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Curriculum and Instruction – Mathematics
Quarter 1
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 1
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 judgement 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 6-8 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, iReady lessons 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




Tools of Geometry
Reasoning & Proof
Transformations, Congruence & Similarity
Lines & Angles
Overview
Rotations, reflections, translations and congruency are developed experimentally in grade 8, and this experience is built upon in geometry, giving greater
attention to precise definitions and formal reasoning. Properties of lines and angles, triangles and parallelograms were investigated in Grades 7 and 8. In
geometry, these properties are revisited in a more formal setting, giving greater attention to precise statements of theorems and establishing these theorems
by means of formal reasoning. During this quarter students will develop the relationship between transformations and congruency. Students will study
Congruence (G-CO), namely experimenting with transformations in the plane, understanding congruence in terms of rigid motions, proving geometric
theorems, prove geometric theorems, and make geometric constructions with a variety of tools. Students will also use congruence and similarity criteria for
triangles to solve problems and to prove relationships (G-SRT). Additionally in this quarter, students will use coordinates to prove simple geometric theorems
algebraically (G-GPE).
Content Standard
G-CO.A.1,2,3,4,5
Type of Rigor
Procedural Skill and Fluency , Conceptual
Understanding & Application
Foundational Standards
8.G.A.1, 2,3, 4,5
G-CO.B.6, 7, 8
G-CO.C.9, 10
G-CO.D.12
G-GPE.B.4, 5
Conceptual Understanding & Application
Conceptual Understanding & Application
Conceptual Understanding & Application
Procedural Skill and Fluency
8.G.A.1, 2,3, 4,5
8.G.A.1, 2,3, 4,5
8.G.A.5; 8.EE.B.6
8.EE.B.6
Sample Assessment Items**
Defining Parallel Lines; Defining
Perpendicular Lines; Fixed Points of
Rigid Motion; C-CO.A.4 Tasks; GCO.A.5 Tasks
Hexagon Art; Parallelogram
G-CO.C.9 Tasks; G-CO.C.10 Tasks
G-CO.C.12 Tasks
Lucio’s Ride
** TN Tasks are available at http://www.edutoolbox.org/ and can be accessed by Tennessee educators with a login and password.
Major Content
 Supporting Content

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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TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Tools of Geometry
(Allow approximately 2 weeks for instruction, review, and assessment)
Domain: G-CO Congruence
Cluster: Experiment with transformations in
the plane

Cluster: G-CO.A.1 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.
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.).
Enduring Understanding(s)
Proving and applying congruence provides a
basis for modeling situations geometrically.
Essential Question(s)
In what ways can congruence be useful?
Objective(s):
• Students will explore and know precise
definitions of basic geometric terms.
• Students will identify the undefined notions
used in geometry (point, line, plane,
distance).
• Students will use tools and methods to
precisely copy a segment, copy an angle,
bisect a segment, and bisect an angle.
• Students will informally perform the
constructions listed above using string,
reflective devices, paper folding, and/or
dynamic geometric software.
Domain: G-CO Congruence
Enduring Understanding(s)
Cluster: Experiment with transformations in the Proving and applying congruence provides a
plane
basis for modeling situations geometrically.
 G-CO.A.1 Know precise definitions of
angle, circle, perpendicular line, parallel
Essential Question(s)
line, and line segment, based on the
Why are geometry and measurement important
undefined notions of point, line, distance
in the real world?
along a line, and distance around a
circular arc.
Objective(s):
•
Students will use a compass and
Major Content
 Supporting Content
Lesson 1-1 Points, Lines and Planes, pp. 5 – 13 Vocabulary
Undefined term, point, line, plane,
collinear, coplanar, intersection, definition,
Use the following resources to ensure that the
defined term, space
intended outcome and level of rigor of the
standards are met.
Include Vocabulary from 3.1 - parallel lines,
Task(s)
skew lines, parallel planes
Select appropriate task(s) from GSE Analytic
Geometry Unit 1: Similarity, Congruence and
Writing in Math
Proofs
Connect the words collinear and coplanar to
the prefix co-.
Additional Resource(s)
CCSS Flip Book with Examples of each Standard
Is it possible for two points on the surface of a
prism to be neither collinear nor coplanar?
Justify your answer.
Points, Lines, and Planes
(Interactive Notebook/Foldables)
Lesson 1.2 – Linear Measure and Precision, pp.
14 – 24
Constructing a Copy of a Line Segment p.17
Vocabulary
Line segment, betweeness of points, between,
congruent segments, construction
Use the following Engageny Lessons to
introduce the concepts/build conceptual
understanding. If used, these lessons should be
used before the lessons from the textbooks.
Discussion
Discuss the Ruler Postulate.
Additional Lesson(s):
Engageny Geometry Module 1, Topic A,
Lesson 1 – Construct an Equilateral Triangle

