Download Objective(s) - Shelby County Schools

Curriculum and Instruction – Office of 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 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 3
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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Quarter 3
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 3
GEOMETRY
Topics Addressed in Quarter
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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. 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 should be able to identify central angles, major and minor arcs, semicircles
and find their measures. They will finish the quarter studying inscribed angles and intercepted arcs.
Content Standard
G-SRT.A.2
Type of Rigor
Conceptual Understanding
Foundational Standards
8.G.A.1, 2,3, 4,5
G-SRT.B.4, 5
Conceptual Understanding
8.G.A.1, 2,3, 4,5
G-SRT.C.6, 7, 8
G-C.A.1, 2
Conceptual Understanding & Application
Conceptual Understanding
8.G.A.1, 2,3, 4,5
8.G.A.5; 8.G.B.7
G-MG.A.3
Application
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
Mathshell: Hopewell Geometry
Illustrative: Similar Circles; Illustrative:
Neglecting the Curvature of the Earth
Illustrative: Ice Cream Cone; Illustrative:
Satellite
** 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 3
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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Quarter 3
GEOMETRY
TN STATE STANDARDS
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.
CONTENT
Similarity and Transformations
Right Triangles and Trigonometry
(Allow approximately 5 weeks for instruction, review, and assessment)
Use the textbook resources to address
Enduring Understanding(s)
procedural skill and fluency.
 Polygons are similar if and only if
Lesson 7.2 Similar Polygons pp.465-473
corresponding angles are congruent and
corresponding sides are proportional.
Lesson 7.6 Similarity Transformations pp. 505-511

Geometric figures can change size and/or
position while maintaining proportional
attributes
Essential Question(s)
 How is similarity defined by transformations?
 How can you prove two figures are similar?
Objective(s):
 Use proportions to Identify similar
polygons.
 Solve problems using the properties of
similar polygons.
 Identify similarity transformations.
 Verify similarity after a similarity
transformation.
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
Major Content
INSTRUCTIONAL SUPPORT & RESOURCES
Enduring Understanding(s)
 Geometric figures can change size and/or
position while maintaining proportional
attributes.
 Supporting Content
Use the following Lesson(s) 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?
Engageny Geometry Module 2, Topic C,
Lesson 12 – Similarity Transformations
Engageny Geometry Module 2, Topic C,
Lesson 14 – Similarity
Task(s):
Illustrative Math: Are They Similar? G-SRT.A.2
Use the textbook resources to address
procedural skill and fluency.
Lesson 7.7 Scale Drawings and Scale Models
pp. 512-517

Additional Content
Vocabulary
Similar polygons, similarity ratio, scale factor
dilation, similarity transformation, center of
dilation, scale factor of a dilation,
enlargement, reduction
Activity with Discussion
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
Explain how you can use scale factor to
determine whether a transformation is an
enlargement, a reduction, or a congruence
transformation.
Writing in Math
Compare and contrast congruent, similar, and
equal figures.
Vocabulary
Scale model, scale drawing, scale
Writing in Math
Felix and Tamara are building a replica of their
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Quarter 3
GEOMETRY
TN STATE STANDARDS
minimize cost; working with typographic grid
systems based on ratios). ★
CONTENT
Essential Question(s)
 How can geometric properties and
relationships be applied to solve problems
that are modeled by geometric objects?
 How do you use proportions to find side
lengths in similar polygons?
INSTRUCTIONAL SUPPORT & RESOURCES
Use the following Lesson(s) to introduce
concepts/build conceptual understanding.
Engageny Geometry Module 2, Topic A,
Lesson 2 – Making Scale Drawings
Task(s):
Illustrative Math: Ice Cream Cone
high school. The high school is 75 feet tall and
the replica is 1.5 feet tall. Felix says the scale
factor of the actual high school to the replica is
50:1, while Tamara says the scale factor is
1:50. Is either of them correct? Explain your
reasoning.
Objective(s):
 Create scale drawings of polygonal
figures by the ratio method.
 Use scale factors to solve problems.
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Cluster(s): Understand similarity in terms of
similarity transformations.
Prove theorems involving similarity



