GATEWAY REGIONAL HIGH SCHOOL
ALGEBRA II GRADE 1012
PACING GUIDE
The Algebra II curriculum is comprised of the following major concepts or ‘Big Ideas’: (1) expressions, equations, and inequalities; (2) polynomial functions and graphs; (3) rational, irrational, and complex numbers; (4) quadratic equations and inequalities; (5) rational functions and graphs; (6) exponential and logarithmic functions; (7) sequences and series; (8) statistics and probability; and (9) matrices. While knowledge of content is being developed, students are engaged in handson and cooperative activities that encourage mathematical reasoning, problem solving, communicating, and making connections. Through these activities students utilize technology such as graphing calculators, computers, and calculatorbased lab equipment. In addition, they are encouraged to think more critically through activities that will involve investigations, explorations, and discovery. Finally, evaluations appear in several formats: pencil and paper tests, performance tasks, and long and shortterm projects.
PACING GUIDE
Month  # Days  Standards  Skills  Activities  Assessments 
September Analyzing Functions  30  MA.ALG2.3.1 MA.ALG2.4.2 MA.ALG2.4.3  Identify Functions Evaluate Functions Interval and Inequality Notation Discrete Vs. Continuous Domain and Range
Operation with Functions Composite Functions  Graphic organizer 1.1 identifying key terms and function relations Graphic Organizer Function Notation 1.2 Identify function notation and evaluate functions PracticeEvaluating functions Graphic Organizer 1.3Graph inequalities on a number line using using inclusive and noninclusive notation. PracticeInterval Notation Graphic Organizer 1.4Identify if functions are discrete or continuous by analyzing graphs, functions, mapping, and tables. Quiz ReviewIntro to functions Quiz Intro to functions Graphic Organizer 1.5state the domain and range of given data, graphs, and functions. Graphic Organizer 1.6Perform indicated operations with functions. (adding, subtracting, multiplying, and dividing) Practice function operations Graphic Organizer 1.7 Evaluate Composite functions for the given values.  Secondary assessment Quiz 1.11.4 Introduction to functions Secondary Assessment Quiz operations and evaluating functions. Primary Assessment Primary assessment on identifying functions and all function operations 
October Graphs of functions and Desmos Project  30 days  MA.ALG2.1.7 MA.ALG.3.1 MA.ALG2.3.4 MA.ALG2.4.2  Graphs of Functions Increasing and Decreasing Finding X and Y Intercepts Exploring Polynomial Functions  Graphic Organizer Identifying functions and the graphs that correlate with them. Graphic Organizer Identify parts of graphs of functions. Identify the maximum and minimum of the graph. Guided notes find the x and y intercepts of functions algebraically Graphic OrganizerDetermine the behaviors of functions (ex. Max, min, translations, and end behaviors) TestFunction Basics and their graphs Performance AssessmentDesmos Graph Activity  Secondary AssessmentAnalyzing graphs of functions and behaviors Primary Assessment Function Basics and their graphs Primary Assessment Create a name using Desmos and the understanding of graphs of functions. 
November Complex Numbers Graphing Quadratic Functions  10 Days 15 days  MA.ALG2.1.1 MA.ALG2.1.2 MA.ALG2.1.2 MA.ALG2.1.6 MA.ALG2.1.7  Complex Numbers Operations with Complex Numbers Complex Numbers Unit Review Quadratic Functionsterms and standard form Characteristics of a quadratic function  Graphic OrganizerDefine a complex number. Find the root of a negative number. Graphic Organizer – Multiplying imaginary numbers and complex numbers. PracticePerforming operations with complex numbers Quiz Complex Numbers Unit Review PacketOverall review of finding roots and performing operations with complex numbers. Test Complex Numbers Graphic Organizer Intro To Quadratic FunctionsKey terms for quadratic functions unit. Standard form of a quadratic function. Graphic Organizer Characteristics of Quadratic functionsUnderstand how to determine the characteristics of a parabola given the equation. Find domain and range. Practice problems built into Organizer  Secondary assessmentOperations with complex numbers (Ed Connect) Primary Assessment Test on Complex numbers unit 
December Graphing Quadratic Functions Continued Solving Quadratic Functions Algebraically  20 Days  MA.ALG2.1.7  Graphing Quadratic Functions Factoring quadratic functions  Graphic Organizer with Practice Graphing Quadratic FunctionsGraph a parabola given the function in standard form. Quiz Graphing Quadratic Functions Guided Practice FactoringGuided practice reviewing methods of factoring quadratics  Secondary AssessmentGraphing quadratic functions in standard form 
January  Solve quadratic equations using the quadratic formula Solve quadratic equations by taking the square root Solve quadratics by completing the square  Graphic Organizer Quadratic FormulaIdentify the discriminant and utilize the quadratic formula to solve. Practice problems solving Graphic Organizer Square root MethodSolve the quadratic equation by taking the square root. Individual practice problems in notes Graphic Organizer Complete the SquareSolve the quadratic equation by completing the square. Individual Practice problems Quiz solving Quadratics Algebraically Chapter Review Quadratics Test Quadratic Equations  Secondary Assessment Solving quadratic equationsSolve the quadratic equations using various algebraic methods Santa’s Special DeliveryActivity using quadratics and Santa delivering gifts (Secondary) Primary AssessmentChapter 5 Test on Quadratic equations  
