Download Objective(s) - Shelby County Schools

Curriculum and Instruction –Mathematics
Quarter 3
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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8. Look for and
express regularity
in repeated
reasoning
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.
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
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:
4. Model with
mathematics
5. Use appropriate
tools strategically
The TN Mathematics Standards
The Tennessee Mathematics Standards:
Teachers can access the Tennessee State standards, which are featured
https://www.tn.gov/education/article/mathematics-standards
throughout this curriculum map and represent college and career ready
learning at reach respective grade level.
Standards for Mathematical Practice
Mathematical Practice Standards
Teachers can access the Mathematical Practice Standards, which are
https://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view featured throughout this curriculum map. This link contains more a more
detailed explanation of each practice along with implications for instructions.
Major Content
 Supporting Content

Additional Content
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GEOMETRY
Purpose of the Mathematics Curriculum Maps
This curriculum framework or map is meant to help teachers and their support providers (e.g., coaches, leaders) on their path to effective, college and career ready
(CCR) aligned instruction and our pursuit of Destination 2025. It is a resource for organizing instruction around the TN State Standards, which define what to teach
and what students need to learn at each grade level. The framework is designed to reinforce the grade/course-specific standards and content—the major work of the
grade (scope)—and provides a suggested sequencing and pacing and time frames, aligned resources—including sample questions, tasks and other planning tools.
Our hope is that by curating and organizing a variety of standards-aligned resources, teachers will be able to spend less time wondering what to teach and searching
for quality materials (though they may both select from and/or supplement those included here) and have more time to plan, teach, assess, and reflect with
colleagues to continuously improve practice and best meet the needs of their students.
The map is meant to support effective planning and instruction to rigorous standards; it is not meant to replace teacher planning or prescribe pacing or instructional
practice. In fact, our goal is not to merely “cover the curriculum,” but rather to “uncover” it by developing students’ deep understanding of the content and mastery of
the standards. Teachers who are knowledgeable about and intentionally align the learning target (standards and objectives), topic, task, and needs (and
assessment) of the learners are best-positioned to make decisions about how to support student learning toward such mastery. Teachers are therefore expected-with the support of their colleagues, coaches, leaders, and other support providers--to exercise their professional judgment aligned to our shared vision of effective
instruction, the Teacher Effectiveness Measure (TEM) and related best practices. However, while the framework allows for flexibility and encourages each
teacher/teacher team to make it their own, our expectations for student learning are non-negotiable. We must ensure all of our children have access to rigor—highquality teaching and learning to grade-level specific standards, including purposeful support of literacy and language learning across the content areas.
Additional Instructional Support
Shelby County Schools adopted our current math textbooks for grades 9-12 in 2010-2011. The textbook adoption process at that time followed the requirements set
forth by the Tennessee Department of Education and took into consideration all texts approved by the TDOE as appropriate. We now have new standards; therefore,
the textbook(s) have been vetted using the Instructional Materials Evaluation Tool (IMET). This tool was developed in partnership with Achieve, the Council of Chief
State Officers (CCSSO) and the Council of Great City Schools. The review revealed some gaps in the content, scope, sequencing, and rigor (including the balance of
conceptual knowledge development and application of these concepts), of our current materials.
The additional materials purposefully address the identified gaps in alignment to meet the expectations of the CCR standards and related instructional shifts while still
incorporating the current materials to which schools have access. Materials selected for inclusion in the Curriculum Maps, both those from the textbooks and
external/supplemental resources (e.g., engageny), have been evaluated by district staff to ensure that they meet the IMET criteria.
Major Content
 Supporting Content

