Download Objective(s) - Shelby County Schools

Curriculum and Instruction – Office of Mathematics
Quarter 2
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 2
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 2
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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Quarter 2
GEOMETRY
Topics Addressed in Quarter
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Triangle Congruence with Applications
Properties of Triangles
Special Segments in Triangles
Properties of Quadrilaterals with Coordinate Proof
Overview
During the second quarter, students will continue to work with the concept of rigid motion and congruency. They will determine if two triangles are congruent by SSS, SAS, ASA, AAS, or HL
and then provide appropriate reasoning for why they are congruent. They also will gain a deeper insight into constructing two-column, paragraph, and coordinate proofs. Students will classify
triangles based on its’ angles and side measures and determine whether a triangle exists given three side measures and find the range of the third side when given two side measures.
Students will compare the sides or angles of a given triangle and apply the Hinge theorem. Students will learn how to find missing angles in triangles both interior and exterior angles. They will
investigate the special segments of a triangle; altitude, angle bisector, perpendicular bisector, and median. They will also practice with the points of concurrency; orthocenter, incenter,
circumcenter, and centroid. Identifying quadrilaterals using given properties concludes the second quarter. Students should be able to solve equations to find various missing parts of the
quadrilaterals as well as write two-column, paragraph and coordinate proofs using definitions and properties.
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 2
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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TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Properties of Triangles and Triangle Congruence with
Applications
(Allow 3 weeks for instruction, review, and assessment)
Domain: G-CO Congruence
Cluster: Prove geometric theorems
 G-CO.C.10
Prove theorems about
triangles.
Domain: G-CO Congruence
Cluster: Make geometric constructions

G-CO.D.12 Make formal geometric
constructions with a variety of tools and
methods (compass and straightedge,
string, reflective devices, paper folding,
dynamic geometric software, etc.).
Domain: G-CO Congruence
Cluster: Prove geometric theorems

G-CO.C.10 Prove theorems about
triangles.
Enduring Understanding(s)
The properties of triangles create a basis for
understanding and reasoning that extends to
other geometric figures.
Lesson 4.1 Classifying Triangles, pp.235-242
Essential Question(s)
How do the properties of triangles contribute
to the geometric understanding of the world
around us?
Activity with Discussion
Pair the categories of classifications of sides of
triangles with the categories of classifications
of angles to determine which combinations can
exist and which ones cannot exist. Explain
why certain combinations cannot exist.
(Example, can a right equilateral triangle
exist?)
Error Analysis
pg. 241, #56 (H.O.T. Problem)
Objective(s):
• Students will identify and classify
triangles by angle measure
• Students will identify and classify
triangles by side measure
Enduring Understanding(s)
Many relationships exist between the measure
of the angles of a triangle and the measure of
the sides of the triangle.
Lesson 4.2 Angles of Triangles, pp. 243-252
Choose from the following resources to
ensure that the intended outcome and level
of rigor (mainly conceptual understanding
and application) of the standards are met.
Essential Question(s)
Task(s)
What can you say about the interior and exterior
Geometry Lab: Angles of Triangles p. 243
angles of a triangle and other polygons?
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
Objective(s):
geometric software, etc.).
• Students will apply the Triangle Angle
Sum Theorem
• Students will prove the measures of
interior angles of a triangle have a sum
Major Content
 Supporting Content
Vocabulary
acute triangle, equiangular triangle, obtuse
triangle, right triangle, equilateral triangle
isosceles triangle, scalene triangle

Additional Content
Vocabulary
Auxiliary line, exterior angle, remote interior
angles, flow proof, corollary
Writing in Math
Explain in words how to find the measure of
a missing angle of a triangle if you know
two of the angles. (Have students write this
as if they were explaining it to someone
who has never taken geometry before.)
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GEOMETRY
TN STATE STANDARDS
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
of 180º.
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster: Prove theorems involving similarity

G-SRT.B.5 Use congruence and
similarity criteria for triangles to solve
problems and to prove relationships in
geometric figures.
Domain: G-CO Congruence
Cluster: Understand congruence in terms of
rigid motions

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.
Domain: G-CO Congruence
Cluster: Understand congruence in terms of
rigid motions

