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Curriculum and Instruction – Mathematics

1st Quarter Advanced Algebra & Trigonometry

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.

Shelby County Schools 2016/2017Revised 6/29/16

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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 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.

Coherence

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.

Rigor

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.



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:


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The TN Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-standards

Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.

Standards for Mathematical PracticeMathematical Practice Standardshttps://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

Teachers can access the Mathematical Practice Standards, which are featured throughout this curriculum map. This link contains more a more detailed explanation of each practice along with implications for instructions.

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 judgement 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—high-quality teaching and learning to grade-level specific standards, including purposeful support of literacy and language learning across the content areas.

Additional Instructional SupportShelby 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;


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https://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

https://www.tn.gov/education/article/mathematics-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.

How to Use the Mathematics Curriculum Maps

OverviewAn 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 StandardsThe 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.

ContentTeachers 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 ResourcesDistrict and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks, i-Ready lessons 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

Equations & Inequalities Relations, Functions & Graphs Polynomials & Rational Functions

OverviewDuring this quarter students will review and extend their previous understanding of number expressions and algebra. They will represent, intercept, compare, and simplify number expressions including roots and fractions of pi. Students will simplify complex radical and rational expressions and discuss and display understanding that rational numbers are dense in the real numbers and the integers are not. Students will perform complex number arithmetic and understand the representation on the complex plane and analyze functions using different representations. Students extend their knowledge of functions and equations to include quadratic, polynomial and rational functions and equations. Students will understand the properties of conic sections and apply them to model real-world phenomena. Students will build new functions from existing functions and analyze their graphs. Students will solve real-world problems that can be modeled using these functions (by hand & technology). 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/ http://tncore.org

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESEquations and Inequalities

(Allow approximately 3 weeks for instruction, assessment, and review)Domain: N-NE – Number ExpressionsCluster: Represent, intercept, compare, and

Enduring Understanding(s)The most fundamental requirement for

R.1 The Language, Notation, and Number of Mathematics (Coburn)

VocabularySets, subsets, real number, natural numbers,


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http://achievethecore.org/

http://www.nctm.org/Standards-and-Positions/Position-Statements/Procedural-Fluency-in-Mathematics/

http://www.corestandards.org/

https://www.engageny.org/



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESsimplify number expressions.N-NE.A.3 Classify real numbers and order real numbers that include transcendental expressions, including roots and fractions of pi and e.

learning algebra is mastering the language which includes words, symbols, and numbers to express mathematical ideas.

Essential Question(s)How is the language of algebra like any other language?

Objective(s):• Students will review sets of numbers,

graphing real numbers, and set notation.• Students will review inequality symbols

and order relations.• Students will review the absolute value of

a real number.• Students will review order of operations.

P.1 Algebraic Expressions, Mathematical Models, and Real Numbers. (Blitzer)

Additional Resource(s)Brightstorm Video: Introduction to the Real Number System Khan Academy Video: Rational & Irrational Numbers

whole numbers, integers, rational numbers, irrational numbers

Writing in MathList the different types of numbers. Give real life examples of when the specific types of numbers are best used.

Can a real number be both rational and irrational? Explain your answer.

Domain: N-NE – Number ExpressionsCluster: Represent, intercept, compare, and simplify number expressions.N-NE.A.4 Simplify complex radical and rational expressions; discuss and display understanding that rational numbers are dense in the real numbers and the integers are not.

Enduring Understanding(s)The most fundamental requirement for learning algebra is mastering the language which includes words, symbols, and numbers to express mathematical ideas.

Essential Question(s)• How do we use the properties of

exponents to simplify expressions?• How are radical expressions used in real-

world phenomena?Objective(s):• Students will evaluate radicals, simplify

radicals, add & subtract radical expressions, and multiply and divide radical expressions.

• Students will evaluate formulas involving radicals.

R.6/P.3 Radicals and Rational Exponents (Coburn/Blitzer)

Additional Resource(s)Brightstorm Videos: Introduction to Radicals Khan Academy Video: Simplifying Radicals Khan Academy Video: Square Root & Real Numbers Khan Academy Video: Adding & Simplifying Radicals

VocabularyRadical, radicand, square root, radical expression, Product Rule, Quotient Rule, rationalizing the denominator

Writing in MathCompare and contrast the words “radical” and “rational.”