Additional Content
Writing in Math
Why is it important to have a standard of
measure? Refer to p. 14, and include an
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TN STATE STANDARDS
CONTENT
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.).
GEOMETRY
straightedge to draw a segment and use
a ruler to measure it.
Students will identify the tools
used in formal constructions.
Students will use tools and
methods to precisely copy a
segment, copy an angle, bisect a
segment, and bisect an angle.
Domain: G-CO Congruence
Enduring Understanding(s)
Cluster: Experiment with transformations in the •
Proving and applying congruence provides
plane
a basis for modeling situations
geometrically.
 G-CO.A.1 Know precise definitions of
angle, circle, perpendicular line, parallel
•
Algebra can be used to efficiently and
line, and line segment, based on the
effectively describe and apply geometric
undefined notions of point, line, distance
properties.
along a line, and distance around a
circular arc.
Essential Question(s)
Domain: G-CO Congruence
Why are the Distance and Midpoint Formulas
Cluster: Make geometric constructions
important in the real world?
 G-CO.D.12 Make formal geometric
constructions with a variety of tools and
Objective(s):
methods (compass and straightedge,
• Students will connect two points on a
string, reflective devices, paper folding,
coordinate plane to form a segment and use
dynamic geometric software, etc.).
the Distance Formula to find its length.
Domain: G-GPE Expressing Geometric
•
Students will find the midpoint of a
Properties with Equations
segment and in the coordinate plane.
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
Major Content
INSTRUCTIONAL SUPPORT & RESOURCES
 Supporting Content
advantage and disadvantage to the builders of
the pyramids.
Lesson 1.3 – Distance and Midpoint, pp. 25 – 35 Vocabulary
Distance, irrational number, midpoint, segment
bisector
Use the following resources to ensure that the
intended outcome and level of rigor of the
standards are met.
Task(s)
As the Crow Flies
Writing in Math
Compare the Distance and Midpoint Formulas.
Draw an example of each on a grid.
TN Task Arc, Geometry - Investigating
Coordinate Geometry and Its Use in Solving
Mathematical Problems
Task 1- My Point is That There Are Many Points!
Task 2 - The Distance Between Us
Task 3 - Will That Work for ANY Two Points?
Select appropriate tasks from GSE Analytic
Geometry Unit 1: Similarity, Congruence and
Proofs

