Mathematics Curriculum:
Geometry/Geometry Honors
Geometry Mapping
Dates
Math
September 4- October
24, 2014
5 Weeks
2 Weeks
Instruction Assessment/
Enrichment/
Unit 1
Asmnt
1/Unit 1
October 27 – December
22 2014
5 Weeks
2 Weeks
Instruction Assessment/
Enrichment/
Unit 2
Asmnt
2/Unit2
Mathematics: Geometry
Standard
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G.CO.1
G.CO.4
G.CO.2
G.CO.3
G.CO.5
G.CO.6
G.CO.7
G.CO8
G.CO.9
G.CO.10
G.CO.11
Description


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.
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
January 5 –Feb 27 2015
March 2 – Apr 24, 2015
Apr 27-June 19, 2015
5 Weeks
Instruction
5 Weeks
Instruction
5 Weeks
Instruction
Unit 3
2 Weeks
Assessment/
Enrichment/
Asmnt
3/Unit 3
Unit 4
Unit #1: Congruence, Proof, and
Construction
9/4/14-10/24/14
Student Learning Objectives




Use the undefined notion of a
point, line, distance along a line
and distance around a circular arc
to develop definitions for angles,
circles,
parallel
lines,
perpendicular lines and line
segments.
Apply the definitions of angles,
circles,
parallel
lines,
perpendicular lines and line
segments to describe rotations,
reflections, and translations.
Develop and perform rigid
transformations
that include
reflections, rotations, translations
and dilations using geometric
software, graph paper, tracing
paper, and geometric tools and
compare them to non-rigid
transformations.
Use rigid transformations to
determine, explain and prove
2 Weeks
Assessment/
Enrichment/
Asmnt
4/Unit 4
Unit 3
2 Weeks
Assessment/
Enrichment/
Asmnt
5/Unit 5
Unit #1
Interdisciplinary Connections/Critical Thinking
 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/reflection.
swf
 Rotations:
Guided Problem Solving: Understanding Math
Problems
Activity: Rotate shapes either 90 or 45 degrees:
http://www.primaryresources.co.uk/online/roration.s
wf

Activity
Lab:
Tracing
Paper
Transformations
Use interactive figures to explore geometric
transformations
(rotations,
translations,
and
reflections and a composition of these):
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


transformations that
preserve distance and
angle to those that do
not (e.g., translation
versus horizontal
stretch).
Given a rectangle,
parallelogram,
trapezoid, or regular
polygon, describe the
rotations and
reflections that carry
it onto itself.
Develop definitions
of rotations,
reflections, and
translations in terms
of angles, circles,
perpendicular lines,
parallel lines, and
line segments
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.
Use geometric
descriptions of rigid

congruence of geometric figures. http://standards.nctm.org/document/eexamples/chap
Create proofs of theorems 6/6.4/index.htm
involving lines, angles, triangles,
and parallelograms.
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

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 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.
Explain how the
criteria for triangle
congruence (ASA,
SAS, and SSS)
follow from the
definition of
congruence in terms
of rigid motions.
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.
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.
Prove theorems about
parallelograms.
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.
Technolgy
Standard
Description
Performance Task
8.2.12.D.1
Apply the design process.
Design and create a prototype to
solve a real world problem using
a design process, identify
constraints addressed during the
creation of the prototype, identify
trade-offs made, and present the
solution for peer review
Explain how material processing
impacts the quality of engineered
and fabricated products.
Develop an innovative solution to
a real world problem or issue in
collaboration with peers and
experts, and present ideas for
feedback through social media or
in an online community
Activity: Create your own kaleidoscope
http://www.zefrank.com/dtoy_vs_byokal/
8.2.12.D.5
Assess the impact of products
and systems.
8.1.12.C.1
Contribute to project teams to
produce original works or solve
problems.
Activity: Rotate shapes either 90 or 45 degrees:
http://www.primaryresources.co.uk/online/roration.swf
Use interactive figures to explore geometric transformations
(rotations, translations, and reflections and a composition of these):
http://standards.nctm.org/document/eexamples/chap6/6.4/index.htm
Differentiation-GNT/ELL
Standard
Description
Performance Task
4.1.1.
Educators maintain high
expectations for all students
with gifts and
talents as evidenced in
meaningful and challenging
activities
Rotations:
Guided Problem Solving: Understanding Math Problems
5.1.1
Educators regularly use
multiple alternative approaches
to accelerate
learning.
Reflections:
Activity Lab: Paper Folding and Reflections
Activity: Reflect the given pattern in a line:
http://www.primaryresources.co.uk/online/reflection.swf
5.1.5.
Educators regularly use current
technologies, including online
learning options and assistive
technologies to enhance access
to high-level programming.
Activity Lab: Tracing Paper Transformations
Use interactive figures to explore geometric transformations
(rotations, translations, and reflections and a composition of these):
http://standards.nctm.org/document/eexamples/chap6/6.4/index.htm
Careers and 21st Century
Standard
Description
Performance Task
9.3.ST‐ET.4
Apply the elements of the design
process.
Activity: Create your own kaleidoscope
http://www.zefrank.com/dtoy_vs_byokal/
9.3.ST.2
Use technology to acquire,
Activity: Reflect the given pattern in a line:
9.3.ST.1
manipulate, analyze and report data.
http://www.primaryresources.co.uk/online/reflection.swf
Apply engineering skills in a project
that requires project management,
process control and quality
assurance.
Activity: Rotate shapes either 90 or 45 degrees:
http://www.primaryresources.co.uk/online/roration.swf
Reading / Writing
Standard
Description
Performance Task
CCSS.ELA-Literacy.WHST.9-10.2.a
Introduce a topic and organize ideas,
concepts, and information to make
important connections and distinctions;
include formatting (e.g., headings),
graphics (e.g., figures, tables), and
multimedia when useful to aiding
comprehension.
CCSS.ELA-Literacy.WHST.9-10.6
Use technology, including the Internet, to
produce, publish, and update individual or
shared writing products, taking advantage
of technology's capacity to link to other
information and to display information
flexibly and dynamically.
Project:
Produce Optical Art and Explain &
Classify all Rotations, Reflections, and
Translations.
CCSS.ELA-Literacy.WHST.9-10.8
Gather relevant information from multiple
authoritative print and digital sources,
using advanced searches effectively; assess
the usefulness of each source in answering
the research question; integrate
Project:
Create and Design Brochure Promoting
Rotations, Reflections, and Translations in
Advertising.
Project:
1. Identify and Classify Rotations,
Reflections, and Translations in Modern
Architecture
information into the text selectively to
maintain the flow of ideas, avoiding
plagiarism and following a standard format
for citation.
Assessment
Geometry Benchmark 1 Exam
Mathematics: Geometry
Standard
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G.SRT.1
G.SRT.2
G.SRT.3
G.SRT.4
G.CO.10
Description


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.
b. The dilation of a
line
segment
is
longer or shorter in
the ratio given by the
scale factor.
Given two figures,
use the definition of
similarity in terms of
similarity
transformations
to
decide if they are
similar; explain using
similarity
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.
Unit #2: Similarity and Proof
10/27/14-12/22/14
Student Learning Objectives




Justify the properties of dilations
given by a center and a scale
factor. 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 (the dilation of
a line segment is longer or shorter
in the ratio given by the scale
factor).
Given two figures, use the
definition of similarity in terms of
similarity transformations to
decide if they are similar; explain
using similarity 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.
Use the properties of similarity
transformations to establish the
AA criterion for two triangles to
be similar.
Prove theorems about triangles.
Unit #2
Interdisciplinary Connections/Critical Thinking

