Grade/Course:11/Algebra 2 First Half of Semester Unit Title: Functions

Jasper County School District Curriculum MAP

Grade/Course:11/Algebra 2 First Half of Semester Unit Title: Functions

Standard(s): / A2.AAPR.1*
Add,subtract,andmultiplypolyomialsand understandthatpolynomialsareclosedundertheseoperations.
A2.ACE.2*
Createequationsintwoor morevariablestorepresentrelationshipsbetweenquantities.Graph
theequationsoncoordinateaxesusing appropriatelabels,units,andscales.
A2.FBF.3*
Describetheeffectofthetransformationskf(x),f(x)+k,f(x+k),andcombinationsofsuch
transformationsonthegraphofy= f(x)forany realnumberk.Findthevalueofkgiventhegraphsand
writetheequationofa transformedparentfunctiongivenitsgraph.
A2.FIF.6* Givena functionin graphical,symbolic,ortabularform,determinetheaveragerateofchangeofthefunctionovera specifiedinterval.Interpretthemeaningoftheaveragerateofchangeina givencontext.
Time Frame
(# of days, weeks) / Performance Indicators:
(skills/learning objectives/ content focus) / Suggested Activities / Resources / Assessment
(Performancetask, portfolio, teacher observation with anecdotal notes, etc.)
2 weeks / A2.AAPR.1
Performoperationswithfunctionsgraphicallyandalgebraically. / Worksheet–IntroductiontoFunctions
Worksheet–OperationswithFunctions / -Holt McDougal
Teacher Resources
-USA testprep
-Khan Academy
- Bing lesson plans / Tests, Quizzes, Projects, & Exams
(A2.FBF.3)
Findthe compositionoftwofunctionsgraphicallyand algebraically. / Worksheet–CompositionsofFunctions
A2.FIF.6
Identifylinearfunctionsas havingaconstantrateofchangewithtables,andgroupsusingrealworlddata.
Findandanalyzetheslopeofa linearfunction. / Worksheet–ModelingLinearEquations
OperationswithLinearFunctions
FunctionOperations
CompositionInverses
FunctionInverses
A2.ACE.2
Representandsolveabsolutevalueequationsandinequalities.

Grade/Course:11/Algebra 2 First Half of Semester Unit Title:Systemsof Equationsand Inequalities

Grade/Course:11/Algebra 2 First Half of Semester Unit Title:Exponentsand Radical Functions

Standard(s): / A2.AREI.2*
Solvesimplerationalandradicalequationsinonevariableandunderstandhowextraneoussolutionsmayarise.
A2.ASE.3c
Usethepropertiesofexponentstotransformexpressionsforexponentialfunctions.
A2.NCNS.1*
Knowthereisa complexnumberisuchthati2= −1,andeverycomplexnumberhastheforma+biwithaandbreal.
Time Frame
(# of days, weeks) / Performance Indicators:
(skills/learning objectives/ content focus) / Suggested Activities / Resources / Assessment
(Performance task, portfolio, teacher observation with anecdotal notes, etc.)
2 weeks / A2.ASE.3c
LawofExponents(includerationalexponents) / Worksheet–PropertiesofExponents
Worksheet–SimplifyingRationalExponents
ExponentJeopardyGame–
LawsofExponentsGame-
ExponentAsteroidGame– / -Holt McDougal
TeacherResources
-USA testprep
-Khan Academy
- Bing lesson plans / Tests, Quizzes, Projects, & Exams
A2.AREI.2
Simplifya radical.
Multiplyradicals / SimplifyRadicalExpression
MoreonSimplifyingRadicals
A2.AREI.2
Addandsubtractradicals
Divideradicalsandrationalizethedenominator. / MoreonOperationswithRadicals
A2.AREI.2
Createand/orsolveradicalequations,verifysolutions,and determinethedomainrestrictions.
Createand/orsolveliteralradical equations. / Worksheet–SolvingRadicalEquations
A2.NCNS.1
Defineandsimplifycomplexnumbers. / Worksheet–ComplexNumbers
OperationswithComplexNumbers
PropertiesofComplexNumbers
RationalizingImaginaryDenominators
A2.NCNS.1
Performoperationsusingcomplexnumbers. / Worksheet–ComplexNumbers
OperationswithComplexNumbers
PropertiesofComplexNumbers
RationalizingImaginaryDenominators

