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Curriculum and Instruction – Mathematics
Quarter 3
Bridge Math
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 concepts of each subject 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 Bridge Math, account for 65-75% of time spent on the major
conccepts of algebra 1, geometry and algebra 2.
• The supporting and additional content from algebra 1, geometry
and algebra 2 are incorporated into the subject to provide more
understanding about the major concepts of those courses.
• Thinking across grades/courses:
• learning of mathematics is carefully connected across
grades and subjects 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/subject level focus.
• 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.
Students are given opportunities to practice core
functions such as solving one-and two-step equations so
that they have access to more complex concepts and
procedures.
• 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.
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8. Look for and
express regularity
in repeated
reasoning
7. Look for and
make use of
structure
1. Make sense of
problems and
persevere in
solving them
2. Reason
abstractly and
quatitatively
Mathematical
Practices
6. Attend to
precision
3. Construct viable
arguments and
crituqe the
reasoning of
others
4. Model with
mathematics
5. Use appropriate
tools strategically
Bridge Math
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 highleverage 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.
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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.
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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.
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Topics Addressed in Quarter



Basic Geometry
Similar Triangles
Measurement
Overview
This quarter introduces and reviews some basic geometry to students including angles, triangles and polygons. Students study angle
relationships, classifications of triangles and their theorems and then the special angles and relationships in polygons and solve problems
involving angles, triangles and polygons. Students then review measurement including perimeter, circumference, area of two-dimensional
figures and surface area and volume of three-dimensional figures and solve problems using these figures, including the use of geometric
probabilities. The quarter concludes with students studying solving real-world problems involving similar triangles and their properties and
theorems.
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.
References:




https://www.engageny.org/
http://www.corestandards.org/
http://www.nctm.org/
http://achievethecore.org/
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TN STATE STANDARDS
Bridge Math
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Basic Geometry
Chapter 4 - McGraw-Hill Bridge Math
McGraw Hill Glencoe Geometry
PLEASE NOTE: TN CURRICULUM EMPHASIZES PROBLEM SOLVING ASPECTS, NOT THE PROOFS.
(Allow approximately 2 weeks for instruction, review, and assessment)
Conceptual Category: Ways of Looking:
Revisiting Concepts
Enduring Understanding(s):

Many relationships exist between the
measure of the angles of a triangle and
the measure of the sides of the triangle.

The properties of triangles create a basis
for understanding and reasoning that
extends to other geometric figures.
Domain: Verbal Mathematics (W-VM)
W-VM3. Use several angle properties to find
an unknown angle measure (i.e.
supplementary, complementary, vertical,
angles along a transversal, and sum of angles
in a polygon.)
Essential Question(s):


How do the properties of triangles
contribute to the geometric
understanding of the world around
us?
What can you say about the interior and
exterior angles of a triangle and other
polygons?

How do you use coordinate geometry to
find relationships within triangles?

How do you solve problems that involve
measurements of triangles?
Objective(s):

Students will identify and use special
pairs of angles.

Students will identify perpendicular lines.

Students will solve equations to find the
measure of angles.
Students classify triangles according to

McGraw-Hill Geometry
Review of angles
1-5 Angle Relationships
4-1 Classifying Triangles
4-2 Angles of Triangles
McGraw-Hill Bridge Math
pp.152-153, Refresh Your Math Skills
4-1 Triangles and Triangle Theorems
4-2 Congruent Triangles
Geometry Lab: Angles of Triangles, p. 243
Task(s):
Mathematics Vision Project- Module 5,
Geometric Figures (select from the eight tasks)
Vocabulary:
Angles, polygon, triangle, vertex, side, interior
angle, exterior angle, postulate, included
angle, included side
Writing in Math/Discussion:

How many exterior angles does a triangle
have? Draw a triangle and label all of its
exterior angles.

Explain why classifying an equiangular
triangle as an acute equiangular triangle is
unnecessary.

Explain why a triangle cannot have an
obtuse, acute, and a right exterior angle.
Additional Lessons/Resources:
Engageny Geometry Module 1, Topic B, Lesson
6 – Solve for Unknown Angles – Angles and
Lines at a Point
Complementary & Supplementary Lesson 1
NCTM Illuminations: Triangle Classification
Learnzillion Lesson: Angle Sum Theorem
Learnzillion Lesson: Exterior angle theorem
CPalms: Discovering Triangle Sum
Khan Academy Videos: Angles
Khan Academy Videos: Triangle Congruence
Khan Academy: Working with Triangles
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Bridge Math
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
their sides or angles.