Interactive webpage allowing students to test
all similarity triangle postulates.
http://www.keymath.com/x3343.xml
 Interactive calculator lesson using a TI 83 to
experiment with the side splitter theorem
http://education.ti.com/calculators/downloads/US/Ac
tivities/Detail?id=12318
 Multiple TI calculator lessons to explore
similar geometric figures
http://education.ti.com/calculators/timathnspired/US/
Activities/?t=5053&sa=5024



Use the properties of
similarity
transformations
to
establish the AA
criterion for two
triangles
to
be
similar.
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.
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.
Technolgy
Standard
Description
Performance Task
8.2.12.D.1
Apply the design process.
Design and create a
prototype to solve a real
world problem using a
design process, identify
constraints addressed
during the creation of the
prototype, identify tradeoffs made, and present the
solution for peer review
Explain how material
processing impacts the
quality of engineered and
fabricated products.
Develop an innovative
solution to a real world
problem or issue in
collaboration with peers
and experts, and present
ideas for feedback
through social media or in
an online community
Activity: Interactive calculator lesson using a TI 83 to experiment with the side
splitter theorem
http://education.ti.com/calculators/downloads/US/Activities/Detail?id=12318
8.2.12.D.5
Assess the impact of
products and systems.
8.1.12.C.1
Contribute to project
teams to produce original
works or solve problems.
Activity: Multiple TI calculator lessons to explore similar geometric figures
http://education.ti.com/calculators/timathnspired/US/Activities/?t=5053&sa=5024
Use interactive figures to explore geometric transformations (rotations,
translations, and reflections and a composition of these):
http://standards.nctm.org/document/eexamples/chap6/6.4/index.htm
Differentiation-GNT/ELL
Standard
Description
Performance Task
4.1.1.
Educators maintain high expectations for
all students with gifts and
talents as evidenced in meaningful and
challenging activities
Similarity:
Guided Problem Solving: Understanding
Math Problems
5.1.1
Educators regularly use multiple
alternative approaches to accelerate
learning.
5.1.5.
Educators regularly use current
technologies, including online learning
options and assistive technologies to
enhance access to high-level programming.
Activity: Students will make a scale
drawing of their bedroom. Students need
to measure their room and use graph paper
to make their drawings. Each drawing
must include a scale
Interactive webpage allowing students to
test all similarity triangle postulates.
http://www.keymath.com/x3343.xml
Careers and 21st Century
Standard
Description
Performance Task
9.3.ST‐ET.4
Apply the elements of
the design process.
Activity: Students fold a sheet of paper in half and then measure and reason to
decide whether the folded sheet is similar to the original sheet.
9.3.ST.2
Use technology to
acquire, manipulate,
analyze and report data.
Multiple TI calculator lessons to explore similar geometric figures
http://education.ti.com/calculators/timathnspired/US/Activities/?t=5053&sa=5024
9.3.ST.1
Apply engineering skills
in a project that requires
project management,
process control and
quality assurance.
Project: Students draw three parallel lines cut by two
transversals. Students use a ruler to measure the segments intercepted on the
transversals and observe they are
proportional, and not congruent
Reading / Writing
Standard
Description
Performance Task
CCSS.ELA-Literacy.WHST.9-10.2.a
Introduce a topic and organize ideas,
concepts, and information to make
important connections and distinctions;
include formatting (e.g., headings),
graphics (e.g., figures, tables), and
multimedia when useful to aiding
comprehension.
Project:
Students connect the midpoints of two
sides of a large triangle, measure all angles
and sides, and then use AA, SAS, and SSS
Similarity to explain why the triangles are
similar.
CCSS.ELA-Literacy.WHST.9-10.6
Use technology, including the Internet, to
produce, publish, and update individual or
shared writing products, taking advantage
of technology's capacity to link to other
information and to display information
flexibly and dynamically.
Project:
Create and Design Brochure introducing
the five ways to prove two quadrilaterals
congruent: four theorems and the
definition of a parallelogram. Then discuss
why both are such a critical term in some
theorems.
CCSS.ELA-Literacy.WHST.9-10.8
Gather relevant information from multiple
authoritative print and digital sources,
using advanced searches effectively; assess
the usefulness of each source in answering
the research question; integrate
Project:
Students think that because the sides of a
rhombus are congruent its diagonals must
also be congruent. Students draw several
counterexamples and explain their
conclusions.
information into the text selectively to
maintain the flow of ideas, avoiding
plagiarism and following a standard format
for citation.
Assessment
Geometry Benchmark Exam 2
Mathematics: Geometry






Standard
G.GPE.6
G.SRT.4
G.SRT.5
G.SRT.6
G.SRT.7
G.SRT.8
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



Description
Find the point on a
directed line segment
between two given
points that partitions
the segment in a
given ratio.
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.
Use congruence and
similarity criteria for
triangles to solve
problems and to
prove relationships in
geometric figures.
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.
Explain and use the
relationship between
Unit #3: Trigonometry
1/5/15-2/27/15
Student Learning Objectives
 Find the point on a directed line
segment between two given
points that partitions the segment
in a given ratio.
 Prove theorems about triangles.
 Use congruence and similarity
criteria for triangles to solve
problems
and
to
prove
relationships in geometric figures.
 Derive the definitions for
trigonometric
ratios
using
similarity of right triangles.
 Explain and use the relationship
between the sine and cosine of
complementary angles.
 Use trigonometric ratios and the
Pythagorean Theorem to solve
right
triangles
in
applied
problems.
Unit # 3
Interdisciplinary Connections/Critical Thinking
Real-World Applications:
 Website introduces geometric shapes and
their properties using everyday objects. Use
classroom objects and household items to
discover 3 dimensional shapes and finding
volume for those shapes
http://www.learner.org/interactives/geometry/index.
html
Science/Chemistry/Physics Applications:
 Density based labs that can be constructed in
the classroom to model situations
http://www.edinformatics.com/math_science/mass_v
olume_density.htm