Additional Content
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GEOMETRY
How to Use the Mathematics Curriculum Maps
Overview
An overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the
students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide some non-summative assessment items.
Tennessee State Standards
The TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a
key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards that
supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teacher’s
responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.
Content
Teachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related
best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, etc.).
Support for the development of these lesson objectives can be found under the column titled ‘Content’. The enduring understandings will help clarify the “big picture”
of the standard. The essential questions break that picture down into smaller questions and the objectives provide specific outcomes for that standard(s). Best
practices tell us that clearly communicating and making objectives measureable leads to greater student mastery.
Instructional Support and Resources
District and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks and
additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as needed for content
support and differentiation.
Major Content
 Supporting Content

Additional Content
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GEOMETRY
Topics Addressed in Quarter




Similarity and Transformations
Using Similar Triangles
Right Triangles with Trigonometry
Properties of Angles and Segments in Circles
Overview
During the third quarter students formalize their understanding of similarity, which was informally studied prior to geometry. Similarity of polygons and triangles is explored and
triangle similarity postulates and theorems are formally proven. The proportionality of corresponding sides of similar figures is applied. Similarity is extended to the side-splitting,
proportional medians, altitudes, angle bisectors, and segments theorems. The geometric mean is defined and related to the arithmetic mean. The special right triangles of 30-60-90
and 45-45-90 are also studied. Students are introduced to the right-triangle trigonometric ratios of sine, cosine, and tangent, and their applications. Angles and the sine, cosine, and
tangent functions are defined in terms of a rotation of a point on the unit circle. Students will end the quarter by starting their study of circles. They will quickly review circumference
and then identify central angles, major and minor arcs, semicircles and find their measures. They will finish the quarter studying inscribed angles and intercepted arcs.
Year at a Glance Document
Content Standard
G-SRT.A.2
Type of Rigor
Procedural Skill and Fluency , Conceptual
Understanding
Foundational Standards
8.G.A.1, 2,3, 4,5
G-SRT.B.4, 5
Procedural Skill and Fluency , Conceptual
Understanding & Application
8.G.A.1, 2,3, 4,5
G-SRT.C.6, 7, 8
Procedural Skill and Fluency , Conceptual
Understanding & Application
Procedural Skill and Fluency , Conceptual
Understanding & Application
Procedural Skill and Fluency , Conceptual
Understanding & Application
8.G.A.1, 2,3, 4,5
G-C.A.1, 2
G-MG.A.3
8.G.A.5; 8.G.B.7
Sample Assessment Items**
Illustrative: Are They Similar; Illustrative:
Congruent and Similar Triangles; Illustrative:
Similar Triangles
Illustrative: Joining Two Midpoints of Sides
of a Triangle; Illustrative: Pythagorean
Theorem; Illustrative: Bank Shot; Illustrative:
Points From Directions
Math shell: Hopewell Geometry
Illustrative: Similar Circles; Illustrative:
Neglecting the Curvature of the Earth
Illustrative: Ice Cream Cone; Illustrative:
Satellite
8.G.A.5; 8.G.B.7
** 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
Similarity and Transformations
(Allow approximately 3 weeks for instruction, review, and assessment)
Domain: G-MG Modeling with Geometry
Cluster: Apply geometric concept in modeling
situations
G-MG.A.3 Apply geometric methods to solve
design problems (e.g., designing an object or
structure to satisfy physical constraints or
minimize cost; working with typographic grid
systems based on ratios). ★
Enduring Understanding(s)
Polygons are similar if and only if corresponding
angles are congruent and corresponding sides
are proportional.
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
Better Lesson: Comparing Sequences
Essential Question(s)
What is the difference between a ratio and a
proportion?
What operations are used to solve a proportion?
Use the textbook resources to address
procedural skill and fluency.
Lesson 7.1 Ratios and Proportions pp. 457 464
Graphing Technology Lab - Fibonacci
Sequence and Ratios p. 464
Objective(s):
•
Write ratios
• Write and solve proportions
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster: Understand similarity in terms of
similarity transformations

