Curriculum Guide
for
Geometry Honors
North Arlington Public Schools
North Arlington Public Schools
Content Area: Geometry Honors Target Course/Grade level: 9
Unit Title: Congruence, Proof, and Constructions
Essential Questions: How do we use Congruence, Proof, and Constructions?
Unit Overview: In previous grades, students were asked to draw triangles based on given measurements. They also have prior experience with rigid motions:
translations, reflections, and rotations and have used these to develop notions about what it means for two objects to be congruent. In this unit, students establish
triangle congruence criteria, based on analyses of rigid motions and formal constructions. They use triangle congruence as a familiar foundation for the
development of formal proof. Students prove theorems—using a variety of formats—and solve problems about triangles, quadrilaterals, and other polygons.
They apply reasoning to complete geometric constructions and explain why they work.
Standards/
CPI’s
G.CO.1
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Know precise definitions of angle,
circle, perpendicular line, parallel
line, and line segment, based on the
undefined notions of point, line,
distance along a line, and distance
around a circular arc.
Evidence of Learning
Formative and
Summative measures
Points, Lines, and Planes:
Activity Lab: How Many Lines
Can You Draw To Create A
Constellation
Participation
Class Discussion
Study Guide
Segments, Rays, Parallel Lines and Planes:
Example: Naming Segments and Rays
Example: Indentifying Parallel and
Skew Segments
Example: Indentifying Parallel Planes
Check Point Quiz
Participation
Class Discussion
Measuring Angles:
Activity Lab: Using a Protractor
to Measure and Classify Angles
http://www.shodor.org/interactivate/activities/An
gles/
Perimeter, Circumference, and Area:
Graphing Calculator Activity:
Comparing Perimeters and Areas
Check Point Quiz
Participation
Class Discussion
Unit Test
Participation
Class Discussion
Study Guide
Resources Books, articles,
text, etc.
Textbook : 1-3 p.16
http://jwilson.coe.uga.edu/
EMT668/EMAT4680.2000
/Satchwell.Niki/4690%20e
ssays/instrunit/instructional
.html
Textbook: 1-4 p.23
http://www.homeschoolma
th.net/teaching/g/angles.ph
p
http://www.homeschoolma
th.net/teaching/g/parallel_a
nd_perpendicular.php
Textbook: 1-6 p.36
http://www.homeschoolma
th.net/teaching/g/measure_
angles.php
Textbook: 1-9 p.61
Content Area: Geometry Honors Target Course/Grade level: 9
Unit Title: Congruence, Proof, and Constructions
Essential Questions: How do we use Congruence, Proof, and Constructions?
Standards/
CPI’s
Evidence of Learning
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Represent transformations in the
plane using, e.g., transparencies and
geometry software; describe
transformations as functions that take
points in the plane as inputs and give
other points as outputs. Compare
transformations that preserve distance
and angle to those that do not (e.g.,
translation versus horizontal stretch).
Translations:
Activity: Create your own kaleidoscope
http://www.zefrank.com/dtoy_vs_byokal/
Reflections:
Activity Lab: Paper Folding and Reflections
Activity: Reflect the given pattern in a line:
http://www.primaryresources.co.uk/online/reflect
ion.swf
Rotations:
Guided Problem Solving: Understanding Math
Problems
Activity: Rotate shapes either 90 or 45 degrees:
http://www.primaryresources.co.uk/online/roratio
n.swf
Participation
Class Discussion
Study Guide
Participation
Class Discussion
Study Guide
Check Point Quiz
Textbook: 9-1 p. 470
http://www.mathsnet.net/tr
ansform/index.html
Textbook: 9-2 p.478
Textbook: p.477
Participation
Class Discussion
Check Point Quiz
Textbook: 9-3 p.483
Textbook: p.489
http://standards.nctm.org/d
ocument/eexamples/chap6/
6.4/index.htm
G.CO.4
Given a rectangle, parallelogram,
trapezoid, or regular polygon,
describe the rotations and reflections
that carry it onto itself.
Symmetry:
Example: Identifying Lines Of Symmetry
Example; Identifying Rotational Symmetry
Symmetry Activity:
http://www.haelmedia.com/OnlineActivities_txh/
mc_txh4_001.html
Participation
Class Discussion
Unit Test
Textbook: 9-4 p.492
http://www.innovationslear
ning.co.uk/subjects/maths/a
ctivities/year3/symmetry/sh
ape_game.asp
G.CO.5
Develop definitions of rotations,
reflections, and translations
in terms of angles, circles,
perpendicular lines, parallel lines, and
line segments.
Lesson Activity: Advanced Transformations
http://www.misterteacher.com/alphabetgeometry/
reflection.html
Lesson Activity: Geometric Solids
http://illuminations.nctm.org/ActivityDetail.aspx?
ID=70
Participation
Class Discussion
Study Guide
Check Point Quiz
http://www.mathsisfun.co
m/geometry/symmetry.htm
l
http://www.explorelearning
.com/index.cfm?method=c
Resource.dspView&Resou
rceID=269
G.CO.2
G.CO.3
3
Formative and
Summative measures
Resources Books, articles,
text, etc.
Content Area: Geometry Honors Target Course/Grade level: 9
Unit Title: Congruence, Proof, and Constructions
Essential Questions: How do we use Congruence, Proof, and Constructions?
Standards/
CPI’s
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
G.CO.6
Given a geometric figure and a
rotation, reflection, or translation,
draw the transformed figure using,
e.g., graph paper, tracing paper, or
geometry software. Specify a
sequence of transformations that will
carry a given figure onto another.
Activity Lab: Tracing Paper Transformations
Participation
Class Discussion
Study Guide
Textbook: p.490
Geometer’s Sketchpad
http://www.youtube.com/w
atch?v=jzmL7-3-92g
G.CO.7
Use geometric descriptions of rigid
motions to transform figures and to
predict the effect of a given rigid
motion on a given figure; given two
figures, use the definition of
congruence in terms of rigid motions
to decide if they are congruent.
Use interactive figures to explore geometric
transformations (rotations, translations, and
reflections and a composition of these):
http://standards.nctm.org/document/eexamples/ch
ap6/6.4/index.htm
Participation
Class Discussion
Study Guide
Check Point Quiz
http://www.girlsgotech.org/
world_around_us.html
http://www.helpingwithmat
h.com/by_subject/geometr
y/geo_congruent_8g2.htm
G.CO.8
Use the definition of congruence in
terms of rigid motions to show that
two triangles are congruent if and
only if corresponding pairs of sides
and corresponding pairs of angles are
congruent.
Congruent Figures:
Activity: Similarity and Congruence
http://www.absorblearning.com/mathematics/de
mo/units/KCA035.html
Participation
Class Discussion
Study Guide
Textbook: p.198
http://www.math.com/scho
ol/subject3/lessons/S3U3L
1GL.html
Explain how the criteria for triangle
congruence (ASA, SAS, and SSS)