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https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/square-roots-for-college/v/more-simplifying-radical-expressions

https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/square-roots-for-college/v/more-simplifying-radical-expressions

https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/square-roots-for-college/v/square-roots-and-real-numbers

https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/square-roots-for-college/v/square-roots-and-real-numbers

https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/square-roots-for-college/v/simplifying-radicals

https://www.brightstorm.com/math/algebra-2/roots-and-radicals/introduction-to-radicals/

http://www.tn.gov/assets/entities/education/attachments/std_math_adv_alg_trig.pdf

https://www.khanacademy.org/math/algebra/rational-and-irrational-numbers

https://www.khanacademy.org/math/algebra/rational-and-irrational-numbers

https://www.brightstorm.com/math/algebra-2/real-numbers/introduction-to-real-numbers/

https://www.brightstorm.com/math/algebra-2/real-numbers/introduction-to-real-numbers/




TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Review as needed- Algebra II (A-REI)Domain: Reasoning With Equations and InequalitiesCluster: Solve equations and inequalities in one variableCluster: Represent and solve equations and inequalities graphically.


Essential Question(s)

Objective(s):• Students will solve inequalities and state

the solution set.• Students will solve linear inequalities.• Students will solve compound

inequalities.• Students will solve applications of

inequalities.

1.2 Linear Inequalities in One Variable (Coburn)1.7 Linear Inequalities and Absolute Value Inequalities(Blitzer)

VocabularySolution set, set notation, number line, interval notation, additive property of inequality, multiplicative property of inequality, compound inequalities, union, intersection

Writing in MathWhen solving an inequality, when is it necessary to change the sense of the inequality? Give an example.

Describe ways in which solving an inequality is similar to solving a linear equations. Describe ways in which they are different.

Domain: N-CN- Complex NumbersCluster: Perform complex number arithmetic and understand the representation on the complex plane.N-CN.A.1 Perform arithmetic operations with complex numbers expressing answers in the form a+bi.N-CN.A.2 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.


Essential Question(s)• Why are complex numbers necessary?• How are operations and properties of

complex numbers related to those of real numbers?

Objective(s):• Students will add, subtract, multiply and

divide complex numbers.• Students will perform operations with

square roots of negative numbers.

1.4 Complex Numbers (Coburn/Blitzer)

Task(s)Imaginary Numbers

Additional Resource(s)Brightstorm Video: Adding & Subtracting Complex Numbers Brightstorm Video: Multiplying Complex NumbersKhan Academy Videos: Imaginary & Complex Numbers

VocabularyImaginary, complex, conjugate

Writing in MathWhat is i?

Research the use of imaginary numbers in the real world and write a description, including an example, to share with the class.

Domain: Interpreting Functions Enduring Understanding(s) 1.5 Quadratic Equations (Coburn/Blitzer) Vocabulary


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https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers

https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers

https://www.brightstorm.com/math/algebra-2/roots-and-radicals/multiplying-complex-numbers/

https://www.brightstorm.com/math/algebra-2/roots-and-radicals/multiplying-complex-numbers/

https://www.brightstorm.com/math/algebra-2/roots-and-radicals/adding-and-subtracting-complex-numbers/

https://www.brightstorm.com/math/algebra-2/roots-and-radicals/adding-and-subtracting-complex-numbers/

http://www.scribd.com/doc/15806630/A2TImaginaryNumbers



http://tn.gov/assets/entities/education/attachments/std_math_adv_alg_trig.pdf

http://tn.gov/assets/entities/education/attachments/std_math_algebra_II.pdf




Cluster: Analyze functions using different representations.F-IF.A.3 Identify the real zeroes of a function and explain the relationship between the real zeros and the x-intercepts of the graph of a function (polynomial, rational, exponential, logarithmic, and trigonometric).

You can solve a quadratic equation in standard form in more than one way.

Essential Question(s)How are the real solutions of a quadratic equation related to the graph of the related quadratic function?

