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Curriculum and Instruction – Mathematics
Quarter 4
GEOMETRY
Introduction
In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is
committed to these goals, as further described in our strategic plan, Destination2025. By 2025,
 80% of our students will graduate from high school college or career ready
 90% of students will graduate on time
 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity
In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready aligned instruction. The
Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and career readiness
is rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in
mathematics instruction: focus, coherence and rigor.
Focus
Coherence
Rigor
• The Standards call for a greater focus in mathematics. Rather
than racing to cover topics in a mile-wide, inch-deep curriculum,
the Standards require us to significantly narrow and deepen the
way time and energy is spent in the math classroom. We focus
deeply on the major work of each grade so that students can
gain strong foundations: solid conceptual understanding, a high
degree of procedural skill and fluency, and the ability to apply the
math they know to solve problems inside and outside the math
classroom.
• For geometry, the major clusters, account for 65% of time
spent on instruction.
• Supporting Content - information that supports the
understanding and implementation of the major work of the
grade.
• Additional Content - content that does not explicitly connect to
the major work of the grade yet it is required for proficiency.
• Thinking across grades:
• The TN Standards are designed around coherent
progressions from grade to grade. Learning is carefully
connected across grades so that students can build new
understanding on to foundations built in previous years.
Each standard is not a new event, but an extension of
previous learning.
• Linking to major topics:
• Instead of allowing additional or supporting topics to
detract from the focus of the grade, these concepts serve
the grade level focus. For example, instead of data
displays as an end in themselves, they are an opportunity
to do grade-level word problems.
• Conceptual understanding:
• The TN Standards call for conceptual understanding of
key concepts. Students must be able to access concepts
from a number of perspectives so that they are able to
see math as more than a set of mnemonics or discrete
procedures.
• Procedural skill and fluency:
• The Standards call for speed and accuracy in calculation.
While high school standards for math do not list high
school fluencies, there are fluency standards for algebra
1, geometry, and algebra 2..
• Application:
• The Standards call for students to use math flexibly for
applications in problem-solving contexts. In content areas
outside of math, particularly science, students are given
the opportunity to use math to make meaning of and
access content.
Major Content
 Supporting Content

Additional Content
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Curriculum and Instruction – Mathematics
Quarter 4
8. Look for and
express regularity
in repeated
reasoning
1. Make sense of
problems and
persevere in
solving them
2. Reason
abstractly and
quatitatively
Mathematical
Practices(MP)
7. Look for and
make use of
structure
GEOMETRY
6. Attend to
precision
3. Construct viable
arguments and
crituqe the
reasoning of
others
4. Model with
mathematics
5. Use appropriate
tools strategically
The Standards for Mathematical Practice describe varieties of expertise, habits of minds and
productive dispositions that mathematics educators at all levels should seek to develop in
their students. These practices rest on important National Council of Teachers of
Mathematics (NCTM) “processes and proficiencies” with longstanding importance in
mathematics education. Throughout the year, students should continue to develop
proficiency with the eight Standards for Mathematical Practice.
This curriculum map is designed to help teachers make effective decisions about what
mathematical content to teach so that, ultimately our students, can reach Destination 2025.
To reach our collective student achievement goals, we know that teachers must change their
practice so that it is in alignment with the three mathematics instructional shifts.
Throughout this curriculum map, you will see resources as well as links to tasks that will
support you in ensuring that students are able to reach the demands of the standards in your
classroom. In addition to the resources embedded in the map, there are some high-leverage
resources around the content standards and mathematical practice standards that teachers
should consistently access:
The TN Mathematics Standards
The Tennessee Mathematics Standards:
Teachers can access the Tennessee State standards, which are featured
https://www.tn.gov/education/article/mathematics-standards
throughout this curriculum map and represent college and career ready
learning at reach respective grade level.
Standards for Mathematical Practice
Mathematical Practice Standards
Teachers can access the Mathematical Practice Standards, which are
https://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view featured throughout this curriculum map. This link contains more a more
detailed explanation of each practice along with implications for instructions.
Major Content
 Supporting Content