follow from the definition of
congruence in terms of rigid motions.
Triangle Congruence by SSS and SAS:
Activity: Hands On: Building Congruent
Triangles
Triangle Congruence by ASA and AAS:
Activity: Technology: Exploring AAA and SSA
Participation
Class Discussion
Study Guide
Participation
Class Discussion
Study Guide
Textbook: p.205
Textbook: p.204
G.CO.9
4
Textbook: p.213
Textbook: p.220
Content Area: Geometry Honors Target Course/Grade level: 9
Unit Title: Congruence, Proof, and Constructions
Essential Questions: How do we use Congruence, Proof, and Constructions?
Standards/
CPI’s
G.CO.10
Evidence of Learning
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Prove theorems about lines and
angles. Theorems include: vertical
angles are congruent; when a
transversal crosses parallel lines,
alternate interior angles are congruent
and corresponding angles are
congruent; points on a perpendicular
bisector of a line segment are exactly
those equidistant from the segment’s
endpoints.
Measuring Angles:
Activity: Measuring Angles
http://www.homeschoolmath.net/teaching/g/meas
ure_angles.php
Participation
Class Discussion
Study Guide
Textbook: p.36
http://www.shodor.org/inte
ractivate/activities/Angles/
Properties of Parallel Lines:
Activity: Technology: Parallel Lines and Related
Angles
Check Point Quiz
Participation
Class Discussion
Study Guide
Participation
Class Discussion
Study Guide
Textbook: p.124
http://www.shodor.org/inte
ractivate/activities/angles/i
ndex.html
Textbook: p.134
Participation
Class Discussion
Study Guide
Check Point Quiz
Unit Test
Textbook: p.141
Textbook: p.145
Proving Lines Parallel:
Activity: Parallel and Perpendicular Lines
http://www.homeschoolmath.net/teaching/g/paral
lel_and_perpendicular.php
Parallel and Perpendicular Lines
Guided Problem Solving: Understanding Proof
Problems
Angle pairs formed by parallel lines cut by a
transversal:
http://www.math10.com/en/geometry/angles/angl
es.html
5
Formative and
Summative measures
Resources Books, articles,
text, etc.
Content Area: Geometry Honors Target Course/Grade level: 9
Unit Title: Congruence, Proof, and Constructions
Essential Questions: How do we use Congruence, Proof, and Constructions?
Standards/
CPI’s
G.CO.11
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Prove theorems about triangles.
Theorems include: measures of
interior angles of a triangle sum to
180°; base angles of isosceles
triangles are congruent; the segment
joining midpoints of two sides of
a triangle is parallel to the third side
and half the length; the medians of
a triangle meet at a point.
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Parallel Lines and the Triangle Angle-Sum
Theorem:
Activity Lab: Hands On: Angle Dynamics
Activity Lab: Exploring Spherial Geometry
Participation
Class Discussion
Study Guide
Textbook: p.147
Isosceles and Equilateral Triangles:
Activity: Equilateral and Isosceles Triangles
http://www.homeschoolmath.net/teaching/g/equil
ateral_isosceles.php
Participation
Class Discussion
Study Guide
Textbook: p.228
http://library.thinkquest.org
/20991/geo/ietri.html
Proportions in Triangles:
Activity Lab: Technology: Exploring Proportions
in Triangles
Participation
Class Discussion
Study Guide
Check Point Quiz
Textbook: p.398
Textbook: p.397
Concurrent Lines, Medians, and Altitudes:
Activity Lab: Technology: Special Segments in
Triangles
Participation
Class Discussion
Study Guide
Unit Test
Textbook: p.272
http://www.google.com/url
?sa=t&source=web&cd=4
&ved=0CC0QFjAD&url=h
ttp%3A%2F%2Fwww.onli
nemathlearning.com%2Fsi
de-splittertheorem.html&ei=DDzuTZ
nPFZL4sAO44NGeAw&u
sg=AFQjCNHPCCv2vX39
xFKl32Lm8UehQCkA8Q
The Midpoint Theorem:
http://www.cliffsnotes.com/study_guide/TheMidpoint-Theorem.topicArticleId18851,articleId-18799.html
6
Textbook: p.146
Textbook: p.154
Content Area: Geometry Honors Target Course/Grade level: 9
Unit Title: Congruence, Proof, and Constructions
Essential Questions: How do we use Congruence, Proof, and Constructions?
Standards/
CPI’s
G.CO.12
Evidence of Learning
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Prove theorems about parallelograms.
Theorems include: opposite sides are
congruent, opposite angles are
congruent, the diagonals of a
parallelogram bisect each other, and
conversely, rectangles are
parallelograms with congruent
diagonals.
Properties of Parallelograms:
Activity: Dynamic Rectangle and Parallelogram
http://standards.nctm.org/document/eexamples/ch
ap5/5.3/index.htm
Participation
Class Discussion
Study Guide
Textbook: p.312
Proving That a Quadrilateral is a Parallelogram:
Activity: Hands-On: Geo-Models
Participation
Class Discussion
Study Guide
Check Point Quiz
Participation
Class Discussion
Study Guide
Unit Test
Textbook: p.321
Textbook: p.320
Special Parallelograms:
Activity: Technology: Diagonals of
Parallelograms
The Midpoint Theorem:
http://www.cliffsnotes.com/study_guide/TheMidpoint-Theorem.topicArticleId18851,articleId-18799.html
7
Formative and
Summative measures
Resources Books, articles,
text, etc.
Textbook: p.329
Textbook: p.328
http://www.mathsisfun.co
m/geometry/quadrilateralsinteractive.html
Content Area: Geometry Honors Target Course/Grade level: 9
Unit Title: Congruence, Proof, and Constructions
Essential Questions: How do we use Congruence, Proof, and Constructions?
Standards/
CPI’s
G.CO.13
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Make formal geometric constructions
with a variety of tools and methods
(compass and straightedge, string,
reflective devices, paper folding,
dynamic geometric software, etc.).
Copying a segment; copying an
angle; bisecting a segment; bisecting
an angle; constructing perpendicular
lines, including the perpendicular
bisector of a line segment; and
constructing a line parallel to a given
line through a point not on the line.
Construct an equilateral triangle, a
square, and a regular hexagon
inscribed in a circle.
Basic Constructions:
Activity: Hands-On: Compass Designs
Activity: Technology: Exploring Constructions
Activity: Simulations of Ruler and Compass
Constructions
http://wims.unice.fr/wims/wims.cgi?session=1V7
7FB9E9B.5&+lang=en&+cmd=intro&+module=t
ool%2Fgeometry%2Frulecomp.en&+special_par
m=1
Activity: Construct an Inscribed Equilateral
Triangle:
http://www.nvcc.edu/home/tstreilein/construction
s/Inscribed/inscribe2.htm
Activity: Construct an Inscribed Regular
Hexagon:
http://www.nvcc.edu/home/tstreilein/construction
s/Inscribed/inscribe4.htm
Activity: Construct an Inscribed Square
http://www.nvcc.edu/home/tstreilein/construction
s/Inscribed/inscribe3.htm
8
Evidence of Learning
Formative and
Summative measures
Participation
Class Discussion
Study Guide
Check Point Quiz
Resources Books, articles,
text, etc.
Textbook: p.44