Objective(s):Students will solve quadratic equations by:

• using the zero product property• using the square root property

of equality• completing the square• using the quadratic formula

• Students will use the discriminant to identify solutions.

• Students will solve applications of quadratic equations.

Additional Lesson(s)Engage ny Algebra II, Module1, Topic D

Task(s)Quadratic Equations Puzzles

Additional Resource(s)Khan Academy Videos: Quadratic Equations and Functions

Quadratic equation, standard form, zero product property, square root property of equality, completing the square, quadratic formula discriminant

Writing in MathHow is the quadratic formula derived?

If you are given a quadratic equation, how do you determine which method to use to solve it?

Domain: Interpreting FunctionsCluster: Analyze functions using different representations.F-IF.A.3 Identify the real zeroes of a function and explain the relationship between the real zeros and the x-intercepts of the graph of a function (polynomial, rational, exponential, logarithmic, and trigonometric).

Enduring Understanding(s)• Relations and functions can be

represented numerically, graphically, algebraically, and/or verbally.

• The properties of functions and function operations are used to model and analyze real-world applications and quantitative relationships.

Essential Question(s)• How do I solve polynomial equations?• How do I solve radical equations?• How do I solve equations with rational

exponents?

1.6 Solving Other Types of Equations (Coburn)1.6 Other types of Equations (Blitzer)

Additional Lesson(s)Engage ny Precalculus & Advanced Topics, Module 3, Topic A Additional Resource(s)Khan Academy Videos: Polynomial Expressions, Equations, and Functions

VocabularyPolynomial equation, rational equation, extraneous roots, radical equation, power property of equality

Writing in MathExplain how to recognize an equation that is quadratic in form. Provide two original examples with your explanation.


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https://www.khanacademy.org/math/algebra2/polynomial-functions


https://www.engageny.org/resource/precalculus-and-advanced-topics-module-3-topic-a-overview

https://www.engageny.org/resource/precalculus-and-advanced-topics-module-3-topic-a-overview




https://www.khanacademy.org/math/algebra/quadratics

https://www.khanacademy.org/math/algebra/quadratics

https://www.scribd.com/doc/27362113/Quadratic-Equations-Puzzle

https://www.engageny.org/resource/algebra-ii-module-1-topic-d-overview







Objective(s):• Students will solve polynomial equations

of higher degree.• Students will solve rational equations.• Students will solve radical equations and

equations with rational exponents.• Students will solve equations that are

quadratic in form.• Students will solve applications of various

equation types.

Relations, Functions & Graphs(Allow approximately 3 weeks for instruction, assessment, and review)

Domain: Conic SectionsCluster: Understand the properties of conic sections and apply them to model real-world phenomena.A-C.A.2 From an equation in standard form, graph the appropriate conic section: ellipses, hyperbolas, circles, and parabolas. Demonstrate an understanding of the relationship between their standard algebraic form and the graphical characteristics.



The properties of functions and function operations are used to model and analyze real-world applications and quantitative relationships.

Graphs of quadratic equations of the form ax2 + by2 + cx + dy + e = 0 can be circles, parabolas, ellipses, or hyperbolas

Essential Question(s) How do relationships exist between

quantities and how can you represent these relationships?

How do you identify the graphs of quadratic equations of the form ax2 + by2 + cx + dy + e = 0?

Objective(s):

2.1 Rectangular Coordinates; Graphing Circles and Other Relations (Coburn)2.8 Distance and Midpoint Formulas; Circles (Blitzer)

Additional Resource(s)Dom a in and R a n g e of C o m m on F un c t i ons Khan Academy Videos: Conics

VocabularyRelation, ordered pair, dependent variable, independent variable, mapping notation, domain, range, equation form, rectangular coordinate system, quadrants, coordinate plane, continuous, midpoint of a line segment, the distance formula, the equation of a line, circle, radius, center

Writing in MathIn your own words, describe how to find the distance between two points in the rectangular coordinate system.

In your own words, describe how to find the midpoint of a line segment if its endpoints are known.


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https://www.khanacademy.org/math/precalculus/conics-precalc







• Students will express a relation in mapping notation and ordered pair form.

• Students will graph a relation.• Students will develop the equation of a

circle using the distance and the midpoint formulas exponents.

