Download Objective(s) - Shelby County Schools

Curriculum and Instruction – Office of 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 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 Standards call for conceptual understanding of key
concepts, such as place value and ratios. 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 – Office of 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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Curriculum and Instruction – Office of Mathematics
Quarter 1
GEOMETRY
Purpose of the Mathematics Curriculum Maps
The Shelby County Schools curriculum maps are intended to guide planning, pacing, and sequencing, reinforcing the major work of the grade/subject. Curriculum
maps are NOT meant to replace teacher preparation or judgment; however, it does serve as a resource for good first teaching and making instructional decisions
based on best practices, and student learning needs and progress. Teachers should consistently use student data differentiate and scaffold instruction to meet the
needs of students. The curriculum maps should be referenced each week as you plan your daily lessons, as well as daily when instructional support and resources
are needed to adjust instruction based on the needs of your students.
How to Use the Mathematics Curriculum Maps
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 the
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 teachers'
responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.
Content
Weekly and daily objectives/learning targets should be included in your plan. These 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 learning targets/objectives provide
specific outcomes for that standard(s). Best practices tell us that making objectives measureable increases student mastery.
Instructional Support and Resources
District and web-based resources have been provided in the Instructional Support and Resources column. 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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Curriculum and Instruction – Office of Mathematics
Quarter 1
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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Quarter 1
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:
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
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 – Office of Mathematics
Quarter 1
GEOMETRY
TN STATE STANDARDS
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Tools of Geometry
(Allow 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.
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-.
Is it possible for two points on the surface of a
prism to be neither collinear nor coplanar?
Justify your answer.
Lesson 1.2 – Linear Measure and Precision, pp.
14 – 24
Constructing a Copy of a Line Segment p.17
Discussion
Discuss the Ruler Postulate.
Writing in Math
Why is it important to have a standard of
measure? Refer to p. 14, and include an
Objective(s):
Major Content
 Supporting Content
Vocabulary
Line segment, betweeness of points, between,
congruent segments, construction

Additional Content
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Quarter 1
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
•
•
advantage and disadvantage to the builders of
the pyramids.
Students will use a compass and
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
Major Content
INSTRUCTIONAL SUPPORT & RESOURCES
 Supporting Content
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.
Select appropriate tasks from GSE Analytic
Geometry Unit 1: Similarity, Congruence and
Proofs

Additional Content
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Quarter 1
TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
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-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 resources to ensure that the
intended outcome and level of rigor of the
standards are met.
Writing in Math
Explain the prefix bi- when discussing segment
bisector.
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):
circular arc.
• Students will identify and use special
pairs of angles.
•
Students will identify perpendicular lines.
Lesson 1.5 – Angle Relationships, pp. 46 – 55
Task(s)
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
Bisecting an Angle Task
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
Connect the word degree to the idea of
measurement.
Discuss the similarity between the Protractor
Postulate and the Ruler Postulate.
Vocabulary
Adjacent angles, linear pair, vertical angles,
complementary angles, supplementary angles,
perpendicular
Writing in Math
Discuss the similarity between the postulates
for angles and the postulates for segments.
Describe three different ways you can
determine that an angle is a right angle.
Domain: G-CO Congruence
Major Content
 Supporting Content

Additional Content
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Curriculum and Instruction – Office of Mathematics
Quarter 1
TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
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.).
Reasoning and Proof
(Allow 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
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
Lesson 2.1 – Inductive Reasoning and
Conjecture, pp. 89 – 96
Essential Question(s)
How do you use inductive reasoning to make a
conjecture?
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.
Objective(s):
• Students will make conjectures based
on inductive reasoning.
• Students will find counterexamples.
Lesson 2.3 – Conditional Statements, pp. 105 –
113
Lesson 2.3 Extension – Geometry Lab:
Biconditional Statements p. 114
Essential Question(s)
How can theorems help prove figures
congruent?
Vocabulary
Conditional statement, if-then statement,
hypothesis, conclusion, related conditionals,
converse, inverse, contrapositive, logically
equivalent
Writing in Math
Describe a relationship between a conditional,
its converse, its inverse, and its contrapositive.
Objective(s):
• Students will analyze statements in if-then
form.
• Students will write converses,
 Supporting Content
Vocabulary
Inductive reasoning, conjecture,
counterexample

Additional Content
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Quarter 1
TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
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
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 –
column proofs.
•
Students will use properties of equality to
write geometric proofs.
 Supporting Content
Vocabulary
Algebraic proof, two-column proof, formal
proof

Additional Content
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Quarter 1
TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Transformations and Congruence;
Transformations and Symmetry
(Allow 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
What are rigid motions and how can they be
transformations as functions that take
defined?
points in the plane as inputs and give other
points as outputs. Compare
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
used before the lessons from the textbooks.
Engageny
Additional Lesson(s):
Geometry Module 1, Topic C,

Additional Content
Vocabulary
Transformation, preimage, image, congruence
transformation, isometry, reflection, translation,
rotation
Writing in Math
Explain the prefix pre- when discussing preimage.
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Quarter 1
TN STATE STANDARDS
transformations that preserve distance and
angle to those that do not (e.g., translation
versus horizontal stretch).
GEOMETRY
CONTENT
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).
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
Major Content
 Supporting Content
INSTRUCTIONAL SUPPORT & RESOURCES
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
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)
Task: Introduction to Reflections,
Translations, and Rotations
Translations, Reflections and Rotations
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.

