Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics

Quarter 1 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 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 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. 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

Curriculum and Instruction – Office of Mathematics

Quarter 1 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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Quarter 1 Algebra II

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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Quarter 1 Algebra II

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 Expressions, Equations, and Inequalities Various Functions, Equations & Their Graphs Linear Systems Quadratic Functions & Equations

Overview During this quarter students will extend their understanding of functions and the real numbers system, and increase their toolset for modeling in the real world. Students extend their notion of number to include complex numbers and see how the introduction of this set of numbers yields the solutions of quadratic equations. Students deepen their understanding of the concept of function, and apply equation-solving and function concepts to many different types of functions. Students also build upon previous units and prior courses that explored linear equations and expressions, and apply equation-solving and function concepts to many different types of functions. Students continue to interpret graphs and reason about rates of change of functions. Students learned in Grade 8 that the rate of change of a linear function is equal to the slope of its graph. And because the slope of a line is constant, the phrase “rate of change” is clear for linear functions. For nonlinear functions, however, rates of change are not constant, and students therefore discuss and understand average rates of change over an interval.

Students build on their work with linear and quadratic functions in this quarter. Students work closely with the expressions that define the functions and continue to expand and refine their abilities to model situations and to solve equations, including simplifying radical expressions and solving quadratic equations over the set of complex numbers.

Content Standard Type of Rigor Foundational Standards Sample Assessment Items**A-CED.A.1 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.A.1, A-REI. D.11 Conceptual Understanding & Application A-REI.1, 3, A-REI B. 4a, A-REI C. 5, A-REI D.10, 12

TN Task Alg. 1- Downloads;

F-IF.B.4, 6 Conceptual Understanding & Application F-IF.A.1,2, 7a, 7b, 8 TN Task Alg. 1 - Cliffhanger

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Quarter 1 Algebra II

F-BF.A.1 Conceptual Understanding & Application F-BF.A.1a, F-BF B.3 TN Task Alg. 2 – Car DepreciationA-SSE.A.2, A-SSE.B.3 Procedural Skill, Conceptual

Understanding & ApplicationA-SSE.A.1 TN Task Alg. 2 – One Rocket Three

EquationsA-APR.B. 3 Procedural Skill, Conceptual

Understanding & ApplicationA-APR.B.2 TN Task Alg. 2 – Root of the

ProblemN-RN.A.1, 2 Procedural Skill, Conceptual

UnderstandingN-RN.A.3 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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Quarter 1 Algebra II

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESExpressions, Equations, and Inequalities

(Allow 1 week for instruction, review, and assessment)Domain: Creating EquationsCluster: Create equations that describe number relationships. A-CED.A.1Create equations and

inequalities in one variable and use them to solve problems. ★

Domain: Reasoning with Equations and InequalitiesCluster: Create equations that describe numbers or a relationship. 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.

Enduring Understanding(s):Relationships with numbers can be represented by equations, inequalities, and systems.

Essential Question(s):How can algebra describe the relationship between a set of numbers?

Objective(s):Students will write and solve equations and justify the solution path chosen.

Pearson1-4 Solving EquationsGlencoe1-3 Solving Equations

Additional Resource(s):Solving equations with variables on both sides VideoSolving multi-step equations by combining like terms VideoWriting a multi-step equation to solve problems VideoUsing formulas to solve real-world problems VideoTransforming formulas VideoUse 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):Engage ny Algebra I Module 1, Topic C, Lesson 10, True and False Equations

Engage ny Algebra I Module 1, Topic C, Lesson 12, Solving Equations

Engage ny Algebra I Module 1, Topic C, Lesson 13, Some Potential Dangers When Solving Equations

Use the following resources to ensure that the

VocabularyEquation, solution of an equation, inverse operations, identity, literal equation

Writing in MathSuppose you solve an equation and find that your school needs 4.3 buses for a class trip. Explain how to interpret this solution.

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Quarter 1 Algebra II

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESintended outcome and level of rigor of the standards are met.

Task(s)TN Task Alg. 1 –Buddy Bags Task TN Task Alg. 1- Paulie’s Pen TN Task Alg. 1-- Disc Jockey (expressions)

T-shirt Sale Equations and Identities

Reasoning with Equations and Inequalities Domain: Creating EquationsCluster: Create equations that describe number relationships. A-CED.A.1Create equations and

inequalities in one variable and use them to solve problems. ★

Domain: Reasoning with Equations and InequalitiesCluster: Create equations that describe numbers or a relationship. 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.