February Graph quadratic in vertex form and graph circles Solving Linear and nonLinear systems  15 days 25 Days  MA.ALG2.1.7 MA.ALG2.2.6 MA.ALG2.3.7 MA.ALG2.2.4 MA.ALG2.2.6  Graphing a quadratic in Vertex form Graphing Circles from standard form Use the distance formula and completing the square to create the standard form of a circle Review graphing lines, absolute values, and inequalities  Graphic Organizer Vertex FormIdentify the vertex and locate points from vertex form Practice Graphing in Vertex Form Graphic Organizer graphing circles Part 1 Use the standard form of a circle to identify the center and the radius Practice Graphing Circles Graphic Organizer graphing circles Part 2 Students will use the distance formula and completing the square to graph circles Set up in standard form and graph Graphing Quadratics and Circles Quiz Guided PracticeGraphing linear equations Guided PracticeGraphing Absolute value equations Guided PracticeGraphing linear inequalities  Performance AssessmentStudents will use quadratics to compare 3 different Iphone plans Secondary AssessmentGraphing quadratics and circles in standard form Primary Assessment vertex form and circlesStudents will graph quadratics in Vertex form and circles in standard form. 
March  Graphing Systems of equations Solving systems of equations algebraically Solving Systems of Inequalities Solving systems with 3 variables and 3 equations  Graphic Organizer Graphing systemsSolve a linear system by graphing and locating a point of intersection. Practice Graphing systems of linear equations Graphic Organizer EliminationUse the Elimination method to solve the system of equations. Practice solving systems using elimination method Graphic Organizer SubstitutionUse the substitution method to solve the system of equations Practice solving systems using substitution Quiz solving systems graphing and algebraically Graphic Organizer Systems of InequalitiesGraphing systems of inequalities and identifying the solution set Practice graphing systems of inequalities Graphic Organizer Systems with 3 variablesUsing substitution and Elimination to solve systems with 3 variables. Guided Practice solving systems with 3 variables Test Systems of Equations  Secondary Assessment SystemsSolve the systems of equations by graphing and algebraically Secondary AssessmentSolving systems using different methods and comparing solutions. (Small Group) Primary Assessment Systems of EquationsSolving linear and nonlinear systems of equations with various methods  
April Arithmetic and Geometric Sequences and Series  20 days  MA.ALG.2.3.2  Arithmetic Sequences Geometric Sequences Arithmetic Series Geometric Series  Graphic Organizer Arithmetic SequencesExplore arithmetic patterns and use the explicit formula to find missing terms Guided practice using the explicit formula Graphic Organizer Geometric SequencesExplore Geometric patterns and find the missing terms Guided Practice Exploring geometric sequqences Quiz Arithmetic and Geometric Sequences Graphic Organizer Arithmetic SeriesUse summation notation to find the sum of an arithmetic series Guided Practice Arithmetic Series Graphic Organizer Geometric SeriesUse Sums Formulas to find the sum of finite and infinite geometric series Guided Practice Geometric Series Quiz Arithmetic and Geometric Series Test Sequences and Series Performance AssessmentExplore fractals web quest, Create a pattern using iterations  Secondary Assessment SequencesFind the missing terms and explicit formulas for the patterns Secondary Assessment SeriesFind the sum of finite and infinite series Primary Assessment Sequences and SeriesUse the explicit and sums formulas to find missing terms and sums of all sequences and series Performance Assessment PatternsCreate fractals and patterns by exploring series and iterations 
May Polynomials  20 days  MA.ALG2.1  Polynomial Functions Adding and subtracting polynomials Multiplying polynomials Long Division of Polynomials  Graphic Organizer Polynomials IntroIdentify polynomials and understand writing in descending order Practice identifying polynomials and writing in standard form Graphic Organizer Adding and Subtracting PolynomialsPerform basic polynomial operations with understanding of like terms Practice combining like terms Graphic Organizer Multiplying PolynomialsMultiply larger polynomials and combine like terms Practice multiplying polynomials Quiz operations with polynomials Graphic Organizer Long Division of PolynomialsUse long division of polynomials to identify factors Guided practice long division  Secondary Assessment operations with polynomialsPerform operations with polynomials to write in simplest terms Secondary Assessment Dividing PolynomialsUse synthetic and long division to factor polynomials 
June End of Year Benchmark  5 days  Synthetic Division of Polynomials Prepare for End of Year Benchmark  Graphic Organizer Synthetic Division of PolynomialsUse synthetic division of polynomials to identify factors Practice synthetic division Quiz polynomial division Guided and Individual PracticePractice with sequences and series and all polynomial operations EOY Benchmark Test  Primary Assessment PolynomialsPerform basic operations with polynomials and use division to identify factors of polynomials End of year BenchmarkSequences and series and Polynomials Assessment  
GATEWAY GROUP CURRICULUM UNIT PLAN  
Content Area: Algebra II  
Unit Title: Polynomials  Timeframe: 6 weeks/MP I  
Lesson Components  
UNIT SUMMARY  
In this unit, Students will be able to…
 