• Students will graph circles.

Domain: Building FunctionsCluster: Build new functions from existing functions.F-BF.A.2 Develop an understanding of functions as elements that can be operated upon to get new functions: addition, subtraction, multiplication, division, and composition of functions.




Essential Question(s)• How can you represent and describe

functions?• How can functions describe real-world

situations, model predictions and solve problems?

Objective(s):• Students will distinguish the graph of a

function from that of a relation.• Students will determine the domain and

range of a function.• Students will use function notation and

evaluate functions.• Students will apply the rate-of-change

concept to nonlinear functions.

2.4 Functions, Function Notation, and the Graph of a Function (Coburn)2.1 Basics of Functions and Their Graphs (Blitzer)

Task(s) P rinting Tic ke ts:

VocabularyFunction, linear function, constant function, identity function, vertical boundary line, horizontal boundary line, point of inflection, implied domain, function notation, average rate of change

Writing in MathWhat is the difference in the usage of “y=” and “f(x)=”? Explain the multiple uses of “f(x)” that cannot be accomplished by using “y.”

If a relation is represented by a set of ordered pairs, explain how to determine whether the relation is a function.


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Domain: Building FunctionsCluster: Build new functions from existing functions.F-BF.A.4 Construct the difference quotient for a given function and simplify the resulting expression.







Objective(s):• Students will determine whether a

function is even, odd, or neither.• Students will determine intervals where a

function is positive or negative.• Students will determine where a function

is increasing or decreasing.• Students will identify the maximum and

minimum values of a function.• Students will develop a formula to

calculate rates of change for any function.

2.5 Analyzing the Graph of a Function (Coburn)2.2 More on Functions and Their Graphs (Blitzer)

Task(s)Functions and Everyday SituationsMeasuring MammalsBacteria PopulationsCompleting the square

VocabularySymmetry/symmetric, even function, odd function, maximum, minimum

Writing in MathDiscuss one disadvantage to using point plotting as a method for graphing functions.

Explain how to use a function’s graph to find the function’s domain and range.

Explain how the vertical line test is used to determine whether a graph is a function.

Domain: Building FunctionsCluster: Build new functions from existing functions.F-BF.A.1 Understand how the algebraic properties of an equation transform the geometric properties of its graph.




2.6 The Toolbox Function (Coburn)2.5 Transformations of Functions (Blitzer)Vid e o Tutori a l Using T I - 84

Vocabulary

Writing in MathWhat must be done to a function’s equation so that its graph is shifted vertically upward?

What must be done to a function’s equation so


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http://www.illustrativemathematics.org/illustrations/1690

http://www.illustrativemathematics.org/illustrations/370

http://www.insidemathematics.org/problems-of-themonth/pom-measuringmammals.pdf

http://map.mathshell.org/lessons.php?collection=8&unit=9260










Objective(s):• Students will distinguish the graph of a

function from that of a relation.• Students will determine the domain

and range of a function.

that its graph is shifted horizontally to the right?

What must be done to a function’s equation so that its graph is reflected about the x-axis?

What must be done to a function’s equation so that its graph is reflected about the y-axis?

Domain: Interpreting FunctionsCluster: Analyze functions using different representations.F-IF.A.5 Visually locate critical points on the graphs of functions and determine if each critical point is a minimum, a maximum, or point of inflection. Describe intervals of concavity and increasing and decreasing.







Objective(s):• Students will state the equation and

domain of a piecewise-defined function.• Students will graph functions that are

piecewise-defined.• Students will solve applications involving

2.7 Piecewise-Defined Functions (Coburn)2.2 More on Functions and Their Graphs. (Blitzer)Additional Resource(s)Khan Academy Videos: Piecewise Functions

Vocabularypiecewise-defined function, step functions, greatest integer function

Writing in MathExplain why a piecewise-defined function would ever be used.


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https://www.khanacademy.org/math/algebra/algebra-functions#piecewise-functions




TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESpiecewise-defined functions.

Domain: Building FunctionsCluster: Build new functions from existing functions.F-BF.A.2 Develop an understanding of functions as elements that can be operated upon to get new functions: addition, subtraction, multiplication, division, and composition of functions.F-BF.A.3 Compose functions.