Conceptual Category: Ways of Looking:
Revisiting Concepts
Domain: Verbal Mathematics (W-VM)
W-VM3. Use several angle properties to find
an unknown angle measure (i.e.
supplementary, complementary, vertical,
angles along a transversal, and sum of angles
in a polygon.)
Students will prove triangles are
congruent.
Enduring Understanding(s):
 Two figures are congruent if, through a
sequence of rigid motions and/or
constructions, one shape maps exactly
onto another.

Many relationships exist between the
measure of the angles of a triangle and
the measure of the sides of the triangle.

The properties of triangles create a basis
for understanding and reasoning that
extends to other geometric figures.
Essential Question(s):
 How do the properties of triangles
contribute to the geometric
understanding of the world around
us?
Conceptual Category: Ways of Looking:
Revisiting Concepts

What can you say about the interior and
exterior angles of a triangle and other
polygons?

How do you solve problems that involve
measurements of triangles?
Objective(s):
 Students will establish congruence
between two triangles to show that
corresponding parts are congruent.

Students will find angle and side
measures of triangles.
Enduring Understanding(s):
There exist certain patterns in the angle
measures of polygons.
McGraw-Hill Bridge Math
4-3 Congruent Triangles and Proofs
McGraw-Hill Geometry
4-6 Isosceles and Equilateral Triangles
Task(s):
CPalms Task: Are the Triangles Congruent?
TN Task Arc- Investigating Congruence in
Terms of Rigid Motion, Task 5
Mathematics Vision Project- Module 5,
Geometric Figures (select from the eight tasks)
Vocabulary: legs, base, base angles, vertex
angles, corollary, theorem
Writing in Math/Discussion:
Have students create multiple representations
of binomial multiplication.
Have students write a response to the
following: Can the product of two binomials
ever have more than three terms? Explain your
thinking.
Additional Lessons/Resources:
Engageny Geometry Module 1, Topic D,
Lesson 22 – Triangle Congruence
Equilateral and Isosceles Triangle
McGraw-Hill Bridge Math
4-7 Polygons and Angles
Vocabulary:
Polygon, vertex, convex, concave, interior
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Domain: Verbal Mathematics (W-VM)
W-VM3. Use several angle properties to find
an unknown angle measure (i.e.
supplementary, complementary, vertical,
angles along a transversal, and sum of angles
in a polygon.)
W-VM4. Describe, compare, and contrast
plane and solid figures using their attributes.
Bridge Math
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
Essential Question(s):
Is there a limit to the sum of the
interior/exterior angles of a polygon why or
why not?
McGraw-Hill Geometry
6-1 Angles of Polygons
Spreadsheet Lab Angles of Polygon, p. 398
Objective(s):
 Students will find and use the measures
of interior angles of polygons.
 Students will find and use the measures
of exterior angles of polygons.
Task(s):
CPalms Task: Interior Angles of a Polygon
Illustrative: Sum of Angles in a Polygon
Additional Lessons/Resources:
Khan Academy: Triangle Angles
Illuminations : Angle Sums
angles, exterior angles, consecutive sides,
consecutive vertices, diagonal, the PolygonSum Theorem ( Polygon Interior Angles Sum
Theorem), the Polygon Exterior Angle Theorem
Writing in Math/Discussion:
As the number of sides of a regular polygon
becomes larger and larger, what happens to
the measure of each exterior angle of the
polygon?
As the number of sides of a regular polygon
becomes larger and larger, what happens to
the measure of each interior angle of the
polygon?
Explain how triangles are related to the
Polygon-Sum Theorem (Polygon Interior
Angles Sum Theorem).
Conceptual Category: Ways of Looking:
Revisiting Concepts
Domain: Verbal Mathematics (W-VM)
W-VM4. Describe, compare, and contrast
plane and solid figures using their attributes.
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 apply properties of
parallelograms to find missing lengths and
angle measures.
McGraw-Hill Bridge Math
4-8 Special Quadrilaterals: Parallelograms
McGraw-Hill Geometry
6-3 Tests for Parallelograms
Task(s)
TN Task: Expanding Triangles
TN Task: Parallelograms
MARS Task: Floor Pattern
Mathematics Vision Project- Module 5,
Geometric Figures (select from the eight tasks)
Additional Lessons/Resources:
CPalms: Quadrilateral Classification Game
CPalms: To Be or Not to Be a Parallelogram
Vocabulary:
Opposite sides, opposite angles,