LEARNING TARGETS  
ESSENTIAL QUESTIONS  ENDURING UNDERSTANDINGS  
What is the Fundamental Theorem of Algebra? How are basic elements labeled and used to solve problems? How do we find the sum of a finite geometric series? How do we factor? How do we apply those formulas?  Use properties of operations for complex numbers. Restructure polynomials/rational expressions. Derive Formulas Explain relationships of polynomials  
Global Awareness: Understanding how rational functions are communicated in other cultures. Financial, Economic, Business, and Entrepreneurial Literacy: Examining how Geometric series are used in the workplace to make businesses more profitable.  
Creativity and Innovation: Working in collaborative teams to express original methods for solving realworld problems. Critical Thinking and Problem Solving: Learning the components of logical arguments and applying this skill to geometric problems. Communication and Collaboration: Using cooperative teams to develop notes and problem solving strategies. Information Literacy: Maintaining complete and accurate notes of terms and formulas in Algebra. Media Literacy: Using conditional statements to examine the veracity of advertisements. ICT LiteracyInformation, Communications and Technology: Accessing necessary information to solve problems using Chrome Books and Smart Phones and demonstrating that information on presentation technology. Life and Career Skills: Completing selfevaluations throughout the year to gage individual progress.  
EVIDENCE OF LEARNING  
Assessment Students will:
 
