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Quarter 2 Algebra II

Introduction

In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,

80% of our students will graduate from high school college or career ready 90% of students will graduate on time 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready 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.

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Focus

The TN Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. For algebra 2, the major clusters account for 65% of time spent on instruction.Supporting Content - information that supports the understanding and implementation of the major work of the grade.Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency.

Coherence

Thinking across grades:The TN 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 TN Standards call for conceptual understanding of key concepts. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures.Application: The Standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.

Major Content Supporting Content Additional Content

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Quarter 2 Algebra II

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. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards the supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teachers' responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

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.

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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.

Topics Addressed in Quarter Polynomials & Polynomial Functions Radical Functions & Equations Inverses Logarithmic Functions & Equations Exponential Functions & Equations

Overview During this quarter, students will extend their understanding of functions and the real numbers, and increase their toolset for modeling in the real world. Students extend their notion of number to include rational exponents. Students deepen their understanding of the concept of function, and apply equation-solving and function concepts to many different types of functions. They will explore polynomial, radical, exponential, and logarithmic functions through graphing, solving, and learning their properties. The system of polynomial functions, analogous to the integers, is extended to the field of rational functions, which is analogous to the rational numbers and the graphs of these functions are explored. Building on their work with linear, quadratic, and exponential functions, in Algebra II students extend their repertoire of functions to include polynomial and rational functions. Students work closely with the expressions that define the functions and continue to expand and hone their abilities to model and analyze situations that involve polynomial, radical, exponential, and logarithmic equations over the set of complex numbers.

Content Standard Type of Rigor Foundational Standards Sample Assessment Items**A-CED Procedural Skill, Conceptual Understanding &

ApplicationN-RN.3, N-Q.1,3, A-CED.2,3,4 TN Task Alg. 1- Paulie’s Pen

A-REI Conceptual Understanding & Application A-REI.1, 10 TN Task Alg. 1- DownloadsF-IF Conceptual Understanding & Application F-IF.1,2 TN Task Alg. 1 - CliffhangerF-BF Conceptual Understanding & Application F-BF.1b, F-LE.1,3 TN Task Alg. 2 – Car DepreciationF-LE Procedural Skill, Conceptual Understanding &

ApplicationF-LE.1a,1b,1c,2,3,5 Illustrative: Algae Blooms;

Illustrative: RumorsA-SSE Procedural Skill, Conceptual Understanding & N-RN.1, A-SSE.1 TN Task Alg. 2 – Forms of a

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Application FunctionTN Task Alg. 2 – One Rocket Three Equations

A-APR Procedural Skill, Conceptual Understanding & Application

A-APR.1 TN Task Alg. 2 – Root of the Problem

N-RN Procedural Skill, Conceptual Understanding TN Task Alg. 2 – Natural Order of Things

** TN Tasks are available at http://www.edutoolbox.org/ and can be accessed by Tennessee educators with a login and password.

Fluency

The high school standards do not set explicit expectations for fluency, but fluency is important in high school mathematics. Fluency in algebra can help students get past the need to manage computational and algebraic manipulation details so that they can observe structure and patterns in problems. Such fluency can also allow for smooth progress toward readiness for further study/careers in science, technology, engineering, and mathematics (STEM) fields. These fluencies are highlighted to stress the need to provide sufficient supports and opportunities for practice to help students gain fluency. Fluency is not meant to come at the expense of conceptual understanding. Rather, it should be an outcome resulting from a progression of learning and thoughtful practice. It is important to provide the conceptual building blocks that develop understanding along with skill toward developing fluency.

The fluency recommendations for Algebra II listed below should be incorporated throughout your instruction over the course of the school year. A‐APR.D.6 Divide polynomials with remainder by inspection in simple cases A‐SSE.A.2 See structure in expressions and use this structure to rewrite expressions F.IF.A.3 Fluency in translating between recursive definitions and closed forms

References:

https://www.engageny.org/ http://www.corestandards.org/ http://www.nctm.org/ http://achievethecore.org/

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONSPolynomials and Polynomial Functions

(Allow approximately 4 weeks for instruction, review, and assessment)Domain: Arithmetic with Polynomials and Rational Expressions

Cluster: Understand the relationship between zeros and factors of Polynomials

A-APR.A.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Domain: QuantitiesCluster: Reason quantitatively and use units to solve problems. N-Q.B.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Enduring Understanding(s):• The algebraic form of a polynomial function

gives information about its graph. Its graph gives information about its algebraic form.