G-SRT.B.3 Use the properties of
similarity transformations to establish
the AA criterion for two triangles to be
similar.
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.
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)
 Polygons are similar if and only if
corresponding angles are congruent and
corresponding sides are proportional.
Essential Question(s)
 What relationships among sides and other
segments in a triangle are always true?
 How do you use proportions to find side
lengths in similar polygons?
 How do you show two triangles are similar?
Objective(s):
Use the textbook resources to address
procedural skill and fluency.
Lesson 7.3 Similar Triangles pp. 474-483
Writing in Math
Contrast and compare the triangle congruence
theorems with the triangle similarity theorems.
Use the following Lesson(s) to introduce
concepts/build conceptual understanding.
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
Math Shell Lesson: Flood Light Shadows
 Students will prove the angle-angle criterion
for two triangles to be similar and use it to
solve triangle problems
 Identify similar triangles and use their
properties to solve problems.
 Supporting Content

Additional Content
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Curriculum and Instruction – Office of Mathematics
Quarter 3
GEOMETRY
TN STATE STANDARDS
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.
G-SRT.B.5 Use congruence and
similarity criteria for triangles to solve
problems and to prove relationships in
geometric figures.
CONTENT
Enduring Understanding(s)
 Polygons are similar if and only if
corresponding angles are congruent and
corresponding sides are proportional.
 Congruence and similarity criteria for
triangles are used to solve problems and
prove relationships of geometric figures.
Essential Question(s)
 How do you use proportions to find side
lengths in similar polygons?
 How might the features of one figure be
useful when solving problems about a
similar figure?
Objective(s):
 Prove that special segments in similar
triangles are proportional.
 Prove the Pythagorean Theorem by
using similar triangles.
 Recognize and use proportional
relationships of corresponding angle
bisectors, altitudes, and medians of
similar triangles.
 Use the Triangle Angle Bisector
Theorem to find lengths of sides of
similar triangles.
Domain: G-SRT Similarity, Right Triangles
and Trigonometry
Major Content
INSTRUCTIONAL SUPPORT & RESOURCES
Use the textbook resources to address
procedural skill and fluency.
Lesson 7.4 Parallel Lines and Proportional Parts
(mid-segments was previously covered in unit
2) pp. 484-492
Lesson 7.5 Parts of Similar Triangles pp.495-503
Use the following resources to ensure that
the intended outcome and level of rigor
(mainly conceptual understanding and
application) of the standards are met.
Use the following Lesson(s) to introduce
concepts/build conceptual understanding.
Engageny Geometry Module 2, Topic A,
Lesson 4 – Triangle Side Splitter Theorem
Engageny Geometry Module 2, Topic B,
Lesson 10 – Dividing a Line Segment into
Equal Parts
Engageny Geometry Module 2, Topic C,
Lesson 18 – Triangle Angles Bisector
Theorem
Engageny Geometry Module 2, Topic C,
Lesson 19 – Parallel Lines and Proportional
Segments
Activity with Discussion
Use multiple representations to explore angle
bisectors and proportions. (See p. 492, #47)
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
Task(s)
Illustrative Math: Pythagorean Theorem
Illustrative Math: Joining Two Midpoints of Sides
of a Triangle
Use the textbook resources to address
Enduring Understanding(s)
 Similar figures map one shape proportionally procedural skill and fluency.
 Supporting Content
Vocabulary
Mid-segment of a triangle

Additional Content
Vocabulary
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Curriculum and Instruction – Office of Mathematics
Quarter 3
GEOMETRY
TN STATE STANDARDS
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.
G-SRT.B.5 Use congruence and
similarity criteria for triangles to solve
problems and to prove relationships in
geometric figures.
CONTENT
onto another through non-rigid motions.
 Congruence and similarity criteria for
triangles are used to solve problems and
prove relationships of geometric figures.
Essential Question(s)
 Can the geometric mean be used in any
triangle?
 How does geometric mean help us to find
the missing sides in a right triangle?
INSTRUCTIONAL SUPPORT & RESOURCES
Lesson 8.1 Geometric Mean pp.531-539
Geometric mean
Use the following Lesson(s) to introduce
concepts/build conceptual understanding.
Engageny Geometry Module 2, Topic D,
Lesson 21 – Special Relationships within
Right Triangles
Engageny Geometry Module 2, Topic D,
Lesson 24 – Prove the Pythagorean Theorem
Using Similarity
Writing in Math
How does geometric mean help to find the
missing sides in a right triangle?
Use the textbook resources to address
procedural skill and fluency.
Lesson 8.3 Special Right Triangles pp.552-559
Activity with Discussion
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.
Objective(s):
 Students will prove the geometric mean
relationships in a triangle using similarity.
 Students will prove the triangle
proportionality theorem (side splitting
theorem) using similarity.
 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: 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.
Major Content
Enduring Understanding(s)
 The concept of similarity enables us to
explore geometric relationships and apply
trigonometric ratios to solve real world
problems.
Essential Question(s)
 How does the understanding of triangle
similarity develop an understanding of
trigonometric ratios and relationships in
triangles?
 Supporting Content
Use 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)
Discovering Special Right Triangles Learning
Task
Finding Right Triangles in your Environment