http://www.mathsnet.net/ca
mpus/construction/index.ht
ml
http://www.mathsisfun.co
m/geometry/constructions.
html
Geometric Constructions
Illustrated with Interactive
Java Applets:
http://www.nvcc.edu/home
/tstreilein/constructions/con
tents.htm
Geometer’s Sketchpad
Content Area: Geometry Honors
and Trigonometry
Target Course/Grade level: 9
Unit Title: Similarity, Proof,
Essential Questions: What are the relationships between Similarity, Proof, and Trigonometry?
Unit Overview: Students apply their earlier experience with dilations and proportional reasoning to build a formal understanding of similarity. They identify
criteria for similarity of triangles, use similarity to solve problems, and apply similarity in right triangles to understand right triangle trigonometry, with particular
attention to special right triangles and the Pythagorean theorem. Students develop the Laws of Sines and Cosines in order to find missing measures of general
(not necessarily right) triangles. They are able to distinguish whether three given measures (angles or sides) define 0, 1, 2, or infinitely many triangles.
Standards/
CPI’s
SRT.1
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Verify experimentally the properties
of dilations given by a center and a
scale factor.
a. A dilation takes a line not
passing through the center of
the dilation to a parallel line,
and leaves a line passing
through the center unchanged.
Evidence of Learning
Formative and
Summative measures
http://www.mathsnet.net/transformations/inde
x.html Interactive website that allows the
basic four transformations
Teacher Based test
Activity: Have students search for scale
models and then find actual measurements of
the object
Cooperative learning
http://www.absorblearning.com/mathematics/
demo/units/KCA035.html#Summary
Interactive lesson with follow up questions.
Actively use similar
shapes to create
transformations
Activity: use geometers sketchpad to create
Cooperative learning
Participation
Actively working on
computer models
Resources Books, articles,
text, etc.
Textbook
9-5 Dilations
Pg. 498-503
http://www.brightstorm.c
om/math/geometry/transf
ormations/dilations lesson
in dilation and scale
factors
b. The dilation of a line segment
is longer or shorter in the ratio
c. given by the scale factor.
G.SRT.2
Given two figures, use the definition
of similarity in terms of similarity
transformations to decide if they are
similar; explain using similarity
Textbook
7-2Similar Polygons
Pg. 373-379
7-3Proving Triangles
Similar
Content Area: Geometry Honors
and Trigonometry
Target Course/Grade level: 9
Unit Title: Similarity, Proof,
Essential Questions: What are the relationships between Similarity, Proof, and Trigonometry?
Standards/
CPI’s
G.SRT.3
G.SRT.4
G.SRT.5
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
transformations the meaning of
similarity for triangles as the
equality of all corresponding pairs of
angles and the proportionality of
all corresponding pairs of sides.
two similar shapes and explore their
similarities
Use the properties of similarity
transformations to establish the
AA criterion for two triangles to be
similar.
http://www.keymath.com/x3343.xml
interactive webpage allowing students to test
all similarity triangle postulates.
Evidence of Learning
Formative and
Summative measures
text, etc.
in groups
Pg. 382-388
http://www.absorblearnin
g.com/mathematics/demo
/units/KCA024.html
Participation
Textbook
7-3 Proving Triangles
Similar
Pg. 382-389
http://www.analyzemath.
com/Geometry/similar_tr
iangles.html Lesson on
similar triangles
Teacher based test
Sketch pad
assessments
Prove theorems about triangles.
Theorems include: a line parallel to
one side of a triangle divides the
other two proportionally, and
conversely; the Pythagorean Theorem
proved using triangle similarity.
http://education.ti.com/calculators/downloads/
US/Activities/Detail?id=12318
Interactive calculator lesson using a TI 83 to
experiment with the side splitter theorem
Active group work
Use congruence and similarity
http://education.ti.com/calculators/timathnspir
Scientific Calculator
10
Resources Books, articles,
Scientific calculator
activities
Textbook
7-4 Similarity in Right
Triangles
Pg. 391-397
http://www.mathwarehou
se.com/geometry/similar/t
riangles/side-splittertheorem.php
Web page illustrating the
side splitter theorem
Textbook
Content Area: Geometry Honors
and Trigonometry
Target Course/Grade level: 9
Unit Title: Similarity, Proof,
Essential Questions: What are the relationships between Similarity, Proof, and Trigonometry?
Standards/
CPI’s
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Evidence of Learning
Formative and
Summative measures
criteria for triangles to solve
problems and to prove relationships
in geometric figures.
ed/US/Activities/?t=5053&sa=5024 Multiple TI
calculator lessons to explore similar geometric
figures
activities
Understand that by similarity, side
ratios in right triangles are properties
of the angles in the triangle, leading
to definitions of trigonometric ratios
for acute angles.
http://www.purplemath.com/modules/basirati.
htm Explores the ratios of trigonometry with
problems to solve.
Teacher based test
Explain and use the relationship
between the sine and cosine of
complementary angles.
http://www.cut-theknot.org/pythagoras/cosine2.shtml Proofs and
mathematical problems demonstrating the
relationship between sine and cosine
Participation
G.SRT.8
Use trigonometric ratios and the
Pythagorean Theorem to solve
right triangles in applied problems.★
http://www.themathpage.com/aTrig/trigonome
try.htm Lessons and activities covering right
triangles and trigonometry ratios
Actively working on
computer models
G.MG.1
Use geometric shapes, their
measures, and their properties to
describe objects (e.g., modeling a tree
trunk or a human torso as a
cylinder).*
http://www.learner.org/interactives/geometry/i
ndex.html Website introduces geometric
shapes and their properties using everyday
objects.
Participation
Use classroom objects and household items to
Exploring geometric
G.SRT.6
G.SRT.7
11
Sketchpad activities
Cooperative learning
Cooperative learning
in groups
Resources Books, articles,
text, etc.
7-2 Similar Polygons
Pg. 373-379
Textbook
7-4 Similarity in Right
Triangles
Pg. 391
Textbook
8-4 The sine and cosine
Ratio
Pg. 439-443
Textbook
Chapter 8
Pg. 417-465
Textbook
Chapter 11Surface area
and Volume
Pg. 598-656
Content Area: Geometry Honors
and Trigonometry
Target Course/Grade level: 9
Unit Title: Similarity, Proof,
Essential Questions: What are the relationships between Similarity, Proof, and Trigonometry?
Standards/
CPI’s
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
discover 3 dimensional shapes and finding
