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Curriculum and Instruction – Office of Mathematics
4th Quarter
Algebra II
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 standardsaligned 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 Ready Standards are 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
•
•
•
•
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 algebra 2, 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.
Major Content
Supporting Content
Coherence
Rigor
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 onto
foundations built in previous years. Each
standard is not a new event, but an extension of
previous learning.
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 the high school standards for
math do not list high school fluencies, there are
suggested fluency standards for algebra 1,
geometry and algebra 2.
Linking to major topics:
•
Instead of allowing additional or supporting
topics to detract from course, these concepts
serve the course focus. For example, instead of
data displays as an end in themselves, they are
an opportunity to do grade-level word
problems.
Additional Content
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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Algebra II
Our collective goal is to ensure our students graduate ready for
college and career. The Standards for Mathematical Practice
describe varieties of expertise that mathematics educators at all
levels should seek to develop in their students. These practices rest
on important “processes and proficiencies” with longstanding
importance in mathematics education. The first of these are the
NCTM process standards of problem solving, reasoning and proof,
communication, representation and connections.
Problem Solving
Connecton
Representation
Look for and
express
regularity in
repeated
reasoning
Look for and
make use of
structure
Reasoning and
Proof
Communication
Make sense of
problems and
persevere in
solving them
Reason
abstractly and
quatitatively
Mathematical
Practices
Attend to
precision
Construct viable
arguments and
critique the
reasoning of
others
Model with
mathematics
The second are the strands of mathematical proficiency specified in the
National Research Council’s report Adding It Up: adaptive reasoning,
strategic competence, conceptual understanding (comprehension of
mathematical concepts, operations and relations) procedural fluency
(skill in carrying out procedures flexibly, accurately, efficiently and
appropriately), and productive disposition (habitual inclination to see
mathematics and sensible, useful and worthwhile, coupled with a belief
in diligence and one’s own efficacy). Throughout the year, students
should continue to develop proficiency with the eight Standards for
Mathematical Practice.
Use appropriate
tools
strategically
Major Content
Supporting Content
Additional Content
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Algebra II
How to Use the Mathematic Curriculum Maps
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
instructional practice in alignment with the three College and Career Ready shifts in instruction for Mathematics. We should see these
shifts in all classrooms:
1) Focus
2) Coherence
3) Rigor
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 each of the three shifts that teachers should consistently access:
The TNCore Mathematics Standards
The Tennessee Mathematics Standards:
https://www.tn.gov/education/article/mathematicsstandards
Teachers can access the Tennessee State standards, which
are featured throughout this curriculum map and
represent college and career ready learning at each
respective grade level.
Mathematical Shifts
Focus
The standards are focused on fewer topics so students can
http://achievethecore.org/shifts-mathematics
learn more
Coherence
http://achievethecore.org/shifts-mathematics
Topics within a grade are connected to support focus, and
learning is built on understandings from previous grades
Rigor
http://achievethecore.org/shifts-mathematics
The standards set expectations for a balanced approach to
pursuing conceptual understanding, procedural fluency,
and application and modeling
Major Content
Supporting Content
Additional Content
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Algebra II
Curriculum Maps:







Locate the TDOE Standards in the left column. Analyze the language of the standards and match each standard to a learning target
in the second column.
Consult your Pearson/Prentice Hall or Glencoe Algebra 2 Teachers’ Edition (TE) and other cited references to map out your week(s)
of instruction.
Plan your weekly and daily objectives, using the standards' explanations provided in the second column. Best practices tell us
that making objectives measureable increases student mastery.
Carefully review the web-based resources provided in the 'Content and Tasks' column and use them as you introduce or assess a
particular standard or set of standards. The additional resources provided are supplementary and should be used as needed for
content support and differentiation.
Review the Literacy Connections found in the right column. Make plans to address the content vocabulary, utilizing the
suggested literacy strategies, in your instruction.
Examine the other standards and skills you will need to address in order to ensure mastery of the indicated standard.
Using your Pearson/Prentice Hall or Glencoe TE and other resources cited in the curriculum map, plan your week using the
SCS lesson plan template. Remember to include differentiated activities for small-group instruction and math stations.