Objective(s):• Students will compute a sum or difference

of functions and determine the domain of the result.

• Students will compute a product or quotient of functions and determine the domain.

• Students will compose two functions and determine the domain; decompose a function.

• Students will interpret operations on functions graphically.

• Students will apply the algebra and composition of functions in context.

2.8 The Algebra and Composite of Functions (Coburn)2.6 Combinations of Functions; Composite Functions (Blitzer)

Task(s)Building a Quadratic Function By CompositionTN Task Arc:Building Polynomial Functions, (tasks 1-3)

Additional Resource(s)Khan Academy Videos: Composing Functions

VocabularyAlgebra of functions, composition of functions

Writing in MathExplain in your own words at least two methods to find a composite function.

If the equations of two are given, explain how to obtain the quotient function and its domain.

Polynomial & Rational Functions(Allow approximately 3 weeks for instruction, assessment, and review)

Domain: Interpreting Functions Enduring Understanding(s) 3.1 Quadratic Functions and Applications (Coburn/Blitzer)

Vocabulary


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https://www.khanacademy.org/math/algebra2/manipulating-functions#funciton-composition

https://www.khanacademy.org/math/algebra2/manipulating-functions#funciton-composition

http://tncore.org/sites/www/Uploads/Aug_23/MATH/Alg2_guide_arc.pdf

http://tncore.org/sites/www/Uploads/Aug_23/MATH/Alg2_guide_arc.pdf

https://www.illustrativemathematics.org/content-standards/tasks/744







Cluster: Analyze functions using different representations.F-IF.A.3 Identify the real zeroes of a function and explain the relationship between the real zeros and the x-intercepts of the graph of a function (polynomial, rational, exponential, logarithmic, and trigonometric).

• Relations and functions can be represented numerically, graphically, algebraically, and/or verbally.



quadratic functions?• How can quadratic functions describe

real-world situations, model predictions and solve problems?

Objective(s):• Students will recognize characteristics of

a parabola.• Students will graph parabolas.• Students will determine a quadratic

function’s minimum or maximum value.• Students will solve problems involving a

quadratic function’s minimum or maximum value.

Additional Lesson(s)Representing Quadratic Functions Graphically

Solving Quadratic Equations

Standard form, solution, root, factor, zero

Writing in MathGive examples of real-life situations best suited to the use of quadratic equations.

Domain: Interpreting FunctionsCluster: Analyze functions using different representations.F-IF.A.3 Identify the real zeroes of a function and explain the relationship between the real zeros and the x-intercepts of the graph of a function (polynomial, rational, exponential, logarithmic, and trigonometric).

Enduring Understanding(s)Relationships can be defined as how one member is related to another member by its function in a given situation.

Essential Question(s)• Why is synthetic division used instead of

polynomial long division?• How can you use quadratic procedures to

solve non-quadratic situations?•

3.2 Synthetic Division: The Remainder Factor Theorems (Coburn)3.3 Dividing Polynomials; Remainder and Factor Theorems. (Blitzer)

Additional Resource(s)R e maind e r & F ac tor T h e o re ms T I - 84 A c t i vi t y L e sson 3.2

VocabularySynthetic division, remainder theorem, factor theorem

Writing in MathWhat is a polynomial functions?

What are the zeros of a polynomial function and how are they found?


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Objective(s):• Students will divide polynomials using

long division and synthetic division.• Students will recognize characteristics of

the graphs of polynomial functions.• Students use the remainder theorem to

evaluate polynomials.• Students will use the factor theorem to

factor and build polynomials.• Students will solve applications using the

remainder theorem.

Explain the relationship between the degree of a polynomial and the number of turning points on its graph.

Domain: Complex NumbersCluster: Use complex numbers in polynomial identities and equations.N-CN.B.6 Extend polynomial identities to the complex numbers.N-CN.B.7 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.


Essential Question(s)• How can you find a solution to a

polynomial equation algebraically and graphically?

• How can features of polynomial functions such as the equation, solutions, axis of symmetry, vertex, etc. be represented in tables, equations, and in “real world” contexts?

