Unit 2: Logic
Day Topic(s)/Objectives Covered
Suggested Assignment
1
Supplement
Standards
Addressed
G.G.25
Section 2-1
G.G.25
Section 2-1
Supplement
Section 2-2
Section 2-3
G.G.26
Section 2-4
Section 2-5
Supplement
G.G.27
2
3
4
5
6
7
8
9
Statements, Disjunction, Conjunction,
Negation
Conditional Statements
Counterexamples
Inverse, Converse, Contrapositive,
Logical Equivalence
Biconditionals
Deductive Reasoning
Laws of Detachment and Syllogism
Proving Angles and Segments
Congruent (Logical Reasoning)
Logic Proofs (Required for Honors,
optional for Regents)
Review
Test
G.G.25
G.G.27
G.G.27
Integrated Geometry
Unit 3: Beginning Geometry Proofs
Day Topic(s)/Objectives Covered
Suggested Assignment
1
Section 2-2 (7 – 11, 27)
Section 2-3 (3, 5, 7, 38, 39)
Mini-Proofs Packet
More mini-proofs (packet)
Sec. 2-4 (5-23)
Supplemental Proofs
Select from Sec 2-5 (1 – 32)
Supplemental Proofs
2
3
4
5
6
7
9
10
11
12
13
14
15
16
17
18
Definitions and Mini-Proofs
Postulates vs. Definitions vs.
Theorems
Team Practice with mini-proofs
Substitution, Transitive Property,
Beginning multi-step proofs
Complements and Supplements of
Congruent Angles, Other Angle
Theorems
Practice Proving Segments and
Angles Congruent Using Definitions,
Angle Theorems, and Properties of
Equality
Definition of Congruent Triangles
Proving Triangles Congruent Using
SSS, SAS
Congruent Triangle Proofs Using
ASA and AAS
Proofs involving CPCTC
Theorems regarding Isosceles and
Equilateral Triangles.
Using CPCTC to prove midpoint,
segment bisector, angle bisector,
isosceles triangle
Congruent Triangle Proofs using HL
Double Triangle and Overlapping
Triangle Proofs
Double Triangle and Overlapping
Triangle Proofs
Using Addition and Subtraction
Postulates to Prove Segments and
Angles Congruent
Congruent Triangle Proofs Using
Addition and Subtraction Postulates
More Congruent Triangle Proofs
(Practice Day)
Review
Exam
Standards
Addressed
GG.25
GG.27
GG.27
GG.27
GG.27
Supplemental Proofs
GG.27
Select Problems from
sections 4-1 and 4-2
GG.27 - 29
Select problems from Sec 4-3
Supplemental Proofs
Select problems from Sec 4-4
Supplemental Proofs
Select problems from Sec 4-5
Supplemental Proofs
GG. 27
GG.28
GG. 27
GG. 29
GG. 27 – 29, 31
Select problems from Sec 4-6
Supplemental Proofs
Select problems from Sec 4-7
Supplemental Proofs
Select problems from Sec 4-7
Supplemental Proofs
Supplement
GG. 27 – 29, 31
Supplement
GG. 27 – 29, 31
Chapter 4 Review (p. 249 )
Supplemental Proofs
Review Sheet
GG. 27 – 29, 31
GG. 27 – 29, 31
GG. 27 – 29, 31
GG. 27 – 29, 31
Integrated Geometry
Unit 4: Parallel and Perpendicular Lines,
Angle Relationships in Polygons
Day Topic(s)/Objectives Covered
1
Alternate interior and
corresponding angles
Proving lines parallel
Suggested Assignment
p. 130 #4, p.131 #1-5
#11-13
2
p.137-138 #1-8, 10-21
p.143 #4-10
3 Slopes of parallel and
p.177-178 #1-11,
perpendicular lines
#16-19, 25-28
4 Writing equations of parallel p.178 #12-15, 20-23
and perpendicular lines
5 Congruent triangle proofs
supplement
using parallel and
perpendicular lines
6 Mixed practice
supplement
7 Sum of angles and exterior p.150-151 #1-5,16,
angles of triangles
#18-20,30,32
8 Polygon angle sum
p.161-162 #11-14,
theorem
#16-18, 21, 33-35
9 Interior and exterior angles p.161-162 #22-25,
of regular polygons
#40-43
10 Mixed practice
supplement
11 Review
supplement
12 Test
Standards
Addressed