Additional Content
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GEOMETRY
Purpose of the Mathematics Curriculum Maps
This curriculum framework or map is meant to help teachers and their support providers (e.g., coaches, leaders) on their path to effective, college and career ready
(CCR) aligned instruction and our pursuit of Destination 2025. It is a resource for organizing instruction around the TN State Standards, which define what to teach
and what students need to learn at each grade level. The framework is designed to reinforce the grade/course-specific standards and content—the major work of the
grade (scope)—and provides a suggested sequencing and pacing and time frames, aligned resources—including sample questions, tasks and other planning tools.
Our hope is that by curating and organizing a variety of standards-aligned resources, teachers will be able to spend less time wondering what to teach and searching
for quality materials (though they may both select from and/or supplement those included here) and have more time to plan, teach, assess, and reflect with
colleagues to continuously improve practice and best meet the needs of their students.
The map is meant to support effective planning and instruction to rigorous standards; it is not meant to replace teacher planning or prescribe pacing or instructional
practice. In fact, our goal is not to merely “cover the curriculum,” but rather to “uncover” it by developing students’ deep understanding of the content and mastery of
the standards. Teachers who are knowledgeable about and intentionally align the learning target (standards and objectives), topic, task, and needs (and
assessment) of the learners are best-positioned to make decisions about how to support student learning toward such mastery. Teachers are therefore expected-with the support of their colleagues, coaches, leaders, and other support providers--to exercise their professional judgment aligned to our shared vision of effective
instruction, the Teacher Effectiveness Measure (TEM) and related best practices. However, while the framework allows for flexibility and encourages each
teacher/teacher team to make it their own, our expectations for student learning are non-negotiable. We must ensure all of our children have access to rigor—highquality teaching and learning to grade-level specific standards, including purposeful support of literacy and language learning across the content areas.
Additional Instructional Support
Shelby County Schools adopted our current math textbooks for grades 9-12 in 2010-2011. The textbook adoption process at that time followed the requirements set
forth by the Tennessee Department of Education and took into consideration all texts approved by the TDOE as appropriate. We now have new standards; therefore,
the textbook(s) have been vetted using the Instructional Materials Evaluation Tool (IMET). This tool was developed in partnership with Achieve, the Council of Chief
State Officers (CCSSO) and the Council of Great City Schools. The review revealed some gaps in the content, scope, sequencing, and rigor (including the balance of
conceptual knowledge development and application of these concepts), of our current materials.
The additional materials purposefully address the identified gaps in alignment to meet the expectations of the CCR standards and related instructional shifts while still
incorporating the current materials to which schools have access. Materials selected for inclusion in the Curriculum Maps, both those from the textbooks and
external/supplemental resources (e.g., engageny), have been evaluated by district staff to ensure that they meet the IMET criteria.
Major Content
 Supporting Content

Additional Content
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GEOMETRY
How to Use the Mathematics Curriculum Maps
Overview
An overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the
students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide some non-summative assessment items.
Tennessee State Standards
The TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a
key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards that
supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teacher’s
responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.
Content
Teachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related
best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, etc.).
Support for the development of these lesson objectives can be found under the column titled ‘Content’. The enduring understandings will help clarify the “big picture”
of the standard. The essential questions break that picture down into smaller questions and the objectives provide specific outcomes for that standard(s). Best
practices tell us that clearly communicating and making objectives measureable leads to greater student mastery.
Instructional Support and Resources
District and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks and
additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as needed for content
support and differentiation.
Major Content
 Supporting Content

Additional Content
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GEOMETRY
Topics Addressed in Quarter






Properties of Angles and Segments in Circles
Arc Length, Sector Area, and Equations of Circles
Use Coordinates to Prove Simple Geometric Theorems Algebraically
Volume of Solids
Visualizing Solids
Trigonometry with All Triangles
Overview
During the fourth quarter students continue their study of circles. They explore and apply the properties of angles and segments in circles including the intersection of two secants,
two tangents, two chords or a secant and a tangent. Then they find and apply arc length and area of sectors and write equations of circles and graph them in the coordinate plane.
Students use coordinates to prove simple geometric theorems algebraically and then students explain volume formulas and use them to solve problems in prisms, pyramids,
cylinders, cones and spheres. Students learn how to construct regular hexagons, squares, and triangles in circles. At this point, students have covered most of the content &
standards needed prior to the TNReady End of Course Exam. Since there are 3 to 4 weeks of class after the EOC exam, students will examine some additional content/standards.
Students will then spend some time reviewing and extending their understanding of surface area of solids. The year will conclude by studying law of sines and cosines to find
missing sides in any triangle, not just right triangles.
Year at a Glance Document
Content Standard
G-GPE.B.4
G-MG.A.1
G-MG.A.3
G-CO.D.12
G-CO.D.13
Type of Rigor
Conceptual Understanding
Conceptual Understanding & Application
Application
Procedural skill & fluency, Conceptual
Understanding & Application
Procedural skill & fluency, Conceptual
Understanding & Application
Foundational Standards
A-REI.B.4
8.G.A.1, 2,3, 4,5
8.G.A.5; 8.G.B.7
8.G.A. 2,3, 4,5
Sample Assessment Items
Illustrative: G-GPE.B.4 Tasks
Illustrative: G-MG.A.1 Tasks
Illustrative: G-MG.A.3 Tasks
Illustrative: G-CO.D.12 Tasks
8.G.A.2,3, 4,5
Illustrative: G-CO.D.13 Tasks
TNReady High School Assessment Blueprints
Geometry Practice Test
Major Content
 Supporting Content
(you must login to your EdTools account)