the sine and cosine of
complementary
angles.
Use
trigonometric
ratios
and
the
Pythagorean
Theorem to solve
right triangles in
applied problems.
Technolgy
Standard
Description
Performance Task
8.2.12.D.1
Apply the design process.
Design and create a prototype to solve a
real world problem using a design
process, identify constraints addressed
during the creation of the prototype,
identify trade-offs made, and present
the solution for peer review
Real-World Applications:
 Website introduces geometric shapes and their
properties using everyday objects. Use
classroom objects and household items to
discover 3 dimensional shapes and finding
volume for those shapes
http://www.learner.org/interactives/geometry/index.html
8.2.12.D.5
Assess the impact of products and
systems.
Explain how material processing
impacts the quality of engineered and
fabricated products.
8.1.12.C.1
Contribute to project teams to produce
original works or solve problems.
Activity: Have students explain how to find tan 30° and
tan 60° without using a calculator, and then confirm the
values with a calculator.
Develop an innovative solution to a real Activity: After students learn and apply Theorem 8-5,
world problem or issue in collaboration have them write a formula for the area of an isosceles
with peers and experts, and present
right triangle whose hypotenuse has length s.
ideas for feedback through social media
or in an online community
Differentiation-GNT/ELL
Standard
Description
Performance Task
4.1.1.
Educators maintain high
expectations for all
students with gifts and
talents as evidenced in
meaningful and
challenging activities
Prove Theorems About Theorems:
Guided Problem Solving: Understanding Math Problems
5.1.1
Educators regularly use
multiple alternative
approaches to accelerate
learning.
Activity: Have students draw and measure right triangles to
make a table of sine and cosine values for the angles in the set (10°, 20°, ... , 80°).
5.1.5.
Educators regularly use
current technologies,
including online learning
options and assistive
technologies to enhance
access to high-level
programming.
Activity:
Multiple TI calculator lessons to explore similar geometric figures
http://education.ti.com/calculators/timathnspired/US/Activities/?t=5053&sa=5024
Careers and 21st Century
Standard
Description
Performance Task
9.3.ST‐ET.4
Apply the elements of the
design process.
Activity: Website introduces geometric shapes and their properties
using everyday objects.
http://www.learner.org/interactives/geometry/index.html
9.3.ST.2
Use technology to acquire,
manipulate, analyze and
report data.
Activity: Interactive webpage allowing students to test all similarity
triangle postulates.
http://www.keymath.com/x3343.xml
9.3.ST.1
Apply engineering skills in a
project that requires project
management, process control
and quality assurance.
Science/Chemistry/Physics Applications:
Density based labs that can be constructed in the classroom to model
situations
http://www.edinformatics.com/math_science/mass_volume_density.htm
Reading / Writing
Standard
Description
Performance Task
CCSS.ELA-Literacy.WHST.9-10.2.a
Introduce a topic and organize ideas,
concepts, and information to make
important connections and distinctions;
include formatting (e.g., headings),
graphics (e.g., figures, tables), and
multimedia when useful to aiding
comprehension.
Project:
Students will apply your knowledge of
trigonometry to shadows in order to
calculate the angle of elevation to the sun
at different times of day. Graphic
organizing report will present the students
knowledge of trigonometric ratios.
CCSS.ELA-Literacy.WHST.9-10.6
Use technology, including the Internet, to
produce, publish, and update individual or
shared writing products, taking advantage
of technology's capacity to link to other
information and to display information
Project:
Students develop a story involving the
missing angle or missing side of a right
triangle. They will carefully draw, use a
photograph, a picture clipped from a
magazine or downloaded from the Internet,
illustrating the problem in your story.
Gather relevant information from multiple Project:
Create a powerpoint presentation and an
authoritative print and digital sources,
using advanced searches effectively; assess exercise on the Pythagorean theorem.
the usefulness of each source in answering
the research question; integrate
information into the text selectively to
maintain the flow of ideas, avoiding
plagiarism and following a standard format
for citation.
flexibly and dynamically.
CCSS.ELA-Literacy.WHST.9-10.8
Assessment
Geometry Benchmark Exam 3
Mathematics: Geometry






Standard
G.C.2
G.GPE.1
G.GPE.5
G.CO.11
G.GPE.4
G.GPE.7



Description
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.
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.
Prove theorems about
parallelograms.
Theorems include:
opposite sides are
congruent, opposite
angles are congruent,
the diagonals of a
Unit # 4: Circles and Expressing
Geometric Properties through
Equations
3/2/15-4/24/15
Student Learning Objectives
 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.
 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.
 Prove the slope criteria for
parallel and perpendicular lines
and use 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.)
 Construct formal proofs using
theorems, postulates, and
definitions involving
parallelograms. *
 Use coordinates to prove simple
geometric theorems algebraically.
 Use coordinates to compute
perimeters of polygons and areas
of triangles and rectangles, e.g.,
Unit # 4
Interdisciplinary Connections/Critical Thinking
Data Analysis spiraled with coordinate proofs:
 Proofs Using Coordinate Geometry:
Example: Planning a Coordinate Geometry
Proof
http://regentsprep.org/Regents/math/geometry/GCG
4/CoordinatepRACTICE.htm
Activity Lab: Data Analysis: Interpreting Data
Technology Application: Geometer’s Sketchpad:
 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.
 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.
 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.
 Students will use Geometer’s Sketchpad to
create tangent lines to given circles.
 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.



parallelogram bisect
each other, and
conversely,
rectangles are
parallelograms with
congruent diagonals.
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).
Prove the slope
criteria for parallel
and perpendicular
lines and use 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.
Use coordinates to
compute perimeters
using the distance formula.
Students will then be able to use formulas
for area to show that measured area is the
same as ones they derived themselves.
of polygons and areas
of triangles and
rectangles, e.g., using
the distance formula.
Technolgy
Standard
Description
Performance Task
8.2.12.D.1
Apply the design process.
Design and create a
prototype to solve a real
world problem using a
design process, identify
constraints addressed
during the creation of the
prototype, identify tradeoffs made, and present the
solution for peer review
Explain how material
processing impacts the
quality of engineered and
fabricated products.
Develop an innovative
solution to a real world
problem or issue in
collaboration with peers
and experts, and present
ideas for feedback
through social media or in
an online community
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.
8.2.12.D.5
Assess the impact of
products and systems.
8.1.12.C.1
Contribute to project
teams to produce original
works or solve problems.
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.
Data Analysis spiraled with coordinate proofs:
Proofs Using Coordinate Geometry:
Example: Planning a Coordinate Geometry : Proof
http://regentsprep.org/Regents/math/geometry/GCG4/CoordinatepRACTICE.htm
Differentiation-GNT/ELL
Standard
Description
Performance Task
4.1.1.
Educators maintain high expectations for
all students with gifts and
talents as evidenced in meaningful and
challenging activities
Activity: Students wil calculate which is
greater, the height or the circumference of
a can of three tennis balls.
5.1.1
Educators regularly use multiple
alternative approaches to accelerate
learning.
Activity: Students will calculate the area of
chosen circular logos and compare results
5.1.5.
Educators regularly use current
technologies, including online learning
options and assistive technologies to
enhance access to high-level programming.
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.
Standard
Description
Performance Task
9.3.ST‐ET.4
Apply the elements of the design process.
Activity: Students will use Geometer’s
Sketchpad to create tangent lines to given
circles.
9.3.ST.2
Use technology to acquire, manipulate,
Activity: Students will use the Geometer’s
Sketchpad to create circles. They will then
Careers and 21st Century
analyze and report data.
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.
Apply engineering skills in a project that
requires project management, process
control andquality assurance.
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.
Standard
Description
Performance Task
CCSS.ELA-Literacy.WHST.9-10.2.a
Introduce a topic and organize ideas,
concepts, and information to make
important connections and distinctions;
include formatting (e.g., headings),
graphics (e.g., figures, tables), and
multimedia when useful to aiding
comprehension.
Project:
Create a Geometry Book that explores the
slope criteria for parallel and perpendicular
lines including example and illustrations.
9.3.ST.1
Reading / Writing
CCSS.ELA-Literacy.WHST.9-10.6
Use technology, including the Internet, to
produce, publish, and update individual or
shared writing products, taking advantage
of technology's capacity to link to other
information and to display information
flexibly and dynamically.
Project:
Produce a Quilt Design and Explain &
Classify all Quadrilaterals that are utilized
in the design process.
CCSS.ELA-Literacy.WHST.9-10.8
Gather relevant information from multiple
authoritative print and digital sources,
using advanced searches effectively; assess
the usefulness of each source in answering
the research question; integrate
information into the text selectively to
maintain the flow of ideas, avoiding
plagiarism and following a standard format
for citation.
Project:
Create and Design Brochure that presents
all the concepts and formulas of polygonal
areas.
Assessment
Geometry Benchmark Exam 4
Mathematics: Geometry