volume for those shapes
G.MG.2
Apply concepts of density based on
area and volume in modeling
situations (e.g., persons per square
mile, BTUs per cubic foot).*
http://www.edinformatics.com/math_science/
mass_volume_density.htm Density based labs
that can be constructed in the classroom to
model situations
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
shapes outside the
classrooom
Participation
Cooperative learning
in groups
Textbook
Chapter 11 Surface area
and Volme
Pg. 597-659
Exploring geometric
shapes outside the
classrooom
G.MG.3
G.SRT.9 (+)
Apply geometric methods to solve
design problems (e.g., designing an
object or structure to satisfy physical
constraints or minimize cost; working
with typographic grid systems based
on ratios).*
http://www.bbc.co.uk/schools/ks2bitesize/math
s/shape_space/ apply geometric shapes to solve
puzzles
Derive the formula A = 1/2 ab sin(C)
for the area of a triangle by drawing
an auxiliary line from a vertex
perpendicular to the opposite side.
http://jwilson.coe.uga.edu/EMAT6680/Simmo
ns/6700/Unit%20Lesson1W.pdf file explaining
how to use geometer sketchpad to use and
derive the formula A=1/2 ab sin ©
Cooperative learning
in groups
Participation
Textbook
11-7 Areas and Volumes
of Similar Solids
Pg. 646-651
http://www.ecalc.com/ma
thhelp/worksheet/geometry
Reference sheet
12
Teacher Based test
Participation
Textbook
8-4 The sine and cosine
Ratio
Pg. 439-443
Content Area: Geometry Honors
and Trigonometry
Target Course/Grade level: 9
Unit Title: Similarity, Proof,
Essential Questions: What are the relationships between Similarity, Proof, and Trigonometry?
Standards/
CPI’s
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Prove the Laws of Sines and Cosines
and use them to solve problems.
http://www.brightstorm.com/math/trigonomet
ry/basic-trigonometry/trigonometric-ratiossine
http://www.brightstorm.com/math/trigonomet
ry/basic-trigonometry/trigonometric-ratiossine
Math videos
Understand and apply the Law of
Sines and the Law of Cosines to find
unknown measurements in right and
non-right triangles (e.g., surveying
problems, resultant forces).
http://illuminations.nctm.org/LessonDetail.asp
x?ID=L704
Lesson teaching trigonometry in non right
triangles
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Cooperative learning
G.SRT.10 (+)
G.SRT.11 (+)
13
Actively working on
computer models
Teacher based test
Geometer sketchpad
activities
Textbook
8-4 The sine and cosine
Ratio
Pg. 439-443
Textbook
8-4 The sine and cosine
Ratio
Pg. 439-443
Content Area: Geometry Honors
Three Dimensions
Target Course/Grade level: 9
Unit Title: Extending to
Essential Questions: Extending to Three Dimensions
Unit Overview: Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area
and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a
two-dimensional object about a line.
Standards/
CPI’s
G.GMD.1
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Give an informal argument for the
formulas for the circumference of a
circle, area of a circle, volume of a
cylinder, pyramid, and cone. Use
dissection arguments, Cavalieri’s
principle, and informal limit
arguments.
http://www.exploratorium.edu/pi/pi_activities/
index.html To discover Pi and its relationship
with circumference. Students use string and
scissors to dicover the relationship of circles
and Pi.
http://www.learner.org/courses/learningmath/
measurement/session7/part_b/index.html To
understand area and how to derive a formula.
Interative lesson that disects shapes to create
formulas
Evidence of Learning
Formative and
Summative measures
Participation
Cooperative learning
Actively working on
computer models
Teacher made tests
Resources Books, articles,
text, etc.
Text book
10-6 Circles and Arcs
Pg.566-571
11-3 Surface Areas of
pyramids and cones
Pg. 617-623
http://www.mathgoodies.
com/lessons/vol2/circumfe
rence.html lesson on
circumference
Activity: Students use geometry tools such as
protractor, compasses, rulers, and paper to
derive formulas.
G.GMD.3
Use volume formulas for cylinders,
pyramids, cones, and spheres to solve
problems.★
http://www.shodor.org/interactivate/activities/
SurfaceAreaAndVolume/ Allows student to
construct 3-D shapes and calculate volumes
http://mathforum.org/alejandre/mathfair/pyra
mid2.html Constructing pyramids to find
volume and surface area.
Use circular and square blocks to create
volume formulas for three dimensional
figures.
Actively constructing
models
Cooperative learning
in groups
Finding volume for
everyday materials
Text book
Chapters 10 Area
Chapter 11Surface Area
and Volume
Pages 539-656
Handouts using paper
cutouts
http://www.brightstorm.c
om/math/geometry/volum
e/volume-of-prisms
Content Area: Geometry Honors
Three Dimensions
Target Course/Grade level: 9
Unit Title: Extending to
Essential Questions: Extending to Three Dimensions
Standards/
CPI’s
G.GMD.4
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Identify the shapes of twodimensional cross-sections of threedimensional objects, and identify
three-dimensional objects generated
by rotations of two-dimensional
objects.
http://www.mathsnet.net/geometry/solid/nets.h
tml Nets made virtually on the web that will
construct themselves.
http://www.korthalsaltes.com/ Paper models
and worksheets to create nets for all 3
dimensional shapes
Evidence of Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Constructions
Research constructions
of different
polyhedrons
Textbook
11-1 Space Figures and
cross Sections
Pg. 598-603
Activity: Have students create two
dimensional shapes on geometers sketchpad
and the rotate them to create a three
dimensional object.
G.MG.1
Use geometric shapes, their
measures, and their properties to
describe objects (e.g., modeling a tree
trunk or a human torso as a
cylinder).*
http://www.learner.org/interactives/geometry/i
ndex.html Website introduces geometric
shapes and their properties using everyday
objects.
Participation
Use classroom objects and household items to
discover 3 dimensional shapes and finding
volume for those shapes
Exploring geometric
shapes outside the
classrooom
15
Cooperative learning
in groups
Textbook
Chapter 11Surface area
and Volume
Pg. 598-656
Content Area: Geometry Honors
Target Course/Grade level: 9
Unit Title: Connecting Algebra and Geometry through Coordinates
Essential Questions: How do we Connect Algebra and Geometry through Coordinates?
Unit Overview: Building on their work with the Pythagorean theorem in 8 th grade to find distances, students use a rectangular coordinate system to verify
geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines. Students continue their study of
quadratics by connecting the geometric and algebraic definitions of the parabola.
Standards/
CPI’s
G.GPE.4