parallelogram, rectangle, rhombus, square,
The Parallelogram-Side Theorem, The
Parallelogram-Angle Theorem, The
Parallelogram-Diagonal Theorem, The
Rectangle-Diagonal Theorem, The RhombusDiagonal Theorem
Writing in Math/Discussion:
Are two parallelograms congruent if they both
have four congruent angles? Justify your
answer.
Suppose that you are asked to prove the
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Conceptual Category: Ways of Looking:
Revisiting Concepts
Domain: Verbal Mathematics (W-VM)
W-VM4. Describe, compare, and contrast
plane and solid figures using their attributes. .
Bridge Math
CONTENT
Enduring Understanding(s):
Properties of angles, triangles, quadrilaterals,
and polygons are connected.
Essential Question(s):
What are the properties of kites and
trapezoids?
Objective(s):
Students will apply properties of trapezoids to
find missing lengths and angle measures.
INSTRUCTIONAL SUPPORT & RESOURCES
Characteristics of Quadrilaterals
parallelogram-diagonal theorem. Write a
paragraph that explains how you would
proceed. (Do not write the two-column proof.)
McGraw-Hill Bridge Math
4-9 Special Quadrilaterals: Trapezoids
Graphing Technology Lab: The Triangle
Inequality, p.195a
Spreadsheet Lab: Angle of Polygons, 195b
Vocabulary:
Trapezoid, bases, base angles, legs, median,
isosceles trapezoid, kite, The Isosceles
Trapezoid Theorem
McGraw-Hill Geometry
6-6 Trapezoids and Kites
Task(s)
TN Task: Getting in Shape
TN Task: Go Fly a Kite
Writing in Math/Discussion:
Differentiate between the word median when
used in geometry to the word median used in
statistics.
Compare the median of a trapezoid to the
median of a triangle. How are they alike? How
are they different?
Additional Lessons/Resources:
Khan Academy: Quadrilaterals- Kites As
Geometric Shape
ACT Practice
(sample problems to prepare for the ACT)
McGraw-Hill Bridge Math, pp. 200-201
McGraw-Hill Geometry, pp.388-389
Conceptual Category: Ways of Looking:
Revisiting Concepts
Domain: Diagrammatic Mathematics (W-DM)
Measurement
Chapter 5 -McGraw-Hill Bridge Math
McGraw Hill Glencoe Geometry
(Allow approximately 3.5 weeks for instruction, review, and assessment)
Enduring Understanding(s):
McGraw-Hill Bridge Math
Relationships exist among angles,
5-2 & Perimeter, Circumference, and Area
segments, lengths, perimeter and area of
a polygons, and circumference and area
McGraw-Hill Geometry
Vocabulary:
Perimeter, circumference, area
Writing in Math/Discussion:
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W-DM4. Compute the perimeter of simple
composite geometric figures with unknown
side lengths.
W-DM5. Apply a variety of strategies to
determine the circumference and the area for
circles.
Bridge Math
CONTENT
of circles.
1-6 Two-Dimensional Figures
Essential Question(s):
 How do you find the area of a
polygon or find the circumference
and area of a circle?
 How do perimeters and areas of
similar polygons compare?
Task(s):
Illustrative: Eight Circles
Inside Math: Pizza Crusts
Objective(s):
Students will apply perimeter,
circumference and area formulas.
Conceptual Category: Applications: Ways of
Looking at the World
Domain: Applications with Data
(A-AD)
A-AD3. Solve problems involving
geometric probabilities. .
INSTRUCTIONAL SUPPORT & RESOURCES
Enduring Understanding(s):
The probability of an event can be
expressed as the ration of the number of
favorable outcomes to the number of
possible outcomes.
Essential Question(s):
How can you explain the concepts of
probability and use probability to solve
real-world problems?
Additional Lessons/Resources:
Khan Academy: Language-and-notation-of-thecircle
Khan Academy: Area and Perimeter
Khan Academy: Area and Circumference of
Circles
CPalms: Area and Circumference 1
CPalms: Area and Circumference 2
CPalms: Area and Circumference 3
McGraw-Hill Bridge Math
5-3 Probability and Area
McGraw-Hill Geometry
13-3 Geometric Probability
Task(s):
Inside Math: Marble Game
Additional Lessons/Resources:
Khan Academy: Probability Basics
Since  is an irrational number, many
calculations involving  are found using
approximations 3.14 or 227. When might it be
easier to use 22/7 rather than 3.14 to estimate
area or circumference?
Vocabulary:
probability
Writing in Math/Discussion:
The probability of an event is a number
between 0 and 1. What is the probability that
an event will always occur? What is the
probability of an impossible event? Give an
example of each.
Objective(s):