Standard
G. GMD.3
G.MG.1
G.MG.2
G.MG.3




Description
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.
Use geometric
shapes, their
measures, and their
properties to describe
objects
Apply concepts of
density based on area
and volume in
modeling situations
Apply geometric
methods to solve
design problems
Unit # 5: Extending to Three
Dimensions
4/27/15-6/19/15
Student Learning Objectives
 Solve problems using volume
formulas for cylinders, pyramids,
cones, and spheres.
 Use geometric shapes, their
measures, and their properties to
describe objects (e.g., modeling a
tree trunk or a human torso as a
cylinder).
 Use density concepts in modeling
situations based on area and
volume. (e.g., persons per square
mile, BTUs per cubic foot).
 Solve design problems using
geometric methods. (e.g.,
designing an object or structure to
satisfy physical constraints or
minimize cost; working with
typographic grid systems based
on ratios).
Unit # 5
Interdisciplinary Connections/Critical Thinking
Real-World Applications:
•
Website introduces geometric shapes and
their properties using everyday objects. Use
classroom objects and household items to discover 3
dimensional shapes and finding volume for those
shapes
http://www.learner.org/interactives/geometry/index.
html
Technolgy
Standard
Description
Performance Task
8.2.12.D.1
Apply the design process.
Design and create a prototype to solve
a real world problem using a design
process, identify constraints addressed
during the creation of the prototype,
identify trade-offs made, and present
the solution for peer review
Explain how material processing
impacts the quality of engineered and
fabricated products.
Activity: Students are introduced to geometric shapes
and their properties using everyday objects by utilizing
the following website:
http://www.learner.org/interactives/geometry/index.html
Develop an innovative solution to a
real world problem or issue in
collaboration with peers and experts,
and present ideas for feedback through
social media or in an online community
Activity: Students discover Pi and its relationship with
circumference. Students use string and scissors to
dicover the relationship of circles and Pi.
http://www.exploratorium.edu/pi/pi_activities/index.html
8.2.12.D.5
Assess the impact of products and
systems.
8.1.12.C.1
Contribute to project teams to produce
original works or solve problems.
Activity: Students will construct paper models and
worksheets to create nets for all 3 dimensional shapes
using the following web tool:
http://www.korthalsaltes.com/
Differentiation-GNT/ELL
Standard
Description
Performance Task
4.1.1.
Educators maintain
high expectations for
all students with gifts
and
talents as evidenced in
meaningful and
challenging activities
Area Exploration: To understand area and how to derive a formula. Interactive lesson
that dissects shapes to create formulas:
http://www.learner.org/courses/learningmath/measurement/session7/part_b/index.html
5.1.1
Educators regularly use Activity: Nets made virtually on the web that will construct themselves.
multiple alternative
http://www.mathsnet.net/geometry/solid/nets.html
approaches to
accelerate
learning.
5.1.5.
Educators regularly use Activity: Density based labs that can be constructed in the classroom to model
current technologies,
situations.
including online
http://www.edinformatics.com/math_science/mass_volume_density.htm
learning options and
assistive technologies
to enhance access to
high-level
programming.
Careers and 21st Century
Standard
Description
Performance Task
9.3.ST‐ET.4
Apply the elements of the
design process.
Activity: Students will use classroom objects and household items to
discover 3 dimensional shapes and finding volume for those shapes
9.3.ST.2
Use technology to acquire,
manipulate, analyze and
report data.
Activity: Following website allows student to construct 3-D shapes and
calculate and record volumes:
http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/
9.3.ST.1
Apply engineering skills in a
project that requires project
management, process control
Real-World Applications:
Website introduces geometric shapes and their properties using
everyday objects. Use classroom objects and household items to
and
quality assurance.
discover 3 dimensional shapes and finding volume for those shapes
http://www.learner.org/interactives/geometry/index.html
Reading / Writing
Standard
Description
Performance Task
CCSS.ELA-Literacy.WHST.9-10.2.a
Introduce a topic and organize ideas,
concepts, and information to make
important connections and distinctions;
include formatting (e.g., headings),
graphics (e.g., figures, tables), and
multimedia when useful to aiding
comprehension.
Project: Students will unfold an empty
cereal box. Students will use this real life
application to develop the concept of nets.
Students will measure each attribute:
length, width, and height. Students record
all measurements in a spreadsheet.
Students utilize the formulas to calculate
the surface area of a rectangular prism.
Students will record all results in
spreadsheet and present their results.
CCSS.ELA-Literacy.WHST.9-10.6
Use technology, including the Internet, to
produce, publish, and update individual or
shared writing products, taking advantage
of technology's capacity to link to other
information and to display information
flexibly and dynamically.
Project:
Students will research the different
methods of packaging design and create a
business presentation that promotes their
own packaging design.
CCSS.ELA-Literacy.WHST.9-10.8
Gather relevant information from multiple
authoritative print and digital sources,
using advanced searches effectively; assess
the usefulness of each source in answering
Project:
Create and Design an Informational
Brochure highlighting all the aspects of
three –dimensional solids.
the research question; integrate
information into the text selectively to
maintain the flow of ideas, avoiding
plagiarism and following a standard format
for citation.
Assessment
Geometry Final Exam
Resources by Standard
for
Geometry
North Arlington Public
Schools
North Arlington Public
Schools
Content Area: Geometry
Target Course/Grade level: 10
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
segment of learning, students will…
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.
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Points, Lines, and Planes:
Activity Lab: How Many Lines
Can You Draw To Create A
Constellation
Participation
Class Discussion
Study Guide
Textbook : 1-3 p.16
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
Textbook: 1-4 p.23
http://www.homescho
olmath.net/teaching/g/
angles.php
http://www.homescho
olmath.net/teaching/g/
parallel_and_perpendi
cular.php
Textbook: 1-6 p.36
http://www.homescho
olmath.net/teaching/g/
measure_angles.php
Measuring Angles:
Activity Lab: Using a Protractor
to Measure and Classify Angles
http://www.shodor.org/interactivate/activ
ities/Angles/
Perimeter, Circumference, and Area:
Graphing Calculator Activity:
Check Point Quiz
Participation
Class Discussion
Unit Test
Participation
Class Discussion
Textbook: 1-9 p.61
Content Area: Geometry
Target Course/Grade level: 10
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
segment of learning, students will…
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Comparing Perimeters and Areas
G.CO.2
G.CO.3
G.CO.4
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).
Given a rectangle, parallelogram,
trapezoid, or regular polygon,
describe the rotations and
reflections that carry it onto itself.
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/onlin
e/reflection.swf
Rotations:
Guided Problem Solving: Understanding
Math Problems
Activity: Rotate shapes either 90 or 45
degrees:
http://www.primaryresources.co.uk/onlin
e/roration.swf
34
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Study Guide
Participation
Class Discussion
Study Guide
Participation
Class Discussion
Study Guide
Check Point Quiz
Participation
Class Discussion
Check Point Quiz
Participation
Class Discussion