Additional Content
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GEOMETRY
Fluency
The high school standards do not set explicit expectations for fluency, but fluency is important in high school mathematics. Fluency in algebra can help students get
past the need to manage computational and algebraic manipulation details so that they can observe structure and patterns in problems. Such fluency can also allow
for smooth progress toward readiness for further study/careers in science, technology, engineering, and mathematics (STEM) fields. These fluencies are highlighted
to stress the need to provide sufficient supports and opportunities for practice to help students gain fluency. Fluency is not meant to come at the expense of
conceptual understanding. Rather, it should be an outcome resulting from a progression of learning and thoughtful practice. It is important to provide the conceptual
building blocks that develop understanding along with skill toward developing fluency.
The fluency recommendations for geometry listed below should be incorporated throughout your instruction over the course of the school year.
 G-SRT.B.5
Fluency with the triangle congruence and similarity criteria
 G-GPE.B.4,5,7
Fluency with the use of coordinates
 G-CO.D.12
Fluency with the use of construction tools
References:




http://www.tn.gov/education/article/mathematics-standards
http://www.corestandards.org/
http://www.nctm.org/
http://achievethecore.org/
Major Content
 Supporting Content

Additional Content
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Curriculum and Instruction – Mathematics
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GEOMETRY
TN STATE STANDARDS
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Properties of Angles and Segments in Circles
(Allow approximately 1 week for instruction, review, and assessment)
Domain: G-C Circles
Cluster: Understand and apply theorems
about circles


G-C.A.2 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.
G-C.A.3 Construct the inscribed and
circumscribed circles of a triangle, and
prove properties of angles for a
quadrilateral inscribed in a circle.
Enduring Understanding(s)
All circles are similar and that relationships exist
between angles formed by radii, chords, secants
and tangents.
Essential Question(s)
How can the properties of circles, polygons,
lines and angles be useful when solving
geometric problems?
Objective(s):
Students will

Identify and describe relationships among
tangents and radii;
Domain: G-CO Congruence
Cluster: Make geometric constructions

Identify and describe relationships among
circumscribed angles and central angles;


Construct a tangent line from a point.
G-CO.D.12 Make formal geometric
constructions with a variety of tools and
methods (compass and straightedge,
string, reflective devices, paper folding,
dynamic geometric software, etc.).
Domain: G-CO Congruence
Cluster: Make geometric constructions

G-CO.D.12 Make formal geometric
constructions with a variety of tools and
methods (compass and straightedge,
string, reflective devices, paper folding,
dynamic geometric software, etc.).
Domain: G-CO Congruence
Major Content
Enduring Understanding(s)
All circles are similar and that relationships exist
between angles formed by radii, chords, secants
and tangents.
Essential Question(s)
 Supporting Content
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry Module 5, Topic C,
Lesson 11: Properties of Tangents
Use the textbook resources to address
procedural skill and fluency.
Lesson 10.5 Tangents pp.718-725
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
Task(s)
Tangent Lines and the Radius of a Circle
Task
Vocabulary
Tangent, point of tangency, common tangent
Writing in Math/Discussion
How many tangents can be drawn from a point
outside a circle, from a point on a circle, and
from a point inside a circle? Explain your
reasoning.
GSE Analytic Geometry Unit 3: Circles and
Volume (select from the tasks)
Use the textbook resources to address
procedural skill and fluency.
Extend Lesson 10-5 Geometry Lab: Inscribed
and Circumscribed Circles, p. 726
Writing in Math/Discussion
Why is the term “incenter” a good term for the
intersection of the three angle bisectors?
Explain your reasoning.
Use geometry software or graphing calculator
such as TI-Nspire or the Cabri Jr. APP on the
TI-84 to investigate. A regular compass and

Additional Content
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Curriculum and Instruction – Mathematics
Quarter 4
GEOMETRY
TN STATE STANDARDS
Cluster: Make geometric constructions

G-CO.D.13 Construct an equilateral
triangle, a square, and a regular hexagon
inscribed in a circle
Domain: G-C Circles
Cluster: Understand and apply theorems
about circles

G-C.A.3 Construct the inscribed and
circumscribed circles of a triangle, and
prove properties of angles for a
quadrilateral inscribed in a circle.
Domain: G-C Circles
Cluster: Understand and apply theorems
about circles

G-C.A.2 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.
CONTENT
How can the properties of circles, polygons,
lines and angles be useful when solving
geometric problems?
Objective(s):
Students will

Construct an equilateral triangle, a square,
and a regular hexagon inscribed in a circle.

Construct the inscribed and circumscribed
circles of a triangle
Enduring Understanding(s)
All circles are similar and that relationships exist
between angles formed by radii, chords, secants
and tangents.
Essential Question(s)
 How can the properties of circles, polygons,
lines and angles be useful when solving
geometric problems?
Objective(s):
Students will

Find measures of angles formed by lines
intersecting on or inside a circle and
describe the relationships;

Find measures of angles formed by lines
intersecting outside the circle and describe
the relationships.
INSTRUCTIONAL SUPPORT & RESOURCES
straight edge can also be used.
ACT Practice
(sample problems to prepare for the ACT)
Glencoe, pp.692-693 & pp.774-775
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry Module 5, Topic C, Lesson
16: Similar Triangles in Circle-Secant (or
Circle-Secant-Tangent) Diagrams
Vocabulary
Secant
Ticket Out the Door
Select examples and ask students to name
the segments in the figure as they leave.
Use the textbook resources to address
procedural skill and fluency.
Lesson 10-6 Secants, Tangents, and Angle
Measures, pp. 727-735
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
Task(s)
Chords, Secants, and Tangents Tasks, pp. 56
& 69
GSE Analytic Geometry Unit 3: Circles and
Volume (select from the tasks)
Major Content
 Supporting Content