Enduring Understanding(s):There are various methods of manipulating equations and inequalities to solve problems.

Essential Question(s):How can a problem be solved and why is one method chosen over another?

Objective(s):Students will write, solve and graph inequalities and justify the solution path chosen.

Pearson1-5 Solving Inequalities (Parts 1& 2)

Glencoe1-5 Solving Inequalities

Additional Resource(s):Writing and solving a compound inequality containing “And” VideoWriting and solving a compound inequality containing “Or” VideoSolving and graphing multi-step inequalities VideoInequalities with no solutions or all real numbers as solutions Video

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):Engage ny Algebra I Module 1, Topic C, Lesson 11, Solution Sets for Equations and Inequalities

Engage ny Algebra I Module 1, Topic C, Lesson 14, Solving Inequalities

Engage ny Algebra I Module 1, Topic C, Lesson 15, Solution Sets of Two or More Equations (or Inequalities) Joined by “And” or “Or”

Engage ny Algebra I Module 1, Topic C, Lesson 16,

VocabularyCompound inequalitiesWriting in MathWhat is the difference between solutions to a compound inequality joined by and compared to those joined by or?

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Quarter 1 Algebra II

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESSolving and Graphing Inequalities Joined by “And” or “Or”

Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.

Task(s)Ivy Smith Grows Up

Functions, Equations, and Graphs(Allow 2 weeks for instruction, review, and assessment)

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.

Domain: Linear, Quadratic, and Exponential Models ★Cluster: Conduct and compare linear, quadratic, 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

Enduring Understanding(s):Functions can be used to model all kinds of real-world problems.

Essential Question(s):What is a relation and when is a relation a function?

Objective(s):Students will identify, interpret, and graph relations and functions.

Pearson2-1 Relations and Functions (Parts 1& 2) Glencoe2-1 Relations and Functions

Additional Lesson(s):Domain Representations

Additional Resource(s)Identifying functions using a mapping diagram VideoIdentifying functions using the vertical line test VideoGraphing relations VideoFinding domain and range of a relation Video

Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.

Task(s)TN Alg. 1 Task Arc, Creating & Interpreting Functions

• Task 1 –Joe’s on the Beach Ice Cream • Task 2 - Jose’s Surfboard • Task 3 - Ocoee Sand Dunes • Task 4 - More Sand Dunes • Task 5- Swimming Pool Depth • Sugar Prices Task

VocabularyRelation, domain, range, function, vertical-line test, function rule, function notation, independent variable, dependent variable

Writing in Math Your friend writes, “In a function, every vertical

line must intersect the graph in exactly one point.” Explain your friend’s error and rewrite the statement so that it is correct.

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Quarter 1 Algebra II

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES(include reading these from a table).

Domain: Linear, Quadratic, and Exponential Models ★Cluster: 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: Linear, Quadratic, and Exponential Models ★Cluster: 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. ★

Enduring Understanding(s):Many real-world problems involve rates of change/slope.

Essential Question(s):How can the relationship between quantities best be represented?

Objective(s):Students will graph and write linear equations and calculate and interpret the rate of change of a function.

Pearson2-3 Linear Functions and Slope-Intercept FormGlencoe2-3 Rate of Change and Slope

Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.

Additional Lesson(s)Armstrong Numbers National Debt and WarsHow to Weigh an Alligator Weight of Money-linear function Weight of Money Reflect and Apply

Tasks:TN Task, Alg. 1 – Downloads TN Task, Alg. 1-What’s the Point Oil spills on land Medical Testing Television and Test Grades You’re Toast Dude!

VocabularySlope, linear function, linear equations, x-intercept, y-intercept, slope-intercept

Writing in MathDescribe the process of finding the rate of change for each of the following:a. a table of values b. a graph c. an equation

Graphic OrganizerSlope-intercept Form (dgelman)

Domain: Interpreting Categorical and Quantitative Data

Cluster: Summarize, represent, and interpret

Enduring Understanding(s):Many real-world problems involve modeling data with a linear equation. The equation

Pearson 2-5 Using Linear Models

VocabularyScatter plot, correlation, line of best fit, correlation coefficient

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

data on a single count or measurement. variable S-ID.B.6 Represent data on two

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.

can be used to draw conclusions about the situation.Essential Question(s):How can you model data with a linear function?