Additional Content
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TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
disprove that the point (1,√3) lies on the
circle centered at the origin and
containing the point (0, 2).
Domain: G-CO Congruence
Enduring Understanding(s)
Cluster: Experiment with transformations in the Proving and applying congruence provides a
plane
basis for modeling situations geometrically
 G-CO.A.1 Know precise definitions of
Essential Question (s)
angle, circle, perpendicular line, parallel
How are number operations used to find and
line, and line segment, based on the
compare the measures of angles.
undefined notions of point, line, distance
along a line, and distance around a
Objective(s):
circular arc.
• Students will describe the characteristics,
Domain: G-CO Congruence
and identify angles, circles, perpendicular
Cluster: Make geometric constructions
lines, parallel lines, rays, and line segments.
 G-CO.D.12 Make formal geometric
• Students will use tools and methods
constructions with a variety of tools and
to precisely copy a segment, copy an
methods (compass and straightedge,
angle, bisect a segment, and bisect
string, reflective devices, paper folding,
an angle.
dynamic geometric software, etc.).
Lesson 1.4 – Angle Measure, pp. 36 – 45
Constructing a Copy of an Angle p. 39
Constructing an Angle Bisector p. 40
Vocabulary
Ray, angle, vertex, degree, right angle, acute
angle, obtuse angle
Use the following Engageny Lessons to
introduce the concepts/build conceptual
understanding. If used, these lessons should be
used before the lessons from the textbooks.
Writing in Math
Explain the prefix bi- when discussing segment
bisector.
Additional Lesson(s):
Geometry Module 1, Topic
A, Lesson 3 – Copy and Bisect and
Angle
Connect the word degree to the idea of
measurement.
Engageny
Use the following resources to ensure
that the intended outcome and level of
rigor of the standards are met.
Discuss the similarity between the Protractor
Postulate and the Ruler Postulate.
Task(s)
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
Bisecting an Angle Task
Domain: G-CO Congruence
Enduring Understanding(s)
Cluster: Experiment with transformations in the Proving and applying congruence provides a
plane
basis for modeling situations geometrically
 G-CO.A.1 Know precise definitions of
Essential Question(s)
angle, circle, perpendicular line, parallel
What are some real-life applications of
line, and line segment, based on the
congruence?
undefined notions of point, line, distance
along a line, and distance around a
Objective(s):
Major Content
 Supporting Content
Lesson 1.5 – Angle Relationships, pp. 46 – 55
Use the following Engageny Lessons to
introduce the concepts/build conceptual
understanding. If used, these lessons should be
used before the lessons from the textbooks.
Additional Lesson(s):
Geometry Module 1, Topic B,
Lesson 6 – Solve for Unknown Angles –
Engageny

Additional Content
Vocabulary
Adjacent angles, linear pair, vertical angles,
complementary angles, supplementary angles,
perpendicular
Writing in Math
Discuss the similarity between the postulates
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GEOMETRY
TN STATE STANDARDS
CONTENT
circular arc.
•
Domain: G-CO Congruence
Cluster: Make geometric constructions

•
Students will identify and use special
pairs of angles.
Students will identify perpendicular lines.
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.).
INSTRUCTIONAL SUPPORT & RESOURCES
Angles and Lines at a Point
for angles and the postulates for segments.
Use the following resources to ensure that the
intended outcome and level of rigor of the
standards are met.
Describe three different ways you can
determine that an angle is a right angle.
Task(s)
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
See the Teacher version of the Engageny lesson
which has a thorough graphic organizer of
previously learned angle facts.
Reasoning and Proof
(Allow approximately 2 weeks for instruction, review, and assessment)
Domain: G-CO Congruence
Cluster: Prove geometric theorems
 G.CO.C.9 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.
Enduring Understanding(s)
Proving and applying congruence provides a
basis for modeling situations geometrically
Domain: G-CO Congruence
Cluster: Prove geometric theorems
 G.CO.C.9 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
Enduring Understanding(s)
Proving and applying congruence provides a
basis for modeling situations geometrically
Major Content
Lesson 2.1 – Inductive Reasoning and
Conjecture, pp. 89 – 96
Vocabulary
Inductive reasoning, conjecture,
counterexample
Additional Resource(s)
Essential Question(s)
How do you use inductive reasoning to make a
conjecture?
CCSS Flip Book with Examples of each
Standard
Writing in Math
Consider the conjecture: If two points are
equidistant from a third point, then the three
points are collinear. Is this conjecture true or
false? If false, give a counterexample.
Lesson 2.3 – Conditional Statements, pp. 105 –
113
Lesson 2.3 Extension – Geometry Lab:
Biconditional Statements p. 114
Vocabulary
Conditional statement, if-then statement,
hypothesis, conclusion, related conditionals,
converse, inverse, contrapositive, logically
equivalent
Objective(s):
• Students will make conjectures based
on inductive reasoning.
• Students will find counterexamples.
Essential Question(s)
How can theorems help prove figures
congruent?
Writing in Math
Describe a relationship between a conditional,
Objective(s):
 Supporting Content