Additional Content
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Curriculum and Instruction – Mathematics
Quarter 4
GEOMETRY
TN STATE STANDARDS
Domain: G-C Circles
Cluster: Understand and apply theorems
about circles

G-C.A.2 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.
Domain: G-C Circles
Cluster: Understand and apply theorems
about circles

G-C.A.2 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.
CONTENT
Enduring Understanding(s)
All circles are similar and that relationships exist
between angles formed by radii, chords, secants
and tangents.
Use the textbook resources to address
procedural skill and fluency.
Lesson 10-7 Special Segments in Circles, pp.
736-742
Ask students to describe how the lesson on
secants, tangents, and angles (10-6)
helped them better understand the lesson
on special segments in a circle.
Objective(s):
Students will

Find measures of segments that intersect in
the interior of a circle and describe the
relationships;

Find measures of segments that intersect in
the exterior of a circle and describe the
relationships.
Enduring Understanding(s)
All circles are similar and that relationships exist
between angles formed by radii, chords, secants
and tangents.
Essential Question(s)
 How can the properties of circles, polygons,
lines and angles be useful when solving
geometric problems?
Objective(s):
Students will
Find measures of angles formed by lines
intersecting on or inside a circle and
 Supporting Content
Vocabulary
Chord segment, secant, external secant
segment, tangent segment
Writing in Math/Discussion
Describe the relationship among segments
in a circle when two secants intersect inside
a circle.
Essential Question(s)
How can the properties of circles, polygons,
lines and angles be useful when solving
geometric problems?

Major Content
INSTRUCTIONAL SUPPORT & RESOURCES
Use the textbook resources to address
procedural skill and fluency.
Lesson 10-6 Secants, Tangents, and Angle
Measures, pp. 727-735
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
Task(s)
Chords, Secants, and Tangents Tasks, pp. 56
& 69
Writing in Math/Discussion
Explain how to find the measure of an angle
formed by a secant and a tangent that intersect
outside a circle.
GSE Analytic Geometry Unit 3: Circles and
Volume (select from the tasks)

Additional Content
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Curriculum and Instruction – Mathematics
Quarter 4
GEOMETRY
TN STATE STANDARDS
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
describe the relationships;

Find measures of angles formed by lines
intersecting outside the circle and describe
the relationships.
Arc Length, Sector Area, and Equations of Circles
(Allow approximately 1.5 weeks for instruction, review, and assessment)
Domain: G-C Circles
Cluster: Understand and apply theorems
about circles

G-C.A.2 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.
Domain: G-C Circles
Cluster: Find arc lengths and areas of sectors
of circles

G-C.B.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.
Domain: G-C Circles
Cluster: Find arc lengths and areas of sectors
Major Content
Enduring Understanding(s)
The properties of polygons, lines, and angles
can be used to understand circles; the
properties of circles can be used to solve
problems involving polygons, lines and angles.
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry Module 5, Topic A,
Lesson 4; Experiments with Inscribed Angles
Essential Question(s)
How can the properties of circles, polygons,
lines and angles be useful when solving
geometric problems?
Use the textbook resources to address
procedural skill and fluency.
Lesson 10-2 – Measuring Angles and Arcs, pp.
692-700
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
Task(s)
Circles and Spheres Tasks
Circles and their Relationships among Central
Angles, Arcs and Chords Task , p.15
Investigating Angle Relationships in Circles
Tasks, p. 46 & p.52
Objective(s):
Students will

Derive and apply the formula for arc
length;

Derive the fact that the length of the arc
intercepted by an angle is proportional to
the radius;

Define and apply radian measure.

Explore the relationship between inscribed
angles and central angles and their
intercepted arcs.
Enduring Understanding(s)
The properties of polygons, lines, and angles
 Supporting Content
Use the following lesson(s) first to
introduce concepts/build conceptual

Additional Content
Vocabulary
Central angle, arc, minor arc, major arc,
semicircle, congruent arcs, adjacent arcs, arc
length
Writing in Math/Discussion
Describe the three different types of arcs in a
circle and the method for finding the measure of
each one.
Vocabulary
Sector of a circle, segment of a circle
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Curriculum and Instruction – Mathematics
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GEOMETRY
TN STATE STANDARDS
of circles

G-C.B.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.
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
can be used to understand circles; the
properties of circles can be used to solve
problems involving polygons, lines and angles.
understanding.
engageny Geometry Module 3, Topic A,
Lesson 4
Essential Question(s)
How can the properties of circles, polygons,
lines and angles be useful when solving
geometric problems?
Use the textbook resources to address
procedural skill and fluency.
Lesson 11-3 – Areas of Circles, pp.782 788
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
Task(s)
Arc Length and Area of Sector Tasks, p. 82 &
p.91
Grain Storage Task
Objective(s):
Students will

Derive a formula for the area of a
sector of a circle;