Major Content
Supporting Content
Additional Content
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TN State Standards
Algebra II
Essential Understandings
Content & Tasks
Literacy Connections
Chapter 10: Quadratic Relations & Conic Sections
(Allow 2 weeks for instruction, review, and assessments)
G-GPE Expressing Geometric Properties with
Equations
Translate between the geometric description
and the equation for a conic section.
G-GPE.2 Derive the equation of a
parabola given a focus and directrix.
Algebra can be used to efficiently and
effectively describe and apply
geometric properties.
Students will:
• Write the equation of a parabola and
graph parabolas.
Essential Question
How can algebra be useful when expressing
geometric properties?
Pearson 10-2 Parabolas
Glencoe 10-2 Parabolas
Additional Resources
The resources below are supplementary and
should be used as needed for additional
content support and differentiation
Writing in Math
What is true about the set of points on a
parabola, its focus, and its directrix?
What can you determine about the orientation
of a parabola by looking at its vertex
equation?
Pearson Videos
Writing the equation of a parabola
Finding the equation of a parabola
Graphing the equation of a parabola
Vocabulary
Focus of a parabola, directrix, focal length
Save the Kindle Task
Mica Item
G-GPE.2 Question # 78 ID # 44293
Engageny Algebra II Module 1, Topic C,
Lesson 33, The Definition of a Parabola
Students model the locus of points at equal
distance between a point (focus) and a line
(directrix). They construct a parabola and
understand this geometric definition of the curve.
They use algebraic techniques to derive the
analytic equation of the parabola.
GPE.A.1 Derive the equation of a circle of
given center and radius using the
Pythagorean Theorem; complete the
square to find the center and radius of a
circle given by an equation.
Major Content
An equation of a circle with center (0, 0)
and radius r in the coordinate plane is x2 +
y2 = r2.
Students will:
• Write and graph the equation of a
Supporting Content
Additional Content
Pearson 10-3 Circles
Glencoe 10-3 Circles
Pearson Videos
Writing in Math
What is the standard form of a circle, and what
do the variables h, k, and r represent?
Writing the equation of a circle
Writing the equation of the translation of a circle
Vocabulary
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TN State Standards
•
GPE.A.3 (+) Derive the equations of
ellipses and hyperbolas given the foci,
using the fact that the sum or difference
of distances from the foci is constant.
GPE.A.3 (+) Derive the equations of
ellipses and hyperbolas given the foci,
using the fact that the sum or difference
of distances from the foci is constant.
Algebra II
Essential Understandings
circle;
Find the center and radius of a circle
and use them to graph the circle.
A circle is the set of points a fixed
distance from one point. An ellipse
“stretches” a circle in one direction and is
the set of points that have a total fixed
distance from two points.
Content & Tasks
Writing the equation of a circle to model a realworld situation
Using the center and radius of a circle
Pearson 10-4 Ellipses
Glencoe 10-4 Ellipses
Additional Resources
The resources below are supplementary and
should be used as needed for additional
content support and differentiation
Students will:
• Write and graph the equation of a
ellipse;
• Find the foci of an ellipse.
Pearson Videos
Essential Question
How can algebra be useful when expressing
geometric properties?
Loci and Conics Task
Like an ellipse, the hyperbola’s shape is
determined by its distance from two foci.
Students will:
• Graph the equation of a hyperbola;
• Find and use the foci of a hyperbola.
Literacy Connections
Circle, center of a circle, radius, standard form
of an equation of a circle
Writing in Math
The area of a circle is r2. The area of an
ellipse is ab. Explain the connection.
Vocabulary
Ellipse, focus of an ellipse, major axis, center
of an ellipse, minor axis, vertices of an ellipse,
co-vertices of an ellipse
Writing the equation of an ellipse given vertex, covertex, and the center
Finding the foci of an ellipse
Pearson 10-5 Hyperbolas
Glencoe 10-5 Hyperbolas
Additional Resources
The resources below are supplementary and
should be used as needed for additional
content support and differentiation
Pearson Videos
Graphing a hyperbola
Finding the foci of a hyperbola
Using the foci of a hyperbola
Writing in Math
Compare and contrast the characteristics of
the equations and graphs of ellipses and
hyperbolas.