Unit Test
Textbook: 9-1 p. 470
http://www.mathsnet.n
et/transform/index.htm
l
Textbook: 9-2 p.478
Textbook: p.477
Textbook: 9-3 p.483
Textbook: p.489
http://standards.nctm.o
rg/document/eexample
s/chap6/6.4/index.htm
Textbook: 9-4 p.492
http://www.innovation
Content Area: Geometry
Target Course/Grade level: 10
Unit Title: Congruence, Proof, and Constructions
Essential Questions: How do we use Congruence, Proof, and Constructions?
Standards/
CPI’s
G.CO.5
G.CO.6
G.CO.7
Unit Learning Targets As a result of this
segment of learning, students will…
Develop definitions of rotations,
reflections, and translations
in terms of angles, circles,
perpendicular lines, parallel lines,
and line segments.
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.
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.
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Symmetry:
Example: Identifying Lines Of
Symmetry
Example; Identifying Rotational
Symmetry
Symmetry Activity:
http://www.haelmedia.com/OnlineActivit
ies_txh/mc_txh4_001.html
Lesson Activity: Advanced
Transformations
http://www.misterteacher.com/alphabetg
eometry/reflection.html
Lesson Activity: Geometric Solids
http://illuminations.nctm.org/ActivityDet
ail.aspx?ID=70
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
slearning.co.uk/subject
s/maths/activities/year
3/symmetry/shape_ga
me.asp
Participation
Class Discussion
Study Guide
Check Point Quiz
http://www.mathsisfun
.com/geometry/symme
try.html
Participation
Class Discussion
Study Guide
Textbook: p.490
Geometer’s Sketchpad
Activity Lab: Tracing Paper
Transformations
Participation
Class Discussion
Study Guide
Check Point Quiz
Use the definition of congruence in
35
http://www.girlsgotech
Content Area: Geometry
Target Course/Grade level: 10
Unit Title: Congruence, Proof, and Constructions
Essential Questions: How do we use Congruence, Proof, and Constructions?
Standards/
CPI’s
G.CO.8
Unit Learning Targets As a result of this
segment of learning, students will…
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.
Explain how the criteria for triangle
congruence (ASA, SAS, and SSS)
follow from the definition of
congruence in terms of rigid
motions.
G.CO.9
G.CO.10
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.
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
.org/world_around_us.
html
Use interactive figures to explore
geometric transformations (rotations,
translations, and reflections and a
composition of these):
http://standards.nctm.org/document/eexa
mples/chap6/6.4/index.htm
Participation
Class Discussion
Study Guide
Textbook: p.198
http://www.math.com/
school/subject3/lesson
s/S3U3L1GL.html
Participation
Class Discussion
Congruent Figures:
Study Guide
Activity: Similarity and Congruence
Participation
http://www.absorblearning.com/mathema Class Discussion
tics/demo/units/KCA035.html
Study Guide
Participation
Class Discussion
Study Guide
Triangle Congruence by SSS and SAS:
Activity: Hands On: Building Congruent
Triangles
36
Check Point Quiz
Participation
Class Discussion
Textbook: p.205
Textbook: p.204
Textbook: p.213
Textbook: p.220
Textbook: p.36
http://www.shodor.org
/interactivate/activities
/Angles/
Content Area: Geometry
Target Course/Grade level: 10
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
segment of learning, students will…
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Triangle Congruence by ASA and AAS:
Activity: Technology: Exploring AAA
and SSA
Measuring Angles:
Activity: Measuring Angles
http://www.homeschoolmath.net/teachin
g/g/measure_angles.php
Properties of Parallel Lines:
Activity: Technology: Parallel Lines and
Related Angles
Evidence of
Learning
Formative and
Summative measures
Study Guide
Participation
Class Discussion
Study Guide
Participation
Class Discussion
Study Guide
Check Point Quiz
Unit Test
G.CO.11
Parallel and Perpendicular Lines
Guided Problem Solving: Understanding
Proof Problems
Participation
Class Discussion
37
text, etc.
Textbook: p.124
http://www.shodor.org
/interactivate/activities
/angles/index.html
Textbook: p.134
Textbook: p.141
Textbook: p.145
Proving Lines Parallel:
Activity: Parallel and Perpendicular
Lines
http://www.homeschoolmath.net/teachin
g/g/parallel_and_perpendicular.php
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.
Resources Books, articles,
Content Area: Geometry
Target Course/Grade level: 10
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
segment of learning, students will…
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Study Guide
Parallel Lines and the Triangle AngleSum Theorem:
Activity Lab: Hands On: Angle
Dynamics
Activity Lab: Exploring Spherial
Geometry
Prove theorems about
parallelograms. Theorems include:
opposite sides are congruent,
opposite angles are congruent, the
diagonals of a parallelogram bisect
each other, and conversely,
Isosceles and Equilateral Triangles:
Activity: Equilateral and Isosceles
Triangles
http://www.homeschoolmath.net/teachin
g/g/equilateral_isosceles.php
Proportions in Triangles:
Activity Lab: Technology: Exploring
Proportions in Triangles
38
Participation
Class Discussion
Study Guide
Textbook: p.147
Participation
Class Discussion
Study Guide
Check Point Quiz
Textbook: p.228
http://library.thinkques
t.org/20991/geo/ietri.h
tml
Participation
Class Discussion
Study Guide
Unit Test
Textbook: p.398
Textbook: p.397
Textbook: p.146
Textbook: p.154
Textbook: p.272
http://www.google.co
m/url?sa=t&source=w
eb&cd=4&ved=0CC0
QFjAD&url=http%3A
%2F%2Fwww.online
mathlearning.com%2F
side-splitter-
Content Area: Geometry
Target Course/Grade level: 10
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
segment of learning, students will…
rectangles are parallelograms with
congruent diagonals.
G.CO.12
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Concurrent Lines, Medians, and
Altitudes:
Activity Lab: Technology: Special
Segments in Triangles
Evidence of
Learning
Formative and
Summative measures
Participation
Class Discussion
Study Guide
Participation
Class Discussion
Study Guide
Check Point Quiz
Participation
Class Discussion
Study Guide
Unit Test
Resources Books, articles,
text, etc.
theorem.html&ei=DD
zuTZnPFZL4sAO44N
GeAw&usg=AFQjCN
HPCCv2vX39xFKl32
Lm8UehQCkA8Q
Textbook: p.312
Textbook: p.321
Textbook: p.320
Make formal geometric
constructions with a variety of tools
and methods (compass and
Properties of Parallelograms:
Activity: Dynamic Rectangle and
Parallelogram
http://standards.nctm.org/document/eexa
mples/chap5/5.3/index.htm
Proving That a Quadrilateral is a
39
Textbook: p.329
Textbook: p.328
http://www.mathsisfun
.com/geometry/quadril
aterals-interactive.html
Content Area: Geometry
Target Course/Grade level: 10
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
segment of learning, students will…
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.
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Parallelogram:
Activity: Hands-On: Geo-Models
Special Parallelograms:
Activity: Technology: Diagonals of
Parallelograms
Participation
Class Discussion
Study Guide
Check Point Quiz
Textbook: p.44
http://www.mathsnet.n
et/campus/constructio
n/index.html
http://www.mathsisfun
.com/geometry/constru
ctions.html
40
Content Area: Geometry
Target Course/Grade level: 10
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
segment of learning, students will…
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
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?sessi
on=1V77FB9E9B.5&+lang=en&+cmd=i
ntro&+module=tool%2Fgeometry%2Fru
lecomp.en&+special_parm=1
Activity: Construct an Inscribed
Equilateral Triangle:
http://www.nvcc.edu/home/tstreilein/con
structions/Inscribed/inscribe2.htm
Activity: Construct an Inscribed Regular
Hexagon:
http://www.nvcc.edu/home/tstreilein/con
structions/Inscribed/inscribe4.htm
Activity: Construct an Inscribed Square
http://www.nvcc.edu/home/tstreilein/con
structions/Inscribed/inscribe3.htm
41
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Geometric
Constructions
Illustrated with
Interactive Java
Applets:
http://www.nvcc.edu/h