Grade/Course:11/ Algebra 2 First Half of Semester Unit Title:QuadraticFunctions

Standard(s): / A2.ACE.2*
Createequationsintwoor morevariablestorepresentrelationshipsbetweenquantities.Graph
theequationsoncoordinateaxesusing appropriatelabels,units,andscales.
A2.ACE.3
Usesystemsofequationsandinequalitiestorepresentconstraintsarisinginreal-worldsituations.Solvesuchsystemsusinggraphicaland analyticalmethods,includinglinearprogramming.Interpretthesolutionwithinthecontextofthesituation.(Limittolinearprogramming.)
A2.ACE.4*Solveliteralequationsand formulasfora specifiedvariableincluding
equationsandformulasthatariseina varietyofdisciplines.
A2.AREI.4* Solvemathematicalandreal-worldproblemsinvolvingquadraticequationsin
one variable.
A2.AREI.4b
Solvequadraticequationsbyinspection,takingsquareroots,completingthe square,thequadratic
formulaandfactoring,asappropriatetothe initialformoftheequation.Recognizewhenthe
quadraticformulagivescomplexsolutionsandwritethemasa+biforreal numbersaandb.
A.ASE.2*Analyzethestructureofbinomials,trinomials,andotherpolynomialsin ordertorewriteequivalentexpressions.
A2.FBF.1*Writea functionthatdescribesa relationshipbetweentwoquantities.
A2.FIF.8*Translatebetweendifferentbutequivalentformsofafunctionequationtorevealandexplaindifferentpropertiesofthe function.
A2.FIF.9*
Comparepropertiesoftwo functiongivenindifferentrepresentationssuchasalgebraic,graphical,tabular,or verbal.
A2.ACE.3
Usesystemsofequationsandinequalitiestorepresentconstraintsarisinginreal-worldsituations.Solvesuchsystemsusinggraphicaland analyticalmethods,includinglinearprogramming.
Interpretthesolutionwithinthecontextofthesituation.(Limittolinearprogramming.)
A2.ASE.3*
Chooseand produceanequivalentformofanexpressiontorevealandexplainpropertiesofthequantityrepresentedbytheexpression.
A2.ASE.3b
Determinethemaximumandminimumvalueofa quadraticfunctionby completingthesquare.
A2.FBF.3*
Describetheeffectofthetransformationskf(x),f(x)+k,f(x+k),andcombinationsofsuchtransformationsonthegraphofy= f(x)forany realnumberk.Findthevalueofkgiventhegraphsandwritetheequationofa transformedparentfunctiongivenitsgraph.
A2.FIF.6*
Givena functionin graphical,symbolic,ortabularform,determinetheaveragerateofchangeofthefunctionovera specifiedinterval.Interpret themeaningoftheaveragerateofchangeina givencontext.
A2.FIF.8*
Translatebetweendifferentbutequivalentformsofafunctionequationtorevealandexplaindifferentpropertiesofthe function.
A2.FIF.9*
Comparepropertiesoftwo functiongivenindifferentrepresentationssuchasalgebraic,graphical,tabular,or verbal.
A2.NCNS.7*
Solvequadraticequationsinone variablethathavecomplexsolutions.
Time Frame
(# of days, weeks) / Performance Indicators:
(skills/learning objectives/ content focus) / Suggested Activities / Resources / Assessment
(Performance task, portfolio, teacher observation with anecdotal notes, etc.)
3 weeks / A2.ACE.2,A2.ACE.3,A2.ACE.4,A2.FBF.1,A2.FIF.8,A2.FIF.9 Createand/orgraphquadraticfunctionsusinga graphing calculatorand identifyimportantfeaturesincludingthe maximum/minimum,thezeros,andtheintervalswherethe functionisincreasing/decreasing.
Comparedifferentformsofquadraticfunctions.
Determinethedomainand range(usingintervalnotation)for quadraticfunctions. / Worksheet–IntroductiontoQuadratics
PropertiesofParabolas
Worksheet–WordProblemsandSolvingwiththe Calculator / -Holt McDougal Teacher
Resources
-USA testprep
-Khan Academy
- Bing lesson plans / Tests, Quizzes, Projects, & Exams
A2.AREI.4b,A2.ASE.2
Factor quadraticexpressions / FactoringQuadraticForm
FactoringQuadraticExpressions
Factoringby Grouping
FactoringAllTechniques
Worksheet–MixedFactoringPractice
Worksheet–PerfectSquares
Worksheet–FactoringTrinomials
A2.AREI.4,A2.AREI.4b,A2.ASE.2
Solvequadraticfunctionsbyfactoring. / Worksheet–SolvebyFactoring
Worksheet–Factoringand SolvebyFactoring
QuadraticEquationsbyFactoring
A2.FIF.6
Calculateandinterpretaveragerateofchangeofquadratic functionsovera specificinterval.
A2.FIF.8,A2.FIF.9,A2.FBF.3,A2.ASE.3b,A2.ASE.3
Completethesquaretowritea
quadraticfunctioninvertexform. Graphquadraticfunctionsusingvertexform.
Determinethedomainand range(usingintervalnotation)for quadraticfunctions(withgraphs). / CompletingtheSquare
Worksheet–WriteinVertexFormand Graph
Worksheet–Completethe Squareto FindtheVertex
Worksheet–MoreonCompletingtheSquareto
Findthe Vertex
A2.NCNS.7
Solvequadraticfunctionsusingthequadraticformula. / Worksheet–SolveUsingQuadraticFormula
QuadraticFormula
A2.ACE.3
Usethediscriminanttodeterminethenatureofthesolutions. / Activity–Lab for Natureof Roots
The Discriminant
A2.FIF.8
Writetheequationofa quadraticfunctionwhengivenitsroots. / Worksheet–FindingEqfromRoots
Factorsand Zeros