Vocabulary
Hyperbola, focus of the hyperbola, vertex of a
hyperbola, transverse axis, axis of symmetry,
center of a hyperbola, conjugate axis
Engageny Precalculus and Advanced Topics
Module 3, Topic A, Lesson 8; Curves from
Geometry
Major Content
Supporting Content
Additional Content
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Curriculum and Instruction – Office of Mathematics
4th Quarter
TN State Standards
Algebra II
Essential Understandings
Content & Tasks


Literacy Connections
Students learn to graph equations of the
form x2/a2 – y2/b2 =1.
Students derive the equations of
hyperbolas given the foci, using the fact
that the difference of distances from the
foci is constant.
Chapter 12: Matrices
(Allow 3 weeks for instruction, review, and assessments)
N-Q Vector & Matrix Quantities
Perform operations on matrices and use
matrices in applications.
VM.C.6 Use matrices to represent
and manipulate data
VM.C.8 Add, subtract, and multiply
matrices of appropriate dimensions
Operations and properties of the real
number system can be extended to
situations involving vectors and matrix
quantities.
Essential Question
How does the knowledge of real numbers and
geometry help when working with vectors and
matrices?
Students will:
• Add and subtract matrices;
• Solve matrix equations.
Pearson 12-1 Adding and Subtracting
Matrices
Glencoe 4.1 Introduction to Matrices & 4.2
Operations with Matrices
Writing in Math
Explain how a matrix can be helpful when
deciding what college you want to attend.
Additional Resources
The resources below are supplementary and
should be used as needed for additional
content support and differentiation
Vocabulary
Corresponding elements, matrix equation,
zero matrix, equal matrices
Pearson Videos
Adding matrices
Using the additive identity and additive
inverse matrices
Subtracting matrices
Solving matrix equations
Finding unknown matrix elements
Fast Food Order (Project Graduation Activity)
N-Q Vector & Matrix Quantities
Perform operations on matrices and use
matrices in applications.
The product of two matrices is a matrix.
To find an element in the product matrix,
you multiply the elements of a row from
the first matrix by the corresponding
elements of a column from the second
Major Content
Additional Content
Supporting Content
Pearson 12-2 Matrix Multiplication
Glencoe 4.3 Multiplying Matrices
Writing in Math
When can you multiply two matrices, and
how?
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TN State Standards
VM.C.7 Multiply matrices by scalars
to produce new matrices
VM.C.8 Add, subtract, and multiply
matrices of appropriate dimensions
VM.C.9 Understand that, unlike
multiplication of numbers, matrix
multiplication for square matrices is not a
commutative operation, but still satisfies
the associative and distributive
properties.
Algebra II
Essential Understandings
matrix. Then add the products.
Students will:
• Multiply matrices using scalar and
matrix multiplication.
Content & Tasks
Additional Resources
The resources below are supplementary and
should be used as needed for additional
content support and differentiation
Literacy Connections
Vocabulary
Scalar, scalar multiplication
Pearson Videos
Using scalars and matrix multiplication
Solving matrix equations with scalars
Multiplying Matrices
Using matrix multiplication to solve problems
Engageny Precalculus and Advanced Topics
Module 1, Topic C, Lesson 25; Matrix
Multiplication and Addition

Students work with 2 × 2 matrices as
transformations of the plane.

Students combine matrices using matrix
multiplication and addition.
Students understand the role of the zero
matrix in matrix addition

A-REI Reasoning with Equations and
Inequalities
Solve systems of equations.
A-REI.6 Solve systems of linear
equations exactly and approximately
(e.g., with graphs), focusing on pairs of
linear equations in two variables.
Some matrix equations Ax = B can be
solved by multiplying each side by A-1, the
inverse of matrix A.
Pearson 12-4 Inverse Matrices and Systems
Glencoe 4.6 Inverse Matrices and Systems
of Equations
Students will:
• Solve systems of equations using
matrix inverses and multiplication.
Additional Resources
The resources below are supplementary and
should be used as needed for additional
content support and differentiation
Pearson Videos
Writing in Math
Explain how matrix equations can be used to
solve systems of equations.