G.G.35
G.G.9, G.G.35
G.G.62, G.G.63
G.G.64, G.G.65
G.G.30, G.G.32
G.G.36
G.G.37
Integrated Geometry
Unit 5: Relationships Within Triangles
Day Topic(s)/Objectives Covered
Suggested Assignment
1
2
3
P262 (1-21, 38,39)
P267-268 (1-25,31)
P275-276
(1-5,8-12, 14-16,19-23)
P279 (1-10)
P282 has notes
P283 (10-19)
Need to Supplement with
actual 2 column proofs
P292 (1-28)
Needs to be supplemented
4
5
Mid-segments
Angle and Segment Bisectors
Concurrent Lines, Medians, and
Altitudes
Quiz
Indirect Proofs
6
7
8
9
Triangle Inequalities
Inequality Proofs (honors only)
Review
Test
Standards
Addressed
G.G.21, G.G.42
G.G.21
G.G.21, G.G.43
G.G.24
G.G.33, G.G.34
Integrated Geometry
Unit 6: Quadrilaterals
Day Topic(s)/Objectives Covered
Suggested Assignment
1
2
6-2
Standards
Addressed
G.G.38
6-3, supplement proofs
G.G.41
6-4
6-4
6-4, supplement proofs
G.G.39
G.G.39
G.G.41
Supplement with algebraic
problems and proofs
6-5, supplement
G.G.39
G.G.41
G.G.40
3
4
5
6
7
8
9
10
11
12
13
14
15
Properties of a Parallelogram
More work on Parallelograms
(Algebraic)
Parallelogram Proofs
Proving a Parallelogram
More work on Parallelograms
Properties of a Rectangle
Properties of a Rhombus
Proving a Rectangle
Proving a Rhombus
Review Day
Properties of a Square
Proving a Square
Properties of Trapezoids and
Isosceles Trapezoids including
mid-segments
Trapezoids Proofs
Review of all Parallelograms
Properties of Kites
Review of all Parallelograms
Review Day
Unit Test on Quadrilaterals
6-5, supplement proofs
6-5
Integrated Geometry
Unit 7: Coordinate Geometry
Day Topic(s)/Objectives Covered
1
2
3
4
5
6
7
8
9
10

Review Pythagorean
Theorem & Its converse
 Distance Formula
 Review simplifying
radicals (and cube roots
in HONORS)
 3D distance formula –
optional for HONORS
 Midpoint and Slope
formulas
 Equations of Lines
 Parallel, Perp. Or neither
 3D midpoint formula –
optional for HONORS
Writing the equation of the
perpendicular bisector of a
segment given the endpoints of
the line segment
Coordinate Geometry Proofs
Coordinate Geometry Proofs
For Regents – practice more
coordinate geometry proofs
For HONORS – do coordinate
geometry proofs with variables
Equations of Circles and
Appropriate Problem Solving
FOR HONORS ONLY – write
the eq. of a circle given any
three points that lie on the circle
For Regents – Practice Day
Review solving linear-quadratic
system graphically and
algebraically (including those
that involve circles)
Review
TEST
Suggested Assignment
Section 8-1 p.417-423
Section 1-8
p.56 #1-17,32-40,43,44-52
p.58 #65,67
Standards
Addressed
G.G.48
G.G.67
p.73 #34-36, 38
supplement for honors
Section 1-8
Section 3-7
G.G.62-66
supplement for honors
p.178 #23,46
G.G.68
needs to be supplemented
Section 6-6
Section 6-7
Proofs in text are too easy,
needs to be supplemented
Section 6-6
Section 6-7
Proofs in text are too easy,
needs to be supplemented
Section 12-5
G.G.69
G.G.38-41
G.G.69
G.G.38-41
G.G.71-74
Needs to be supplemented
p.355 #13-20
p.699 #53-58
Review from Algebra 1
G.G.70
Integrated Geometry
Unit 8: Similar Triangles
Day Topic(s)/Objectives Covered
Suggested Assignment
1
Ratios and Proportions
2
3
Similar Polygons
Proving Triangles Similar
P368-370 (2-28 evens,
40,41,42
Review of solving
quadratics p372
P375-377 (1-35 odd)
P385-387 (1-19)
4
Proving Triangles Similar using
2-column proofs
Quiz
Similarity in Right Triangles