Objective(s):• Students will write linear equations that

model real-world data.• Students will make predictions from linear

models based upon the data.

Glencoe 2-5 Scatter Plots and Lines of Regression and

Correlation

Additional Resource(s): Writing an equation for a trend line Video Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.

Additional Lesson(s):Guess the Age Price of Apples Exploring Linear Data Line of Best Fit

Tasks:Bird Eggs

Having Kittens

Writing in MathWhat is the difference between a positive correlation and a negative correlation? Provide real-world quantities that represent each.

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); 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.

Enduring Understanding(s):The absolute value function is a good parent function to use to apply translations, stretches, compressions, and reflections.Essential Question(s):What is an absolute value function?

Objective(s):Students will graph and find solutions of absolute value functions using a variety of strategies.

Pearson 2-7 Absolute Value Functions and Graphs Glencoe 2-7 Parent Functions and Transformations

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):Engage ny Algebra I Module 3, Topic C, Lesson 15, Piecewise Functions Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.Absolute Value Functions Lesson & resources

VocabularyAbsolute value function, axis of symmetry, vertex

Writing in MathExplain why the reflection of the graph off(x) = x2 in the y-axis is the same as the graph of f(x) = x2. Is this true for all reflections of quadratic equations? If not, describe a case when it is false.

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Quarter 1 Algebra II

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Linear Systems(Allow 2 weeks for instruction, review, and assessment)

Domain: Reasoning with Equations and InequalitiesCluster: Solve systems of equations. A-REI.C.6 Solve systems of linear

equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Enduring Understanding(s):A system of equations can be solved by finding a set of values that replace the variables in the equations and make each true.

Essential Question(s):How does representing functions graphically help you solve systems of equations?

Objective(s):Students will solve a linear system using a graph or a table.

Pearson 3-1 Solving Systems Using Tables and Graphs

Glencoe 3-1 Solving Systems of Equations by Graphing

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): Engage ny Algebra II Module 1, Topic C, Lesson 31,

Systems of Equations Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.

Tasks: Don't Get Zapped TN Task, Alg. 2- Amusement Park TN Task, Alg. 1-Gorp Task TN Alg. 1 Task Arc-Bike and Truck TN Task, Alg. 1 –Delivery Truck TN Task, Alg. 1 - Knitting Knots Printing Tickets Cycling Situations Talk is Cheap

Additional Resource(s) Solving and interpreting a system of linear

equations by graphing Video Interpreting solutions of systems of linear

equations Video

VocabularySystem of equations, linear system, solution of a system

Writing in MathExplain how you can determine the consistency and dependence of a system without graphing the system.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Classifying systems of equations without

graphing Video

Domain: Reasoning with Equations and InequalitiesCluster: Solve systems of equations. A-REI.C.5 Prove that, given a system of

two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

A-REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Enduring Understanding(s):A system of equations can be solved by utilizing various methods including substitution, elimination, and using matrices.

Essential Question(s):When can you use substitution to solve a system?When can you use elimination to solve a system of linear equations?Why is it helpful to use matrices to solve systems of linear equations?

Objective(s):Students will solve a linear system using substitution.Students will solve a linear system using elimination.• Students will represent a system of linear

equations with a matrix.• Students will solve a system of linear

equations with matrices.

Pearson 3-2 Solving Systems Algebraically 3-2 Solving Systems Algebraically (Part 2)

3-6 Solving Systems Using Matrices

Glencoe 3-2 Solving Systems of Equations Algebraically

4-6 Augmented MatricesUse the following resources to ensure that the intended outcome and level of rigor of the standards are met.

Tasks:Best Buy Tickets Cash Registers System of Equations and Inequalities Accurately Weighing Pennies

Flying Through the St Louis Gateway Arch Stacking Cups

Additional Resource(s): Solving linear systems using substitution Video Solving linear systems for real-world situations

using substitution Video Solving linear systems using elimination,

adding Video Solving linear systems using elimination,

multiplying first Video Writing the dimensions of a matrix Video Identifying a matrix element Video Using matrices to organize data Video

VocabularyEquivalent systems, matrix, matrix element, row operation

Writing in MathWhy might you use different methods for solving a system of equations?