Vocabulary
Coefficient matrix, variable matrix, constant
matrix
Solving a matrix equation containing 3 x 3 matrices
Using matrices to solve a system of two equations
Using matrices to solve a system of three
equations
Applying matrices of systems of equations
Major Content
Supporting Content
Additional Content
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TN State Standards
Algebra II
Essential Understandings
N-Q Vector & Matrix Quantities
Perform operations on matrices and use
matrices in applications.
VM.C.11 Multiply a vector (regarded as a
matrix with one column) by a matrix of
suitable dimensions to produce another
vector. Work with matrices as
transformations of vectors.
You can multiply a 2 X 1 matrix
representing a point by a 2 X 2 matrix to
rotate the point about the origin or reflect
the point across a line.
Students will:
• Solve systems of equations using
matrix inverses and multiplication.
Content & Tasks
Pearson 12-5 Geometric Transformations
Glencoe 4.4 Transformations with Matrices
Additional Resources
The resources below are supplementary and
should be used as needed for additional
content support and differentiation
Pearson Videos
Using matrices to translate a figure
Using matrices to dilate a figure
Using matrices to reflect a figure
Using matrices to rotate a figure
Literacy Connections
Writing in Math
Describe how matrices can be used to
transform figures in two-dimensional space.
Describe the physical characteristics of a
figure after each transformation.
Vocabulary
Image, preimage, dilation, rotation, center of
rotation
Engageny Algebra II Module 1, Topic C,
Lesson 35
Students apply the geometric transformation of
dilation to show that all parabolas are similar.
N-Q Vector & Matrix Quantities
Represent and model with vector quantities
VM.A.1 Recognize vector quantities
as having both magnitude and
direction. Represent vector
quantities by directed line segments,
and use appropriate symbols for
vectors and their magnitudes
VM.A.2 Find the components of a
vector by subtracting the
coordinates of an initial point from
the coordinates of a terminal point.
VM.A.3 Solve problems involving velocity
and other quantities that can be
represented by vectors.
Major Content
A vector is a mathematical object that has
both magnitude (size) and direction.
Pearson 12-6 Vectors
Glencoe 4.4 Vectors and Matrices
Students will:
• Use basic vector operations and the
dot product.
Additional Resources
The resources below are supplementary and
should be used as needed for additional
content support and differentiation
Supporting Content
Pearson Videos
Learning about vectors and vector sums
using dynamic software
Additional Content
Writing in Math
Subtract any vector from itself. The result is
still a vector, but a unique one. Explain what
this vector is, and what it means for vector
addition.
Vocabulary
Vector, magnitude, initial point, terminal point,
dot product, normal vectors
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TN State Standards
Algebra II
Essential Understandings
Content & Tasks
Literacy Connections
Solving Polynomial, Rational, and Radical Equations
(Allow 3 weeks including TNReady assessment, instruction after TNReady, review, and assessments)
(TNReady Part II, April 25-May 6, 2016)
In preparation for students’ next school
year in mathematics please select from the
following lessons to build and reinforce the
Algebra II content.
Arithmetic with Polynomials and Rational
Expressions
Rewrite rational expressions.
A-APR.6 Rewrite simple rational expressions in
different forms; write a(x)/b(x) in the form q(x) +r(x)/b(x),
where a(x), b(x), q(x), and r(x) are polynomials with
the degree of r(x) less than the degree of b(x), using
inspection, long division, or, for the more
complicated examples, a computer algebra system.
Engageny Algebra II Module 1, Topic C
Solving and Applying Equations--- Polynomial,
Rational, and Radical
Lesson 22: Equivalent Rational Expressions
Lesson 23: Comparing Rational Expressions
Lesson 24: Multiplying and Dividing Rational Expressions
Lesson 25: Adding and Subtracting Rational Expressions
Lesson 26: Solving Rational Equations
Lesson 27: Word Problems Leading to Rational Equations
Lesson 28: A Focus on Square Roots
Lesson 29: Solving Radical Equations
Lesson 30: Linear Systems in Three Variables
Lesson 31: Systems of Equations
Lesson 32: Graphing Systems of Equations
Reasoning with Equations and Inequalities
Understand solving equations as a process of
reasoning and explain the reasoning
A-REI.1 Explain each step in solving a simple
equation as following from the equality of numbers
asserted at the previous step, starting from the
assumption that the original equation has a solution.