G-SRT.A.2 Given two figures, use the
definition of similarity in terms of
similarity transformations to decide if
they are similar; explain using similarity
transformations the meaning of
similarity for triangles as the equality of
all corresponding pairs of angles and
the proportionality of all corresponding
pairs of sides.
Enduring Understanding(s)
Polygons are similar if and only if corresponding
angles are congruent and corresponding sides
are proportional.
Essential Question(s)
How do you use proportions to find side lengths
in similar polygons?
How do you identify corresponding parts of
similar triangles?
Objective(s):
• Use proportions to Identify similar
polygons
• Solve problems using the properties of
similar polygons
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry Module 2, Topic C,
Lesson 12 – Similarity Transformations
Use the textbook resources to address
procedural skill and fluency.
Lesson 7.2 Similar Polygons pp.465-473
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
Vocabulary
Ratio, extended ratios, proportion,
extremes, means, cross products
Activity with Discussion
Research and Report- The Fibonacci
Sequence and the Golden Ratio - what are
they, why are they important, and how are they
related.
Vocabulary
Similar polygons, similarity ratio, scale factor
Activity with Discussion
p. 472 #54 Draw two regular pentagons that
are different sizes. Are the pentagon’s similar?
Will any two regular polygons with the same
number of sides be similar? Explain
Writing in Math/Discussion
p. 472 #55 Compare and contrast congruent,
similar, and equal figures.
HS Flip Book with examples of each
Standard
(Designed as a resource tool to assist teachers in deepening
Major Content
 Supporting Content

Additional Content
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TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
their understanding of what each standard means in terms of
what students must know and be able to do.
It outlines only a sample of instructional strategies and
examples. Links to conceptual categories and specific
standards in the document can be accessed from page 5
Mathematics Standards for High School.)
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster: Understand similarity in terms of
similarity transformations

G-SRT.A.2 Given two figures, use the
definition of similarity in terms of
similarity transformations to decide if
they are similar; explain using similarity
transformations the meaning of
similarity for triangles as the equality of
all corresponding pairs of angles and
the proportionality of all corresponding
pairs of sides.
Enduring Understanding(s)
Geometric figures can change size and/or
position while maintaining proportional
attributes.
Essential Question(s)
How do you show two triangles are similar?
Objective(s):
• Identify similarity transformations
• Verify similarity after a similarity
transformation
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry Module 2, Topic A,
Lesson 2 – Scale Drawings by Ratio Method
engageny Geometry Module 2, Topic A,
Lesson 3 – Scale Drawings by the Parallel
Method
engageny Geometry Module 2, Topic B
Lesson 6 – Dilations
engageny Geometry Module 2, Topic B,
Lesson 7 – Do Dilations Map Segments?
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster: Define trigonometric ratios and solve
problems involving right triangles
Use the textbook resources to address
procedural skill and fluency.
Lesson 7.6 Similarity Transformations pp. 505-511

Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
G-SRT.C.6 Understand that by
similarity, side ratios in right triangles
are properties of the angles in the
triangle, leading to definitions of
trigonometric ratios for acute angles.
Domain: G-MG Modeling with Geometry
Cluster: Apply geometric concepts in
modeling situations
Major Content
Vocabulary
dilation, similarity transformation, center of
dilation, scale factor of a dilation,
enlargement, reduction
Activity with Discussion
Explain how you can use scale factor to
determine whether a transformation is an
enlargement, a reduction, or a congruence
transformation.
HS Flip Book with examples of each
Standard
Enduring Understanding(s)
Geometric figures can change size and/or
position while maintaining proportional
 Supporting Content
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.