Graphic OrganizerSystems by Substitution(dgelman)

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Quadratic Functions and Equations( Allow 4 weeks for instruction, review, and assessment)

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

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); 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.★

Enduring Understanding(s):A parabola is the graph of the quadratic function f(x) = ax2 + bx + cThe vertex form of a quadratic function is f(x) = a(x – h)2 + k, where a ≠ 0.

Objective(s):• Students will identify, compare, and graph

quadratic functions.• Students will find and explain solutions of

equations using various methods.

Pearson 4-1 Quadratic Functions and TransformationsGlencoe 5-1 Graphing Quadratic FunctionsUse the following resources to ensure that the intended outcome and level of rigor of the standards are met.

Tasks: TN Task, Alg. 2 –Forms of a Function TN Task, Alg. 1 -Vegetable Garden TN Alg. 1 Task Arc, Task 1 -Log Flume Ride TN Alg. 1 Task Arc, Task 2 -Linear or Quadratic Quadratic Function Dominos Season Pass Throwing a Ball Breaking Distance Building Functions

Additional Resource(s) Graphing Families of Quadratic Functions

(Texas Instruments) Changing Lots Finding the minimum of a parabola Video Using the maximum or minimum of a parabola

Video Using vertex form of a parabola to graph the

parabola Video Using vertex form to write the equation of a

parabola Video Using vertex form of a parabola to solve real

world problems Video

VocabularyParabola, quadratic function, vertex form, axis of symmetry, vertex of the parabola, minimum value, maximum value

Writing in MathDescribe how you determine whether a function is quadratic and if it has a maximum or minimum value.

Domain: Seeing Structure in Expressions Enduring Understanding(s): Pearson VocabularyShelby County Schools 2016/2017

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

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

expression to identify ways to rewrite it.

Any quadratic function is a stretch or compression, reflection, and/or a translation of y = x2.

• The standard form of a quadratic function is f(x) = ax2 + bx + c, where a ≠ 0.

Essential Question(s):Why is the standard form of a quadratic function useful?

Objective(s):Students will identify and graph quadratic functions written in standard form.

4-2 Standard Form of a Quadratic FunctionGlencoe5-1 Graphing Quadratic FunctionsUse the following resources to ensure that the intended outcome and level of rigor of the standards are met.

Additional Lesson(s): Kangaroo Conundrum/Tower of Hanoi Hanging Chains The Winning Three Pointer The Winning Three Pointer Reflect

and Apply Over Da Watta Math Shadows

Tasks:TN Task, Alg. 1 –Bottle Rocket

TN Task, Alg. 2 – One Rocket Three Equations TN Alg. 1Task Arc, Task 3, Roller Coaster Ride

TN Alg. 1Task Arc, Task 4 , Fireworks at the Park

TN Alg. 1Task Arc, Task 5 -Riding the Ramp TN Alg. 1Task Arc, Task 8 -Skywalking the Grand Canyon

Additional Resource(s) Identifying points on a parabola Video Using a quadratic function to model the height

of an object - Example 1- Video Graphing a quadratic function, y = ax^2 + bx

+ c Video Using a quadratic function to model the

height of an object - Example 2- Video

Standard form

Writing in MathDescribe how you determine whether a function is quadratic and if it has a maximum or minimum value.

Domain: Creating EquationsCluster: Create equations that describe numbers or relationships.

Essential Question(s):How can you write the equation of a parabola without knowing the vertex?

Pearson 4-3 Modeling With Quadratic Functions

Use the following resources to ensure that the

VocabularyStandard form

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

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.★

Objective(s):Students will model data with quadratic functions.

intended outcome and level of rigor of the standards are met.

Tasks:TN Alg.2 Task Arc, Task 5 –The Root of the Problem TN Alg. 1 Task Arc, Task 6 -Food to GoTN Alg. 1 Task Arc, Task 5 -Circus Acts Sidewalk Patterns in Prague

Additional Resource(s): Math Nspired: Modeling with a quadratic

function Ball Bounce (Texas Instruments) Mirror, Mirror Reflect and Apply Fitting a quadratic function to 3 points Video Using quadratic models Video Graphing a quadratic function using a table, y

= ax^2 + c Video

Writing in MathDescribe how you determine whether a function is quadratic and if it has a maximum or minimum value.