Find the area of circles and sectors of
circles.
Writing in Math/Discussion
If the radius of a circle doubles, will the
measure of a sector of that circle double? Will it
double if the arc measure of that sector
doubles?
Ticket Out the Door
Have students describe how to find the area of a
circle, given its circumference.
GSE Analytic Geometry Unit 3: Circles and
Volume (select from the tasks)
ACT Practice
(sample problems to prepare for the ACT)
Glencoe, pp.774-775
Domain: G-GPE Expressing Geometric
Properties with Equations
Cluster: Translate between the geometric
description and the equation for a conic
section

G-GPE.A.1 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.
Enduring Understanding(s)
The properties of polygons, lines, and angles
can be used to understand circles; the
properties of circles can be used to solve
problems involving polygons, lines and angles
Essential Question(s)
How can the properties of circles, polygons,
lines and angles be useful when solving
geometric problems?
Domain: G-GPE Expressing Geometric
Major Content
 Supporting Content
Use the textbook resources to address
procedural skill and fluency.
Lesson 10-8 – Equations of Circles and
Graphing Technology Lab 10.8 (using TINspire), pp.743 - 749
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.

Additional Content
Vocabulary
Compound locus
Writing in Math/Discussion
Describe how the equation for a circle changes
if the circle is translated a units to the right and
b units down.
Shelby County Schools 2016/2017
Revised 2/6/17
11 of 20
Curriculum and Instruction – Mathematics
Quarter 4
GEOMETRY
TN STATE STANDARDS
Properties with Equations
Cluster: Use coordinates to prove simple
geometric theorems algebraically

G-GPE.B.4 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).
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Objective(s):
Students will
HS Flip Book with examples of each
Standard

Derive the equation of a circle given
the center and the radius.
(Designed as a resource tool to assist teachers in deepening
their understanding of what each standard means in terms of
what students must know and be able to do.

Complete the square to find the center and
radius of a circle by an equation.
It outlines only a sample of instructional strategies and
examples. Links to conceptual categories and specific
standards in the document can be accessed from page 5
Mathematics Standards for High School.)
Task(s)
Equations of Circles Lesson
GSE Analytic Geometry Unit 3: Circles and
Volume (select from the tasks)
Use coordinates to prove simple geometric theorems algebraically
(Allow approximately 1 week for instruction, review, and assessment)
Domain: G-GPE Expressing Geometric
Properties with Equations
Cluster: Use coordinates to prove simple
geometric theorems algebraically
Enduring Understanding(s)
Geometric definitions, properties and theorems
allow one to describe, model, and analyze
situations in the real world.

G-GPE.B.4 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).
Domain: G-GPE Expressing Geometric
Properties with Equations
Cluster: Use coordinates to prove simple
geometric theorems algebraically
G-GPE.B.6 Find the point on a directed line
segment between two given points that
partitions the segment in a given ratio
Major Content
Essential Question(s)
How is coordinate algebra used when writing
geometric proofs?
Objective(s):
Students will
Find midpoints of segments and points that
divide segments into 3, 4, or more proportional,
equal parts.
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry, Module 4, Topic D
Lesson 12: Dividing Segments Proportionately
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
Task(s)
Scaling a Triangle in the Coordinate Plane
Partitioning Segments in the Coordinate Plane
Use the interactive resources to address
procedural skill and fluency.
Dividing Line Segments
 Supporting Content

Additional Content
Shelby County Schools 2016/2017
Revised 2/6/17
12 of 20
Curriculum and Instruction – Mathematics
Quarter 4
TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Expressing Geometric Properties with
Equations HSG-GPE.B.6
Volume of Solids
(Allow approximately 1.5 week for instruction, review, and assessment)t)
Domain: G-GMD Geometric Measurement
and Dimension
Cluster: Explain volume formulas and use them
to solve problems


Enduring Understanding(s)
Two- and three-dimensional objects with or
without curved surfaces can be described,
classified, and analyzed by their attributes.
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry, Module 3, Topic B
Lesson 5: Three-Dimensional Space
Lesson 6: General Prisms and Cylinders and
Their Cross-Sections
G-GMD.A.1 Give an informal
 Essential Question(s)
argument for the formulas for the
 In what ways do we use cones, cylinders,
circumference of a circle, area of a
spheres, right rectangular prisms, triangular
circle, volume of a cylinder, pyramid,
prisms in real-life?
and cone. Use dissection arguments,
Use the textbook resources to address
Cavalieri’s principle, and informal limit
 How do I find the surface area and volume procedural skill and fluency.
arguments.
of a three dimensional figure?
Lesson 12.4 pp. 847-854
G-GMD.A.3 Use volume formulas for
Use the following resources to deepen
Objective(s):
cylinders, pyramids, cones, and
students' conceptual understanding of
Students will
spheres to solve problems. ★
mathematical content and develop their
ability to apply that knowledge to non Find volumes of prisms and cylinders
routine problems.
in the context of the real world.
Writing in Math/Discussion
Write a helpful response to the following
questions posted on an Internet garden forum.
“I am new to gardening. The nursery will deliver
a truckload of soil, which they say is 4 yards. I
know that a yard is 3 feet, but what is a yard of
soil? How do I know what to order?”
Task(s)
How much money is that? (prism)
Centerpiece (cylinder)
Domain: G-GMD Geometric Measurement
and Dimension
Cluster: Explain volume formulas and use them
to solve problems