More Similarity in Right
Triangles
Proportions in Triangles
Product of Means and Extremes
Review
Test
5
6
7
8
9
10
11
Standards
Addressed
G.CN.4
G.RP.2
G.G.44, G.G.45
Need to be supplemented
G.G.44, G.G.45
P394 (1-22)
Supplement more practice
Use Practice 7-4
P400-401 (1-26)
Need to be supplemented
G.G.45, G.G.47
G.G.45, G.G.46
G.G.45, G.G.46
Integrated Geometry
Unit 9: Right Triangles and Trigonometry
Day Topic(s)/Objectives Covered
Suggested Assignment
1
2
Special Right Triangles
More Special Right Triangles
3
4
The Tangent Ratio
Sine and Cosine Ratios
5
Angles of Elevation and
Depression
Vectors
Review
Test
P428-429 (1-22)
Supplement
Use Practice 8-2
P434-436 (1-20,31,32)
P441-442 (1-24)
Option: Activity Lab p444
P447-449 (1-18,28,29)
6
7
8
P455-459 (1-28)
Standards
Addressed
G.G.48
Integrated Geometry
Unit 10: Transformation Geometry
Day Topic(s)/Objectives Covered
Suggested Assignment
1
Introduction to Transformations
and Isometries
Translations
Preserving Segment and Angle
Congruence
Line Reflections
Preserving Parallelism and
Perpendicularity
9-1
supplement
Rotations
9-3
Mandatory for HONORS ONLY –
Rotation of any degree measure
about any point. Include special
angles. (1 or 2 days)
Mixed Practice
Line Symmetry (Reflectional)
Rotational Symmetry
Dilations
Similarity vs Congruence
Supplement
Compositions
Glide Reflections
Direct Isometries
Opposite Isometries
More Compositions
Mixed Practice
Review
Unit Test
9-6
9-6
2
3
4
5
6
7
8
9
10
11
9-2
supplement
Standards
Addressed
G.G.54
G.G.55
G.G.61
G.G.54
G.G.55
G.G.57
G.G.61
G.G.54
G.G.55
G.G.61
9-4
9-5
supplement
G.G.58
G.G.59
G.G.60
G.G.61
G.G.60
G.G.55
G.G.56
G.G.57
Integrated Geometry
Unit 11: Area, Surface Area, Volume
Day
1
Topic
Assignment
Areas of Triangles, Quadrilaterals, Select problems from sections
Circles, and Composite Figures
10-1, 10-2, and 10-7 (#25 – 27, 36 –
(see examples below)
40)
Supplement composite figures
Find Area of a Polygon Given the
Section 10 – 1 (24 – 33)
Section 10 – 2 (25 – 27)
Coordinates of the Vertices;
Find Area of a Polygon Bound by 3
or 4 Linear Equations
Relationship Between Areas and
Select problems from Section 10 - 4
Perimeters of Similar Figures
Finding Areas Using Trig. and
Select problems from Section 10 - 5
Special Right Triangles
Mandatory for Honors Only:
Select problems from Sections
Areas of Regular Polygons
10 – 3 and 10 - 5
Circles and Sectors
Select problems from Sections
(Arc Length and Area)
10 – 6 and 10 - 7
Surface Area of Prisms and
Select problems from Section 11 - 2
Cylinders
2
3
4
5
6
7
Standards
Covered
GG.10
GG. 14
Honors: Bases are Regular Polygons
8
Surface Area of Pyramids and
Cones
Select problems from Section 11 - 3
GG.13
GG.15
Select problems from Section 11 - 4
GG.11
GG.12
GG.14
GG.13
GG.15
GG.16
Honors: Bases are Regular Polygons
9
Volumes of Prisms and Cylinders
Honors: Bases are Regular Polygons
10
Volumes of Pyramids and Cones
Select problems from Section 11 - 5
Honors: Bases are Regular Polygons
11
Volume and Surface Area of A
Sphere; Great Circle of a Sphere;
Planes Equidistant from Center of
a Sphere Intersect Sphere in 2
Congruent Circles
Mandatory for Honors Only:
Relationship Between Volumes of
Similar Solids
Review
Exam
12
13
14
Select problems from Section 11 – 6
Supplement
Select problems from Section 11 - 7
Examples for Day 1:
x
6
8
Express the area of
the shaded space
in terms of x.