ome/tstreilein/construc
tions/contents.htm
Geometer’s Sketchpad
Content Area: Geometry
Similarity, Proof, and Trigonometry
Target Course/Grade level: 10
Unit Title:
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
segment of learning, students will…
Verify experimentally the properties
of dilations given by a center and a
scale factor.
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
http://www.mathsnet.net/transformati
ons/index.html Interactive website
that allows the basic four
transformations
Evidence of
Learning
Formative and
Summative measures
Teacher Based test
Participation
Cooperative
learning
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.
Actively working
on computer
models
Resources Books, articles,
text, etc.
Textbook
9-5 Dilations
Pg. 498-503
http://www.brightsto
rm.com/math/geomet
ry/transformations/di
lations 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
http://www.absorblearning.com/mathe
matics/demo/units/KCA035.html#Sum
mary Interactive lesson with follow up
Actively use
similar shapes to
Textbook
7-2Similar Polygons
Pg. 373-379
Content Area: Geometry
Similarity, Proof, and Trigonometry
Target Course/Grade level: 10
Unit Title:
Essential Questions: What are the relationships between Similarity, Proof, and Trigonometry?
Standards/
CPI’s
G.SRT.3
G.SRT.4
Unit Learning Targets As a result of this
segment of learning, students will…
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.
Use the properties of similarity
transformations to establish the
AA criterion for two triangles to be
similar.
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.
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
questions.
Evidence of
Learning
text, etc.
create
transformations
7-3Proving Triangles
Similar
Pg. 382-388
http://www.absorblea
rning.com/mathemati
cs/demo/units/KCA0
24.html
Cooperative
learning in groups
http://www.keymath.com/x3343.xml
interactive webpage allowing students Participation
to test all similarity triangle postulates.
Teacher based test
Sketch pad
assessments
http://education.ti.com/calculators/do
wnloads/US/Activities/Detail?id=12318 Active group work
Interactive calculator lesson using a TI
83 to experiment with the side splitter Scientific
calculator
theorem
activities
43
Resources Books, articles,
Formative and
Summative measures
Textbook
7-3 Proving
Triangles Similar
Pg. 382-389
http://www.analyzem
ath.com/Geometry/si
milar_triangles.html
Lesson on similar
triangles
Textbook
7-4 Similarity in
Right Triangles
Pg. 391-397
http://www.mathwar
ehouse.com/geometry
Content Area: Geometry
Similarity, Proof, and Trigonometry
Target Course/Grade level: 10
Unit Title:
Essential Questions: What are the relationships between Similarity, Proof, and Trigonometry?
Standards/
CPI’s
G.SRT.5
G.SRT.6
G.SRT.7
G.SRT.8
Unit Learning Targets As a result of this
segment of learning, students will…
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Evidence of
Learning
Formative and
Summative measures
Use congruence and similarity
criteria for triangles to solve
problems and to prove relationships
in geometric figures.
http://education.ti.com/calculators/tim
athnspired/US/Activities/?t=5053&sa=
5024 Multiple TI calculator lessons to
explore similar geometric figures
Scientific
Calculator
activities
Explain and use the relationship
between the sine and cosine of
complementary angles.
http://www.purplemath.com/modules/
basirati.htm Explores the ratios of
trigonometry with problems to solve.
Teacher based test
Use geometric shapes, their
text, etc.
/similar/triangles/side
-splitter-theorem.php
Web page illustrating
the side splitter
theorem
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.
Use trigonometric ratios and the
Pythagorean Theorem to solve
right triangles in applied problems.★
Resources Books, articles,
Sketchpad
activities
http://www.cut-theknot.org/pythagoras/cosine2.shtml
Proofs and mathematical problems
demonstrating the relationship
between sine and cosine
44
Participation
Textbook
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
Content Area: Geometry
Similarity, Proof, and Trigonometry
Target Course/Grade level: 10
Unit Title:
Essential Questions: What are the relationships between Similarity, Proof, and Trigonometry?
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
measures, and their properties to
describe objects (e.g., modeling a
tree trunk or a human torso as a
cylinder).*
G.MG.1
Apply concepts of density based on
area and volume in modeling
situations (e.g., persons per square
mile, BTUs per cubic foot).*
G.MG.2
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).*
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Cooperative
learning
http://www.themathpage.com/aTrig/tri
gonometry.htm Lessons and activities
covering right triangles and
Actively working
trigonometry ratios
on computer
models
http://www.learner.org/interactives/ge
ometry/index.html Website introduces
geometric shapes and their properties
using everyday objects.
Use classroom objects and household
items to discover 3 dimensional shapes
and finding volume for those shapes
http://www.edinformatics.com/math_s
cience/mass_volume_density.htm
Density based labs that can be
constructed in the classroom to model
situations
45
Textbook
Chapter 8
Pg. 417-465
Textbook
Chapter 11Surface
area and Volume
Pg. 598-656
Participation
Cooperative
learning in groups
Exploring
geometric shapes
outside the
classrooom
Participation
Textbook
Chapter 11 Surface
area and Volme
Pg. 597-659
Content Area: Geometry
Similarity, Proof, and Trigonometry
Target Course/Grade level: 10
Unit Title:
Essential Questions: What are the relationships between Similarity, Proof, and Trigonometry?
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
G.MG.3
Cooperative
learning in groups
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://www.bbc.co.uk/schools/ks2bitesi
ze/maths/shape_space/ apply
geometric shapes to solve puzzles
Prove the Laws of Sines and Cosines
and use them to solve problems.
Exploring
geometric shapes
outside the
classrooom
Textbook
11-7 Areas and
Volumes of Similar
Solids
Pg. 646-651
Cooperative
learning in groups
http://www.ecalc.com
/mathhelp/worksheet/geom
etry Reference sheet
G.SRT.9 (+)
Participation
G.SRT.10 (+)
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://jwilson.coe.uga.edu/EMAT6680/
Simmons/6700/Unit%20Lesson1W.pdf
file explaining how to use geometer
sketchpad to use and derive the
Teacher Based test
formula A=1/2 ab sin ©
Participation
46
Textbook
8-4 The sine and
cosine Ratio
Pg. 439-443
Content Area: Geometry
Similarity, Proof, and Trigonometry
Target Course/Grade level: 10
Unit Title:
Essential Questions: What are the relationships between Similarity, Proof, and Trigonometry?
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Evidence of
Learning
Formative and
Summative measures
Cooperative
learning
G.SRT.11 (+)
http://www.brightstorm.com/math/trig
onometry/basictrigonometry/trigonometric-ratios-sine
http://www.brightstorm.com/math/trig
Actively working
onometry/basictrigonometry/trigonometric-ratios-sine on computer
models
Math videos
text, etc.
Textbook
8-4 The sine and
cosine Ratio
Pg. 439-443
Textbook
8-4 The sine and
cosine Ratio
Pg. 439-443
http://illuminations.nctm.org/LessonD
etail.aspx?ID=L704
Lesson teaching trigonometry in non
right triangles
Teacher based test
Geometer
sketchpad
activities
47
Resources Books, articles,
Content Area: Geometry
Extending to Three Dimensions
Target Course/Grade level: 10
Unit Title:
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
G.GMD.3
Unit Learning Targets As a result of this
segment of learning, students will…
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.
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Evidence of
Learning
Formative and
Summative measures
http://www.exploratorium.edu/pi/pi_a
ctivities/index.html To discover Pi and
its relationship with circumference.
Students use string and scissors to
dicover the relationship of circles and
Pi.
Participation