Students will determine probabilities using
areas.
Conceptual Category: Making Connections
Domain: Symbolic & Diagrammatic
Mathematics (M-SD)
Enduring Understanding(s):
More difficult problems can be solved by
decomposing the problems into smaller
solvable problems.
M-SD5. Apply a variety of strategies using
Essential Question(s):
McGraw-Hill Bridge Math
5-4 Problem Solving Skills: Irregular Shapes
McGraw-Hill Geometry
11-4 Area of Regular Polygons and Composite
Writing in Math/Discussion:
Create your own problem involving the area of
irregular figures that can be solved by first
solving a simpler problem or problems.
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relationships between perimeter, area, and
volume to calculate desired measures in
composite figures.
Bridge Math
CONTENT
How can you break a more complex
problem into smaller problems?
Objective(s):
Students will solve problems involving
irregular shapes.
Conceptual Category: Applications: Ways of
Looking at the World
Domain: Applications with Geometry (A-AG)
A-AG3. Solve problems involving surface
areas and volumes of 3-dimensional figures,
including maximization, scale, and increment
problems.
Conceptual Category: Applications: Ways of
Looking at the World
Domain: Applications with Geometry (A-AG)
A-AG3. Solve problems involving surface
areas and volumes of 3-dimensional figures,
including maximization, scale, and increment
problems.
Enduring Understanding(s):
More difficult problems can be solved by
decomposing the problems into smaller
solvable problems.
Essential Question(s):
How can you break a more complex
problem into smaller problems?
INSTRUCTIONAL SUPPORT & RESOURCES
Figures
Task(s):
NCTM Illuminations: Finding the Area of
Irregular Figures
Additional Lessons/Resources:
Khan Academy: Perimeter-and-Area-of-a-NonStandard-Polygon
LearnZillion: Finding the Area of an Irregular
Figure
McGraw-Hill Bridge Math
5-5 Three-dimensional Figures and Loci
McGraw-Hill Geometry
12-1 Representations of Three-Dimensional
Figures
Objective(s):
Students will analyze space figures.
Additional Lessons/Resources:
NCTM Illuminations: 3-D Interactive
Khan Academy: 2D vs, 3D Objects
Platonic Solids Ornaments
Enduring Understanding(s):
 Visualization can help you connect
properties of real objects with twodimensional drawings of these objects.
 Some attributes of geometric figures,
such as length, area, volume, and angle
measure, are measureable. Units are
used to describe these attributes.
McGraw-Hill Bridge Math
5-6 Surface Area of Three-dimensional Figures
5-7 Volume of Three-dimensional Figures
McGraw-Hill Geometry
12-2 Surface Area of Prisms & Cylinders
12-3 Surface Area of Pyramids & Cones
12-4 Volumes of Pyramids and Cones
12-5 Volumes of Prisms & Cylinders
Essential Question(s):
 How can you determine the
intersection of a solid and a plane?
 How do you find the surface area
Task(s):
Bedroom Remodel
MARS: Fruit Boxes
Vocabulary:
Polyhedron, faces, edge, vertex, prism, base,
pyramid, lateral faces, lateral edges, cylinder,
axis, cone, sphere
Writing in Math/Discussion:
A polyhedron is a regular polyhedron if all of its
faces are congruent regular polygons. The
Greek scholar, Plato, studied these figures,
also known as the five Platonic solids. What
are they and how have you seen examples of
these in the real world?
Vocabulary:
Surface area, volume
Writing in Math/Discussion:
The surface area of a rectangular prism is 178
in2. What is the height of the figure if its length
is 3 in. and its width is 4 in.? Explain how you
got your answer.
How are the formulas for the volume of a prism
and the volume of a cylinder similar? How are
they different?
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Bridge Math
CONTENT
and volume of a solid?
Objective(s):
 Students will find the surface area of
three-dimensional figures.
 Students will find the volume of
three-dimensional figures.
INSTRUCTIONAL SUPPORT & RESOURCES
Additional Lessons/Resources:
Khan Academy: Cylinder Volume and SurfaceArea
Surface Area of Pyramids and Cones
Khan Academy: Volume of a Sphere
LearnZillion: finding Surface Area of ThreeDimensional Figures
LearnZillion: Using Nets to Find Surface Area
LearnZillion: Volume Lessons
LearnZillion: Solve Real-World ProblemsSurface Area and Volume of Rectangular
Prisms
Interactive: Isometric Drawing Tool
Illuminations: Finding Surface Area and Volume
ACT Practice
(sample problems to prepare for the ACT)
McGraw-Hill Bridge Math, pp. 242-243