Integrated Geometry
Unit 12: Circles
Day Topic(s)/Objectives Covered
Suggested Assignment
1
Section 12-1
Standards
Addressed
G.G.50
Section 12-1
G.G.50
Section 12-2
G.G.49
Section 12-2
G.G.49
Section 12-3
p.682 #25 (needs to be
supplemented)
Section 12-4
G.G.51
G.G.52
2
3
4
5
6
7
8
9
10
11
12
13
Tangents – angle formed by
tangent and radius
Tangents – two segments
tangent to a circle from a point
outside the circle are congruent
Chords and Arcs – congruent
chords have congruent arcs
Chords – perpendicular bisector
of a chord contains the center of
the circle
Inscribed Angles and their
relationship to intercepted arcs
Angle Measures and Segment
Lengths – secant lines and their
relationships with intercepted
arcs
FOR HONORS ONLY
Honors Level Questions
Review Day
Circle Proofs w/ Similar
Triangles
More Circle Proofs: Similar
Triangles
FOR HONORS ONLY
Circle Proofs: Congruent
Triangles
Review
TEST
G.G.51
G.G.53
Needs to be supplemented
Needs to be supplemented
G.G.27
Needs to be supplemented
G.G.27
Needs to be supplemented
G.G.27
Integrated Geometry
Unit 13: Locus
Day Topic(s)/Objectives Covered
1
Locus
2
3
4
Compound Locus
More compound locus
Locus with coordinate geometry
5
More locus with coordinate
geometry
6
*
Locus review
Honors Only: 2 – 3 days of
3-D locus and 3-D compound loci
More review
Test
7
8
Suggested Assignment
Packet pp. 2 – 3
(#1-7, 10-12,14,17-19, 21)
Packet pp.4 – 5 (#1-19,22)
worksheet
Packet p. 7 (#2-8even,
11-25 odd, 26-30)
Packet
p.7 (#31-41,44-46)
p.8 (#1-6, 10-12)
review packet
supplement
supplement
Standards
Addressed
G.G.22
G.G.23
Integrated Geometry
Unit 14: Constructions
NOTE: This unit may be taught as a stand alone unit or
incorporated into other units as appropriate
Day Topic(s)/Objectives Covered
Suggested Assignment
1
1-7
supplement (especially
justifications)
2
3
4
5
6
Introduction to Constructions
Constructions and Justifications:
-Congruent Line Segments
-Congruent Angles
-Perpendicular Bisector of a
Line Segment
-Median of a Triangle
-Bisecting an Angle
Constructions and Justifications:
- Perpendicular at a Point on a
Line
- Perpendicular From a Point
to a Line
-Altitude of a Triangle
Constructions and Justifications:
- A line parallel to a given line
- A Parallelogram
- An equilateral Triangle
- Trisecting a line segment
(optional)
Investigate the Concurrence of
medians, altitudes, angle
bisectors, and perpendicular
bisectors of sides of triangles
Review and Practice
Unit Quest
Standards
Addressed
G.G.17
G.G.18
3-8
supplement (especially
justifications)
G.G.19
3-8
supplement
G.G.19
G.G.20
5-2 (HW # 32)
5-2 (HW # 33)
5-3 Geometer’s Sketchpad
Lab Activity
G.G.21
Integrated Geometry
Unit 15: Quadratic Functions
Mandatory for HONORS only
Day Topic(s)/Objectives
Covered
Vertex form of a parabola
1
Pages A-C
Vertex form of a parabola
2
Pages D - E
Writing a Quadratic Equation
3
given the Roots
Solving Quadratic Equations
4
by Completing the Square
5
Writing the Equation of a
Parabola
9
Writing the Equation of a
Parabola
Practice Days 1-6 p.5
QUIZ
Constructing a Circle that
Circumscribes a Triangle
Writing the Equation of the
Circle that passes through 3
given points
Review
10
TEST
6
7
8
Suggested Assignment
Pages F-G #1-6
Pages G-H #7-15
Packet, pg. 1
Packet, pg. 2
Packet, pg. 3 – 4
You can do #10 for bonus, your answer
has to be IN FRACTION FORM
Bring a compass & straight edge to
class on Day 7
Packet, pg. 6 – 7
Bring a compass & straight edge to
class tomorrow
Packet, pg 8
Packet, pg. 9-10
Study!
Due Tomorrow: June 2005 Honors
Final Part 3 ( #1-4)
Standards
Addressed