http://www.shodor.org/interactivate/ac
tivities/SurfaceAreaAndVolume/
Allows student to construct 3-D shapes
and calculate volumes
Actively
constructing
models
Resources Books, articles,
text, etc.
Text book
10-6 Circles and Arcs
Cooperative
Pg.566-571
learning
11-3 Surface Areas of
pyramids and cones
Actively working
Pg. 617-623
on computer
http://www.mathgoo
http://www.learner.org/courses/learnin models
dies.com/lessons/vol2/
gmath/measurement/session7/part_b/i
circumference.html
Teacher made tests lesson on
ndex.html To understand area and
how to derive a formula. Interative
circumference
lesson that disects shapes to create
formulas
Use volume formulas for cylinders,
pyramids, cones, and spheres to
solve problems.★
Text book
Chapters 10 Area
Chapter 11Surface
Area and Volume
Pages 539-656
Content Area: Geometry
Extending to Three Dimensions
Target Course/Grade level: 10
Unit Title:
Essential Questions: Extending to Three Dimensions
Standards/
CPI’s
G.GMD.4
Unit Learning Targets As a result of this
segment of learning, students will…
Identify the shapes of twodimensional cross-sections of threedimensional objects, and identify
three-dimensional objects generated
by rotations of two-dimensional
objects.
Use geometric shapes, their
measures, and their properties to
describe objects (e.g., modeling a
tree trunk or a human torso as a
cylinder).*
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
http://mathforum.org/alejandre/mathf
air/pyramid2.html Constructing
pyramids to find volume and surface
area.
Use circular and square blocks to
create volume formulas for three
dimensional figures.
http://www.mathsnet.net/geometry/soli
d/nets.html 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
Cooperative
learning in groups
Finding volume
for everyday
materials
Constructions
Resources Books, articles,
text, etc.
Handouts using
paper cutouts
http://www.brightsto
rm.com/math/geomet
ry/volume/volume-ofprisms
Textbook
11-1 Space Figures
and cross Sections
Pg. 598-603
Research
constructions of
different
polyhedrons
G.MG.1
http://www.learner.org/interactives/ge
ometry/index.html Website introduces
geometric shapes and their properties
using everyday objects.
49
Participation
Cooperative
learning in groups
Textbook
Chapter 11Surface
area and Volume
Pg. 598-656
Content Area: Geometry
Extending to Three Dimensions
Target Course/Grade level: 10
Unit Title:
Essential Questions: Extending to Three Dimensions
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Use classroom objects and household
items to discover 3 dimensional shapes
and finding volume for those shapes
50
Evidence of
Learning
Formative and
Summative measures
Exploring
geometric shapes
outside the
classrooom
Resources Books, articles,
text, etc.
Content Area: Geometry
Coordinates
Target Course/Grade level: 10
Unit Title: Connecting Algebra and Geometry through
Essential Questions: How do we Connect Algebra and Geometry through Coordinates?
Unit Overview: Building on their work with the Pythagorean theorem in 8th 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
segment of learning, students will…
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).
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).
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Placing Figures in the Coordinate Plane:
Example:Real-World Connection TShirt
Design
Example:Naming Coordinates
Proofs Using Coordinate Geometry:
Example: Planning a Coordinate
Geometry
Proof
http://regentsprep.org/Regents/math/geo
metry/GCG4/CoordinatepRACTICE.htm
Activity Lab: Data Analysis: Interpreting
Data
Lines in the Coordinate Plane:
Example: Graphing Lines In SlopeIntercept
Form
http://www.khanacademy.org/video/grap
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Participation
Class Discussion
Study Guide
Textbook: 6-6 p.343
Check Point Quiz
Participation
Class Discussion
Study Guide
Textbook: 6-7 p.348
http://www.mathwareh
ouse.com/coordinategeometry/
http://regentsprep.org/r
egents/math/geometry/
GCG6/LCir.htm
Participation
Class Discussion
Study Guide
Textbook: 3-6 p.166
http://www.math.com/
school/subject2/lesson
s/S2U4L2GL.html#sm
1
http://www.algebra-
Content Area: Geometry
Coordinates
Target Course/Grade level: 10
Unit Title: Connecting Algebra and Geometry through
Essential Questions: How do we Connect Algebra and Geometry through Coordinates?
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
Find the point on a directed line
segment between two given points
that partitions the segment in a
given ratio.
G.GPE.6
Use coordinates to compute
perimeters of polygons and areas of
triangles and rectangles, e.g., using
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
hing-a-line-in-slope-interceptform?playlist=Algebra+I+Worked+Exam
ples
Example: Using Point-Slope Form
http://www.phschool.com/atschool/acade
my123/english/academy123_content/wlbook-demo/ph-213s.html
Slopes of Parallel and Perpendicular
Lines:
Example: Checking for Parallel Lines
Example: Writing Equations of Parallel
Lines
http://www.phschool.com/atschool/acade
my123/english/academy123_content/wlbook-demo/ph-219s.html
Example: Checking for Perpendicular
Lines
Example: Writing Equations for
Perpendicular
Lines
http://www.phschool.com/atschool/acade
my123/english/academy123_content/wlbook-demo/ph-221s.html
52
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
class.com/slopeintercept-form.html
Check Point Quiz
Participation
Class Discussion
Study Guide
Unit Test
Textbook: 3-7 p.174
http://www.youtube.co
m/watch?v=u3zvkzkQW4
http://www.wtamu.edu
/academic/anns/mps/m
ath/mathlab/col_algebr
a/col_alg_tut28_parpe
n.htm
Check Point Quiz
Participation
Class Discussion
Study Guide
Textbook: 1-8 p.54
Algebra Lab:
http://www.algebralab.
org/lessons/lesson.asp
Content Area: Geometry
Coordinates
Target Course/Grade level: 10
Unit Title: Connecting Algebra and Geometry through
Essential Questions: How do we Connect Algebra and Geometry through Coordinates?
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Evidence of
Learning
Formative and
Summative measures
the distance formula.★
G.GPE.7
The Coordinate Plane:
Finding the Midpoint of a Segment:
Example: Finding the Midpoint
Example Finding an Endpoint
http://www.purplemath.com/modules/mi
dpoint.htm
http://cs.selu.edu/~rbyrd/math/midpoint/
Derive the equation of a parabola
given a focus and directrix.
G.GPE.2
The Coordinate Plane:
Finding Distance on the Coordinate
Plane:
Example: Finding Distance
http://www.purplemath.com/modules/dis
tform.htm
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
53
Check Point Quiz
Participation
Class Discussion
Study Guide
Unit Test
Resources Books, articles,
text, etc.
x?file=geometry_coor
dmidpoint.xml
http://regentsprep.org/r
egents/math/geometry/
GCG2/Lmidpoint.htm
Textbook: 1-8 p.53
http://www.teachersch
oice.com.au/maths_lib
rary/analytical%20geo
metry/alg_15.htm
Textbook: 1-9 p.61
http://hotmath.com/hel
p/gt/genericalg1/sectio
n_8_5.html
Check Point Quiz
Participation
Class Discussion
Study Guide
Textbook: p.69
Graphing Calculator
http://colalg.math.csus
b.edu/~devel/precalcd
emo/conics/src/parabol
a.html
http://www.brightstor
m.com/math/algebra-
Content Area: Geometry
Coordinates
Target Course/Grade level: 10
Unit Title: Connecting Algebra and Geometry through
Essential Questions: How do we Connect Algebra and Geometry through Coordinates?
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Parabolas: Finding the Equation from
Information
http://www.purplemath.com/modules/par
abola3.htm
http://www.physicsforums.com/showthre
ad.php?t=69327
http://www.valleyview.k12.oh.us/vvhs/d
ept/math/agparabhelp.html
54
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
2/quadratic-equationsand-inequalities/focusand-directrix-of-aparabola/
Content Area: Geometry
Target Course/Grade level: 10
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
segment of learning, students will…
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
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
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.