G-GMD.A.1 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,
Major Content
Enduring Understanding(s)
Geometric definitions, properties and theorems
allow one to describe, model, and analyze
situations in the real world.
Essential Question(s)
 In what ways do we use cones, cylinders,
spheres, right rectangular prisms, triangular
prisms in real-life?
 Supporting Content
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry, Module 3, Topic B
Lesson 8: Definition and Properties of Volume
Lesson 9: Scaling Principle for Volumes
Lesson 10: The Volume of Prisms and
Cylinders and Cavalieri’s Principle

Additional Content
Writing in Math/Discussion
Compare and contrast finding volumes of
pyramids and cones with finding volumes of
prisms and cylinders.
Shelby County Schools 2016/2017
Revised 2/6/17
13 of 20
Curriculum and Instruction – Mathematics
Quarter 4
TN STATE STANDARDS
Cavalieri’s principle, and informal limit
arguments.

G-GMD.A.3 Use volume formulas for
cylinders, pyramids, cones, and
spheres to solve problems. ★
Domain: G-GMD Geometric Measurement
and Dimension
Cluster: Explain volume formulas and use them
to solve problems


G-GMD.A.1 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.
G-GMD.A.3 Use volume formulas for
cylinders, pyramids, cones, and
spheres to solve problems. ★
Major Content
GEOMETRY
CONTENT

INSTRUCTIONAL SUPPORT & RESOURCES
How do I find the surface area and volume
of a three dimensional figure?
Use the textbook resources to address
procedural skill and fluency.
Lesson 12.5 pp. 857-863
Objective(s):
Use the following resources to deepen
Students will
students' conceptual understanding of
mathematical content and develop their

Understand the precise language that
ability to apply that knowledge to nondescribes the properties of volume.
routine problems.

Find volumes of pyramids and cones in the
Task(s)
context of the real world.
Doctors Appointment (cone)
Great Egyptian Pyramids (pyramid)
Enduring Understanding(s)
Geometric definitions, properties and theorems
allow one to describe, model, and analyze
situations in the real world.
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry, Module 3, Topic B
Lesson 11: The Volume Formula of a Pyramid
and Cone
Lesson 12: The Volume Formula of a Sphere
Essential Question(s)
 In what ways do we use cones, cylinders,
spheres, right rectangular prisms, triangular
prisms in real-life?
 How do I find the surface area and volume
of a three dimensional figure?
Use the textbook resources to address
procedural skill and fluency.
Objective(s):
Lesson 12.6 pp. 873-878
Students will

Understand the precise language that
describes the properties of volume.

Find and use volumes of spheres to solve
problems.
 Supporting Content
Vocabulary
great circle, pole, hemisphere
Writing in Math/Discussion
Write a ratio comparing the volume of a sphere
with radius r to the volume of a cylinder with
radius r and height 2r. Then describe what the
ratio means.
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
Task(s)
Guessing Gumballs Task

Additional Content
Shelby County Schools 2016/2017
Revised 2/6/17
14 of 20
Curriculum and Instruction – Mathematics
Quarter 4
GEOMETRY
TN STATE STANDARDS
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Visualizing Solids
(Allow approximately 3 weeks for instruction, review, and assessment)
Domain: G-MG Modeling with Geometry
Cluster: Apply geometric concepts in
modeling situations

G-MG.A.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). ★
Domain: G-GMD Geometric Measurement
and Dimension
Cluster: Visualize relationships between two‐
dimensional and three‐ dimensional objects

G-GMD.B.4 Identify the shapes of two‐
dimensional cross‐sections of three
dimensional objects, and identify three‐
dimensional objects generated by
rotations of two‐dimensional objects.
Enduring Understanding(s).
Geometric definitions, properties and theorems
allow one to describe, model, and analyze
situations in the real world.
Essential Question(s)
In what ways, can geometric figures be used to
understand real-world problems?
Objective(s):
Students will

Investigate cross sections of threedimensional figures.
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry, Module 3, Topic B
Lesson 7: General Pyramids and Cones and
Their Cross-Sections
Use the textbook resources to address
procedural skill and fluency.
Lesson 12-1 – Representations of ThreeDimensional Figures, Lesson pp. 823-828
Vocabulary
Isometric view, cross section
Writing in Math/Discussion
When an object on a video game is viewed
from only one side, what are some ways that
the object can be made to appear threedimensional?
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
HS Flip Book with examples of each
Standard
(Designed as a resource tool to assist teachers in deepening
their understanding of what each standard means in terms of
what students must know and be able to do.
It outlines only a sample of instructional strategies and
examples. Links to conceptual categories and specific
standards in the document can be accessed from page 5
Mathematics Standards for High School.)
Task(s)
Volumes of Cylinders, Cones, Pyramids, and
Spheres Videos
Volumes of Cylinders, Cones, Pyramids, and
Spheres Task, p.98
Unit on Area, Perimeter, and Volume with
multiple tasks

Major Content
 Supporting Content
Boxing Basketballs p.5

Additional Content
Shelby County Schools 2016/2017
Revised 2/6/17
15 of 20
Curriculum and Instruction – Mathematics
Quarter 4
TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES



Domain: G-MG Modeling with Geometry
Cluster: Apply geometric concepts in
modeling situations
 G-MG.A.3
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). ★
Enduring Understanding(s)
Geometric definitions, properties and theorems
allow one to describe, model, and analyze
situations in the real world.