Enduring Understanding(s)
There exist methods for proving triangles
congruent.
Essential Question(s)
What does the SAS Triangle Congruence
Theorem tell you about triangles?
What does the SSS Triangle Congruence
Theorem tell you about triangles?
Objective(s):
• Students will use the SSS Postulate to
test for triangle congruence.
• Students will use the SAS Postulate to
test for triangle congruence.
• Students will write two-column proofs to
show that two triangles are congruent by
SSS or SAS.
G-CO.B.8 Explain how the criteria
for triangle congruence (ASA, SAS,
and SSS) follow from the definition
of congruence in terms of rigid
motions.
p. 269 #30, (H.O.T. Problems)
Investigating Congruence in Terms of Rigid
Motion (TN Task Arc)
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.
Proving properties of Geometric Figures,
students use what they have learned in Topics
A through C to prove properties(Students
learn why any two triangles that satisfy the
SAS congruence criter.
G-CO.D.13 Construct an equilateral
triangle, a square, and a regular hexagon
inscribed in a circle
Major Content
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
Additional Lesson(s):
Engageny Geometry Module 1, Topic D,
Lesson 22 – Triangle Congruence
Domain: G-CO Congruence
Cluster: Make geometric constructions

Lesson 4.4 Proving Triangles Congruent – SSS,
Vocabulary
SAS, pp. 262-271
Included angle
Lesson 4.4 Extension – Geometry Lab: Proving Writing in Math
Constructions p. 271
Create a chart for triangle congruence
theorems (theorem, definition, and picture)
Choose from the following resources to
highlighting the sides and angles that are
ensure that the intended outcome and level congruent in each pair of triangles. Compare
of rigor (mainly conceptual understanding
and contrast the theorems in your own
and application) of the standards are met.
words. Be sure to include both similarities
and differences between the theorems.
Task(s)
 Supporting Content

Additional Content
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Quarter 2
TN STATE STANDARDS
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster: Prove theorems involving similarity

G-SRT.B.5 Use congruence and
similarity criteria for triangles to solve
problems and to prove relationships in
geometric figures.
Domain: G-CO Congruence
Cluster: Understand congruence in terms of
rigid motions

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.
Domain: G-CO Congruence
Cluster: Understand congruence in terms of
rigid motions

G-CO.B.8 Explain how the criteria
for triangle congruence (ASA, SAS,
and SSS) follow from the definition
of congruence in terms of rigid
motions.
GEOMETRY
CONTENT
Enduring Understanding(s)
There exist methods for proving triangles
congruent.
Essential Question(s)
What does the ASA Triangle Congruence
Theorem tell you about triangles?
What does the AAS Triangle Congruence
Theorem tell you about triangles?
What does the HL Triangle Congruence
Theorem tell you about two triangles?
Objective(s):
• Students will use the ASA Postulate to
test for triangle congruence.
• Students will use the AAS Postulate to
test for triangle congruence.
• Students will explore congruence in right
triangles.
• Students will write formal proofs to show
that two triangles are congruent by AAS,
ASA or HL.
INSTRUCTIONAL SUPPORT & RESOURCES
Lesson 4.5 Proving Triangles Congruent – ASA,
AAS. Pp.273-280
Lesson 4.5 ext Congruence in Right Triangles
p.281-282
Choose from the following resources to
ensure that the intended outcome and level
of rigor (mainly conceptual understanding
and application) of the standards are met.
Task(s)
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
Vocabulary
Included side
Writing in Math
Explain why identifying two pairs of congruent
angles with their included sides congruent is
enough to prove that two triangles are
congruent.
Analyzing Congruency Proofs
Are the Triangles Congruent?
Domain: G-CO Congruence
Cluster: Make geometric constructions

G-CO.D.13 Construct an equilateral
triangle, a square, and a regular hexagon
inscribed in a circle
Major Content
 Supporting Content