Integration of Technology:
 
Materials/Equipment: Lined paper Pencils Screens/LCD Projector Transparencies/markers Colored pencils Markers Access to mobile labs/computer lab Smartboard, Handouts, texts, articles  
Goals/Objectives Students will:  CPI#  Learning Activities/Instructional Strategies (Interdisciplinary Connections; Technology; Integration of 21st Century Skills)  Assessment Tasks (More on the summative side)  
 A.SSE.2  Notes Cooperative Teams Homework Class Discussion Smart Board Demonstrations Assessments  Traditional Assessment
Alternative Assessment
 
 A.SSE.4  Notes Cooperative Teams Homework Class Discussion Smart Board Demonstrations Assessments  Traditional Assessment
 
 A.APR.2  
 A.APR.3 
 
Differentiation/Adaptations/Modifications:
 
Resources Provided

CPI#  Cumulative Progress Indicator (CPI) 
A.REI.4b  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. 
A.SSE.2  Use the structure of an expression to identify ways to rewrite it.

F.IF.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 behavior 
GATEWAY GROUP CURRICULUM UNIT PLAN  
Content Area: Algebra II  
Unit Title: Expressions and Equations  Timeframe: 6 weeks/MP I  
Lesson Components  
UNIT SUMMARY  
In this unit, Students will be able to… Extend the properties of exponents to rational exponents. Understand solving equations as a process of reasoning and explain the reasoning. Write expressions in equivalent forms to solve problems. Interpret functions that arise in applications in terms of the content.
 
LEARNING TARGETS  
ESSENTIAL QUESTIONS  ENDURING UNDERSTANDINGS  
What are the properties of exponents? How can you solve equations? How do interpret functions?  Identify the properties of exponents Solve equations. Interpret functions.  
Global Awareness: Understanding how Exponents are communicated in other cultures. Financial, Economic, Business, and Entrepreneurial Literacy: Examining how functions are used in the workplace to make businesses more profitable.  
Creativity and Innovation: Working in collaborative teams to express original methods for solving realworld problems. Critical Thinking and Problem Solving: Learning the components of logical arguments and applying this skill to functions. Communication and Collaboration: Using cooperative teams to develop notes and problem solving strategies. Information Literacy: Maintaining complete and accurate notes of terms and formulas in Algebra II. Media Literacy: Using graphs to examine the veracity of advertisements. ICT LiteracyInformation, Communications and Technology: Accessing necessary information to solve problems using Chrome Books and Smart Phones and demonstrating that information on presentation technology. Life and Career Skills: Completing selfevaluations throughout the year to gage individual progress.  
EVIDENCE OF LEARNING  
Assessment
.  
Integration of Technology:
 
Materials/Equipment: Screens/LCD Projector Transparencies/markers Chromebooks Smartboard, Handouts, texts, articles 
Goals/Objectives Students will:  CPI#  Learning Activities/Instructional Strategies (Interdisciplinary Connections; Technology; Integration of 21st Century Skills)  Assessment Tasks (More on the summative side) 
 N.RN.1  For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.  Traditional Assessment
Alternative Assessment

 A.REI.1  Justify each step in the process and the solution and in the case of rational and radical equations show how extraneous solutions may arise.  Traditional Assessment Simple Rational and Radical Equations Alternative Assessment Apply the properties of rational and radical. 
 Produce equivalent expressions for exponential functions using the properties of exponents.  Produce equivalent expressions for exponential functions using the properties of exponents.  
 Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. ★  Using Desmos, create graphs and tables to give a visual example of behaviors.  
Differentiation/Adaptations/Modifications:

CPI#  Cumulative Progress Indicator (CPI) 
A.REI.2  Expressions and Equations 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. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. 
ASSE.3  Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. 
F.IF.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. 
GATEWAY GROUP CURRICULUM UNIT PLAN  
Content Area: Algebra II  
Unit Title: Expressions and Equations (2)  Timeframe: 3 weeks/MP 2  
Lesson Components  
UNIT SUMMARY  
In this unit, Students will be able to Find approximate solutions for the intersections of functions. Write arithmetic and geometric sequences both recursively and with an explicit formula. Graph exponential, logarithmic and trigonometric functions.  
LEARNING TARGETS  
ESSENTIAL QUESTIONS  ENDURING UNDERSTANDINGS  
What do exponential, logarithmic and trigonometric graphs look like? How can find the intersections of functions? What are arithmetic and geometric sequences?  Show the difference between graphs. Approximate Intersections Find arithmetic and geometric sequences.  
Global Awareness: Understanding how sequences are communicated in other cultures. Financial, Economic, Business, and Entrepreneurial Literacy: Examining how logarithmic graphs are used in the workplace to make businesses more profitable.  
Creativity and Innovation: Working in collaborative teams to express original methods for solving realworld problems. Critical Thinking and Problem Solving: Learning the components of logical arguments and applying this skill to algebra problems. Communication and Collaboration: Using cooperative teams to develop notes and problem solving strategies. Information Literacy: Maintaining complete and accurate notes of terms and formulas in Algebra. Media Literacy: Using graphs to examine the veracity of advertisements. ICT LiteracyInformation, Communications and Technology: Accessing necessary information to solve problems using Chrome Books and Smart Phones and demonstrating that information on presentation technology. Life and Career Skills: Completing selfevaluations throughout the year to gage individual progress.  
EVIDENCE OF LEARNING  
Assessment
 