Additional Content
Vocabulary
Translation vector
Shelby County Schools 2016/2017
Revised 5/31/16
12 of 18
Curriculum and Instruction – Office of Mathematics
Quarter 1
TN STATE STANDARDS
rotations, reflections, and translations in
terms of angles, circles, perpendicular
lines, parallel lines, and line segments.
GEOMETRY
CONTENT
Essential Question(s)
How can you represent a transformation in the
coordinate plane?
INSTRUCTIONAL SUPPORT & RESOURCES
Task(s)
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
Describe what a vector is and how it is used to
define a translation.
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
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.
Major Content
 Supporting Content
Writing in Math
Compare and contrast a translation and a
reflection.
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
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

Additional Content
Shelby County Schools 2016/2017
Revised 5/31/16
13 of 18
Curriculum and Instruction – Office of Mathematics
Quarter 1
TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
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,
trapezoid, or regular polygon, describe the
Essential Question(s)
rotations and reflections that carry it onto
How can you identify the type of symmetry that
itself.
a figure has?
Lesson 9.5 – Symmetry, pp. 653 - 659
Transforming 2-D Figures
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
Major Content
Enduring Understanding(s)
Proving and applying congruence provides a
basis for modeling situations geometrically.
Essential Question(s)
 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
understanding. If used, these lessons should be
used before the lessons from the textbooks.
Additional Lesson(s)
ny
Engage Geometry Module 1, Topic C,
Lesson 15 – Rotations, Reflections, and
Symmetry
Extra lesson – Congruence Transformation
Rigid Motions and Congruence Activity
(just the activity page)
Congruence and Triangles Lesson (Lesson
3.1)

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,
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.
Shelby County Schools 2016/2017
Revised 5/31/16
14 of 18
Curriculum and Instruction – Office of Mathematics
Quarter 1
TN STATE STANDARDS
on a given figure; given two figures, use
the definition of congruence in terms of
rigid motions to decide if they are
congruent.
GEOMETRY
CONTENT
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
Use the following resources to ensure that the
intended outcome and level of rigor of the
standards are met.
Task(s)
Investigating Congruence in Terms of Rigid
Motion (TN Task Arc 4 -Looks Can Be
Deceiving)
Lines, Angles and Triangles’ Lines and Angles
(Allow 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
Enduring Understanding(s)
Proving and applying congruence provides a
basis for modeling situations geometrically.
Major Content
Essential Question(s)
How can you identify relationships between two
lines or two planes?
Objective(s):
•
Students will identify the relationships
between two lines.
•
Students will name angle pairs
formed by parallel lines and
transversals.
Essential Question(s)
 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
Task(s)
angles, corresponding angles
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Writing in Math
Congruence and Proofs
Determine what the term alternate means and
demonstrate its using a series of figures.
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.

Additional Content
Shelby County Schools 2016/2017
Revised 5/31/16
15 of 18
Curriculum and Instruction – Office of Mathematics
Quarter 1
TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
congruent and corresponding angles are
How are the angles formed by two parallel lines
congruent; points on a perpendicular
cut by a transversal related?
bisector of a line segment are exactly those
equidistant from the segment’s endpoints.
Objective(s):
•
Students will use theorems to
determine the relationship[s between
specific pairs of angels.
•
Students will use algebra to find angle
measurements.
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.
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.,
Major Content
Enduring Understanding(s)
Proving and applying congruence provides a
basis for modeling situations geometrically.
Essential Question(s)
How can coordinates and the coordinate plane
be used to prove theorems algebraically?
Objective(s):
•
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
Connect converse to the word conversation.
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.
Task(s)
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
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?
 Supporting Content
Writing in Math
Write and solve a problem involving finding
the equation of a line that is parallel to a given
line.
Vocabulary
Slope, rate of change
Writing in Math
A classmate says that all lines have positive or
negative slope. Write a question that would

Additional Content
Shelby County Schools 2016/2017
Revised 5/31/16
16 of 18
Curriculum and Instruction – Office of Mathematics
Quarter 1
TN STATE STANDARDS
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).
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Objective(s):
Students will find slopes of lines and use the
slope of a line to identify parallel and
perpendicular lines.
challenge her conjecture.
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
Vocabulary
Slope-intercept form, point-slope form
Objective(s):
•
Students will write an equation
of a line given information about
the graph.
•
Students will solve problems by writing
equations.
introduce the concepts/build conceptual
understanding. If used, these lessons should be
used before the lessons from the textbooks.
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
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 5/31/16
17 of 18
Curriculum and Instruction – Office of 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 5/31/16
18 of 18