Additional Content
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Curriculum and Instruction – Office of Mathematics
Quarter 2
TN STATE STANDARDS
Domain: G-CO Congruence
Cluster: Prove geometric theorems
 G-CO.C.10
Prove theorems about
triangles.
Domain: G-CO Congruence
Cluster: Make geometric constructions
 G-CO.D.12 Make formal geometric
constructions with a variety of tools and
methods (compass and straightedge,
string, reflective devices, paper folding,
dynamic geometric software, etc.).
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster: Prove theorems involving similarity
 G-SRT.B.5 Use congruence and
similarity criteria for triangles to solve
problems and to prove relationships in
geometric figures.
GEOMETRY
CONTENT
Enduring Understanding(s)
Many relationships exist between the measure
of the angles of a triangle and the measure of
the sides of the triangle.
Essential Question(s)
What are the special relationships among
angles and sides in isosceles and equilateral
triangles?
Objective(s):
• Students will use properties of isosceles
triangles.
• Students will use properties of equilateral
triangles.
• Students will prove base angles of
isosceles triangles are congruent.
INSTRUCTIONAL SUPPORT & RESOURCES
Lesson 4.6 Isosceles and Equilateral Triangles, pp. Vocabulary
283-291
Pythagorean triple
Choose from the following resources to
ensure that the intended outcome and level
of rigor (mainly conceptual understanding
and application) of the standards are met.
Writing in Math
p. 290 #45 Challenge – proof (H.O.T.
problem)
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):
Engageny Geometry Module 1, Topic D,
Lesson 23 – Isosceles Triangles
Special Segments in Triangles
(Allow 2.5 weeks for instruction, review, and assessment)
Domain: G-CO Congruence
Cluster: Prove geometric theorems
 G-CO.C.10
Prove theorems about
triangles.
Domain: G-MG Modeling with Geometry
Cluster: Apply geometric concepts in
modeling situations

G-MG.A.3 Apply geometric methods
Major Content
Enduring Understanding(s)
The properties of triangles create a basis for
understanding and reasoning that extends to
other geometric figures.
Lesson 5.1 Bisectors of Triangles pp. 321-331
Choose from the following resources to
ensure that the intended outcome and level
of rigor (mainly conceptual understanding
and application) of the standards are met.
Essential Question(s)
Task(s)
How can you use perpendicular bisectors to find
the point that is equidistant from all the vertices Centers of Triangles
of a triangle?
Centers of Triangles Solutions
How can you use angle bisectors to find the
 Supporting Content

Additional Content
Vocabulary
Perpendicular bisector, concurrent lines,
point of concurrency, circumcenter, incenter
Writing in Math
Compare and contrast the perpendicular
bisectors and angle bisectors of a triangle. Be
sure to include their points of concurrency.
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TN STATE STANDARDS
to solve design problems (e.g.,
designing an object or structure to
satisfy physical constraints or
minimize cost; working with
typographic grid systems based on
ratios). ★
Domain: G-MG Modeling with Geometry
Cluster: Apply geometric concepts in
modeling situations

G-MG.A.3 Apply geometric methods
to solve design problems (e.g.,
designing an object or structure to
satisfy physical constraints or
minimize cost; working with
typographic grid systems based on
ratios). ★
Major Content
GEOMETRY
CONTENT
point that is equidistant from all the sides of a
triangle?
INSTRUCTIONAL SUPPORT & RESOURCES
Hospital Locator
Dividing a Town into Pizza Delivery Regions
Geometry Lab - Constructing Bisectors p. 321
Why are the points of concurrency called
incenter for angle bisectors of triangles and
circumcenter for the perpendicular bisectors?
Enduring Understanding(s)
The properties of triangles create a basis for
understanding and reasoning that extends to
other geometric figures.
Lesson 5.2 Medians and Altitudes of Triangles pp.
332-341
Vocabulary
Median, centroid, altitude, orthocenter
Essential Question(s)
How can you find the balance point or center of
gravity of a triangle?
Additional Lesson(s):
Engageny Geometry Module 1, Topic E, Lesson
30 – Medians of Triangles
Objective(s):
• Students will identify and use
perpendicular bisectors in triangles
• Students will identify and use angle
bisectors in triangles.
• Students will construct the special
segments (perpendicular bisectors and
angle bisectors) in acute, right and obtuse
triangles.
• Students will prove the perpendicular
bisectors and the angle bisectors of a
triangle meet at a point.
Objective(s):
• Students will identify and use medians in
triangles
• Students will identify and use altitudes in
triangles.
• Students will construct the special
segments (medians and altitudes) in
acute, right and obtuse triangles.
 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.
Writing in Math
Summarize the special segments of a triangle
including their names, properties and diagrams
into a chart or booklet.
Choose from the following resources to
ensure that the intended outcome and level
of rigor (mainly conceptual understanding
and application) of the standards are met.
Task(s)
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,