• Knowing the zeros of a polynomial function gives information about its graph.

• A polynomial of degree n has n linear factors. The graph of the related function crosses the x-axis an even or odd number of times depending if n is even or odd.

Essential Question(s):How can algebra describe the relationship between a function and its graph?

Objective(s):• Students will classify polynomials.• Students will graph polynomials and

describe end behavior.

Pearson 5-1 Polynomial FunctionsGlencoe 6.1 Operations with PolynomialsChoose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.Additional Lesson(s):Engageny Algebra I Module 5, Topic A, Lesson 1, Recognize Features of Graphs

Engageny Algebra I Module 5, Topic A, Lesson 2, Recognize and Formulate a Model

Engageny Algebra II Module 1, Topic A, Lesson 5, Standard Form

Engageny Algebra II Module 1, Topic B, Lesson 15, End Behavior

VocabularyMonomial, degree of a monomial, polynomial, degree of a polynomial, polynomial function, standard form of a polynomial function, turning point, end behavior

Writing in MathWhy does the end behavior depend on the leading term?

Have students to write a sentence(s) and create at least two examples about their thinking.

Graphic OrganizerPolynomial Foldable

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONSEngageny Algebra II Module 1, Topic B, Lesson 20, Fit Polynomial Function to Data

Tasks:Arithmetic with Polynomials and Rational ExpressionsMath Nspired: Application of PolynomialsSorting FunctionsAdditional Resource(s):Classifying polynomials using the degree and number of termsClassify PolynomialsPolynomial ExpressionsClassifying PolynomialsPolynomial End BehaviorGraphs of Higher Degree PolynomialsEnd Behavior

A-APR.A.3

Domain: Linear, Quadratic, and Exponential ModelsCluster: Interpret functions that arise in applications in terms of the context. F-IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Domain: Interpreting FunctionsCluster: Analyze functions using different representations.

F-IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Essential Question(s):How are the linear factors of a polynomial related to the zeros of the polynomial?

Objective(s):• Students will analyze the factored form of a

polynomial.• Students will write a polynomial function

given its zeros and use the zeros to construct a rough graph of the function defined by the polynomial.

Pearson5-2 Polynomials, Linear Factors, and Zeros

Glencoe6.3 Polynomials FunctionsChoose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.

Additional Lesson(s):Engageny Algebra II Module 1, Topic A, Lesson11, Finding Zeros

Tasks:Math Nspired: Exploring Polynomials:Factors,

VocabularyFactor theorem, multiple zero,

multiplicity, relative maximum, relative minimum

Writing in MathCan zero be a solution of a polynomial function?

Have students to write a sentence(s) and create and solve an example about their thinking.

Graphic OrganizerFactoring Flow Chart

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONSRoots, and Zeros

Additional Resource(s):Writing a Polynomial in Factored Form VideoUsing a polynomial function and its factors to solve problems VideoFinding the zeros of a polynomial Function VideoWriting a Polynomial from its zeros VideoFactoring a Sum or Difference of Cubes Video

Domain: Arithmetic with Polynomials and Rational Expressions

Cluster: Understand the relationship between zeros and factors of Polynomials

A-APR.A.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Domain: Interpreting FunctionsCluster: Interpret functions that arise in applications in terms of the context. F-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Domain: Building FunctionsCluster: Build a function that models a relationship between two quantities F-BF.A.1 Write a function that describes a relationship between two quantities.★a. Determine an explicit expression, a recursive process, or steps for calculation from a context.b. Combine standard function types using arithmetic operations. For example, build a

Enduring Understanding(s):If (x-a) is a factor of a polynomial, then the polynomial has value zero when x=a. If a is a real number, then the graph of a polynomial has (a, 0) as an x-intercept.

Essential Question(s):Will a graph help you to check all solutions to a polynomial equation? How can you check imaginary solutions?

Objective(s):• Students will solve polynomial equations by

factoring and by graphing.• Students will interpret key features of

graphs and tables in terms of quantities, given a function that models a relationship between two quantities.

• Students will sketch graphs showing key features given a verbal description of the relationship.

Pearson 5-3 Solving Polynomial Equations

Glencoe 6.5 Solving Polynomial Functions

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.