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

to solve problems. 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. ★

Enduring Understanding(s):• Expressions can be written in a variety

of ways.• Many quadratic trinomials can be

factored into products of two binomials.

Essential Question(s):How is factoring related to the Distributive Property?

Objective(s):• Students will find common and binomial

factors of quadratic expressions and explain their properties.

Pearson4-4 Factoring Quadratic Expressions(Parts 1 & 2)Glencoe5-3 Solving Quadratic Equations by Factoring

Additional Lesson(s): Polynomial puzzler Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.

Tasks:The Protein Bar Toss Task ,p.18Two Squares are Equal

Additional Resource(s):

VocabularyFactoring, greatest common factor (GCF) of an expression, perfect square trinomial, difference of two squares

Writing in MathWhat is the purpose of factoring quadratic expressions?

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• Students will factor special quadratic expressions and solve problems using equivalent forms.

Factoring trinomials of the type x^2 + bx + c where b is positive Video

Factoring trinomials of the type x^2 + bx + c where b is negative Video

Factoring trinomials of the type x^2 + bx - c Video

Factoring trinomials of the type ax^2 + bx + c where c is positive Video

Factoring trinomials of the type ax^2 + bx + c where c is negative Video

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

equations with real coefficients that have complex solutions.

Domain: Arithmetic with Polynomials and Rational ExpressionsCluster: Understand the relationship between zeros and factors of polynomials. A-APR 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.

Enduring Understanding(s):Operations and properties of the real number system can be extended to situations involving complex numbers.

Essential Question(s):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 solve quadratic equations by

factoring, by using a table, and by graphing.• Students will identify the zeros of a

polynomial where appropriate and graph the function defined by the polynomial.

Pearson4-5 Quadratic Equations (Parts 1& 2)Glencoe5-2 Solving Quadratic Equations by GraphingUse the following resources to ensure that the intended outcome and level of rigor of the standards are met.

Tasks:TN Task , Alg. 2 - Boxed In TN Task, Alg. 1 - Cliffhanger TN Task , Alg. 1 - Fencing For Josephine’s garden (linear and quadratic) The Pig Problem

Additional Resource(s): Solving quadratic equations by graphing Video Solving quadratic equations by factoring Video

VocabularyZero of a function, Zero-Product Property

Writing in MathExplain how to solve a quadratic equation by graphing its related quadratic function.

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

Enduring Understanding(s):• A single quantity may be represented

by many different expressions.• Corresponding to every power, there is

a root.Essential Question(s):

Pearson6-1 Roots and Radical ExpressionsGlencoe7-4 Nth Roots

VocabularyNth root, principal root, radicand, index

Writing in MathExplain when and why absolute value symbols are needed when taking an nth

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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.

What does it mean to take the nth root of a number?

Objective(s):Students will find and explain the roots of an expression.

Additional Resource(s): Simplifying radical expressions Video Simplifying radical expressions with cube roots

Video

root.

Domain: Reasoning with Equations and InequalitiesCluster: Solve systems of equations. A-REI.B.4 Solve quadratic equations in one

variable.b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Enduring Understanding(s):There are various methods of solving equations and inequalities when solving problems.

Essential Question(s):Why structure expressions in different ways?

Objective(s):• Students will find common and binomial

factors of quadratic expressions.• Students will solve equations, and solve

problems involving functions by completing the square.

Pearson 4-6 Completing the Square (Parts 1 & 2)Glencoe5-5 Completing the SquareAdditional Lesson(s):Building Connections

Additional Resource(s): Math Nspired: Completing the Square Math Nspired: Completing the square

algebraically Solving quadratic equations using square roots

Video Solving quadratic equations using completing

the square Video Solving quadratic equations using completing

the square when a does not equal 1 Video Rewriting a function in vertex form by

completing the square Video

VocabularyCompleting the square

Writing in MathExplain what it means to complete the square. Describe each step.

Enduring Understanding(s):There are various methods of solving equations and inequalities when solving problems.

Essential Question(s):Why is the Quadratic Formula important?

Pearson 4-7 The Quadratic Formula Glencoe 5.6 Quadratic Formula and the Discriminant

Additional Resource(s): Math Nspired: Discriminant testing Solving quadratic equations using the

VocabularyQuadratic Formula, discriminant

Writing in MathDescribe three different ways to solvex2 – 2x – 15 + 0. Which method do you prefer and why?