Additional Content
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TN STATE STANDARDS
are exactly those equidistant from the
segment’s endpoints.
GEOMETRY
CONTENT
its converse, its inverse, and its contrapositive.
• Students will analyze statements in if-then
form.
• Students will write converses,
inverses, and contrapositives.
• Students will write biconditional statements.
Domain: G-CO Congruence
Cluster: Prove geometric theorems
 G.CO.C.9 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.
Enduring Understanding(s)
Proving and applying congruence provides a
basis for modeling situations geometrically
Domain: G-CO Congruence
Cluster: Prove geometric theorems
 G.CO.C.9 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.
Enduring Understanding(s)
Proving and applying congruence provides a
basis for modeling situations geometrically
Major Content
INSTRUCTIONAL SUPPORT & RESOURCES
Lesson 2.5 – Postulates and Paragraph
Proofs, pp. 125-132
Essential Question(s)
How are the properties used in geometry helpful
in solving problems?
Vocabulary
Postulate, axiom, proof, theorem, deductive
reasoning, paragraph proof, informal proof
Writing in Math
Explain how undefined terms, definitions,
postulates, and theorems are alike and how are
they different.
Objective(s):
•
Students will identify and use the
properties of congruence and equality in
proofs.
•
Students will interpret geometric diagrams
by identifying what can and cannot be
assumed.
Lesson 2.6 – Algebraic Proof, pp. 134-141
Essential Question(s)
How can information, definitions, postulate,
properties and theorems helpful in writing
proofs?
Writing in Math
Compare and contrast informal or paragraph
proofs with formal or two-column proofs. Which
type of proof do you find easier to write? Justify
your answer.
Objective(s):
•
Students will use algebra to write two –
 Supporting Content
Vocabulary
Algebraic proof, two-column proof, formal
proof

Additional Content
Shelby County Schools 2016/2017
Revised 6/27/16
11 of 20
Curriculum and Instruction – Mathematics
Quarter 1
TN STATE STANDARDS
GEOMETRY
CONTENT
•
INSTRUCTIONAL SUPPORT & RESOURCES
column proofs.
Students will use properties of equality to
write geometric proofs.
Transformations and Congruence;
Transformations and Symmetry
(Allow approximately 3 weeks for instruction, review, and assessment)
Domain: G-CO Congruence
Cluster: Understand congruence in terms of
rigid motion
 G-CO.B.7 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.
Enduring Understanding(s)
Proving and applying congruence provides a
basis for modeling situations geometrically
Lesson 4.3 – Congruent Triangles, pp. 253 –
261
Teaching Resource for this section (Lesson
1.2 in document)
Vocabulary
Congruent, congruent polygons, corresponding
parts
Essential Question(s)
•
How do you identify corresponding parts of
congruent triangles?
Use the following resources to ensure that the
intended outcome and level of rigor of the
standards are met.
Writing in Math
Determine whether the following statement is
always, sometimes, or never true. Explain your
reasoning.
Equilateral triangles are congruent.
•
How do you show that two triangles are
congruent?
Task(s)
TN Geometry Instructional TaskComparing Shapes
Objective(s):
•
Students will identify corresponding sides
and corresponding triangles of congruent
triangles.
•
Students will explain that in a pair of
congruent triangles, corresponding sides
are congruent (distance is preserved) and
corresponding angles are congruent
(angle measure is preserved).
Domain: G-CO Congruence
Enduring Understanding(s)
Cluster: Experiment with transformations in the Proving and applying congruence provides a
plane
basis for modeling situations geometrically
 G.CO.A.2 Represent transformations in
the plane using, e.g., transparencies and
Essential Question(s)
geometry software; describe
Major Content
 Supporting Content
Lesson 4.7 –Congruence Transformations, pp.
294 – 295
Use the following Engageny Lessons to
introduce the concepts/build conceptual
understanding. If used, these lessons should be