McGraw-Hill Geometry, pp.456-457
Conceptual Category: Making Connections
Domain: Symbolic & Numeric Mathematics
(M-SV)
M-SV3. Write ratios, proportions, and solve
proportions in a contextual setting for an
unknown value.
Similar Triangles
Chapter 7 - McGraw-Hill Bridge Math
McGraw Hill Glencoe Geometry
(Allow approximately 3.5 weeks for instruction, review, and assessment)
McGraw-Hill Bridge Math
Enduring Understanding(s):
5-1 Ratios and Units of Measure
Many types/varieties of situations in life
McGraw-Hill Geometry
depend on or require the application of
proportional reasoning.
7-1 Ratios and Proportions
7-1 Graphing Technology Lab - Fibonacci
Essential Question(s):
Sequence and Ratios p. 464
How do we use proportional relationships
in solving real-world problems?
Task(s)
Dan Myer 3-Act Tasks – Ratios and
Objective(s):
Proportions
Students will use ratios and rates to
Vocabulary:
Measurement, customary, metric, compass,
protractor, calipers, micrometers, precision,
greatest possible error (GPE), ratio, rate, unit
rate, unit price.
Writing in Math/Discussion:
Compare and contrast a ratio and a proportion.
Explain how you would use both to solve a
problem.
Shelby County Schools 2016/2017
Revised 11/28/16
12 of 17
Curriculum and Instruction – Mathematics
Quarter 3
TN STATE STANDARDS
Conceptual Category: Applications: Ways of
Looking at the World
Domain: Applications with Numbers (A-AN)
A-AN3. Solve rate, distance, and work
problems using proportions and percentages.
Conceptual Category: Making Connections
Domain: Symbolic & Verbal Mathematics (MSV)
Bridge Math
CONTENT
solve problems.
Additional Lessons/Resources:
Khan Academy: Ratios, Rates and Proportions
Enduring Understanding(s):
Ratios can be used to describe proportional
situations.
McGraw-Hill Bridge Math
7-1 Ratios and Proportions
Essential Question(s):
 Why are ratios and proportions
important?
 How are they used in the real world?
M-SV3. Write ratios, proportions, and
solve proportions in a contextual setting
for an unknown value.
Objective(s):
 Students will find equivalent ratios.
 Students will use ratios and proportions
to solve problems.
Conceptual Category: Applications: Ways of
Looking at the World
Domain: Applications with Geometry (A-AG)
Enduring Understanding(s):
The use of proportional relationships between
similar figures can help solve problems.
A-AG1. Solve problems involving ratios in
geometric settings, such as similar figures and
right triangle distance problems.
Essential Question(s):
 How do you show two polygons are
similar?
 How do you use proportions to find side
lengths in similar polygons?
Conceptual Category: Applications: Ways of
Looking at the World
Domain: Applications with Geometry (A-AG)
INSTRUCTIONAL SUPPORT & RESOURCES
Objective(s):
 Students will identify similar polygons.
 Students will find missing measures of
similar polygons.
Enduring Understanding(s):
The use of proportional relationships between
similar figures can help solve problems.
McGraw-Hill Geometry
7-1 Ratios and Proportions
Task(s):
TN Task Arc: Reasoning With Ratios and Rates
(Select from Tasks 1 through 8)
Vocabulary:
Equivalent ratios, proportion, terms, extremes,
means, cross products
Writing in Math/Discussion:
If a/b = c/d, is it always true that a/c = b/d?
Explain.
Additional Lessons/Resources:
Khan Academy: Ratios
Khan Academy: Writing Proportions
Khan Academy: Ratio and Proportion
McGraw-Hill Bridge Math
7-2 Similar Polygons
McGraw-Hill Geometry
7-2 Similar Polygons
Task(s):
TN Task: Ratios, Proportions, and Similar
Figures
Vocabulary:
Similar
Writing in Math/Discussion:
When given two similar figures, how can you
tell which angles are corresponding angles?
Additional Lessons/Resources:
Similar Polygons - Lesson & Worksheets
Lesson: Congruent and Similar Figures
McGraw-Hill Bridge Math
7-3 Scale Drawings
McGraw-Hill Geometry
7-7 Scale Drawings and Models
Vocabulary:
Scale drawing, scale
Writing in Math/Discussion:
Shelby County Schools 2016/2017
Revised 11/28/16
13 of 17
Curriculum and Instruction – Mathematics
Quarter 3
TN STATE STANDARDS
A-AG1. Solve problems involving ratios
in geometric settings, such as similar
figures and right triangle distance
problems.
Bridge Math
CONTENT
Essential Question(s):
How do you use proportions to find real
and scale measurements?
Objective(s):
Students will find actual or scale length
using scale drawings.
Conceptual Category: Applications: Ways of
Looking at the World