Integration of Technology:
 
Materials/Equipment: Lined paper Pencils Screens/LCD Projector Transparencies/markers Colored pencils Markers Access to mobile labs/computer lab Smartboard, Handouts, texts, articles  
Goals/Objectives Students will:  CPI#  Learning Activities/Instructional Strategies (Interdisciplinary Connections; Technology; Integration of 21st Century Skills)  Assessment Tasks (More on the summative side)  
Find approximate solutions for the intersections of functions  A.REI.11  Explain why the xcoordinates 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) involving linear, polynomial, rational, absolute value, logarithmic and exponential functions.  Traditional Assessment
Alternative Assessment
 
Write arithmetic and geometric sequences both recursively and with an explicit formula.  4.2.12A  Use them to model situations, and translate between the two forms.  Traditional Assessment
Alternative Assessment
 
Graph exponential, logarithmic and trigonometric functions.  F.IF.4  Graph exponential, logarithmic and trigonometric functions expressed symbolically or verbally and show key features of the graph (including intercepts, intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity) by hand in simple cases and using technology for more complicated cases  Traditional Assessment
Alternative Assessment
 
Differentiation/Adaptations/Modifications: Study Guides Individual instruction Use of review guides  

CPI#  Cumulative Progress Indicator (CPI) 
A.REI.11  Expressions and Equations Explain why the xcoordinates 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. 
F.IF.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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity 
F.BF.2  Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 
GATEWAY GROUP CURRICULUM UNIT PLAN  
Content Area: Geometry  
Unit Title: Functions/Inferences & Conclusions  Timeframe: 4 weeks/MP 2  
Lesson Components  
UNIT SUMMARY  
In this unit, Students will be able to…
 
LEARNING TARGETS  
ESSENTIAL QUESTIONS  ENDURING UNDERSTANDINGS  
What is rate of change? How do you construct a function? What is the data?  Identify and apply rate of change Determine when you construct a function. Use data to create reports.  
Global Awareness: Understanding how data is communicated in other cultures. Financial, Economic, Business, and Entrepreneurial Literacy: Examining how data is used in the workplace to make businesses more profitable.  
Creativity and Innovation: Working in collaborative teams to express original methods for solving realworld problems. Critical Thinking and Problem Solving: Learning the components of logical arguments and applying this skill to apple data roblems. Communication and Collaboration: Using cooperative teams to develop notes and problem solving strategies. Information Literacy: Maintaining complete and accurate notes of terms and formulas in Algebra. Media Literacy: Using conditional statements to examine the veracity of advertisements. ICT LiteracyInformation, Communications and Technology: Accessing necessary information to solve problems using Chrome Books and Smart Phones and demonstrating that information on presentation technology. Life and Career Skills: Completing selfevaluations throughout the year to gage individual progress.  
EVIDENCE OF LEARNING  
Assessment Students will be able to…
 
Integration of Technology:
 
Materials/Equipment: Lined paper Pencils Screens/LCD Projector Transparencies/markers Colored pencils Markers Access to mobile labs/computer lab Smartboard, Handouts, texts, articles 
Goals/Objectives Students will:  CPI#  Learning Activities/Instructional Strategies (Interdisciplinary Connections; Technology; Integration of 21st Century Skills)  Assessment Tasks (More on the summative side) 
Calculate and interpret the average rate of change of a function.  4.2.12A  Present symbolically or as a table over a specified interval.  Estimate the rate of change from a graph 
Write a function that describes a relationship between two quantities.  Combine standard function types using arithmetic operations.  Build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model  
Use data from a randomized experiment to compare two treatments  Compare two treatments  Use simulations to decide if differences between parameters are significant  
Differentiation/Adaptations/Modifications:
 
Resources Provided

CPI#  Cumulative Progress Indicator (CPI) 
F.IF.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. 
F.8F.1  Write a function that describes a relationship between two quantities 
S.IC.3  Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each 