G-MG.A.3 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). ★
Major Content
Walter and Juanita’s Water Troughs p.17
Greenhouse p.23
Use the textbook resources to address
procedural skill and fluency.
Lesson 12-2 – Surface Area of Prisms and
Cylinders, pp.830-837
Use the following resources to deepen
 In what ways, can geometric figures be students' conceptual understanding of
mathematical content and develop their
used to understand real-world
ability to apply that knowledge to nonproblems?
routine problems.
 How do surface volume and area
HS Flip Book with examples of each
compare to each other?
Standard
Objective(s):
Task(s)
Students will
 Find the lateral area and surface area of Cereal Box Project (Surface Area & Volume)
Tasks
prisms to solve problems.
Essential Question(s)

Domain: G-MG Modeling with Geometry
Cluster: Apply geometric concepts in
modeling situations
Great Pyramid p.13
Vocabulary
Lateral face, lateral edge, base edge, altitude,
height, lateral area, axis, composite solid
Writing in Math/Discussion
Compare and contrast finding the surface area
of a prism and finding the surface area of a
cylinder.
Find the lateral area and surface area of
cylinders to solve problems.
Enduring Understanding(s)
Geometric definitions, properties and theorems
allow one to describe, model, and analyze
situations in the real world.
Essential Question(s)

In what ways, can geometric figures be
used to understand real-world problems?

How do surface volume and area compare
to each other?
 Supporting Content
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny -Lessons 23–24: The Volume of a
Right Prism
Lessons 25–26: Volume and Surface Area
Use the textbook resources to address
procedural skill and fluency.
Lesson 12-3 – Surface Area of Pyramids and
Cones, pp.838-846

Additional Content
Vocabulary
Regular pyramid, slant height, right cone,
oblique cone
Writing in Math/Discussion
p. 845, #41 Describe how to find the surface
area of a regular polygonal pyramid with an ngon base, height h units and an apothem of a
units.
Shelby County Schools 2016/2017
Revised 2/6/17
16 of 20
Curriculum and Instruction – Mathematics
Quarter 4
GEOMETRY
TN STATE STANDARDS
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Objective(s):
Students will
Domain: G-MG Modeling with Geometry
Cluster: Apply geometric concepts in
modeling situations

G-MG.A.3 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). ★

Find the lateral area and surface area of
pyramids to solve problems.

Find the lateral area and surface area of
cones to solve problems.
Enduring Understanding(s)
Geometric definitions, properties and theorems
allow one to describe, model, and analyze
situations in the real world.
Essential Question(s)

In what ways, can geometric figures be
used to understand real-world problems?

How do surface volume and area compare
to each other?
Objective(s):
Students will

Use the textbook resources to address
procedural skill and fluency.
Lesson 12-6 – Surface Areas of Spheres,
pp.864-871
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
Vocabulary
Great circle, pole, hemisphere
Writing in Math/Discussion
Describe the difference between the surface
area of a sphere and the volume of a sphere.
HS Flip Book with examples of each
Standard
Find the surface area of a sphere to solve
problems
Trigonometry with All Triangles
(Allow approximately 1 week for instruction, review, and assessment)t)
(Advanced Algebra & Trigonometry)
Domain: A-AT.1 Applied Trigonometry
Cluster: Use trigonometry to solve problems
 G-AT.A.5. Understand and apply the
Law of Sines (including the ambiguous
case) and the Law of Cosines to find
unknown measurements in right and
non-right triangles (e.g., surveying
problems, resultant forces).
Major Content
Enduring Understanding(s).
Dilations, similarity, and the properties of similar
triangles allow for the application of
trigonometric ratios to solve real-world
situations.
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry Module 2, Topic E,
Lesson 30
Essential Question(s)
Use the textbook resources to address
How can the Law of Sines and Cosines be used procedural skill and fluency.
to solve problems involving non-right triangles? Lesson 8-6 – The Law of Sines and Cosines
 Supporting Content

Additional Content
Vocabulary
Law of Sines, Law of Cosines
Writing in Math/Discussion
Draw and label a triangle that can be solved: a.
using only the Law of Sines; b. using only the
Law of Cosines. Explain why each triangle
cannot be solved using the other Law.
Shelby County Schools 2016/2017
Revised 2/6/17
17 of 20
Curriculum and Instruction – Mathematics
Quarter 4
GEOMETRY
TN STATE STANDARDS
CONTENT
Objective(s):
Students will

Derive a trigonometric formula for the area
of a triangle

Prove and apply the Law of Sines;