Additional Lesson(s):Engageny Algebra I Module 1, Topic B, Lesson 9, Multiply Polynomials

Engageny Algebra I Module 1, Topic C, Lesson 17, Solving Equations by Factoring

Engageny Algebra I Module 5, Topic A, Lesson 3, Analyze Word Problems

Tasks: Population and Food Supply

Introduction to Polynomials - College FundIdeal Gas Law

VocabularySum of cubes, differences of cubes

Writing in MathWhen should you use the quadratic formula to solve a polynomial?

Have students to write a sentence(s) and create and solve an example about their thinking.

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONSfunction that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

Domain: The Complex Number SystemCluster: Use complex numbers in polynomial identities and equations. .B. 7 Solve quadratic equations

with real coefficients that have complex solutions.

Domain: Building Functions

Cluster: Build new functions from existing functions F-BF.B.3 Identify the effect on the

graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Domain: Reasoning with Equations and InequalitiesCluster: Represent and solve equations and

inequalities graphically. A-REI. D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x);

Additional Resource(s):Modeling Data with a Polynomial FunctionSolving Polynomial Equations by FactoringSolving Polynomial Equations of higher degrees using factoring and the quadratic formulaSolve polynomial equations of higher degree using factoring Video

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find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

N-Q.B.2Domain: Arithmetic with Polynomials and Rational Expressions

Cluster: Understand the relationship between zeros and factors of Polynomials

A-APR.A.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

Domain: Arithmetic with Polynomials and Rational Expressions

Cluster: Understand the relationship between zeros and factors of Polynomials

A-APR.C.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

Enduring Understanding(s):Polynomials can be divided using steps that are similar to long division steps that are used to divide whole numbers.

Essential Question(s):When is it best to use long division vs. synthetic division?

Objective(s):• Students will divide polynomials by long

division.• Students will divide polynomials by

synthetic division.

Pearson5-4 Dividing PolynomialsGlencoe

6.2 Dividing Polynomials Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.

Additional Lesson(s)Engageny Algebra II Module 1, Topic A, Lesson 3, Division Algorithm

Engageny Algebra II Module 1, Topic A, Lesson 4, Long Division

Engageny Algebra II Module 1, Topic A, Lesson 6, Long Division Practice

Engageny Algebra II Module 1, Topic B, Lesson 19, Remainder Theorem

VocabularySynthetic division, remainder theorem

Writing in MathHow does dividing a polynomial by a binomial determine if that binomial is a factor of the polynomial?

Have students to write a sentence(s) and create and solve an example and counterexample about their thinking.

Graphic OrganizerGraphic Organizer division(dgelman)

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Additional Resources:Dividing a polynomial by a binomial VideoDividing Polynomials Using Synthetic Division Video

A-APR.A.2Enduring Understanding(s):(x-a) is a factor of a polynomial if and only if a is a root of the related polynomial equation.Essential Question(s):How can the rational root theorem help to find the factors/roots of a polynomial?Objective(s):• Students will solve equations using the

Rational Root Theorem.• Students will use the Conjugate Root

theorem to solve equations.

Pearson 5-5 Theorems About Roots of Polynomial equations Glencoe 6.7 Roots and ZerosChoose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.

Additional Lesson(s):Engageny Algebra II Module 1, Topic D, Lesson 36, Complex Zeros

Engageny Algebra II Module 1, Topic D, Lesson 40, Fundamental Theorem of Algebra

Tasks: Math Nspired: Watch Your p's and q's

Additional Resource(s):Using the Rational Root Theorem to Find Roots VideoSolving Equations Using the Rational Root Theorem VideoUsing the Irrational Root Theorem to Find Irrational

VocabularyRational Root Theorem, Conjugate Root Theorem, Descartes’ Rule of Signs

Writing in MathAfter applying the Conjugate Root Theorem, how do you know that you have found all of the roots of a polynomial?

Have students to write a sentence(s) and create and solve an example about their thinking.

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONSRoots VideoWriting A Polynomial From Its Roots Video

Domain: Interpreting FunctionsCluster: Analyze functions using different representations

F-IF.C.7c Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior7

Enduring Understanding(s):The behavior of the graphs of polynomial functions of different degrees can suggest which will best fit a particular real-world data set.

Essential Question(s):How can regression analysis help determine the best fit polynomial to given data?

Objective(s):Students will fit data to linear, quadratic, cubic, or quartic models.