Additional Content
Vocabulary
Transformation, preimage, image, congruence
transformation, isometry, reflection, translation,
rotation
Shelby County Schools 2016/2017
Revised 6/27/16
12 of 20
Curriculum and Instruction – Mathematics
Quarter 1
TN STATE STANDARDS
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).
GEOMETRY
CONTENT
What are rigid motions and how can they be
defined?
Objective(s):
•
Students will identify reflections,
translations, and rotations.
•
Students will define rigid motions as
reflections, rotations, translations, and
combinations of these, all of which
preserve distance and angle measure.
•
Students will define congruent
figures as figures that have the
same shape and size and state that
a composition of rigid motions will
map one congruent figure onto the
other.
Domain: G-CO Congruence
Enduring Understanding(s)
Cluster: Experiment with transformations in the Proving and applying congruence provides a
plane
basis for modeling situations geometrically.
 G-CO.A.4 Develop definitions of rotations,
reflections, and translations in terms of
Essential Question(s)
angles, circles, perpendicular lines, parallel
How can you represent a transformation in the
lines, and line segments.
coordinate plane?
Objective(s):
•
Students will construct the reflection
definition by connecting any point on the
pre-image to is corresponding parts on
the reflected image and describe the line
segment’s relationship to the line of
reflection (i.e., the line of reflection is the
perpendicular bisector of the segment).
Major Content
 Supporting Content
INSTRUCTIONAL SUPPORT & RESOURCES
used before the lessons from the textbooks.
Additional Lesson(s):
ny
Engage Geometry Module 1, Topic C,
Lesson 12 – Transformations—The Next
Level
Engageny Geometry Module 1, Topic C,
Lesson 16 – Translations
Lessons 9.1 –Reflections, pp. 615 – 623
Use the following Engageny Lessons to
introduce the concepts/build conceptual
understanding. If used, these lessons should be
used before the lessons from the textbooks.
Additional Lesson(s)
Geometry Module 1, Topic C,
Lesson 14 – Reflections
Writing in Math
Explain the prefix pre- when discussing preimage.
Explain, give an example and write the rules
for the translations and nonrigid motion
transformation on a coordinate plane of a
reflection, a translation, a rotation and a
nonrigid motion transformation.
Vocabulary
Line of reflection
Writing in Math
Describe how to reflect a coordinate figure not
on a plane across a line.
Engageny
Use the following resources to ensure that the
intended outcome and level of rigor of the
standards are met.
Task(s)
TN Task Arc, Geometry -Investigating
Congruence in Terms of Rigid Motion
Task 3 – Reflect on This
(Use patty paper to differentiate for struggling
learners.)

Additional Content
Shelby County Schools 2016/2017
Revised 6/27/16
13 of 20
Curriculum and Instruction – Mathematics
Quarter 1
TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Task: Introduction to Reflections,
Translations, and Rotations
Translations, Reflections and Rotations
Domain: G-CO Congruence
Enduring Understanding(s)
Cluster: Experiment with transformations in the Proving and applying congruence provides a
plane
basis for modeling situations geometrically.
 G-CO.A.4 Develop definitions of
rotations, reflections, and translations in
Essential Question(s)
terms of angles, circles, perpendicular
How can you represent a transformation in the
lines, parallel lines, and line segments.
coordinate plane?
Lesson 9.2 –Translations, pp. 624 – 631
Use the following resources to ensure that the
intended outcome and level of rigor of the
standards are met.
Task(s)
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
Objective(s):
Students will construct the translation definition
by connecting any point on the pre-image to its
corresponding point on the translated image,
and connecting a second point on the preimage to its corresponding point on the
translated image, and describe how the two
segments are equal in length, point in the same
direction, and are parallel.
Domain: G-CO Congruence
Enduring Understanding(s)
Cluster: Experiment with transformations in the Proving and applying congruence provides a
plane
basis for modeling situations geometrically.
 G-CO.A.4 Develop definitions of
rotations, reflections, and translations in
Essential Question(s)
terms of angles, circles, perpendicular
How can you represent a transformation in the
lines, parallel lines, and line segments.
coordinate plane?
Objective(s):
Students will construct rotation definition by
connecting the center of rotation to any point
Major Content
 Supporting Content
Vocabulary
Translation vector
Writing in Math
Compare and contrast a translation and a
reflection.
Describe what a vector is and how it is used to
define a translation.
Describe any similarities between the meaning
of translation as it us used in geometry and
the word’s meaning when used to describe the
process of converting words from one
language to another.
Lesson 9.3 – Rotations, pp. 632 - 638
Lesson 9.3 Explore – Geometry Lab:
Rotations p. 631
Use the following Engageny Lessons to
introduce the concepts/build conceptual
understanding. If used, these lessons should be
used before the lessons from the textbooks.
Vocabulary
Center of rotation, angle of rotation
Writing in Math
Use a graphic organizer to keep track of the
types of transformations and their properties in
a sequence of transformations.
Additional Lesson(s)
Engageny Geometry Module 1, Topic C,
Lesson 13 – Rotations