Prove and apply the Law of Cosines.
INSTRUCTIONAL SUPPORT & RESOURCES
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
Task(s)
Right Triangle Trigonometry Tasks
Students explore the relationships that exist
among and between sides and angles of right
triangles. They build upon their previous
knowledge of similar triangles and of the
Pythagorean Theorem to determine the side
length ratios in special right triangles and to
understand the conceptual basis for the
functional ratios sine, cosine, and tangent.
They explore how the values of these
trigonometric functions relate in
complementary angles and how to use these
trigonometric ratios to solve problems.
Through the work with these eight tasks,
students not only develop the skills and
understanding needed for the study of many
technical areas but also build a strong
foundation for future study of trigonometric
functions.
Major Content
 Supporting Content

Additional Content
Shelby County Schools 2016/2017
Revised 2/6/17
18 of 20
Curriculum and Instruction – Mathematics
Quarter 4
GEOMETRY
RESOURCE TOOLBOX
The Resource Toolbox provides additional support for comprehension and mastery of subject-level skills and concepts. While some of these resources are embedded in the map, the use of these categorized materials can assist educators with
maximizing their instructional practices to meet the needs of all students.
Textbook Resources
Standards
ConnectED Site - Textbook and Resources Glencoe
Video Lessons
Hotmath - solutions to odd problems
Common Core Standards - Mathematics
Common Core Standards - Mathematics Appendix A TN Core
HS Flip Book with Examples of each Standard
Comprehensive Geometry Help:
Online Math Learning (Geometry)
I LOVE MATH
NCTM Illuminations
New Jersey Center for Teaching & Learning (Geometry)
(Designed as a resource tool to assist teachers in deepening their understanding of what each standard
means in terms of what students must know and be able to do.
It outlines only a sample of instructional strategies and examples. Links to conceptual
categories and specific standards in the document can be accessed from page 5 Mathematics
Standards for High School.)
https://www.livebinders.com/play/play?id=464831
http://www.livebinders.com/play/play?id=571735
NWEA MAP
Geometry Model Curriculum
http://www.ccsstoolbox.org/
http://insidemathematics.org/index.php/high-school-geometry
http://learnzillion.com/common_core/math/hs
http://www.livebinders.com/play/play/454480
North Carolina – Unpacking Common Core http://thegeometryteacher.wordpress.com/thegeometry-course/
Finding Your Way Around TI-83+ & TI-84+ (mathbits.com)
http://mathtermind.blogspot.com/2012/07/common-core- geometry.html
Utah Electronic School -Geometry
Major Content
Tasks
Edutoolbox (formerly TNCore) Tasks
Inside Math
Tasks
Mars Tasks
Dan Meyer's ThreeAct Math Tasks
NYC tasks
Illustrative Math Tasks
UT Dana Center
SCS Math Tasks
GSE Analytic Geometry Unit 2: Right Triangle
Trigonometry
GSE Analytic Geometry Unit 3: Circles and
Volume
http://www.azed.gov/azcommoncore/mathstandards/hsmath/
Calculator
Videos
Math TV Videos
The Teaching Channel
Khan Academy Videos (Geometry)
 Supporting Content

Additional Content
Resources:https://teach.mapnwea.org/assist/help_map/Applicat
ionHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in
and Click the Learning Continuum Tab – this resources will help
as you plan for intervention, and differentiating small group
instruction on the skill you are currently teaching. (Four Ways to
Shelby County Schools 2016/2017
Revised 2/6/17
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Curriculum and Instruction – Mathematics
Quarter 4
GEOMETRY
RESOURCE TOOLBOX
The Resource Toolbox provides additional support for comprehension and mastery of subject-level skills and concepts. While some of these resources are embedded in the map, the use of these categorized materials can assist educators with
maximizing their instructional practices to meet the needs of all students.
Ohio Common Core Resources
Impact Teaching with the Learning Continuum)
Texas Instruments Calculator Activity Exchange
Texas Instruments Math Nspired
STEM Resources
Casio Education for Teachers
*Graphing Calculator Note: TI tutorials are available through
Atomic Learning and also at the following link: Math Bits graphing calculator steps Some activities require calculator
programs and/or applications.
Use the following link to access FREE software for your MAC.
This will enable your computer and TI Calculator to
communicate: Free TI calculator downloads
Major Content
Chicago Public Schools Framework and Tasks
https://support.nwea.org/khanrit - These Khan
Academy lessons are aligned to RIT scores.
Mathy McMatherson Blog - Geometry in Common Core
ACT
TN ACT Information & Resources
ACT College & Career Readiness Mathematics Standards
Interactive Manipulatives
Literacy Resources
GeoGebra – Free software for dynamic math and science learning
Literacy Skills and Strategies for Content Area Teachers (Math,
p. 22)
NCTM Core Math Tools http://www.keycurriculum.com/products/sketchpad (Not free) Any activity
using Geometer’s Sketchpad can also be done with any software that allows construction of
figures and measurement, such as Cabri, Cabri Jr. on the TI-83 or 84 Plus,TI-92 Plus, or TINspire.
 Supporting Content

Additional Content
Glencoe Reading & Writing in the Mathematics Classroom
Graphic Organizers (9-12) (teachervision.com)
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Revised 2/6/17
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