G.GPE.5
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Evidence of Learning
Formative and
Summative measures
Use coordinates to prove simple
geometric theorems algebraically. For
example, prove or disprove that a
figure defined by four given points in
the coordinate plane is a rectangle;
prove or disprove that the point (1,
√3) lies on the circle centered at the
origin and containing the point (0, 2).
Placing Figures in the Coordinate Plane:
Example:Real-World Connection T-Shirt
Design
Example:Naming Coordinates
Participation
Class Discussion
Study Guide
Proofs Using Coordinate Geometry:
Example: Planning a Coordinate Geometry
Proof
http://regentsprep.org/Regents/math/geometry/G
CG4/CoordinatepRACTICE.htm
Activity Lab: Data Analysis: Interpreting Data
Check Point Quiz
Participation
Class Discussion
Study Guide
Prove the slope criteria for parallel
and perpendicular lines and uses
them to solve geometric problems
(e.g., find the equation of a line
parallel or perpendicular to a given
line that passes through a given
point).
Lines in the Coordinate Plane:
Example: Graphing Lines In Slope-Intercept
Form
http://www.khanacademy.org/video/graphing-aline-in-slope-interceptform?playlist=Algebra+I+Worked+Examples
Example: Using Point-Slope Form
http://www.phschool.com/atschool/academy123/
english/academy123_content/wl-book-demo/ph213s.html
Slopes of Parallel and Perpendicular Lines:
Example: Checking for Parallel Lines
Example: Writing Equations of Parallel Lines
http://www.phschool.com/atschool/academy123/
english/academy123_content/wl-book-demo/ph219s.html
Participation
Class Discussion
Study Guide
Resources Books, articles,
text, etc.
Textbook: 6-6 p.343
http://www.mathwarehouse
.com/coordinategeometry/prove-triangleisosceles.php
Textbook: 6-7 p.348
http://www.mathwarehouse
.com/coordinate-geometry/
http://regentsprep.org/rege
nts/math/geometry/GCG6/
LCir.htm
Textbook: 3-6 p.166
http://www.math.com/scho
ol/subject2/lessons/S2U4L
2GL.html#sm1
http://www.algebraclass.com/slope-interceptform.html
Check Point Quiz
Participation
Class Discussion
Study Guide
Unit Test
Textbook: 3-7 p.174
http://www.youtube.com/w
atch?v=u3zvk-zkQW4
Content Area: Geometry Honors
Target Course/Grade level: 9
Unit Title: Connecting Algebra and Geometry through Coordinates
Essential Questions: How do we Connect Algebra and Geometry through Coordinates?
Standards/
CPI’s
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Evidence of Learning
Formative and
Summative measures
Example: Checking for Perpendicular Lines
Example: Writing Equations for Perpendicular
Lines
http://www.phschool.com/atschool/academy123/
english/academy123_content/wl-book-demo/ph221s.html
Resources Books, articles,
text, etc.
http://www.wtamu.edu/aca
demic/anns/mps/math/math
lab/col_algebra/col_alg_tut
28_parpen.htm
G.GPE.6
Find the point on a directed line
segment between two given points
that partitions the segment in a given
ratio.
The Coordinate Plane:
Finding the Midpoint of a Segment:
Example: Finding the Midpoint
Example Finding an Endpoint
http://www.purplemath.com/modules/midpoint.ht
m
http://cs.selu.edu/~rbyrd/math/midpoint/
Check Point Quiz
Participation
Class Discussion
Study Guide
Textbook: 1-8 p.54
Algebra Lab:
http://www.algebralab.org/l
essons/lesson.aspx?file=ge
ometry_coordmidpoint.xml
http://regentsprep.org/rege
nts/math/geometry/GCG2/
Lmidpoint.htm
G.GPE.7
Use coordinates to compute
perimeters of polygons and areas of
triangles and rectangles, e.g., using
the distance formula.★
The Coordinate Plane:
Finding Distance on the Coordinate Plane:
Example: Finding Distance
http://www.purplemath.com/modules/distform.ht
m
http://www.mathwarehouse.com/algebra/distance
_formula/index.php
Perimeter, and Area:
Example: Finding Perimeter in the Coordinate
Plane
Activity Lab: Technology: Comparing Perimeters
and Areas
Check Point Quiz
Participation
Class Discussion
Study Guide
Unit Test
Textbook: 1-8 p.53
http://www.teacherschoice.
com.au/maths_library/anal
ytical%20geometry/alg_15.
htm
Textbook: 1-9 p.61
http://hotmath.com/help/gt/
genericalg1/section_8_5.ht
ml
17
Textbook: p.69
Graphing Calculator
Content Area: Geometry Honors
Target Course/Grade level: 9
Unit Title: Connecting Algebra and Geometry through Coordinates
Essential Questions: How do we Connect Algebra and Geometry through Coordinates?
Standards/
CPI’s
G.GPE.2
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Derive the equation of a parabola
given a focus and directrix.
Parabolas: Finding the Equation from
Information
http://www.purplemath.com/modules/parabola3.h
tm
http://www.physicsforums.com/showthread.php?t
=69327
http://www.valleyview.k12.oh.us/vvhs/dept/math
/agparabhelp.html
18
Evidence of Learning
Formative and
Summative measures
Check Point Quiz
Participation
Class Discussion
Study Guide
Resources Books, articles,
text, etc.
http://colalg.math.csusb.ed
u/~devel/precalcdemo/coni
cs/src/parabola.html
http://www.brightstorm.co
m/math/algebra2/quadratic-equations-andinequalities/focus-anddirectrix-of-a-parabola/
Content Area: Geometry Honors
Target Course/Grade level: 9
Unit Title: Circles With and Without Coordinates
Essential Questions: How do we explore Circles With and Without Coordinates?
Unit Overview: In this unit, students prove basic theorems about circles, with particular attention to perpendicularity and inscribed angles, in order to see
symmetry in circles and as an application of triangle congruence criteria. They study relationships among segments on chords, secants, and tangents as an
application of similarity. In the Cartesian coordinate system, students use the distance formula to write the equation of a circle when given the radius and the
coordinates of its center. Given an equation of a circle, they draw the graph in the coordinate plane, and apply techniques for solving quadratic equations to
determine intersections between lines and circles or parabolas and between two circles.
Standards/
CPI’s
G.C.1
G.C.2
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Prove that all circles are similar.
Identify and describe relationships among
inscribed angles, radii, and chords. Include
the relationship between central, inscribed,
and
circumscribed angles; inscribed angles on a
diameter are right angles; the radius of a
circle is perpendicular to the tangent where
the radius intersects the circle.
Evidence of Learning
Resources Books, articles,
Formative and
Summative measures
Activity: Students will use the Geometer’s
Sketchpad to create different size circles. Then,
they will measure the degrees of all circles, and
set up ratios between. After, they will be able to
take the circumference of one and multiply by the
scale factor to get the other circle.