Additional Content
Shelby County Schools 2016/2017
Revised 6/27/16
14 of 20
Curriculum and Instruction – Mathematics
Quarter 1
TN STATE STANDARDS
GEOMETRY
CONTENT
on the pre-image and to its corresponding
point on the rotated image, and describe the
measure of the angle formed and the equal
measures of the segments that formed the
angles part of the definition.
INSTRUCTIONAL SUPPORT & RESOURCES
Use the following resources to ensure that the
intended outcome and level of rigor of the
standards are met.
Task(s)
TN Task Arc, Geometry -Investigating
Congruence in Terms of Rigid Motion
Task 2: Twisting Triangles
(Use patty paper to differentiate for struggling
learners.)
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
Domain: G-CO Congruence
Enduring Understanding(s)
Cluster: Experiment with transformations in the Proving and applying congruence provides a
plane
basis for modeling situations geometrically.
 G-CO.A.5 Given a geometric figure and a
rotation, reflection, or translation, draw the Essential Question(s)
transformed figure using, e.g., graph
paper, tracing paper, or geometry software. How can you represent a transformation in the
Specify a sequence of transformations that coordinate plane?
Objective(s):
will carry a given figure onto another.
•
Students will draw a specific
transformation given a geometric
figure and a rotation.
•
Students will predict and verify the
sequence of transformations (a
composition) that will map a figure onto
another.
Lesson 9.4 – Compositions of
Transformations, pp. 641 - 649
Lesson 9.4 Explore – Geometry Software Lab:
Compositions of Transformations, p. 640
Domain: G-CO Congruence
Enduring Understanding(s)
Cluster: Experiment with transformations in the Proving and applying congruence provides a
plane
basis for modeling situations geometrically.
 G.CO.A.3 Given a rectangle, parallelogram,
Lesson 9.5 – Symmetry, pp. 653 - 659
Transforming 2-D Figures
Major Content
 Supporting Content
Use the following Engageny Lessons to
introduce the concepts/build conceptual
understanding. If used, these lessons should be
used before the lessons from the textbooks.
Additional Lesson(s)
Geometry Module 1, Topic C,
Lesson 13 – Rotations
Engageny
Use the following Engageny Lessons to
introduce the concepts/build conceptual

Additional Content
Vocabulary
Composition of transformations, glide
reflection
Writing in Math
Explain how the Latin word for rigid helps to
understand nonrigid transformation.
Compare and contrast the methods learned
for combining rigid transformations and
nonrigid transformations in the coordinate
plane.
Vocabulary
Symmetry, line symmetry, line of symmetry,
rotational symmetry, center of symmetry,
order of symmetry, magnitude of symmetry,
Shelby County Schools 2016/2017
Revised 6/27/16
15 of 20
Curriculum and Instruction – Mathematics
Quarter 1
TN STATE STANDARDS
trapezoid, or regular polygon, describe the
rotations and reflections that carry it onto
itself.
GEOMETRY
CONTENT
Essential Question(s)
How can you identify the type of symmetry that
a figure has?
Objective(s):
•
Students will identify line and rotational
symmetries in two-dimensional figures.
Domain: G-CO Congruence
Cluster: Understand congruence in terms of
rigid motion
 G-CO.B.6 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.
Enduring Understanding(s)
Proving and applying congruence provides a
basis for modeling situations geometrically.
Essential Question(s)
How do you define congruence in terms of rigid
motion?
Objective(s):
•
Students will predict the composition
of transformations that will map a
figure onto a congruent figure.
•
Students will determine if two figures are
congruent by determining if rigid motions
will turn one figure into the other.
INSTRUCTIONAL SUPPORT & RESOURCES
understanding. If used, these lessons should be
used before the lessons from the textbooks.
Additional Lesson(s)
Geometry Module 1, Topic C,
Lesson 15 – Rotations, Reflections, and
Symmetry
Engageny
Additional Lesson(s)
Extra lesson – Congruence Transformation
Rigid Motions and Congruence Activity
(just the activity page)
Congruence and Triangles Lesson (Lesson
3.1)
plane symmetry, axis symmetry
Writing in Math
Connect the idea of a reflection to a figure with
line symmetry.
Writing in Math
Define congruent. Relate the word to the
terms equal and equivalent.
Use the following resources to ensure that the
intended outcome and level of rigor of the
standards are met.
Task(s)
TN Task Arc, Geometry -Investigating
Congruence in Terms of Rigid Motion
Task 4 -Looks Can Be Deceiving
Lines, Angles and Triangles’ Lines and Angles
(Allow approximately 2 weeks for instruction, review, and assessment)
Domain: G-CO Congruence
Cluster: Prove geometric theorems
 G-CO.C.9 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
Major Content
Enduring Understanding(s)
Proving and applying congruence provides a
basis for modeling situations geometrically.
Essential Question(s)
How can you identify relationships between two
lines or two planes?
 Supporting Content
Lesson 3.1 – Parallel Lines and Transversals, pp. Vocabulary
171 – 176
Parallel lines, skew lines, parallel planes,
Use the following resources to ensure that the
transversal, interior angles, exterior
intended outcome and level of rigor of the
angles, consecutive interior angles,
standards are met.
alternate interior angles, alternate exterior
angles, corresponding angles