Additional Content
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TN STATE STANDARDS
CONTENT
•
Domain: G-CO Congruence
Cluster: Prove geometric theorems
 G-CO.C.10
triangles.
Prove theorems about
Domain: G-MG Modeling with Geometry
Cluster: Apply geometric concepts in
modeling situations
 G-MG.A.3
Apply geometric methods
to solve design problems (e.g.,
designing an object or structure to
satisfy physical constraints or
minimize cost; working with
typographic grid systems based on
ratios). ★
Domain: G-CO Congruence
Cluster: Prove geometric theorems
 G-CO.C.10
Prove theorems about
triangles.
Domain: G-MG Modeling with Geometry
Cluster: Apply geometric concepts in
modeling situations
Major Content
GEOMETRY
Students will prove the medians and the
altitudes of a triangle meet at a point.
Enduring Understanding(s)
Many relationships exist between the measure
of the angles of a triangle and the measure of
the sides of the triangle.
Essential Question(s)
How can you use inequalities to describe the
relationships among side lengths and angle
measures in a triangle?
Objective(s):
• Students will recognize and apply
properties of inequalities to the measures
of the angles of a triangle.
• Students will recognize and apply
properties of inequalities to the
relationships between the angles and
sides of a triangle.
Enduring Understanding(s)
Many relationships exist between the measure
of the angles of a triangle and the measure of
the sides of the triangle.
Essential Question(s)
In what ways can congruence be useful?
 Supporting Content
INSTRUCTIONAL SUPPORT & RESOURCES
Congruence and Proofs
Geometry Lab - Constructing Medians and
Altitudes p. 332
The Centroid of a Triangle
Balancing Act
Exploring the Centroid of a Triangle
Lesson 5.3 Inequalities in one triangle pp. 342-349 Writing in Math
Lesson 5.5 The Triangle Inequality Theorem
p. 348 #43 & 48 (H.O.T. Problems)
pp.359-366
p. 365 #45 & 48 (H.O.T. Problems)
Choose from the following resources to
ensure that the intended outcome and level
of rigor (mainly conceptual understanding
and application) of the standards are met.
Task(s)
Graphing Technology Lab - The Triangle
Inequality p. 359
Triangle Inequality Task
Triangle Inequalities
Lesson 5.6 Inequalities in Two Triangles pp. 367376
Choose from the following resources to
ensure that the intended outcome and level
of rigor (mainly conceptual understanding
and application) of the standards are met.
Task(s)
Inequalities in Two Triangles Activity

Additional Content
Writing in Math
Compare and contrast the Hinge Theorem to
the SAS Postulate for Triangle Congruence.
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Quarter 2
TN STATE STANDARDS

G-MG.A.3 Apply geometric methods
to solve design problems (e.g.,
designing an object or structure to
satisfy physical constraints or
minimize cost; working with
typographic grid systems based on
ratios). ★
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster: Prove theorems involving similarity

G-SRT.B.4 Prove theorems about
triangles. Theorems include: a line
parallel to one side of a triangle divides
the other two proportionally, and
conversely; the Pythagorean Theorem
proved using triangle similarity.
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster: Prove theorems involving similarity