Domain: Applications with Geometry (A-AG)
A-AG1. Solve problems involving ratios in
geometric settings, such as similar figures and
right triangle distance problems.
Enduring Understanding(s):
There exist methods for proving triangles
similar.
INSTRUCTIONAL SUPPORT & RESOURCES
Task(s):
Additional Lessons/Resources:
LearnZillion: Scale Drawings Lesson 1
(Procedural Skills)
LearnZillion: Scale Drawings Lesson 2
(Conceptual)
LearnZillion: Scale Drawings Lesson 3
(Application)
LearnZillion: Areas of Scale Drawings
McGraw-Hill Bridge Math
7-4 Postulates for Similar Triangles
McGraw-Hill Geometry
7-3 Similar Triangles
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 AA, SSS, and SAS
similarity postulates to determine if two
triangles are similar and solve problems using
similar triangles.
Task(s):
Select appropriate tasks from GSE Analytic
Geometry Unit 1: Similarity, Congruence and
Proofs
Additional Lessons/Resources:
Engageny Geometry Module 1, Topic D,
Lesson 22 – Triangle Congruence
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.
Vocabulary:
The AA Similarity Postulate, the SSS Similarity
Theorem, the SAS Similarity Theorem
Writing in Math/Discussion:
Compare and contrast the AA Similarity
Postulate, the SSS Similarity Theorem, and the
SAS Similarity Theorem
Given a triangle, explain a process you can use
to draw a similar triangle that is twice as large.
Engageny Geometry Module 1,
Topic D, Lesson 24 – Congruence
Criteria for Triangles – ASA and SSS
Khan Academy - Similar Triangle Basics
Shelby County Schools 2016/2017
Revised 11/28/16
14 of 17
Curriculum and Instruction – Mathematics
Quarter 3
TN STATE STANDARDS
Conceptual Category: Ways of Looking:
Revisiting Concepts
Domain: Verbal Mathematics (W-VM)
W-VM1. Understand that a line parallel to one
side of a triangle divides the other two sides
proportionally, and conversely.
W-VM2. Apply similar triangles to solve
problems, such as finding heights and
distances.
Conceptual Category: Applications: Ways of
Looking at the World
Domain: Applications with Geometry (A-AG)
A-AG1. Solve problems involving ratios in
geometric settings, such as similar figures and
right triangle distance problems
Bridge Math
CONTENT
Enduring Understanding(s):
There exist theorems for finding similar
triangles’ lengths of proportional segments.
Essential Question(s):
 If a segment connects the midpoint
of two sides of a triangle, what is
known about the length of the third
side?
 What is the relationship between the
altitudes of two similar triangles?
 If two triangles are similar, what is
known about their medians in
relation to the corresponding sides
of the triangles?
Objective(s):
 Students will prove theorem
involving similar triangles.
 Students will find unknown lengths
of sides of triangles.
Enduring Understanding(s):
There exist theorems for finding lengths of
proportional segments involving parallel lines.
Essential Question(s):
 If a line is parallel to one side of a
triangle and intersects the other
sides at any points except the
vertex, what is known about that
line?
 What do you know about the
median of a trapezoid in relation to
the lengths of the bases?
Objective(s):
 Students will use theorems involving
INSTRUCTIONAL SUPPORT & RESOURCES
McGraw-Hill Bridge Math
7-5 Triangles and Proportional Segments
McGraw-Hill Geometry
7-5 Parts of Similar Triangles
Writing in Math/Discussion:
If two rectangles are similar, do you think their
diagonals are proportional to corresponding
sides? Explain.
Task(s):
Illustrative: Congruent and Similar Triangles
Illustrative: Similar Triangles
Additional Lessons/Resources:
LearnZillion: Triangle Similarity by Checking for
Congruent Angles
Khan Academy: Triangle Similarity
MARS: Identifying Similar Triangles
McGraw-Hill Bridge Math
7-6 Parallel Lines and Proportional Segments
7-7 Problem Solving Skills: Indirect
Measurements
McGraw-Hill Geometry
7-4 Parallel Lines and Proportional Parts
7-5 Extend: Geometry Lab: Fractals
Vocabulary:
Median
Writing in Math/Discussion:
Construct the following segment as directed:
 A segment separated into two
segments in which their lengths have
a ratio of 1 to 3.
Task(s):
Illustrative: Midpoints of Triangle Sides
Additional Lessons/Resources:
Brightstorm: Proportional Segments Between
Parallel lines
Brightstorm: Indirect Measurement
Shelby County Schools 2016/2017
Revised 11/28/16
15 of 17
Curriculum and Instruction – Mathematics
Quarter 3
TN STATE STANDARDS
Bridge Math
CONTENT