Objective(s):• Students will apply the fundamental

theorem of algebra and the linear factorization theorem.

• Students will locate zeros of a polynomial using the immediate value theorem.

• Students find rational zeros of a

3.3 The Zeros of Polynomial Functions3.4 Zeroes of Polynomial Functions

Task(s)P e r son a l Pol y nomia ls

Select tasks from the following (pp.10-93):GSE Algebra II/Advanced Algebra: Polynomial Functions

Additional Resource(s)T I - 84 A c t i vi t y L e sson 3.4 Representing Polynomials Graphically

Khan Academy Videos: Polynomial Expressions, Equations, and Functions (includes a video on the Fundamental Theorem of Algebra, etc.)

VocabularyThe Fundamental Theorem of Algebra, the Linear Factorization Theorem, Zeros of Multiplicity, irreducible, the Immediate Value Theorem, the Rational Zeros Theorem, Descartes’ Rule of Signs, Upper and Lower Bounds Property

Writing in MathIn your own words, state the Remainder Theorem.


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polynomial using the rational zeros theorem.

• Students will use Descartes’ rule of signs and the upper/lower bounds theorem.

• Students will solve applications of polynomials.

Domain: Interpreting FunctionsCluster: Analyze functions using different representations.F-IF.A.1 Determine whether a function is even, odd, or neither.F-IF.A.2 Identify or analyze the distinguishing properties of exponential, polynomial, logarithmic, trigonometric, and rational functions from tables, graphs, and equations.F-IF.A.4 Identify characteristics of graphs based on a set of conditions or on a general equation such as y=ax2+c.F-IF.A.5 Visually locate critical points on the graphs of functions and determine if each critical point is a minimum, a maximum, or point of inflection. Describe intervals of concavity and increasing or decreasing.F-IF.A.7 Solve real world problems that can be modeled using quadratic, exponential, or logarithmic functions (by hand & technology).


Essential Question(s)• How can you find a solution to a

polynomial equation algebraically and graphically?

• How can features of polynomial functions such as the equation, solutions, axis of symmetry, vertex, etc. be represented in tables, equations, and in “real world” contexts?

Objective(s):• Students will identify the graph of a

polynomial function and determine its degree,

• Students will describe the end behavior of a polynomial.

• Students will discuss the attributes of a polynomial graph with zeros of multiplicity.

• Students will graph polynomial functions in standard form.

• Students will solve applications of polynomials.

3.4 Graphing Polynomial Functions (Coburn)3.2 Polynomial Functions and Their Graphs (Blitzer)

Task(s)Polynomial Graphs

Select tasks from the following (pp.10-93):GSE Algebra II/Advanced Algebra: Polynomial Functions

Additional Resource(s)Khan Academy Videos: Polynomial Expressions, Equations, and Functions

VocabularyTurning points, end behavior

Writing in MathDescribe how to find the possible rational zeros of a polynomial.

Describe how to use Descartes’s Rule of Signs to determine the possible number of positive real zeros of a polynomial function.

Why must every polynomial equation with real coefficients of degree 3 have at least one real root?

Domain: Interpreting Functions Enduring Understanding(s) 3.5 Graphing Rational Functions (Coburn) Vocabulary


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https://www.georgiastandards.org/Frameworks/GSO%20Frameworks/Math%20III%20Unit2%20SE.pdf









Cluster: Analyze functions using different representations.F-IF.A.6 Graph rational functions, identifying zeros, asymptotes (including slant), and holes when suitable factorizations are available, and showing end-behavior.

• Real world situations can be modeled and solved by using various functions.

• Graphs of functions can explain the observed local and global behavior of a function.

Essential Question(s)What are the similarities and differences between linear, quadratic, and polynomial functions?Objective(s):• Students will identify horizontal and

vertical asymptotes.• Students will find the domains of a

rational function.• Students will apply the concept of

“multiplicity” to rational graphs.• Students will find the horizontal

asymptotes of a rational function.• Students will graph general rational

functions.• Students will solve applications of rational

functions.