Pearson 5-8 Polynomial Models in the Real World Glencoe 6.4 Analyzing Graphs and Modeling Data of Polynomial FunctionsChoose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.Additional Lesson(s):Engageny Algebra II Module 1, Topic B, Lesson 21, Polynomial Model

Tasks:Absolute Value Functions Lesson & resourcesFind dimensions of a piece of land and riding the busAdditional Resource(s):Modeling data using a linear, quadratic, or cubic model

Vocabulary Linear regression (linreg), quadratic

regression (quadreg), cubic regression (cubicreg)

Writing in MathExplain how to find the degree of a polynomial by finding differences.

Have students to write a sentence(s) and create two different examples about their thinking.

F-IF.C.7c Enduring Understanding(s):The graph y=af(x-h)+k is a vertical stretch or compression by the absolute value of a, a horizontal shift of h u nits, and a vertical shift of k units of the graph of y=f(x).

Essential Question(s):What are the different transformations that can

Pearson 5-9 Transforming Polynomial FunctionsChoose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Use the following Engageny Lessons to

VocabularyPower function, constant of proportionality

Writing in MathWhat are the different ways that a parent function can be transformed? Is this the same or different from power functions to

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be applied to a power function?

Objective(s):Students will apply transformations to graphs of polynomials.

introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.Additional Lesson(s):Engage ny Algebra II Module 1, Topic C, Lesson 31, Systems of Equations

other functions studied this year?

Have students to write a sentence(s) and create two different examples about their thinking.

Radical Functions and Rational Exponents(Allow approximately 2 weeks for instruction, review, and assessment)

Domain: The Real Number SystemCluster: Extend the properties of exponents to rational exponents. N-RN.A.1 Explain how the definition of the

meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

N-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Enduring Understanding(s):A radical expression can be written in an equivalent form using a fractional (rational) exponent instead of a radical sign.

The nth root of an expression that contains an nth power as a factor can be simplified.

Essential Question(s):How does the index relate to the rational exponent of a radical?

Objective(s):• Students will simplify expressions with

rational exponents.

Pearson6.4 Rational Exponents

Glencoe 7.6 Rational Expressions

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Additional Lessons:Engageny Algebra II Module 1, Topic A, Lesson 9, Simplify Radical Expressions

Tasks:TN Task Arc –Investigating Exponents TI Classroom Activity: Rational ExponentsBacterial Growth Additional Resource(s):Simplifying expressions with rational exponentsConverting to and from radical formSimplifying numbers with rational exponentsWriting expressions with rational exponents in

VocabularyRational exponent

Writing in MathWhen is it necessary to use absolute value bars when simplifying radicals?

Have students to write a sentence(s) and create two different examples about their thinking.

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simplest form

Domain: Reasoning with Equations and Inequalities

Cluster: Represent and solve equations and inequalities graphically.

A-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Domain: Reasoning with Equations and InequalitiesCluster: Represent and solve equations and

inequalities graphically. A-REI. A.1 Explain each step in solving

a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Domain: Reasoning with Equations and InequalitiesCluster: Represent and solve equations and

inequalities graphically. A-REI. A.2 Solve simple rational and radical equations in one variable, and give

Enduring Understanding(s):Solving a square root equation may require squaring each side of the equation. This can introduce extraneous solutions.

A radical equation can be solved by isolating the radial on one side of the equation, then raising each side to the power suggested by the index.

The nth root of an expression that contains an nth power as a factor can be simplified.

Essential Question(s):How do you determine the inverse you need to use when solving radical equations?

Objective(s):• Students will solve square root and other

radical equations.

Pearson6.5 Solving Square Root and Other Radical Equations

Glencoe 7.7 Solving Radical Equations andChoose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.

Additional Lessons:Engageny Algebra I Module 5, Topic A, Lesson 3, Analyze Word Problems

Engageny Algebra II Module 1, Topic C, Lesson 28, Solve Radical Equations

Engageny Algebra II Module 1, Topic C, Lesson 29, Solve Radical Equations

Task(s):Evaluating Statements About Radicals

Additional Resource(s): Solving radical equations by isolating the radicalSolving radical equations with rational

VocabularyRadical equation, square root equation

Writing in MathWhy does squaring both sides of a square root equation not always create an equivalent equation?

Have students to write a sentence(s) and create an example about their thinking.

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examples showing how extraneous solutions may arise.