Construct a viable argument to justify a solution
method
Mica Items
A-APR.6 Question #17 ID #42997
A-APR.6 Question #18 ID #42999
A-APR.6 Question #19 ID #44268
A-REI.1 Question # 25 ID # 42992
A-REI.2 Question # 26 ID # 42956
A-REI.2 Question #27 ID #42989
A-REI.2 Question #28 ID #42991
A-REI.2 Question #29 ID #44302
A-REI.2 Question #30 ID #44384
A-REI.7 Question #31 ID #44128
A-REI.7 Question #32 ID #43856
A-REI.7 Question #33 ID #42953
A-REI.7 Question #34 ID #42955
A-REI.7 Question #35 ID #43841
A-REI.7 Question #36 ID #42954
A-REI.2 Solve simple rational and radical
equations in one variable, and give examples
showing how extraneous solutions may arise.
Reasoning with Equations and Inequalities
Solve equations and inequalities in one variable.
A-REI 4 Solve quadratic equations in one
variable.
b. Solve quadratic equations by inspection (e.g., for
x2 = 49), taking square roots, completing the
square, the quadratic formula and factoring, as
Major Content
Supporting Content
See Engageny Lessons for Exit
Tickets/Discussion Questions
Additional Content
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4th Quarter
TN State Standards
Algebra II
Essential Understandings
Content & Tasks
Literacy Connections
appropriate to the initial form of the equation.
Recognize when the quadratic formula gives
complex solutions and write them as a ± bi for real
numbers a and b.
Reasoning with Equations and Inequalities
Solve systems of equations.
A-REI.6 Solve systems of linear equations
exactly and approximately (e.g., with graphs),
focusing on pairs of linear equations in two
variables.
A-REI.7 Solve a simple system consisting of a
linear equation and a quadratic equation in
two variables algebraically and graphically.
For example, find the points of intersection
between the line y = –3x and the circle x2 + y2
= 3.
G-GPE Expressing Geometric Properties with
Equations
Translate between the geometric description and
the equation for a conic section.
G-GPE.2 Derive the equation of a parabola
given a focus and directrix.
Major Content
Supporting Content
Additional Content
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Algebra II
RESOURCE TOOLBOX
Textbook Resources
Standards
Pearson Tools:
www.phschool.com/math
http://www.poweralgebra.com
http://www.pearsonsuccessnet.com
( ELL, Enrichment, Re-teaching, Quizzes/Tests, Think About a Plan, Test Prep,
Extra Practice, Find the Errors, Activities/Games/Puzzles, Video Tutor, Chapter
Project, Performance Task, and Student Companion)
Glencoe Tools:
Student Edition
Teacher Edition
Problem Solving
Vocabulary Puzzle Maker
http://interactmath.com/
Common Core State Standards Initiative
Common Core Standards - Mathematics
Common Core Standards - Mathematics Appendix A
TN Core
The Mathematics Common Core Toolbox
Tennessee Blueprints
PARCC Blueprints and Test Specifications FAQ
CCSS Toolbox
NYC tasks
New York Education Department Tasks
PARCC High School Math Tasks
TICommonCore.com
TN Department of Education Math Standards
Algebra 2 TN State Standards
Videos
Brightstorm
Teacher Tube
The Futures Channel
Khan Academy
Math TV
Lamar University Tutorial
Literacy:
Literacy Skills and Strategies for Content Area Teachers
(Math, p. 22)
Glencoe Reading & Writing in the Mathematics Classroom
Graphic Organizers (9-12)
Graphic Organizers (dgelman)
PARCC Practice Test
Calculator
Interactive Manipulatives
Kuta Software- worksheet generator
Illuminations (NCTM)
Math Nspired
Texas Instrument Activities
Casio Activities
Stem Resources
National Math Resources
MARS Course 2
NASA Space Math
Other:
UT Dana Center
Mars Tasks
Inside Math Tasks
Math Vision Project
UT Dana Center
Mars Tasks
Purple Math
Mica Items
Major Content
Supporting Content
Additional Content
Additional Sites
Dana Center Algebra 2 Assessments
Illinois State Assessment strategies
University of Idaho Literacy Strategies
SCS Math Tasks (Algebra II)
NWEA MAP
Resources:https://teach.mapnwea.org/assist/help_map/Appli
cationHelp.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.
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