Additional Content
Vocabulary
Scale model, scale drawing, scale
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Quarter 3
GEOMETRY
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). ★
CONTENT
attributes.
Essential Question(s)
How do you use proportions to find side lengths
in similar polygons?
Objective(s):
• Interpret scale models
• Use scale factors to solve problems
INSTRUCTIONAL SUPPORT & RESOURCES
engageny Geometry Module 2, Topic A,
Lesson 1 – Scale Drawings
Writing in Math/Discussion
Compare and contrast scale and scale factor.
Use the textbook resources to address
procedural skill and fluency.
Lesson 7.7 Scale Drawings and Scale Models
pp. 512-517
You can produce a scale model of a certain
object by extending each dimension by a
constant. What must be true of the shape of the
object? Explain your reasoning.
Using Similar Triangles
(Allow approximately 3 weeks for instruction, review, and assessment)
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.
Enduring Understanding(s)
Polygons are similar if and only if corresponding
angles are congruent and corresponding sides
are proportional.
Essential Question(s)
How do you use proportions to find side lengths
in similar polygons?
How do you show two triangles are similar?
Objective(s):
• Identify and prove similar triangles
using the AA Similarity Postulate and
the SSS and SAS similarity Theorems
• Use similar triangles to solve problems
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry Module 2, Topic C,
Lesson 14 – Similarity
engageny Geometry Module 2, Topic C,
Lesson 15 – AA Similarity
engageny Geometry Module 2, Topic C,
Lesson 17 – SSS & SAS Similarity
engageny Geometry Module 2, Topic C,
Lesson 16 – Applying Similar Triangles
Writing in Math/Discussion
Contrast and compare the triangle congruence
theorems with the triangle similarity theorems.
Use the textbook resources to address
procedural skill and fluency.
Lesson 7.3 Similar Triangles pp. 474-483
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to non-
Major Content
 Supporting Content

Additional Content
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TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
routine problems.
HS Flip Book with examples of each
Standard
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.
Enduring Understanding(s)
Use the following lesson(s) first to
Polygons are similar if and only if corresponding introduce concepts/build conceptual
understanding.
angles are congruent and corresponding sides
are proportional.
engageny Geometry Module 2, Topic A,
Lesson 4 – Triangle Side Splitter Theorem
engageny Geometry Module 2, Topic B,
Essential Question(s)
How do you use proportions to find side lengths Lesson 10 – Dividing a Line Segment into
Equal Parts
in similar polygons?
engageny Geometry Module 2, Topic C, Lesson
19 – Parallel Lines and Proportional Segments
Objective(s):
• Use proportional parts within triangles
• Use proportional parts with parallel lines
Vocabulary
Mid-segment of a triangle
Activity with Discussion
Use multiple representations to explore angle
bisectors and proportions. See p. 492, #47
Use the textbook resources to address
procedural skill and fluency.
Lesson 7.4 Parallel Lines and Proportional Parts
(midsegments was previously covered in unit 2)
pp. 484-492
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
HS Flip Book with examples of each
Standard
Major Content
 Supporting Content

Additional Content
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TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Task(s)
See Mathematics, Instructional Resources,
Geometry, Task Arc: Investigating Coordinate
Geometry
Partitioning
However You Want to Slice It
Comparing Shapes
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
HS Flip Book with examples of each
Standard
(Designed as a resource tool to assist teachers
in deepening their understanding of what each
standard means in terms of what students must
know and be able to do.
It outlines only a sample of instructional
strategies and examples. Links to conceptual
categories and specific standards in the
document can be accessed from page 5
Mathematics Standards for High School.)
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.
Enduring Understanding(s)
•
Similar figures map one shape
proportionally onto another through nonrigid motions.
•
Congruence and similarity criteria for
triangles are used to solve problems and
prove relationships of geometric figures.
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry Module 2, Topic D,
Lesson 21 – Special Relationships within
Right Traingles
engageny Geometry Module 2, Topic D,
Lesson 24 – Prove the Pythagorean Theorem
Using Similarity
Vocabulary
Geometric mean
Writing in Math/Discussion
What is an arithmetic mean and a geometric
mean of two numbers? Are they ever equal?
Justify your answer.
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Major Content
 Supporting Content

Additional Content
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TN STATE STANDARDS
CONTENT
Cluster: Prove theorems involving similarity