3.5 Rational Functions and Their Graphs (Blitzer)Task(s) Asymptotes and Rational Functions

Transforming the Graph of a Function

Select tasks from the following (pp.12-157):CCGPS Advanced Algebra: Unit 2 Polynomial Functions

Additional Resource(s)S k e tching G r a phs Relate the domain of a function to its graph, accounting for asymptotes and restricted domains

Khan Academy Videos: Rational Expressions, Equations, and Functions

Rational function, reciprocal square function, asymptotic behavior, vertical asymptote, horizontal asymptote, arrow notation,

Writing in MathWhy is a function called “rational?” What could make a function “irrational?” How do these mathematical terms differ from common English usage of the same terms?

Domain: N-NE – Number ExpressionsCluster: Represent, intercept, compare, and simplify number expressions.N-NE.A.5 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Enduring Understanding(s)• Real world situations can be modeled and

solved by using various functions.• Graphs of functions can explain the

observed local and global behavior of a function.

Essential Question(s)What are the similarities and differences between linear, quadratic, and polynomial functions?

3.6 Additional Insights Into Rational Functions (Coburn)P.6 Rational Expressions (Blitzer)

Task(s)Select tasks from the following (pp.14-224):CCGPS Advanced Algebra: Unit 6: Mathematical Modeling

Additional Resource(s)S olvi ng Non -li near Inequ ali ti es

VocabularyOblique asymptote


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http://www.intmath.com/inequalities/3-solving-non-linear-inequalities.php

https://www.georgiastandards.org/Archives/Documents/CCGPS-Math-9-12-Advanced-Algebra-Unit-6.pdf


https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions


https://learnzillion.com/resources/72800-relate-the-domain-of-a-function-to-its-graph-accounting-for-asymptotes-and-restricted-domains



http://www.analyzemath.com/Graphing/GraphRationalFunction.html




https://www.georgiastandards.org/Frameworks/GSO%20Frameworks/Math%20IV%20unit%203%20SE.pdf





Objective(s):• Students will graph rational functions with

removable discontinuities.• Students will graph rational functions with

oblique or nonlinear asymptotes.• Students will solve applications involving

rational functions.

Khan Academy Videos: Rational Expressions, Equations, and Functions

Domain: Solve Equations and InequalitiesCluster: Solve systems of equations and nonlinear inequalities.A-REI.A.3 Solve nonlinear inequalities (quadratic, trigonometric, conic, exponential, logarithmic, and rational) by graphing (solutions in interval notation if one-variable), by hand and with appropriate technology.

Enduring Understanding(s)• Real world situations can be modeled and

solved by using various functions.• Graphs of functions can explain the

observed local and global behavior of a function.

Essential Question(s)What are the similarities and differences between linear, quadratic, and polynomial functions?

Objective(s):• Students will solve quadratic inequalities.• Students will solve polynomial

inequalities.• Students will solve rational inequalities.• Students will use interval tests to solve

inequalities.• Students will solve applications of

inequalities.

3.7 Polynomial and Rational Inequalities (Coburn)3.6 Polynomial and Rational Inequalities (Blitzer)Additional ResourcesP o l y nom i a l a nd Ration a l Inequalities

Khan Academy Videos: Advanced Equations and Inequalities

Writing in MathWhat is a polynomial inequality?

What is a rational inequality?

Domain: N-NE – Number ExpressionsCluster: Represent, intercept, compare, and simplify number expressions.N-NE.A.5 Understand that rational expressions form a system analogous to the rational

Enduring Understanding(s)Real world situations can be modeled and solved by using various functions.

Essential Question(s)

3.8 Variation: Function Models in Action (Coburn)3.7 Modeling Using Variation (Blitzer)

Task(s)

VocabularyDirect variation, constant of variation, inverse variation, joint variation

Writing in MathShelby County Schools 2016/2017

Revised 6/29/1619 of 21

https://www.khanacademy.org/math/algebra2/advanced-equations-and-inequalities

https://www.khanacademy.org/math/algebra2/advanced-equations-and-inequalities

http://www.regentsprep.org/Regents/math/algtrig/ATE11/RationalInequalitiesLes.htm







numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.Represent, interpret, compare, and simplify number expressions.

What are the similarities and differences between linear, quadratic, and polynomial functions?