Additional Content
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Curriculum and Instruction – Office of Mathematics
Quarter 3
GEOMETRY
TN STATE STANDARDS
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.
G-SRT.C.7 Explain and use the
relationship between the sine and
cosine of complementary angles.
G-SRT.C.8 Use trigonometric ratios
and the Pythagorean Theorem to solve
right triangles in applied problems. ★
CONTENT
Objective(s):
Learning Task
 Compare common ratios for similar
right triangles and develop a
relationship between the ratio and the
acute angle leading to the trigonometry
ratios.
Create your own triangles Learning Task
Use the textbook resources to address
 Trigonometry can be used to measure sides procedural skill and fluency.
Lesson 8.4 Trigonometry pp.562-271
and angles indirectly in right triangles.
Enduring Understanding(s)
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?
Objective(s):

G-SRT.C.8 Use trigonometric ratios
and the Pythagorean Theorem to solve
right triangles in applied problems. ★
Major Content
Use the following resources to ensure that
the intended outcome and level of rigor
(mainly conceptual understanding and
application) of the standards are met.
 Use trigonometric rations and Pythagorean
Theorem to solve right triangles.
Discovering Trigonometric Ratio Relationships
Learning Task p.22
Inside Mathematics: Hopewell Geometry
Performance Task
Use the textbook resources to address
 Trigonometry can be used to measure sides procedural skill and fluency.
Lesson 8.5 – Angles of Elevation and Depression
and angles indirectly in right triangles.
pp.574-581
Essential Question(s)
 Supporting Content
Activity with Discussion
Explain how you can use ratios of the side
lengths to find the angle measures of the acute
angles in a right triangle.
Task(s)
Enduring Understanding(s)
 How do you find a side length or angle
measure in a right triangle?
Vocabulary
Trigonometry, trigonometry ratio, sine,
cosine, tangent, inverse sine, inverse
cosine, inverse tangent
Learnzillion: Apply Sine and Cosine Functions
Similar Right Triangles and Trig Ratios Lesson
 Define trigonometric ratios for acute angles
in right triangles.
 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
INSTRUCTIONAL SUPPORT & RESOURCES
Use the following resources to ensure that
the intended outcome and level of rigor
(mainly conceptual understanding and

Additional Content
Vocabulary
Angle of elevation, angle of depression
Writing in Math
How is a right triangle used to find the sine and
cosine of an acute angle? Is there a unique
right triangle that must be used?
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Quarter 3
GEOMETRY
TN STATE STANDARDS
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
 When you know the lengths of the sides of a application) of the standards are met.
right triangle, how can you find the
measures of the two acute angles?
Learnzillion Lesson: Develop an Understanding
and Apply Right Triangle Rules
Objective(s):
Learnzillion: Apply Relationships of Right
Triangles Using Pythagorean Theorem
 Students will solve trigonometry and
Pythagorean Theorem problems based on
written descriptions.
Task(s)
 Students will apply trigonometric ratios and Find that Side or Angle Task
Pythagorean Theorem to solve angle of
elevation and angle of depression problems. TN Task :Interstate
TN Task: Making Right Triangles
Illustrative Math: Ask the Pilot
Domain: G-C Circles
Cluster: Understand and apply theorems
about circles

G-C.A.1 Prove that all circles are similar.
Properties of Angles and Segments in Circles
(Allow approximately 4 weeks for instruction, review, and assessment)t)
Use the textbook resources to address
Enduring Understanding(s)
procedural skill and fluency.
 The concept of similarity as it relates to
circles can be extended with proof.
Lesson 10.1 – Circles and Circumference pp.683691
Essential Question(s)
Domain: G-CO Congruence
Cluster: Experiment with transformations in the  What role do circles play in modeling the
word around us?
plane