GEOMETRY
Essential Question(s)
 Can the geometric mean be used in any
triangle?
G-SRT.B.5 Use congruence and
similarity criteria for triangles to solve
problems and to prove relationships in
geometric figures.
 Why does geometric mean help us to find
the missing sides in a right triangle?
Objective(s):
• Find the geometric mean between two
numbers
• Solve problems involving relationships
between parts of a right triangle and the
altitude to its hypotenuse
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.
Major Content
Enduring Understanding(s)
•
Similar figures map one shape
proportionally onto another through nonrigid motions.
•
Congruence and similarity criteria for
triangles are used to solve problems and
prove relationships of geometric figures.
.
Essential Question(s)
How might the features of one figure be useful
when solving problems about a similar figure?
Objective(s):
•
Recognize and use proportional
relationships of corresponding angle
bisectors, altitudes, and medians of
similar triangles
•
Use the Triangle Angle Bisector
Theorem
 Supporting Content
INSTRUCTIONAL SUPPORT & RESOURCES
Use the textbook resources to address
procedural skill and fluency.
Lesson 8.1 Geometric Mean pp.531-539
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
HS Flip Book with examples of each
Standard
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry Module 2, Topic C,
Lesson 18 – Triangle Angles Bisector
Theorem
Activity with Discussion
Find a counterexample: If the measure of an
altitude and side of a triangle are proportional
to the corresponding altitude and
corresponding side of another triangle, then the
triangles are similar
Use the textbook resources to address
procedural skill and fluency.
Lesson 7.5 Parts of Similar Triangles pp.495-503
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
HS Flip Book with examples of each
Standard

Additional Content
Shelby County Schools 2016/2017
Revised 12/1/16
12 of 19
Curriculum and Instruction –Mathematics
Quarter 3
TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
ACT Practice
(sample problems to prepare for the ACT)
Glencoe, pp.456-457
Right Triangles and Trigonometry
(Allow approximately 1.5 weeks for instruction, review, and assessment)t)
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster: Define trigonometric ratios and solve
problems involving right triangles

G-SRT.C.6 Understand that by
similarity, side ratios in right triangles
are properties of the angles in the
triangle, leading to definitions of
trigonometric ratios for acute angles.
Enduring Understanding(s)
Use the following lesson(s) first to
Trigonometry can be used to measure sides and introduce concepts/build conceptual
understanding.
angles indirectly in right triangles.
engageny Geometry Module 2, Topic D, Lesson
24 - Prove the Pythagorean Theorem Using
Essential Question(s)
Similarity
How do you find a side length or angle measure
in a right triangle?
Use the textbook resources to address
procedural skill and fluency.
Objective(s):
Lesson 8.3 Special Right Triangles pp.552-559
• Identify and apply side ratios in 45-4590 right triangles.
Use the following resources to deepen
• Identify and apply side ratios in 30-60students' conceptual understanding of
90 right triangles
mathematical content and develop their
Activity with Discussion
p.559 #50
Explain how you can find the lengths of two legs
of a 30-60-90 triangle in radical form if you are
given the length of the hypotenuse.
ability to apply that knowledge to nonroutine problems.
HS Flip Book with examples of each
Standard
Task(s)
Discovering Special Right Triangles Learning
Task
Finding Right Triangles in your Environment
Learning Task
Create your own triangles Learning Task
Major Content
 Supporting Content

Additional Content
Shelby County Schools 2016/2017
Revised 12/1/16
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Curriculum and Instruction –Mathematics
Quarter 3
TN STATE STANDARDS
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster: Define trigonometric ratios and solve
problems involving right triangles

G-SRT.C.7 Explain and use the
relationship between the sine and
cosine of complementary angles.
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster: Define trigonometric ratios and solve
problems involving right triangles

G-SRT.C.8 Use trigonometric ratios
and the Pythagorean Theorem to solve
right triangles in applied problems. ★
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster: Define trigonometric ratios and solve
problems involving right triangles

GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Enduring Understanding(s)
Use the following lesson(s) first to
Trigonometry can be used to measure sides and introduce concepts/build conceptual
understanding.
angles indirectly in right triangles.
engageny Geometry Module 2, Topic E
Lesson 25: Incredibly Useful Ratios
Essential Question(s)
How do you find a side length or angle measure Lesson 26: The Definition of Sine, Cosine, and
Tangent
in a right triangle?
How do trigonometric ratios relate to similar right Lesson 27: Sine and Cosine of
Complementary Angles and Special Angles
triangles?
Lesson 28: Solving Problems Using Sine and
Cosine
Objective(s):
Lesson 29: Applying Tangents Lesson 30:
• Define trigonometric ratios for acute
Trigonometry and the Pythagorean Theorem
angles in right triangles
• Use trigonometric rations and Pythagorean
Use the textbook resources to address
Theorem to solve right triangles
procedural skill and fluency.
• Use the relationship between the sine and
Lesson 8.4 Trigonometry pp.562-271
cosine of complementary angles.
G-SRT.C.6 Understand that by
similarity, side ratios in right triangles
are properties of the angles in the
triangle, leading to definitions of
trigonometric ratios for acute angles.
Vocabulary
Trigonometry, trigonometry ratio, sine,
cosine, tangent, inverse sine, inverse
cosine, inverse tangent
Activity with Discussion
p.570 #65
Explain how you can use ratios of the side
lengths to find the angle measures of the acute
angles in a right triangle.
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
HS Flip Book with examples of each
Standard
Task(s)
Discovering Trigonometric Ratio Relationships
learning task p.22
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster: Define trigonometric ratios and solve
problems involving right triangles
Major Content
Enduring Understanding(s)
Use the following lesson(s) first to
Trigonometry can be used to measure sides and introduce concepts/build conceptual
understanding.
angles indirectly in right triangles.
engageny Geometry Module 2, Topic D, Lesson
 Supporting Content

Additional Content
Vocabulary
Angle of elevation, angle of depression
Shelby County Schools 2016/2017
Revised 12/1/16
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Curriculum and Instruction –Mathematics
Quarter 3
TN STATE STANDARDS

G-SRT.C.8 Use trigonometric ratios
and the Pythagorean Theorem to solve
right triangles in applied problems. ★
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Lesson 31: Using Trigonometry to Determine
Area
Lesson 32: Using Trigonometry to Find Side
Lengths of an Acute Triangle
Lesson 33: Applying the Laws of Sines and
Cosines
Lesson 34: Unknown Angles
Objective(s):
Use the textbook resources to address
• Solve problems involving angles of elevation. procedural skill and fluency.
• Solve problems involving angles of
Lesson 8.5 – Angles of Elevation and Depression
depression.
pp.574-581
Essential Question(s)
How do you find a side length or angle measure
in a right triangle?
How do trigonometric ratios relate to similar right
triangles?
Writing in Math/Discussion
p.580 #25
Classify the statement below as true or
false. Explain. “As a person moves closer
to an object he or she is sighting, the angle
of elevation increases”
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
HS Flip Book with examples of each
Standard
Task(s)
Find that Side or Angle Task
Edutoolbox: Interstate Task
ACT Practice
(sample problems to prepare for the ACT)
Glencoe, pp.618-619
Properties of Angles and Segments in Circles
(Allow approximately 1.5 weeks for instruction, review, and assessment)t)
Domain: G-C Circles
Cluster: Understand and apply theorems
about circles
Major Content
Enduring Understanding(s)
The concept of similarity as it relates to circles
can be extended with proof.
 Supporting Content
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
engageny Geometry Module 3, Topic A, Lesson