G-SRT.B.5 Use congruence and
similarity criteria for triangles to solve
problems and to prove relationships in
geometric figures.
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Objective(s):
• Students will apply the Hinge Theorem or
its converse to make comparisons in two
triangles
• Prove triangle relationships using the
hinge theorem or its converse
Enduring Understanding(s)
Many relationships exist between the measure
of the angles of a triangle and the measure of
the sides of the same triangle.
Essential Question(s)
How are the segments that join the midpoints of
a triangle’s sides related to the triangle’s sides?
Objective(s):
• Students will use proportional parts within
triangles.
• Students will use proportional parts with
parallel lines.
• Students will prove the segment joining
midpoints of two sides of a triangle is
parallel to the third side and half the
length.
Lesson 7.4 Parallel Lines and Proportional Parts
(mid-segments of triangles) pp. 484-493
Vocabulary
mid-segment of a triangle
Choose from the following resources to
ensure that the intended outcome and level
of rigor (mainly conceptual understanding
and application) of the standards are met.
Task(s)
TN Geometry Task: Midpoint Madness See
Mathematics, Instructional Resources,
Geometry
Writing in Math
Draw all of the mid-segments of one triangle.
Explain what you see. Give as much detail as
possible.
Research and report on Sierpinski's
triangle
TN Task Arc: How Should We Divide This
See Mathematics, Instructional Resources,
Geometry, Task Arc: Investigating Coordinate
Geometry
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):
Engageny Geometry Module 1, Topic E,
Lesson 29 – Mid-segments of Triangles
Properties of Quadrilaterals and Coordinate Proof
(Allow 2.5 weeks for instruction, review, and assessment)
Domain: G-MG Modeling with Geometry
Major Content
Enduring Understanding(s)
 Supporting Content
Lesson 6.1 Angles of Polygons pp. 389-398

Additional Content
Vocabulary
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TN STATE STANDARDS
Cluster: Apply geometric concepts in
modeling situations

G-MG.A.1 Use geometric shapes,
their measures, and their properties to
describe objects (e.g., modeling a
tree trunk or a human torso as a
cylinder). ★
GEOMETRY
CONTENT
There exist certain patterns in the angle
measures of polygons.
Essential Question(s)
Is there a limit to the sum of the interior/exterior
angles of a polygon why or why not?
INSTRUCTIONAL SUPPORT & RESOURCES
Choose from the following resources to
ensure that the intended outcome and level
of rigor (mainly conceptual understanding
and application) of the standards are met.
Task(s)
Angle Sums
Spreadsheet Lab p. 398
diagonal
Lesson 6.2 Parallelograms, pp. 399-408
Choose from the following resources to
ensure that the intended outcome and level
of rigor (mainly conceptual understanding
and application) of the standards are met.
Vocabulary
parallelogram
Objective(s):
• Students will find and use the sum of the
measures of the interior angles of a
polygon
• Find and use the sum of the measures of
the exterior angles of a polygon
Domain: G-CO Congruence
Cluster: Prove geometric theorems

G-CO.C.11 Prove theorems about
parallelograms.
Domain: G-GPE Expressing Geometric
Properties with Equations
Cluster: Use coordinates to prove simple
geometric theorems algebraically

G-GPE.B.4 Use coordinates to prove
simple geometric theorems
algebraically. For example, prove or
disprove that a figure defined by four
given points in the coordinate plane is
a rectangle; prove or disprove that the
point (1, 3) lies on the circle centered
at the origin and containing the point
(0, 2).
Major Content
Enduring Understanding(s)
The properties of quadrilaterals help you to
categorize quadrilaterals.
Essential Question(s)
What can you conclude about the sides, angles,
and diagonals of a parallelogram?
Objective(s):
• Students will recognize and apply
properties of the sides and angles of
parallelograms
• Students will recognize and apply
properties of parallelograms
Task(s)
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
TN Task: Expanding Triangles See
Mathematics, Instructional Resources,
Geometry
TN Task: Parallelograms
Writing in Math
p. 396 #52 Open ended - Sketch a polygon
and find the sum of its interior angles. How
many sides does a polygon with twice this
interior angles sum have? Justify your
answer
Writing in Math
p. 406 # 43 Open ended - Provide a
counterexample to show that
parallelograms are not always congruent if
their corresponding sides are congruent.
(H.O.T. Problem)
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.
 Supporting Content

Additional Content
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TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Additional Lesson(s):
Geometry Module 1, Topic E, Lesson
28 – Properties of Parallelograms
Engageny
Domain: G-CO Congruence
Cluster: Prove geometric theorems

G-CO.C.11 Prove theorems about
parallelograms.
Domain: G-GPE Expressing Geometric
Properties with Equations
Cluster: Use coordinates to prove simple
geometric theorems algebraically