Additional Content
Shelby County Schools 2016/2017
Revised 6/27/16
16 of 20
Curriculum and Instruction – Mathematics
Quarter 1
GEOMETRY
TN STATE STANDARDS
bisector of a line segment are exactly those
equidistant from the segment’s endpoints.
CONTENT
Objective(s):
•
Students will identify the relationships
between two lines.
•
Students will name angle pairs
formed by parallel lines and
transversals.
Domain: G-CO Congruence
Cluster: Prove geometric theorems
 G-CO.C.9 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.
Enduring Understanding(s)
Proving and applying congruence provides a
basis for modeling situations geometrically.
Domain: G-CO Congruence
Cluster: Prove geometric theorems
 G-CO.C.9 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.
Enduring Understanding(s)
Proving and applying congruence provides a
basis for modeling situations geometrically.
Major Content
Essential Question(s)
How are the angles formed by two parallel lines
cut by a transversal related?
INSTRUCTIONAL SUPPORT & RESOURCES
Task(s)
Parallel Lines and Transversals
(Interactive Notebook/Foldables)
Writing in Math
Determine what the term alternate means and
demonstrate its using a series of figures.
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
Lesson 3.2 – Angles and Parallel Lines, pp. 178 - Writing in Math
184
Explain how to construct parallel lines using
Lesson 3.2 Explore – Geometry Software
one of the postulates or theorems.
Lab: Angles and Parallel Lines p. 177
Define converse using the Latin meaning.
Connect converse to the word conversation.
Objective(s):
•
Students will use theorems to
determine the relationship[s between
specific pairs of angels.
•
Students will use algebra to find angle
measurements.
Essential Question(s)
How can coordinates and the coordinate plane
be used to prove theorems algebraically?
Objective(s):
 Supporting Content
Lesson 3.5 – Proving Lines Parallel, pp. 205 212 Constructing Parallel Lines
Use the following resources to ensure that the
intended outcome and level of rigor of the
standards are met.
Writing in Math
Write and solve a problem involving finding
the equation of a line that is parallel to a given
line.
Task(s)
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Congruence and Proofs