Grade/Course: 11 / Algebra 2 Second Half of Semester Unit Title:PolynomialFunctions

Standard(s): / A2.AAPR.1*
Add,subtract,andmultiplypolyomialsand understandthatpolynomialsareclosedundertheseoperations.
A2.AAPR.3
Graphpolynomialsidentifyingzeroswhensuitable factorizationsareavailableandindicatingendbehavior.Writea polynomialfunctionofleast degreecorrespondingtoagivengraph.(Limittopolynomialswithdegrees3orless.)
A2.ASE.1*
Interpretthemeaningsofcoefficients,factors,terms,andexpressionsbasedontheirreal-worldcontexts.Interpretcomplicatedexpressionsas beingcomposedofsimplerexpressions.
A2.ASE.2*
Analyzethestructureofbinomials,trinomials,andotherpolynomialsin ordertorewriteequivalentexpressions.
A2.FBF.1b
Combinefunctionsusingtheoperationsaddition,subtraction,multiplication,anddivisiontobuild newfunctionsthatdescribetherelationship betweentwoquantitiesin mathematicalandreal-worldsituations.
A2.FIF.4*
Interpretkeyfeaturesofa functionthatmodelstherelationshipbetweentwoquantitieswhengiveningraphicalortabularform.Sketchthe graphofafunctionfroma verbaldescriptionshowingkeyfeatures.Keyfeaturesincludeintercepts;intervalswherethefunctionisincreasing,decreasing,constant,positive,ornegative;relativemaximumsandminimums;symmetries;endbehaviorandperiodicity.
A2.FIF.7*
Graphfunctionsfromtheirsymbolicrepresentations.Indicatekeyfeaturesincludingintercepts;intervals
wherethefunctionisincreasing, decreasing,positive,or negative;relativemaximumsandminimums;symmetries;endbehaviorandperiodicity.Graphsimplecasesby handand usetechnologyforcomplicatedcases.
A2.FIF.9*
Comparepropertiesoftwo functiongivenindifferentrepresentationssuchasalgebraic,graphical,tabular,or verbal.
Time Frame
(# of days, weeks) / Performance Indicators:
(skills/learning objectives/ content focus) / Suggested Activities / Resources / Assessment
(Performance task, portfolio, teacher observation with anecdotal notes, etc.)
3 weeks / A2.AAPR.3,A2.FIF.4,A2.FIF.7,A2.FIF.9
Graphanddescribetheshapeofpolynomialfunctions
Identifyanddescribeimportantfeaturesofthegraphofa polynomialfunctionincludingabsoluteandrelativemaximum/ minimumpoints,intervalswherethefunctionis increasing/decreasing,zeros(includingthemultiplicityofeach), domainandrange(inintervalnotation),andendbehavior. / GraphingPolynomialFunctionsBasicShape
GraphingPolynomialFunctions / -Holt McDougal
Teacher Resources
-USA testprep
-Khan Academy
- Bing lesson plans / Tests, Quizzes, Projects, & Exams
A2.AAPR.1,A2.FBF.1b
Add,subtract,andmultiplypolynomialfunctions.
Dividepolynomialfunctionsusinglongdivisionandsynthetic.
A2.ASE.1,A2.ASE.2
Factorandsolvepolynomialfunctions,includingspecialproducts like(x+y)3,(x–y)3,etc.
A2.AAPR.3
Usetherationalroottheoremandtheremaindertheoremtofind thezerosofa polynomialfunction / TheRemainderTheorem
RationalRootTheorem
MoreonFactors,Zeros,andDividing
IrrationalandImaginaryRootTheorems
DescartesRuleofSigns
AnalyzingandSolvingPolynomialEquations
Worksheet–RationalRootTheorem(A)to Solve
Worksheet–RationalRootTheorem(B)to Solve
Worksheet–LastPracticeRationalRootTheorem
To FindAllRoots