Domain: Creating EquationsCluster: Create equations that describe numbers or relationships. A-CED.A.1 Create equations and

inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

N-Q.B.2

exponentsUsing radical equations to solve problems Solving radical equations and checking for extraneous solutionsSolving equations with two rational exponents

Domain: Building FunctionsCluster: Build new functions from existing function.

F-BF.B.4 Find inverse functions.a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

Enduring Understanding(s):The inverse of a function may or may not be a function.

When you square each side of an equation, the resulting equation may have more solutions than the original equation.

Pearson6.7 Inverse Relations and Functions

Glencoe 7.2 Inverse Functions and RelationsChoose from the following resources to ensure that the intended outcome and level

VocabularyInverse relation, one-to-one function

Writing in MathWhat type of function breaks the rule: The range of the relation is the domain of the

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONSFor example, f(x) =2x 3 or f(x) = (x+1)/(x–1) for x ≠ 1.

F-BF.A.1.★ F-BF.A.1 a

The range of the relation is the domain of the inverse. The domain of the relation is the range of the inverse.

Essential Question(s):How can the horizontal line test help you determine if an inverse will be a function?

Objective(s):• Students will find the inverse of a relation

or function

of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s):Math Nspired: Functions and InversesWhat is the Inverse of a Function?

Additional Resource(s):Finding the inverse of a relationGraphing a relation and its inverse

Finding an inverse function

inverse. The domain of the relation is the range of the inverse?

Have students to write a sentence(s) and create an example about their thinking.

F-BF.A.1.★ F-BF.A.1 a

Enduring Understanding(s):A square root function is the inverse of a quadratic function that has a restricted domain.

When you square each side of an equation, the resulting equation may have more solutions than the original equation.

Essential Question(s):Why is the square root function only half of its’ quadratic inverse?

Objective(s):• Students will graph square root and other

radical functions.

Pearson6.8 Graphing Radical Functions

Glencoe7.3 Square Root Functions and OperationsChoose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.

Additional Lessons:Engageny Algebra I Module 4, Topic C,

VocabularyRadical function, square root function

Writing in MathWhy do you have to restrict the domain of a quadratic function’s inverse?

Have students to write a sentence(s) and create an example about their thinking.

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONSLesson 19, Transformations of Graphs

Engageny Algebra I Module 4, Topic C, Lesson 20, Square Root Graphs

Engageny Algebra I Module 4, Topic C, Lesson 18, Domain and Range of Cube Root Functions

Engageny Algebra I Module 4, Topic C, Lesson 22, Compare Square Root and Cube Root Functions

Engageny Algebra I Module 5, Topic A, Lesson 1, Recognize Features of Graphs

Engageny Algebra I Module 5, Topic A, Lesson 2, Recognize and Formulate a Model

Engageny Algebra I Module 5, Topic B, Lesson 4,Write a function Given a Graph

Additional Resource(s):Graphing radical functions using a vertical translationGraphing radical functions using a horizontal translationGraphing square root functionsGraphing cube root functions

Exponential and Logarithmic Functions( Allow approximately 3 weeks for instruction, review, and assessment)

Domain: Linear, Quadratic, and Exponential ModelsCluster: Conduct and compare linear,

Enduring Understanding(s):• Repeated multiplication can be represented

Pearson 7.1 Exploring Exponential

VocabularyExponential function, exponential growth,

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONSquadratic, and exponential models and solve problems.

F-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Domain: Linear, Quadratic, and Exponential ModelsCluster: Interpret expressions for functions in terms of the situation they model. F-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context.

Domain: Interpreting FunctionsCluster: Analyze functions using different representations. F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ F-IF.C.9 F-IF.B.6

A-REI.D.11

Domain: Interpreting Categorical and Quantitative Data

Cluster: Summarize, represent, and interpret data on a single count or measurement. variable S-ID.B.6 Represent data on two

with a function in the form of y=abx where b is a positive number other than 1.

• An exponential function is a function with the general form y=abx, a does not equal zero, with b>0, and b is not equal to one. In an exponential function, the base b is a constant. The exponent x is the independent variable with domain the set of real numbers.

Essential Question(s):How do you distinguish between an exponential function being a growth or decay?

Objective(s):• Students will model exponential growth and

decay.• Students will graph y=bx and observe it as

the parent exponential function, then graph y=abx and observe how the value of a either stretches or compresses the graph of y=bx.

• Students will graph y=abx and y=ab(x-h) and observe that y=ab(x-h) is the same as the vertical stretch or compression of y=(ab-h)bx.