G.C.3
Construct the inscribed and circumscribed
circles of a triangle,
and prove properties of angles for a
quadrilateral inscribed in a circle.
Resources Books, articles,
text, etc.
Formative and
Summative measures

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
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.


Geometer’s Sketchpad
http://mstudley.com/
geosketch/geosketcha
ndcirclespt2.pdf
http://archives.math.
utk.edu/ICTCM/VO
L16/C020/paper.html
Student response
in class.
Worksheet on
material
presented.



Geometer’s Sketchpad
http://www.nvcc.edu/
home/tstreilein/const
ructions/Inscribed/in
scribe2.htm
Content Area: Geometry
Target Course/Grade level: 10
Unit Title: Circles With and Without Coordinates
Essential Questions: Essential Questions: How do we explore Circles With and Without Coordinates?
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
Construct a tangent line from a point
outside a given circle to the circle.
experiences that will facilitate engagement and
achievement
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.
G.C.4 (+)
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.
[Type text]
Activity: Students will use Geometer’s
Sketchpad to create tangent lines to given
circles.
text, etc.

Quiz on material
presented.

Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.


Geometer’s Sketchpad
http://mstudley.com/
geosketch/geosketcha
ndcirclespt2.pdf
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.


Geometer’s Sketchpad
http://jwilson.coe.uga
.edu/EMAT6680Fa08
/Wisdom/EMAT6690
/Circles%20And%20
Spheres/Circles%20a
nd%20SpheresUnit.htm
Student response
in class.
Questions from
textbook.
Quiz on material

12.5 – Circles in the
Coordinate plane, pg.
695.

Worksheets




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
Resources Books, articles,
Formative and
Summative measures

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.
G.C.5
Evidence of
Learning
Lessons and Activities The learning



Content Area: Geometry
Target Course/Grade level: 10
Unit Title: Circles With and Without Coordinates
Essential Questions: Essential Questions: How do we explore Circles With and Without Coordinates?
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
Evidence of
Learning
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
Resources Books, articles,
text, etc.
Formative and
Summative measures
presented.
show that measured area is the same as
ones they derived themselves.
G.GPE.1
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).
G.GPE.1
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 geometric shapes, their measures, and
their properties to
describe objects (e.g., modeling a tree trunk
or a human torso as a cylinder).*
G.MG.1
[Type text]





Activity: Students will use the
Geometer’s Sketchpad to create figures
with given coordinates. They will then
use the distance formula and slopintercept form of a line to prove lines are
perpendicular, thus being able to define
the given shape algebraically.

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://go.hrw.com/re
sources/go_mt/ca/c2
/c2_8-7tl.pdf

Geometer’s Sketchpad
Content Area: Geometry
Target Course/Grade level: 10
Unit Title: Circles With and Without Coordinates
Essential Questions: Essential Questions: How do we explore Circles With and Without Coordinates?
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
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.
[Type text]
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.
Content Area: Geometry
Target Course/Grade level: 10
Unit Title: Circles With and Without Coordinates
Essential Questions: Essential Questions: How do we explore Circles With and Without Coordinates?
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
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”).
S.CP.1
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.
S.CP.2
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.
S.CP.3
S.CP.4 Construct and interpret two-way
frequency tables of data when
[Type text]
Evidence of
Learning
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
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.”




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.
Resources Books, articles,
text, etc.
Formative and
Summative measures




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
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
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.

http://www.mathgoodi
es.com/lessons/vol6/in
dependent_events.html

http://www.mathgoodi
es.com/lessons/vol6/co
nditional.html

http://office.microsoft.
Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.
Student generated
frequency tables
and interpretation
Content Area: Geometry
Target Course/Grade level: 10
Unit Title: Circles With and Without Coordinates
Essential Questions: Essential Questions: How do we explore Circles With and Without Coordinates?
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
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.
S.CP.4
experiences 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.
[Type text]
Resources Books, articles,
text, etc.
Formative and
Summative measures
of data.
show that conditional probability can
change outcomes of events if the cards
are common.
com/en-us/excelhelp/explorehistogramsHA001110948.aspx
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.
S.CP.5
Evidence of
Learning
Lessons and Activities The learning



Lesson: Class discussion about the
difference between conditional
statements. Change of having cancer


Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.
Student response
in class.
Worksheet on

Statistics textbook –
pg 169-173
Content Area: Geometry
Target Course/Grade level: 10
Unit Title: Circles With and Without Coordinates
Essential Questions: Essential Questions: How do we explore Circles With and Without Coordinates?
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
Evidence of
Learning
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
being a smoker is different then being a
smoker and having cancer. Show
differences using charts and graphs.

S.CP.6
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 be given decks

of cards and asked to draw cards at
random. They will do this with an
without replacement. Each time, they
Apply the general Multiplication Rule in a
will be asked to find the probability that
uniform probability
model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), their card was drawn. We will use this to

show that conditional probability can
and interpret the answer
in terms of the model.
change outcomes of events if the cards

are common.
S.CP.7

S.CP.8 (+)
[Type text]
Use permutations and combinations to
compute probabilities of compound events
and solve problems.
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.
Resources Books, articles,
text, etc.
Formative and
Summative measures


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.
Student response
in class.
Worksheet on
material
presented.

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

http://www.mathsisfun
Content Area: Geometry
Target Course/Grade level: 10
Unit Title: Circles With and Without Coordinates
Essential Questions: Essential Questions: How do we explore Circles With and Without Coordinates?
Standards/
CPI’s
S.CP.9 (+)
Unit Learning Targets As a result of this
segment of learning, students will…
Use probabilities to make fair decisions (e.g.,
drawing by lots,
using a random number generator).
experiences that will facilitate engagement and
achievement
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.
Analyze decisions and strategies using
probability concepts (e.g., product testing,
medical testing, pulling a hockey goalie at
the end
of a game).
S.MD.6 (+)
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 2-12. After, they will use this to
Resources Books, articles,
text, etc.
Formative and
Summative measures

Quiz on material
presented.

Worksheet on
material.
Quiz on material
presented.


S.MD.7 (+)
[Type text]
Evidence of
Learning
Lessons and Activities The learning


Student response
in class.
Worksheet on
material
presented.
Quiz on material
presented.
.com/combinatorics/co
mbinationspermutations.html

http://www.random.or
g/

Statistics textbook –
pgs. 387-407
Content Area: Geometry
Target Course/Grade level: 10
Unit Title: Circles With and Without Coordinates
Essential Questions: Essential Questions: How do we explore Circles With and Without Coordinates?
Standards/
CPI’s
Unit Learning Targets As a result of this
segment of learning, students will…
Lessons and Activities The learning
experiences that will facilitate engagement and
achievement
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.
[Type text]
Evidence of
Learning
Formative and
Summative measures
Resources Books, articles,
text, etc.