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.
Objective(s):
 Give an argument to justify the formula
for the circumference of a circle.
 Prove that all circles are similar.
Writing in Math
Provide examples of how distance traveled
can depend on the circumference of a circle
when used with vehicles.
Learnzillion Lesson: G-CO.A.1
Learnzillion Lesson: G-GMD.A.1
Task(s)
Illustrative Math: Similar Circles Task
All Circles are Similar Task
Domain: G-GMD Geometric Measurement
and Dimension
Cluster: Explain volume formulas and use them
to solve problems
Major Content
Use the following resources to ensure that
the intended outcome and level of rigor
(mainly conceptual understanding and
application) of the standards are met.
Vocabulary
Circle, center, radius, chord, diameter, congruent
circles, concentric circles, circumference, pi,
inscribed, circumscribed
 Supporting Content

Additional Content
Shelby County Schools 2016/2017
Revised 11/1/16
11 of 15
Curriculum and Instruction – Office of Mathematics
Quarter 3
GEOMETRY
TN STATE STANDARDS

INSTRUCTIONAL SUPPORT & RESOURCES
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

CONTENT
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.
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):
 Investigate and identify relationships
between parts of a circle and angles formed
by parts of a circle
Use the textbook resources to address
procedural skill and fluency.
Lesson 10.2 Measuring Angles and Arcs pp.692700
Vocabulary
Central angle, arc, minor arc, major arc,
semicircle, congruent arcs, adjacent arcs, arc
length
Use 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
Describe how to use central angles to find
other angles within a triangle
Use the following Lesson(s) 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
Discuss relationships between the arcs
intercepted by an angle and the measure of that
angle.
Task(s)
Circles and their Relationships among Central
Angles, Arcs and Chords
Investigating Angle Relationships in Circles
Getting a Job Task (Click on HCPSS
Task: Getting a Job)
Major Content
 Supporting Content

Additional Content
Shelby County Schools 2016/2017
Revised 11/1/16
12 of 15
Curriculum and Instruction – Office of Mathematics
Quarter 3
TN STATE STANDARDS
Domain: G-C Circles
Cluster: Understand and apply theorems
about circles

G-C.A.2 Identify and describe
relationships among inscribed angles,
radii, and chords. Include the relationship
between central, inscribed, and
circumscribed angles; inscribed angles
on a diameter are right angles; the radius
of a circle is perpendicular to the tangent
where the radius intersects the circle.
GEOMETRY
CONTENT
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)
Use the textbook resources to address
procedural skill and fluency.
Lesson 10.4 Inscribed Angles pp.709-716
Use the following resources to ensure that
the intended outcome and level of rigor
(mainly conceptual understanding and
application) of the standards are met.
 How are segments within circles, such as
radii, diameters, and chords, related to each
other?
Use the following Lesson(s) to introduce
 What is the relationship of their
concepts/build conceptual understanding.
measurements?
Engageny Geometry Module 5, Topic A,
Lesson 5 – Prove Inscribed Angle Theorem
Objective(s):
 Identify and describe relationships involving
inscribed angles.
 Prove properties of angles for a
quadrilateral inscribed in a circle.
Major Content
INSTRUCTIONAL SUPPORT & RESOURCES
 Supporting Content
Vocabulary
Inscribed angle, intercepted arc
Writing in Math
Compare and contrast inscribed angles and
central angles of a circle. If they intercept
the same arc how are they related?
Task(s)
Illustrative Math: Opposite angles in a cyclic
quadrilateral

Additional Content
Shelby County Schools 2016/2017
Revised 11/1/16
13 of 15
Curriculum and Instruction – Office of Mathematics
Quarter 3
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)
Others
TN Ready Geometry Blueprint
State ACT Resources
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
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.
 Supporting Content

Additional Content
Videos
Math TV Videos
The Teaching Channel
Khan Academy Videos (Geometry)
Tasks
Edutoolbox (formerly TNCore) Tasks
Inside Math
Tasks
Mars Tasks
Dan Meyer's ThreeAct Math Tasks
NYC tasks
Illustrative Math Tasks
UT Dana Center
SCS Math Tasks
GSE Analytic Geometry Unit 1: Similarity,
Congruence and Proofs
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)
Shelby County Schools 2016/2017
Revised 11/1/16
14 of 15
Curriculum and Instruction – Office of Mathematics
Quarter 3
Major Content
GEOMETRY
 Supporting Content

Additional Content
Shelby County Schools 2016/2017
Revised 11/1/16
15 of 15