Grade 8 - scsk12.org Alg Trig Q1 16... · Web viewStudents will solve problems involving a quadratic function’s minimum or maximum value. ... Solving Quadratic Equations. Vocabulary

Curriculum and Instruction – Office of 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 6/6/16

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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

The Shelby County Schools curriculum maps are intended to guide planning, pacing, and sequencing, reinforcing the major work of the grade/subject. Curriculum maps are NOT meant to replace teacher preparation or judgment; however, it does serve as a resource for good first teaching and making instructional decisions based on best practices, and student learning needs and progress. Teachers should consistently use student data differentiate and scaffold instruction to meet the needs of students. The curriculum maps should be referenced each week as you plan your daily lessons, as well as daily when instructional support and resources are needed to adjust instruction based on the needs of your students.

How to Use the Mathematics Curriculum Maps

Tennessee State StandardsThe TN State Standards are located in the left column. It is the teachers' responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

ContentWeekly and daily objectives/learning targets should be included in your plan. These can be found under the column titled content. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the learning targets/objectives provide specific outcomes for that standard(s). Best practices tell us that making objectives measureable increases student mastery.

Instructional Support and ResourcesDistrict and web-based resources have been provided in the Instructional Support and Resources column. The additional resources provided are supplementary and should be used as needed for content support and differentiation.


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

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



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


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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 and ResourcesEquations and Inequalities

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

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 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.

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

VocabularySets, subsets, real number, natural 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.

Enduring Understanding(s)The most fundamental requirement for learning algebra is mastering the language

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

VocabularyRadical, radicand, square root, radical expression, Product Rule, Quotient Rule,


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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/

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

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 and Resources

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.

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.

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

rationalizing the denominator

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

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.

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)

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

Enduring Understanding(s)The most fundamental requirement for

1.4 Complex Numbers (Coburn/Blitzer) VocabularyImaginary, complex, conjugate


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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

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/





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.

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

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.

Task(s)Imaginary Numbers

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

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 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)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.

1.5 Quadratic Equations (Coburn/Blitzer)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

VocabularyQuadratic 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?


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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




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






• Students will solve applications of quadratic equations.


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?

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.

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.

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

Domain: Conic SectionsCluster: Understand the properties of conic sections and apply them to model real-world phenomena.



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

VocabularyRelation, ordered pair, dependent variable, independent variable, mapping notation, domain, range, equation form, rectangular coordinate system, quadrants, coordinate


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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







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):• 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.

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

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.

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.




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


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







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.

“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.

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.

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.


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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







• 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.

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.







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.

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 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



• The properties of functions and function

2.7 Piecewise-Defined Functions (Coburn)2.2 More on Functions and Their Graphs. (Blitzer)

Additional Resource(s)

Vocabularypiecewise-defined function, step functions, greatest integer function

Writing in MathShelby County Schools 2016/2017

Revised 6/6/1611 of 20








critical point is a minimum, a maximum, or point of inflection. Describe intervals of concavity and increasing and decreasing.

operations are used to model and analyze real-world applications and quantitative relationships.




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

piecewise-defined functions.

Khan Academy Videos: Piecewise Functions Explain why a piecewise-defined function would ever be used.

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.







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

Task(s)Building a Quadratic Function By Composition

TN 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.


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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




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

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






quadratic functions?• How can quadratic functions describe

real-world situations, model predictions and solve problems?

Objective(s):• Students will recognize characteristics of

a parabola.

3.1 Quadratic Functions and Applications (Coburn/Blitzer)

Additional Lesson(s)Representing Quadratic Functions Graphically

Solving Quadratic Equations

VocabularyStandard form, solution, root, factor, zero

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


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• 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.


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?•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.

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?

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.


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

Task(s)

VocabularyThe Fundamental Theorem of Algebra, the Linear Factorization Theorem, Zeros of Multiplicity, irreducible, the Immediate Value Theorem, the Rational Zeros Theorem,


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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 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.

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.)

Descartes’ Rule of Signs, Upper and Lower Bounds Property

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

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.


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

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

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.


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











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).

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.

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

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

Domain: Interpreting FunctionsCluster: 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.

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 identify horizontal and

vertical asymptotes.• Students will find the domains of a

rational function.• Students will apply the concept of

3.5 Graphing Rational Functions (Coburn)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,

VocabularyRational 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?


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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/Archives/Documents/CCGPS-Math-9-12-Advanced-Algebra-Unit-2.pdf



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









“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.

accounting for asymptotes and restricted domains

Khan Academy Videos: Rational Expressions, Equations, and Functions

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.





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.

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

Khan Academy Videos: Rational Expressions, Equations, and Functions

VocabularyOblique asymptote

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.




Essential Question(s)

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

Writing in MathWhat is a polynomial inequality?

What is a rational inequality?


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


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


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









TN STATE STANDARDS CONTENT Instructional Support and ResourcesWhat 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.

Khan Academy Videos: Advanced Equations and Inequalities

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.Represent, interpret, compare, and simplify number expressions.

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


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

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

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

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

Writing in MathWhat does it mean if two quantities vary directly?

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


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

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



RESOURCE TOOLBOX

Textbook Resourceshttp://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

StandardsCom 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

TN Co r e

ht t p: / /ww w . cc ss t oolbo x . o r g /

Common Core LessonsTennessee's State Mathematics Standards

TN Advanced Algebra & Trigonometry Standards

VideosBrightstorm

Teacher Tube

The Futures Channel

Khan Academy

Math TV

Lamar University Tutorial


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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



RESOURCE TOOLBOX

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

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

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/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 Classroom

Graphic Organizers (9-12)

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

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/

https://compasslearning.com/