Activity: Students will work with the Geometer’s
Sketchpad to construct circles. They will then
draw in radii, angles and chords and measure
angles formed between to show the relationship
between each.





text, etc.
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.

Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.






Geometer’s Sketchpad
http://www.cpm.org/p
dfs/state_supplements/
Similar_Circles.pdf
http://math.rice.edu/
~rusmp/geometrymo
dule/PDFdocuments/
sketchpad.pdf
Geometer’s Sketchpad
http://mstudley.com/
geosketch/geosketcha
ndcirclespt2.pdf
http://archives.math.
utk.edu/ICTCM/VO
L16/C020/paper.html
http://archives.math.
utk.edu/ICTCM/VO
L16/C020/paper.html
Content Area: Geometry Honors
Target Course/Grade level: 9
Unit Title: Circles With and Without Coordinates
Essential Questions: Essential Questions: How do we explore Circles With and Without Coordinates?
Standards/
CPI’s
G.C.3
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Construct the inscribed and circumscribed
circles of a triangle,
and prove properties of angles for a
quadrilateral inscribed in a circle.
Activity: Students will use the Geometer’s
Sketchpad to draw triangles and measure out
midpoints and angle bisectors in order to create
inscribed and circumscribed triangles.
Evidence of Learning



G.C.4 (+)
Construct a tangent line from a point outside
a given circle to the circle.
Activity: Students will use Geometer’s
Sketchpad to create tangent lines to given circles.