parallel lines and proportional
segments to find unknown lengths.
Students will divide a line segment
into congruent parts.
Students will solve problems using
indirect measurement.
INSTRUCTIONAL SUPPORT & RESOURCES
ACT Practice
(sample problems to prepare for the ACT)
McGraw-Hill Bridge Math, pp. 294-295;
pp.336-337
McGraw-Hill Geometry, pp.456-457; pp. 532533
Shelby County Schools 2016/2017
Revised 11/28/16
16 of 17
Curriculum and Instruction – Mathematics
Quarter 3
Bridge Math
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.
NWEA MAP Resources: https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.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.
Textbook Resources
http://www.connected.mcgraw-hill.com/
http://www.pearsonsuccessnet.com/
Standards
Common Core Standards - Mathematics
Common Core Standards - Mathematics Appendix A
Edutoolbox (formerly TNCore)
http://www.ccsstoolbox.org/
Common Core Lessons
Tennessee State Standards
Tennessee’s Bridge Math Standards
CCSS Flip Book with Examples of each Standard
Additional Sites
Illuminations (NCTM)
Stem Resources
http://jc-schools.net/dynamic/math/math12.html
Literacy
Glencoe- Reading and Writing in the Math Classroom
Literacy Skills and Strategies for Content Area Teachers
(Math, p. 22)
Graphic Organizers (9-12) Graphic Organizers (dgelman)
Interactive Manipulatives
National Math Resources
MARS Course 2
NASA Space Math
National Math Resources
http://www.ilovemath.org/index.php?option=com_docman
http://www.mathopenref.com
SMARTboard Lessons
Videos
Brightstorm
Teacher Tube
The Futures Channel
Khan Academy
Math TV
Lamar University Tutorial
Shmoop - We Speak Students
Calculator
Math Nspired
Texas Instrument Activities
Casio Activities
Tasks/Lessons
Mathematics Assessment Project (MARS/ Math Shell Tasks)
Dan Meyer's Three-Act Math Tasks
Illustrative Math Tasks
UT Dana Center
Inside Math Tasks
LearnZillion
Math Vision Project
UT Dana Center
Mars Tasks
Better Lesson
SCS Tasks
ACT
TN ACT Information & Resources
ACT College & Career Readiness Mathematics Standards
Shelby County Schools 2016/2017
Revised 11/28/16
17 of 17