• Students will observe that y=abx +k shifts the horizontal asymptote from y=0 to y=k.Graph y=logbx as the parent logarithmic function, then graph y=alogb(x-h) + k and observe: 1) how the value of a either stretches or compresses the graph of y=logbx and 2) the vertical shift of y=logbx by h and the horizontal shift of y=logbx by

Glencoe 8.1 Graphing Exponential Functions

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.

Additional Lesson(s):Engageny Algebra I Module 1, Topic A, Lesson 3,Exponential Functions

Engageny Algebra I Module 3, Topic A, Lesson 4,Compound Interest

Engageny Algebra I Module 3, Topic A, Lesson 7,Exponential Decay Models

Engageny Algebra I Module 3, Topic B, Lesson 14,Exponential Growth Function

Engageny Algebra I Module 3, Topic C, Lesson 21,Exponential Models

Engageny Algebra I Module 3, Topic D, Lesson 22,Applications of Exponential Functions and Transformations

Engageny Algebra I Module 5, Topic A,

exponential decay, asymptote, growth factor, decay factor

Writing in Math.What is the y-intercept of an exponential function with no stated a value?

Have students to write a sentence(s) and create growth and decay examples about their thinking.

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quantitative variables on a scatter plot, and describe how the variables are related.a. Fit a function to the data; use

functions fitted to data to solve problems in the context of the data. Uses given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential.

F-IF.B.4

Domain: Interpreting FunctionsCluster: Analyze functions using different representations. F-IF.C.7e Graph functions expressed

symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated casese. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. There is no additional scope or clarification information for this standard. 8. Write a function defined by an expression in different but equivalent

F-BF.B.3

k. Lesson 1, Recognize Features of Graphs

Engageny Algebra I Module 5, Topic A, Lesson 2, Recognize and Formulate a Model

Engageny Algebra II Module 3, Topic C, Lesson 22, Real World Exponential Model

Engageny Algebra II Module 3, Topic D, Lesson 23, Properites of Exponents

Engageny Algebra II Module 3, Topic D, Lesson 26, Growth/Decay Rate

Tasks:TN Task Arc –Car Depreciation TN Task Arc-Culture ShockMath Vision Project 2012-Linear and Exponentia lFunctions (various) Lake Algae

Additional Resource(s)Graphing exponential growthModeling exponential growthGraphing exponential decayUsing exponential functions to solve problems

F-LE.A.2 F-LE.B.5

Domain: Seeing Structure in Expressions

Enduring Understanding(s):• The factor a in y=abx can stretch, compress,

and possibly reflect the graph of the parent function y=bx.

Pearson7.2 Properties of Exponential FunctionsChoose from the following resources to ensure that the intended outcome and level

VocabularyNatural base exponential function, continuously compounded interest

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Cluster: Interpret the structure of expressions. A-SSE.A.2 Use the structure of an

expression to identify ways to rewrite it.

Domain: Seeing Structure in ExpressionsCluster: Interpret the structure of expressions. A-SSE.B.4 . Derive the formula for the sum

of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.

Domain: Interpreting FunctionsCluster: Analyze functions using different representations. F-IF.C.8b Write a function defined by an

expression in different but equivalent forms to reveal and explain different properties of the function. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t , y = (0.97)t , y = (1.01) 12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.

Domain: Building FunctionsCluster: Build a function that models a relationship between two quantities F-BF.A.1 ★Write a function that describes a relationship

between two quantities.b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of

• The function y=abx, where a>0, b>01, models exponential growth. y=abx models exponential decay if 0<b<1.

Essential Question(s):Why is y=aex considered to be an exponential function?

Objective(s):• Students will explore the properties of

functions of the form y=abx.• Students will graph exponential functions

that have base e.• Students will determine the growth or decay

factor of an exponential function or situation.• Students will write an exponential function

given a growth or decay situation using y=a(1+r)t.

• Students will write an exponential function for continuously compounded interest using y-aert.

of rigor (mainly conceptual understanding and application) of the standards are met.

Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.