Additional Content
Shelby County Schools 2016/2017
Revised 6/27/16
17 of 20
Curriculum and Instruction – Mathematics
Quarter 1
TN STATE STANDARDS
CONTENT
•
•
•
Domain: G-GPE Expressing Geometric
Properties with Equations
Cluster: Use coordinates to prove simple
geometric theorems algebraically
 G-GPE.B.5 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).
Domain: G-GPE Expressing Geometric
Properties with Equations
Cluster: Use coordinates to prove simple
geometric theorems algebraically
 G-GPE.B.5 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).
Major Content
GEOMETRY
INSTRUCTIONAL SUPPORT & RESOURCES
Students will determine if lines are
parallel using their slopes.
Students will recognize angle pairs
that occur with parallel lines.
Students will prove that two lines are
parallel
Enduring Understanding(s)
Lesson 3.3 – Slopes of Lines, pp. 186 – 194
Algebra can be used to efficiently and effectively
describe and apply geometric properties.
Essential Question(s)
How can algebra be useful when expressing
geometric properties?
Writing in Math
A classmate says that all lines have positive or
negative slope. Write a question that would
challenge her conjecture.
Objective(s):
Students will find slopes of lines and use the
slope of a line to identify parallel and
perpendicular lines.
Enduring Understanding(s)
Lesson 3.4 – Equations of Lines, pp. 196 - 203
Algebra can be used to efficiently and effectively Constructing Perpendicular Lines and
describe and apply geometric properties.
Perpendicular Bisectors p. 55
Lesson 3.4 Extension – Geometry Lab:
Essential Question(s)
Equations of Perpendicular Bisectors p. 204
How can algebra be useful when expressing
geometric properties?
Use the following Engageny Lessons to
Objective(s):
•
Students will write an equation
of a line given information about
the graph.
•
Students will solve problems by writing
 Supporting Content
Vocabulary
Slope, rate of change
introduce the concepts/build conceptual
understanding. If used, these lessons should be
used before the lessons from the textbooks.
Vocabulary
Slope-intercept form, point-slope form
Writing in Math
Create a graphic organizer that shows
how some of the properties, postulates
and theorems build upon one another.
Additional Lesson(s)
Select additional lessons as appropriate from
Engageny Geometry Module 1, Topics A -G

Additional Content
Shelby County Schools 2016/2017
Revised 6/27/16
18 of 20
Curriculum and Instruction – Mathematics
Quarter 1
GEOMETRY
TN STATE STANDARDS
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
equations.
Use the following resources to ensure that the
intended outcome and level of rigor of the
standards are met.
Task(s)
Finding Equations of Parallel and
Perpendicular Lines
Construction of a Perpendicular Bisector
Major Content
 Supporting Content

Additional Content
Shelby County Schools 2016/2017
Revised 6/27/16
19 of 20
Curriculum and Instruction – Mathematics
Quarter 1
GEOMETRY
RESOURCE TOOLBOX
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
CCSS Flip Book with Examples of each Standard
Geometry Model Curriculum
http://www.ccsstoolbox.org/
http://insidemathematics.org/index.php/high-school-geometry
http://www.azed.gov/azcommoncore/mathstandards/hsmath/
http://learnzillion.com/common_core/math/hs
http://www.livebinders.com/play/play/454480
https://www.livebinders.com/play/play?id=464831
http://www.livebinders.com/play/play?id=571735
North Carolina – Unpacking Common Core
http://thegeometryteacher.wordpress.com/the-geometry-course/
http://mathtermind.blogspot.com/2012/07/common-core- geometry.html
Utah Electronic School - Geometry
Ohio Common Core Resources
Chicago Public Schools Framework and Tasks
Mathy McMatherson Blog - Geometry in Common Core
Comprehensive Geometry Help:
Online Math Learning (Geometry)
I LOVE MATH
NCTM Illuminations
New Jersey Center for Teaching & Learning (Geometry)
Calculator
Finding Your Way Around TI-83+ & TI-84+ (mathbits.com)
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
Tasks
Edutoolbox (formerly TNCore) Tasks
Inside Math Tasks
Mars Tasks
Dan Meyer's Three-Act Math Tasks
NYC tasks
Illustrative Math Tasks
UT Dana Center
GSE Analytic Geometry Unit 1: Similarity, Congruence and Proofs
Major Content
Interactive Manipulatives
GeoGebra – Free software for dynamic math and science learning
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 TI-Nspire
Videos
Math TV Videos
The Teaching Channel
Khan Academy Videos (Geometry)
NWEA MAP
Resources:https://teach.mapnwea.org/assist/help_
map/ApplicationHelp.htm#UsingTestResults/MAPRe
portsFinder.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 Impact Teaching with the Learning
Continuum)
https://support.nwea.org/khanrit - These
Khan Academy lessons are aligned to RIT
scores.
Literacy Resources
Literacy Skills and Strategies for Content Area
Teachers (Math, p. 22)
Glencoe Reading & Writing in the Mathematics
Classroom
Graphic Organizers (9-12) (teachervision.com)
Others
TN Ready Geometry Blueprint
State ACT Resources
 Supporting Content

Additional Content
Shelby County Schools 2016/2017
Revised 6/27/16
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