Objective(s):• Students will solve direct variations.• Students will solve inverse variations• Students will solve joint variations.

Select tasks from the following (pp.14-224):CCGPS Advanced Algebra: Unit 6: Mathematical Modeling

What does it mean if two quantities vary directly?

In your own words, explain how to solve a variation problem.

RESOURCE TOOLBOX

Textbook Resources

http://glencoe.mcgraw-hill.com/sites/0003112010/

http://highered.mcgrawhill.com/sites/0003112010/instructor_view0/instructor_s_solutions_manual.htm

http://highered.mcgrawhill.com/sites/0003112010/instructor_view0/preformatted_tests.htm

http://highered.mcgrawhill.com/sites/0003112010/instructor_view0/powerpoint_presentations.html

http://highered.mcgrawhill.com/sites/0003112010/instructor_view0/computerized_testing.htm

http://highered.mcgrawhill.com/sites/0003112010/instructor_view0/additional_topics.html

http://highered.mcgrawhill.com/sites/0003112010/instructor_view0/modeling_with_technology.html

Standards

Com m on Core S tand a rds - Math e matics

Com m on Core S tand a rds - Math e matics A pp e ndix A

http://www.edutoolbox.org/tntools (formerly tncore.org) ht t p: / /ww w . cc ss t oolbo x . o r g /

Common Core Lessons

Tennessee's State Mathematics Standards

TN Advanced Algebra & Trigonometry Standards

Videos

Brightstorm

Teacher Tube

The Futures Channel

Khan Academy

Math TV

Lamar University Tutorial

Calculator

ht t p: / /ww w .t i -m athnspir e d. c om

ht t p: / /edu ca t i on.t i . c om / e du ca t i onpo r tal/a c t i vi t y e x c h a n g e / a c t i vi t y

ht t p: / /ww w . ca sioedu ca t i on. c om / e du ca tors

Interactive Manipulatives

ht t p: / /ww w .i l ov e math.o r g / i nd e x .ph p ? opt i on =c om_docm a n

http://www.mathopenref.com

Edugoodies

Additional Sites

ht t p: / /ww w .in t e rn e t4cl a s srooms. c om / g a t e w a y _ a l g e b ra .htm ht t p: / /ww w .kutaso f tw a r e . c om / f ree .ht m ht t p: / / i l lu m inations.n c t m . o r g / ht t p: / /ww w .stemr e sour c e s.com/ https://compasslearning.com/


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https://compasslearning.com/

http://edugoodies.com/scs/

http://tutorial.math.lamar.edu/

http://www.mathtv.com/

https://www.khanacademy.org/

http://thefutureschannel.com/#loaded

http://www.teachertube.com/

http://www.brightstorm.com/


http://state.tn.us/education/standards/math.shtml

http://www.edutoolbox.org/tntools





RESOURCE TOOLBOX

www.explorelearning.comht t p: / / j c - s c hools.n e t / d y n a m i c / m a th / math12.ht m l

Literacy

Glencoe Reading & Writing in the Mathematics ClassroomGraphic Organizers (9-12)Literacy Skills and Strategies for Content Area Teachers(Math, p. 22)

ACTTN ACT Information & ResourcesACT College & Career Readiness Mathematics Standards

Tasks/LessonsUT Dana CenterMars TasksInside Math TasksMath Vision Project Tasks Better Lesson


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http://betterlesson.com/common_core

http://www.mathematicsvisionproject.org/secondary-mathematics-i.html

http://www.insidemathematics.org/performance-assessment-tasks

http://map.mathshell.org/materials/tasks.php

http://www.utdanacenter.org/k12mathbenchmarks/secondary/index.php

http://www.act.org/content/dam/act/unsecured/documents/CCRS-MathStandards.pdf

http://www.tn.gov/education/topic/act-sat

http://www.valrc.org/resources/docs/MHS_Literacy_Strategy_Book.pdf

https://www.teachervision.com/tv/tvsearch/site=TV&lowest_grade=109&highest_grade=112&type=graphic-organizer

http://www.glencoe.com/sec/teachingtoday/downloads/pdf/ReadingWritingMathClass.pdf

http://www.explorelearning.com/