G.C.5
Derive using similarity the fact that the
length of the arc intercepted by an angle is
proportional to the radius, and define the
radian measure of the angle as the constant
of proportionality; derive the formula for the
area of a sector.
Activity: Students will use the Geometer’s
Sketchpad to create circles. They will then create
and shade a sector of a given circle, then draw in
to create a triangle within the sector. Students
will then be able to use formulas for area to show
that measured area is the same as ones they
derived themselves.
Resources Books, articles,
Formative and
Summative measures



Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.
text, etc.









20
Geometer’s Sketchpad
http://www.nvcc.edu/
home/tstreilein/const
ructions/Inscribed/in
scribe2.htm
http://archives.math.
utk.edu/ICTCM/VO
L16/C020/paper.html
Geometer’s Sketchpad
http://mstudley.com/
geosketch/geosketcha
ndcirclespt2.pdf
http://archives.math.
utk.edu/ICTCM/VO
L16/C020/paper.html
Geometer’s Sketchpad
http://jwilson.coe.uga
.edu/EMAT6680Fa08
/Wisdom/EMAT6690
/Circles%20And%20
Spheres/Circles%20a
nd%20SpheresUnit.htm
http://archives.math.
utk.edu/ICTCM/VO
L16/C020/paper.html
Content Area: Geometry Honors
Target Course/Grade level: 9
Unit Title: Circles With and Without Coordinates
Essential Questions: Essential Questions: How do we explore Circles With and Without Coordinates?
Standards/
CPI’s
G.GPE.1
G.GPE.1
G.MG.1
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Derive the equation of a circle of given
center and radius using the Pythagorean
Theorem; complete the square to find the
center and radius of a circle given by an
equation.
Activity: Student’s will use graph paper to
construct circles with given radii. Then, students
will be able to draw in right triangles using radii,
and show how to find lengths using Pythagorean
Theorem. Students will then use this to find the
formula for the circle itself.
Use coordinates to prove simple geometric
theorems algebraically. For example, prove
or disprove that a figure defined by four
given points in the coordinate plane is a
rectangle; prove or disprove that the point (1,
√3) lies on the circle centered at the origin
and containing the point (0, 2).
Activity: Students will use the Geometer’s
Sketchpad to create figures with given
coordinates. They will then use the distance
formula and slop-intercept form of a line to prove
lines are perpendicular, thus being able to define
the given shape algebraically.
Use geometric shapes, their measures, and
their properties to
describe objects (e.g., modeling a tree trunk
or a human torso as a cylinder).*
Activity: Students will use Geometer’s
Sketchpad to create their own pictures using only
the shape tools provided within the program.
Students must list all polygons and shapes used
within their drawings.
21
Evidence of Learning
Resources Books, articles,
Formative and
Summative measures









Student response
in class.
Questions from
textbook.
Quiz on material
presented.
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.
text, etc.

12.5 – Circles in the
Coordinate plane, pg.
695.

Worksheets

Geometer’s Sketchpad
http://go.hrw.com/re
sources/go_mt/ca/c2
/c2_8-7tl.pdf


Geometer’s Sketchpad
Content Area: Geometry Honors
Target Course/Grade level: 9
Unit Title: Applications of Probability
Essential Questions: How do use Probability?
Unit Overview: Building on probability concepts that began in the middle grades, students use the languages of set theory to expand their ability to compute and
interpret theoretical and experimental probabilities for compound events, attending to mutually exclusive events, independent events, and conditional probability.
Students should make use of geometric probability models wherever possible. They use probability to make informed decisions.
Standards/
CPI’s
S.CP.1
S.CP.2
S.CP.3
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Evidence of Learning
Resources Books, articles,
Formative and
Summative measures
Describe events as subsets of a sample space
(the set of
outcomes) using characteristics (or
categories) of the outcomes, or
as unions, intersections, or complements of
other events (“or,” “and,” “not”).
Activity: Students will create “trees” of given
samples (e.g. “You are going to buy a new
snowboard, bindings, and boots. You have a
choice of Burton, Forum, Foursquare, and
Stepchild boards; Burton, DC and Forum boots,
and Altec, Union, or Rome bindings.”

Understand that two events A and B are
independent if the
probability of A and B occurring together is
the product of their
probabilities, and use this characterization to
determine if they are independent.
Activity: Students will take turns rolling dice
and recording their results. Numbers 4 and 6 are
worth 1 point, 1 is -1, and the rest are 0. Students
will each take 10 rolls and record the results.
After, we will discuss and find the probability of
all events, and see if previous throws change later
outcomes.