Additional Lesson(s):Engageny Algebra I Module 3, Topic A, Lesson 5,Model with Exponential Formulas

Engageny Algebra I Module 3, Topic A, Lesson 6,Population Growth

Engageny Algebra I Module 3, Topic C, Lesson 17,Vertical Transformation

Engageny Algebra I Module 3, Topic C, Lesson 18,Horizontal Transformations

Engageny Algebra I Module 3, Topic D, Lesson 23,Exponential Models

Engageny Algebra I Module 5, Topic B, Lesson 4,Write a function Given a Graph

Engageny Algebra I Module 5, Topic B, Lesson 7,Exponential Regression

Tasks:TN Task Arc – Natural Order of Things The Bank Account Making Money

Writing in MathWrite three different examples of exponential functions that stretch, compress, and reflect. Explain why each function moves the way that it does.

Have students to write a sentence(s) and create examples about their thinking.

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONSa cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

Maintaining the Balance

Additional Resource(s)Graphing exponential functions by translatingUsing exponential functions to solve problems

A-REI.D.11

Domain: Linear, Quadratic, and Exponential ModelsCluster: Construct and compare linear, quadratic, and exponential models and solve problems. F-LE.A.4 Use the structure of an expression to identify ways to rewrite it.

F-IF.B.4

F-IF.B.6

F-IF.C.7e

F-BF.B.3

Essential Question(s):• The exponential function y=bx is one-

to-one, so its inverse x=by is a function. To express y as a function of x for the inverse, write y=logbx.

• Logarithms are exponents. In fact, logba =c if and only if bc=a.

Objective(s):• Students will write and evaluate logarithmic

expressions.• Students will graph logarithmic functions.• Students will graph y=logbx as the parent

logarithmic function, then graph y=alogb(x-h) + k and observe: 1) how the value of a either stretches or compresses the graph of y=logbx and 2) the vertical shift of y=logbx by h and the horizontal shift of y=logbx by k.

Pearson 7.3 Logarithmic Functions as Inverses

Glencoe8.3 Logarithms and Logarithmic FunctionsChoose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.

Additional Lesson(s):Engageny Algebra II Module 3, Topic B, Lesson 8,Simplify Simple Logarithms

Engageny Algebra II Module 3, Topic B, Lesson 9,Earthquake Model

Engageny Algebra II Module 3, Topic B, Lesson 10,Logarithms Base 10

Engageny Algebra II Module 3, Topic B, Lesson 11,Logarithms Base 10 Patterns

Engageny Algebra II Module 3, Topic B, Lesson

VocabularyLogarithm, logarithmic function, common logarithm, logarithmic scale

Writing in MathHow are the domain and range related from the exponential function to the logarithmic function?

Have students to write a sentence(s), create examples, and graph about their thinking.

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONS12,Logarithm Properties

Engageny Algebra II Module 3, Topic C, Lesson 16,Irrational Numbers in Context of Logarithms

Engageny Algebra II Module 3, Topic C, Lesson 17 Graph Logarithms,

Engageny Algebra II Module 3, Topic C, Lesson 18 Compare Exponential and Logarithmic graphs

Engageny Algebra II Module 3, Topic C, Lesson 19, Exponential and Logarithmic functions are inverses

Engageny Algebra II Module 3, Topic C, Lesson 20, Transformations of logarithmic functions

Engageny Algebra II Module 3, Topic C, Lesson 21, Sketch natural logarithms

Engageny Algebra II Module 3, Topic D, Lesson 28, Graph Logarithms in Context

Tasks:Math Vision Project 2014- Logarithmic Functions (various) Additional Resource(s):Evaluating logarithmic expressionsUsing logarithmic expressionsGraphing a logarithmic function using its inverseGraphing a logarithmic function using a translation

Domain: Seeing Structure in ExpressionsCluster: Write expressions in equivalent forms

to solve problems.

Enduring Understanding(s):Logarithms and exponents have corresponding

Pearson7.4 Properties of Logarithms

VocabularyChange of base formula

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A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

properties.

Essential Question(s):What are the distinguishing features of the properties of logarithms: product property, quotient property, and power property

Objective(s):• Students will use the properties of

logarithms.

Glencoe8.5 Properties of Logarithms8.6 Common LogarithmsChoose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.

Additional Lesson(s):

Engageny Algebra II Module 3, Topic B, Lesson 13,Change of Base

Additional Resource(s):Simplifying logarithmsUsing logarithms to model sound

Writing in MathWhen would you need to use a Change of Base formula? What does the logarithm look like?

Have students to write a sentence(s) and create examples about their thinking.

A-CED.A.1

F-IF.C.8b .

N-Q.B.2

Enduring Understanding(s):Logarithms can be used to solve exponential equations. Exponents can be used to solve logarithmic equations.