Additional Content
Vocabulary
Circle, center, radius, chord, diameter, congruent
circles, concentric circles, circumference, pi,
Shelby County Schools 2016/2017
Revised 12/1/16
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Curriculum and Instruction –Mathematics
Quarter 3
GEOMETRY
TN STATE STANDARDS

CONTENT
Essential Question(s)
What role do circles play in modeling the word
Domain: G-CO Congruence
Cluster: Experiment with transformations in the around us?
plane
Objective(s):
 G-CO.A.1 Know precise definitions of
• Give an argument to justify the formula
angle, circle, perpendicular line, parallel
for the circumference of a circle.
line, and line segment, based on the
undefined notions of point, line, distance
• Prove that all circles are similar.
along a line, and distance around a
circular arc.
G-C.A.1 Prove that all circles are similar.
Domain: G-GMD Geometric Measurement
and Dimension
Cluster: Explain volume formulas and use them
to solve problems


G-C.A.2 Identify and describe
relationships among inscribed angles,
radii, and chords. Include the relationship
between central, inscribed, and
circumscribed angles; inscribed angles
on a diameter are right angles; the radius
of a circle is perpendicular to the tangent
where the radius intersects the circle.
inscribed, circumscribed
Use the textbook resources to address
procedural skill and fluency.
Lesson 10.1 – Circles and Circumference pp.683691
Writing in Math/Discussion
p.690 #54
Research and write about the history of pi
and its importance to the study of geometry.
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
Task(s)
Illustrative Math: Similar Circles Task
All Circles are Similar Task
Enduring Understanding(s)
•
Relationships between angles, radii and
chords will be investigated.
•
Similarities will be applied to derive an arc
length and a sector area.
Essential Question(s)
When lines intersect a circle, or within a circle,
how do you find the measures of resulting
angles, arcs, and segments?
Objective(s):
Major Content
4 – Proving the Area of a Disk
HS Flip Book with examples of each
Standard
G-GMD.A.1 Give an informal
argument for the formulas for the
circumference of a circle, area of a
circle, volume of a cylinder, pyramid,
and cone. Use dissection arguments,
Cavalieri’s principle, and informal limit
arguments.
Domain: G-C Circles
Cluster: Understand and apply theorems
about circles
INSTRUCTIONAL SUPPORT & RESOURCES
 Supporting Content
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
.
engageny Geometry Module 5, Topic A, Lesson
4 – Explore Relationships between Inscribed
Angles, Central Angles and their Intercepted
Arcs
Use the textbook resources to address
procedural skill and fluency.
Lesson 10.2 Measuring Angles and Arcs pp.692-

Additional Content
Vocabulary
Central angle, arc, minor arc, major arc,
semicircle, congruent arcs, adjacent arcs, arc
length
Writing in Math/Discussion
p.699 #62
Describe the three different types of arcs in
a circle and the method for finding the
measure of each one.
Shelby County Schools 2016/2017
Revised 12/1/16
16 of 19
Curriculum and Instruction –Mathematics
Quarter 3
TN STATE STANDARDS
GEOMETRY
CONTENT
•
Identify central angles, major arcs, minor
arcs, and semicircles and find their
measures.
INSTRUCTIONAL SUPPORT & RESOURCES
700
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
HS Flip Book with examples of each
Standard
Task(s)
Circles and their Relationships among Central
Angles, Arcs and Chords (p. 15)
Investigating Angle Relationships in Circles (pp.
46 & 52)
Domain: G-C Circles
Cluster: Understand and apply theorems
about circles