S.CP.3 Understand the conditional
probability of A given B as P(A
and B)/P(B), and interpret independence of A
and B as saying that the conditional
probability of A given B is the same as the
probability
of A, and the conditional probability of B
given A is the same as the probability of B.
Activity: Students will be given decks of cards
and asked to draw cards at random. They will do
this with an without replacement. Each time,
they will be asked to find the probability that
their card was drawn. We will use this to show
that conditional probability can change outcomes
of events if the cards are common.







text, etc.
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.

Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.

Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.




http://www.hgs.k12.va
.us/Bruce_Norton_fold
er/MISC/Probability_
Trees.pdf
http://www.studyzone.
org/mtestprep/math8/e
/samplespace6p.cfm
http://www.mathgoodi
es.com/lessons/vol6/in
dependent_events.html
http://www.studyzone.
org/mtestprep/math8/e
/probwith6p.cfm
http://www.mathgoodi
es.com/lessons/vol6/co
nditional.html
http://www.studyzone.
org/mtestprep/math8/e
/probwithquiz6p.cfm
Content Area: Geometry Honors
Target Course/Grade level: 9
Unit Title: Applications of Probability
Essential Questions: How do use Probability?
Standards/
CPI’s
S.CP.4
S.CP.5
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
S.CP.4 Construct and interpret two-way
frequency tables of data when
two categories are associated with each
object being classified. Use the
two-way table as a sample space to decide if
events are independent
and to approximate conditional probabilities.
For example, collect
data from a random sample of students in
your school on their favorite subject among
math, science, and English. Estimate the
probability that a randomly selected student
from your school will favor science given
that the student is in tenth grade. Do the
same for other subjects and compare the
results.
Activity: Given in description of Learning
Target.
Recognize and explain the concepts of
conditional probability
and independence in everyday language and
everyday situations. For example, compare
the chance of having lung cancer if you are a
smoker with the chance of being a smoker if
you have lung cancer.
Lesson: Class discussion about the difference
between conditional statements. Change of
having cancer being a smoker is different then
being a smoker and having cancer. Show
differences using charts and graphs.
Evidence of Learning
Resources Books, articles,
Formative and
Summative measures

Student generated
frequency tables
and interpretation
of data.
text, etc.





23
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.


http://office.microsoft.
com/en-us/excelhelp/explorehistogramsHA001110948.aspx
http://www.studyzon
e.org/mtestprep/math
8/e/histograms6p.cfm
Statistics textbook –
pg 169-173
http://www.studyzone.
org/mtestprep/math8/e
/probcompoundquiz6p.
cfm
Content Area: Geometry Honors
Target Course/Grade level: 9
Unit Title: Applications of Probability
Essential Questions: How do use Probability?
Standards/
CPI’s
S.CP.6
S.CP.7
S.CP.8 (+)
Evidence of Learning
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Find the conditional probability of A given B
as the fraction of B’s outcomes that also
belong to A, and interpret the answer in
terms of the model.
Activity: Students will be given decks of cards
and asked to draw cards at random. They will do
this with an without replacement. Each time,
they will be asked to find the probability that
their card was drawn. We will use this to show
that conditional probability can change outcomes
of events if the cards are common.

Apply the Addition Rule, P(A or B) = P(A) +
P(B) – P(A and B),
and interpret the answer in terms of the
model.
Activity: Students will take decks of cards and
go through the probability of pulling different
pairs of cards out, showing how depending if the
cards have something in coming, this will change
our probability.

Apply the general Multiplication Rule in a
uniform probability
model, P(A and B) = P(A)P(B|A) =
P(B)P(A|B), and interpret the answer
in terms of the model.
Activity: Students will create probability trees,
which will show all possible results from a given
experiment. With these trees, students will be
able to show how to find the probability of a
given event using the multiplication rule.






24
Resources Books, articles,
Formative and
Summative measures
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.
Student response
in class.
Worksheet on
material.
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.
text, etc.

http://www.mathgoodi
es.com/lessons/vol6/co
nditional.html

http://www.algebralab.
org/lessons/lesson.asp
x?file=Algebra_Proba
bilityAdditionRule.xm
l

http://people.richland.e
du/james/lecture/m170
/ch05-rul.html
Content Area: Geometry Honors
Target Course/Grade level: 9
Unit Title: Applications of Probability
Essential Questions: How do use Probability?
Standards/
CPI’s
S.CP.9 (+)
S.MD.6 (+)
S.MD.7 (+)
Unit Learning Targets As a result of this
Lessons and Activities The learning experiences
segment of learning, students will…
that will facilitate engagement and achievement
Use permutations and combinations to
compute probabilities of compound events
and solve problems.
Use probabilities to make fair decisions (e.g.,
drawing by lots,
using a random number generator).
Analyze decisions and strategies using
probability concepts (e.g., product testing,
medical testing, pulling a hockey goalie at
the end
of a game).
Activity: Students will be given ingredients for a
sandwich. Students must show all possible ways
in which 4 items can be placed on the sandwich
out of 6 possible items. We will then discuss if
it’s the same sandwich if the same ingredients are
on in the different order.
Activity: Students will use the TI-83/89
calculators to generate 100 random digits from 212. After, they will use this to determine if this is
representative of all possible dice rolls.
Lesson: Students will use their knowledge of
probability to determine if they should continue
producing a product with given results. Using
probability, standard deviation, and hypothesis
testing, students will be able to determine if they
are making a correct decision.
25
Evidence of Learning
Resources Books, articles,
Formative and
Summative measures








Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.
text, etc.


http://www.mathsisfun
.com/combinatorics/co
mbinationspermutations.html
http://www.studyzone.
org/mtestprep/math8/e
/tablestally6p.cfm
Worksheet on
material.
Quiz on material
presented.
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.

http://www.random.or
g/

Statistics textbook –
pgs. 387-407