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Objective(s):• Students will solve quadratic equations

using the Quadratic Formula.• Students will determine the number of

solutions by using the discriminant.

quadratic formula Video Using the discriminant to find the number of

solutions and solve problems Video Solving quadratic equations using the

quadratic formula, complex solution Video

Domain: The Complex Number System Cluster: Perform arithmetic operations with complex numbers. N-CN.A.1 Know there is a complex

number i such that i2 = –1, and every complex number has the form a + bi with a and b real.

N-CN.A.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Enduring Understanding(s):Operations and properties of the real number system can be extended to situations involving complex numbers.

Essential Question(s):What are complex numbers?

Objective(s):• Students will identify, graph, and perform

operations with complex numbers.• Students will determine the number of

solutions by using the discriminant.

Pearson4-8 Complex Numbers (Parts 1 & 2)Glencoe5.4 Complex Numbers and the Complex PlaneUse the following resources to ensure that the intended outcome and level of rigor of the standards are met.

Additional Lesson(s):Classifying Complex Numbers Complex Number Properties

Additional Resource(s): Math Nspired: Complex Numbers Simplifying the square root of negative

numbers Video Simplifying imaginary numbers Video Adding complex numbers Video Multiplying complex numbers Video Finding complex solutions Video

VocabularyImaginary unit, imaginary number,

complex number, pure imaginary number, complex number plane, absolute value of a complex number, complex conjugates

Writing in MathExplain how are complex number related to the solutions of quadratic equations?

Domain: Reasoning with Equations and InequalitiesCluster: Solve systems of equations. A-REI.C.7 Solve a simple system

consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection

Enduring Understanding(s):A system of equations and inequalities can be solved by utilizing various methods.

Essential Question(s):What are the various methods that one can use to solve quadratic inequalities?

PearsonConcept Byte - Quadratic Inequalities (p.279)Glencoe5.8 Quadratic Inequalities Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.

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between the line y = -3x and the circle x2

+ y2 = 3. Objective(s):• Students will investigate and use different

methods to solve quadratic inequalities.

Additional Resource(s):Graphing Calculator Investigation

Domain: Expressing Geometric Properties with EquationsCluster: Translate between the geometric description and the equation for a conic section. G-GPE.A.2 Derive the equation of a

parabola given a focus and directrix.

Enduring Understanding(s):Algebra can be used to efficiently and effectively describe and apply geometric properties.

Essential Question(s):How can algebra be useful when expressing geometric properties?

Objective(s):Students will write the equation of a parabola, graph parabolas and translate between the description and the equation.

Pearson10-2 Parabolas

Glencoe10.1 Midpoint and Distance Formulas10.2 Parabolas

Additional Resource(s): Parabola Word Problem Writing the equation of a parabola Video Finding the equation of a parabola Video Graphing the equation of a parabola Video

VocabularyFocus of a parabola, directrix, focal length

Writing in MathWhat is true about the set of points on a parabola, its focus, and its directrix?What can you determine about the orientation of a parabola by looking at its vertex equation?

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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 Puzzle Maker

Pearson Textbookshttp://interactmath.com/

StandardsCommon Core State Standards InitiativeCommon Core Standards - MathematicsCommon Core Standards - Mathematics Appendix AEdutoolbox (formerly TNCore)The Mathematics Common Core ToolboxPARCC Blueprints and Test Specifications FAQ TICommonCore.com TN Department of Education Math StandardsAlgebra 2 TN State StandardsPARCC Practice Test

VideosBrightstormThe 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)University of Idaho Literacy Strategies

Additional SitesUT Dana CenterMars TasksInside Math TasksMath Vision Project Tasks Better LessonAlgebra II BlueprintDana Center Algebra 2 AssessmentsIllinois State Assessment strategiesSCS Math Tasks (Algebra II)NYC tasksNew York Education Department Tasks

Interactive ManipulativesKuta SoftwareIlluminations (NCTM)Stem ResourcesNational Math ResourcesMARS Course 2NASA Space MathMath Vision ProjectPurple Math

CalculatorMath NspiredTexas Instrument ActivitiesCasio Activities

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.

ACTTN ACT Information & ResourcesACT College & Career Readiness Mathematics Standards