G-C.A.2 Identify and describe
relationships among inscribed angles,
radii, and chords. Include the relationship
between central, inscribed, and
circumscribed angles; inscribed angles
on a diameter are right angles; the radius
of a circle is perpendicular to the tangent
where the radius intersects the circle.
Enduring Understanding(s)
•
Relationships between angles, radii and
chords will be investigated.
•
Similarities will be applied to derive an arc
length and a sector area.
Use the following lesson(s) first to
introduce concepts/build conceptual
understanding.
Engageny Geometry Module 5, Topic A,
Lesson 5 – Prove Inscribed Angle Theorem
Essential Question(s)
When lines intersect a circle, or within a circle,
how do you find the measures of resulting
angles, arcs, and segments?
Use the textbook resources to address
procedural skill and fluency.
Lesson 10.4 Inscribed Angles pp.709-716
Objective(s):
• Identify and describe relationships involving
inscribed angles.
• Prove properties of angles for a quadrilateral
inscribed in a circle.
Use the following resources to deepen
students' conceptual understanding of
mathematical content and develop their
ability to apply that knowledge to nonroutine problems.
Vocabulary
Inscribed angle, intercepted arc
Writing in Math/Discussion
p.715 #50
Compare and contrast inscribed angles and
central angles of a circle. If they intercept
the same arc, how are they related?
HS Flip Book with examples of each
Standard
Task(s)
Major Content
 Supporting Content

Additional Content
Shelby County Schools 2016/2017
Revised 12/1/16
17 of 19
Curriculum and Instruction –Mathematics
Quarter 3
TN STATE STANDARDS
GEOMETRY
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Illustrative Math: Opposite angles in a cyclic
quadrilateral
Major Content
 Supporting Content

Additional Content
Shelby County Schools 2016/2017
Revised 12/1/16
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Curriculum and Instruction –Mathematics
Quarter 3
GEOMETRY
RESOURCE TOOLBOX
The Resource Toolbox provides additional support for comprehension and mastery of subject-level skills and concepts. While some of these resources are embedded in the map, the use of these
categorized materials can assist educators with maximizing their instructional practices to meet the needs of all students.
Textbook Resources
Standards
ConnectED Site - Textbook and Resources Glencoe
Video Lessons
Hotmath - solutions to odd problems
Common Core Standards - Mathematics
Common Core Standards - Mathematics Appendix A TN Core
HS Flip Book with Examples of each Standard
(The Flip Book is designed as a resource tool to assist teachers in deepening their understanding of what
each standard means in terms of what students must know and be able to do. It outlines only a sample of
instructional strategies and examples. Links to conceptual categories and specific standards in the
document can be accessed from page 5 Mathematics Standards for High School.)
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
Major Content
Geometry Model Curriculum
http://www.ccsstoolbox.org/
http://insidemathematics.org/index.php/high-school-geometry
http://learnzillion.com/common_core/math/hs
http://www.livebinders.com/play/play/454480
https://www.livebinders.com/play/play?id=464831
http://www.livebinders.com/play/play?id=571735
Utah Electronic School - Geometry
Ohio Common Core Resources
Chicago Public Schools Framework and Tasks
Videos
Math TV Videos
The Teaching Channel
Khan Academy Videos (Geometry)
Tasks
Edutoolbox (formerly TNCore) Tasks
Inside Math
Tasks
Mars Tasks
Dan Meyer's ThreeNYC tasks
Illustrative Math Tasks
UT Dana Center
GSE Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
NWEA MAP
Resources:https://teach.mapnwea.org/assist/help_map/Applic
ationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sig
n 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.
ACT
TN ACT Information & Resources
ACT College & Career Readiness Mathematics Standards
Interactive Manipulatives
Literacy Resources
GeoGebra – Free software for dynamic math and science learning
Literacy Skills and Strategies for Content Area Teachers (Math,
p. 22)
NCTM Core Math Tools http://www.keycurriculum.com/products/sketchpad (Not free) Any activity
using Geometer’s Sketchpad can also be done with any software that allows construction of
figures and measurement, such as Cabri, Cabri Jr. on the TI-83 or 84 Plus,TI-92 Plus, or TINspire.
 Supporting Content

Additional Content
Glencoe Reading & Writing in the Mathematics Classroom
Graphic Organizers (9-12) (teachervision.com)
Shelby County Schools 2016/2017
Revised 12/1/16
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