The exponential function y=b^x and the logarithmic function y=log(subscript b)x are inverse functions.

Essential Question(s):

Pearson7.5 Exponential and Logarithmic Equations

Glencoe8.2 Solving Exponential Equations and Inequalities8.4 Solving Logarithmic Equations and Inequalities8.8 Using Exponential and Logarithmic Functions

VocabularyExponential equation, logarithmic equation

Writing in MathHow can use the log of any base to solve an exponential equation?

Have students to write a sentence(s) and create an example about their thinking.

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How is the relationship between exponents and logarithms used to solve problems?Objective(s):• Students will solve exponential and

logarithmic equations.

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.

Additional Lessons:Engageny Algebra I Module 5, Topic A, Lesson 3, Analyze Word Problems

Engageny Algebra II Module 3, Topic B, Lesson 7, Solve Exponential Equations Numerically

Engageny Algebra II Module 3, Topic B, Lesson 14, Solve Logarithmic Equations

Engageny Algebra II Module 3, Topic B, Lesson 15, Solve Logarithmic Equations

Engageny Algebra II Module 3, Topic D, Lesson 24, Exponential Equations

Engageny Algebra II Module 3, Topic D, Lesson 27, Create and Solve Exponential Equations

Tasks:Multiplying CellsMedical Diagnosis TaskCompounding with a 100% Interet Rate Compounding with a 5% Interest Rate

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Additional Resource(s):Solving an exponential equation using propertiesSolving an exponential equation using graphingSolving an exponential equation using tablesUsing the change of base formulaSolving logarithmic equations

A-REI.D.11 F-LE.A.4 F-IF.B.4 F-IF.B.6 F-IF.C.7e

Enduring Understanding(s):.The function y=e^x and y =ln x are inverse functions. Just as before, this means that if a=e^b, then b= ln a and vice versa.

Essential Question(s):How can you use the relationship between y=e^x and y =ln x to solve exponential and logarithmic equations?

Objective(s):• Students will evaluate and simplify natural

logarithmic expressions• Students will solve equations using natural

logarithms.

Pearson7.6 Natural Logarithms

Glencoe8.7 Base e and Natural Logarithms

Tasks:Natural Phenomena on Earth

Additional Resource(s):Solving natural logarithmic equationsSolving natural exponential equations

VocabularyNatural logarithmic function

Writing in MathCan ln 5 +log (base 2) 10 be written as a single log?

Have students to write a sentence(s) about their thinking.

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RESOURCE TOOLBOXTextbook Resources

Pearson Tools:www.phschool.com/mathhttp://www.poweralgebra.comhttp://www.pearsonsuccessnet.com( ELL, Enrichment, Re-teaching, Quizzes/Tests, Think About a Plan, Test Prep, Extra Practice, Find the Errors, Activities/Games/Puzzles, Video Tutor, Chapter Project, Performance Task, and Student Companion)Glencoe Tools:Student EditionTeacher EditionProblem SolvingVocabulary Puz zle Maker

StandardsCommon Core State Standards InitiativeCommon Core Standards - MathematicsCommon Core Standards - Mathematics Appendix AEdutoolbox (formerly TNCore)The Mathematics Common Core ToolboxTennessee BlueprintsPARCC Blueprints and Test Specifications FAQCCSS ToolboxNYC tasksNew York Education Department TasksPARCC High School Math TasksTICommonCore.comTN Department of Education Math StandardsAlgebra 2 TN State StandardsPARCC Practice TestCCSS Flip Book with Examples of each Standard

VideosBrightstormTeacher TubeThe Futures ChannelKhan AcademyMath TVLamar University Tutorial

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

Calculator

Math NspiredTexas Instrument ActivitiesCasio Activities Others:

UT Dana CenterMars TasksInside Math TasksMath Vision Project Tasks Better LessonSCS Math Tasks

Interactive ManipulativesKuta SoftwareIlluminations (NCTM)Stem ResourcesNational Math ResourcesMARS Course 2NASA Space MathMath Vision ProjectPurple MathACTTN ACT Information & ResourcesACT College & Career Readiness Mathematics Standards

Additional SitesDana Center Algebra 2 AssessmentsIllinois State Assessment strategiesUniversity of Idaho Literacy StrategiesSCS Math Tasks (Algebra II)NWEA MAP Resources:https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum)https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.