Enduring Understanding(s)
The properties of quadrilaterals help you to
categorize quadrilaterals
Essential Question(s)
What criteria can you use to prove that a
quadrilateral is a parallelogram?
Objective(s):
G-GPE.B.4 Use coordinates to prove
• Students will recognize the conditions
simple geometric theorems algebraically.
that ensure a quadrilateral is a
For example, prove or disprove that a
parallelogram.
figure defined by four given points in the
• Students will prove that a set of points
coordinate plane is a rectangle; prove or
forms a parallelogram in the coordinate
disprove that the point (1, 3) lies on the
plane.
circle centered at the origin and containing
the point (0, 2).
Lesson 6.3 Tests for Parallelograms pp.409-417
Choose from the following resources to
ensure that the intended outcome and level
of rigor (mainly conceptual understanding
and application) of the standards are met.
Task(s)
Select appropriate tasks from GSE
Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
Graphing Technology Lab - Parallelograms p.
408
Whitebeard's Treasure Task
TN Task: Park City
Similarity, Congruence & Proofs
Writing in Math
Journal Question: Are two parallelograms
congruent if they both have four congruent
angles? Justify your answer
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 4, Topic D, Lesson
13 – Coordinate Proof
Engageny
Domain: G-CO Congruence
Cluster: Prove geometric theorems

G-CO.C.11 Prove theorems about
Major Content
Enduring Understanding(s)
The properties of quadrilaterals help you to
categorize quadrilaterals
 Supporting Content
Lesson 6.4 Rectangles
Lesson 6.5 Rhombi and Squares

Additional Content
Vocabulary
rectangle, rhombi, and square.
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TN STATE STANDARDS
GEOMETRY
CONTENT
parallelograms.
Domain: G-GPE Expressing Geometric
Properties with Equations
Cluster: Use coordinates to prove simple
geometric theorems algebraically

G-GPE.B.4 Use coordinates to prove
simple geometric theorems algebraically.
For example, prove or disprove that a
figure defined by four given points in the
Objective(s):
coordinate plane is a rectangle; prove or
• Students will recognize and use the
disprove that the point (1, 3) lies on the
properties of rectangles
circle centered at the origin and containing
the point (0, 2).
• Students will determine whether
parallelograms are rectangles
• Students will recognize and apply the
properties of rhombi and squares.
• Students will determine whether
quadrilaterals are rectangles, rhombi, or
squares.
Domain: G-MG Modeling with Geometry
Cluster: Apply geometric concepts in
modeling situations

Essential Question(s)
How are the properties of rectangles, rhombi,
and squares used to classify quadrilaterals?
How can you use given conditions to prove that
a quadrilateral is a rectangle, rhombus or
square?
G-MG.A.3 Apply geometric methods to
solve design problems (e.g., designing an
object or structure to satisfy physical
constraints or minimize cost; working with
typographic grid systems based on
ratios). ★.
Major Content
INSTRUCTIONAL SUPPORT & RESOURCES
Choose from the following resources to
ensure that the intended outcome and level
of rigor (mainly conceptual understanding
and application) of the standards are met.
Task(s)
TN Task: Getting in Shape
TN Task: Lucio’s Ride
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 D, Lesson
33 – Review of the Assumptions 1
Engageny
Engageny Geometry Module 1, Topic D,
Lesson 34– Review of the Assumptions 2
Enduring Understanding(s)
The properties of quadrilaterals help you to
categorize quadrilaterals
Lesson 6.6 Trapezoids and Kites, pp.435-446
Choose from the following resources to
ensure that the intended outcome and level
of rigor (mainly conceptual understanding
and application) of the standards are met.
Essential Question(s)
Task(s)
What are the properties of kites and trapezoids?
TN Task: Go Fly a Kite
Objective(s):
• Students will apply properties of
trapezoids
• Students will apply properties of kites
 Supporting Content
Writing in Math
See Engageny lessons

Additional Content
Vocabulary
trapezoid, bases, legs of a trapezoid, base
angles, isosceles trapezoid, midsegment of
a trapezoid
Graphic Organizer
Use a Venn Diagram to show the
relationship of the quadrilaterals you
studied in Chapter 6
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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
SCS Math Tasks
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
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Major Content
GEOMETRY
 Supporting Content

Additional Content
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