Grade/Course: 11/ Algebra 2 Second Half of Semester Unit Title:Rational Functions

Standard(s): / A2.AAPR.1*
Add,subtract,andmultiplypolyomialsand understandthatpolynomialsareclosedunder
A2.AREI.2 Solvesimplerationalandradicalequationsinonevariableandunderstandhowextraneoussolutionsmayarise.
A2.FIF.7
Graphfunctionsfromtheirsymbolicrepresentations.Indicatekeyfeaturesincludingintercepts;intervalswherethefunctionisincreasing, decreasing,positive,or negative;relativemaximumsandminimums;symmetries;endbehaviorandperiodicity.Graphsimplecasesby handand usetechnologyforcomplicatedcases.
Time Frame
(# of days, weeks) / Performance Indicators:
(skills/learning objectives/ content focus) / Suggested Activities / Resources / Assessment
(Performance task, portfolio, teacher observation with anecdotal notes, etc.)
2 weeks / Identifyandevaluaterationalfunctions / -Holt McDougal
-USA testprep
-Khan Academy
- Bing lesson plans / Tests, Quizzes, Projects, & Exams
A2.AREI.2
Multiplyanddividerationalexpressionsincluding complex fractions. / Worksheet–MultiplyandDivideRationalExpressions
A2.AREI.2
Addandsubtractrationalexpressions / Worksheet–ReviewofOperations
Worksheet–Addand SubtractwithLikeDenominators
Worksheet–MoreonAddingandSubtracting
Worksheet-MixedReviewofOperations
A2.FIF.7
Grapharationalfunctionandfinditsdomainandrange
(inintervalnotation),writeequationsforits asymptotes,andidentifyanyholesinitsgraph / Worksheet–GraphingRationals(a)
Worksheet–GraphingRationals(b)
Worksheet–GraphingRationals(c)
.
A2.AREI.2
Solverationalequations. / Worksheet–SolvingRationalExpressions
Worksheet–MoreonSolvingRationalExpressions

Grade/Course:11 / Algebra 2 Second Half of Semester Unit Title: Exponential &LogarithmicFunctions

Standard(s): / A2.ACE.1*
Createandsolveequationsand inequalitiesinone variablethatmodelreal-worldproblemsinvolvinglinear,quadratic,simplerational,and exponentialrelationships.Interpretthesolutionsand determinewhethertheyarereasonable.
A2.ACE.2*
Createequationsintwoor morevariablestorepresentrelationshipsbetweenquantities.Graphtheequationsoncoordinateaxesusing appropriatelabels,units,andscales.
A2.ASE.1*
Interpretthemeaningsofcoefficients,factors,terms,andexpressionsbasedontheirreal-worldcontexts.Interpretcomplicatedexpressionsas beingcomposedofsimplerexpressions.
A2.ASE.3c
Usethepropertiesofexponentstotransformexpressionsforexponentialfunctions.
A2.FBF.1b
Combinefunctionsusingtheoperationsaddition,subtraction,multiplication,anddivisiontobuild newfunctionsthatdescribetherelationship betweentwoquantitiesin mathematicalandreal-worldsituations.
A2.FIF.4*
Interpretkeyfeaturesofa functionthatmodelstherelationshipbetweentwoquantitieswhengiveningraphicalortabularform.Sketchthe graphofafunctionfroma verbaldescriptionshowingkeyfeatures.Keyfeaturesincludeintercepts;intervalswherethefunctionisincreasing,decreasing,constant,positive,ornegative;relativemaximumsandminimums;symmetries;endbehaviorandperiodicity.
A2.FIF.5*
Relatethedomainandrangeofa functiontoitsgraphand,whereapplicable,to thequantitativerelationshipit describes.
A2.FIF.6*
Givena functionin graphical,symbolic,ortabularform,determinetheaveragerateofchangeofthefunctionovera specifiedinterval.Interpret themeaningoftheaveragerateofchangeina givencontext.
A2.FIF.7*
Graphfunctionsfromtheirsymbolicrepresentations.Indicatekeyfeaturesincludingintercepts;intervalswherethefunctionisincreasing,decreasing,positive,or negative;relativemaximumsandminimums;symmetries;endbehaviorandperiodicity.Graphsimplecasesby handand use
technologyforcomplicatedcases.
A2.FIF.8b
Interpretexpressionsforexponentialfunctionsby usingthepropertiesofexponents.
A2.FLQE.1*
Distinguishbetweensituationsthatcanbemodeledwithlinearfunctionsorexponentialfunctionsby recognizingsituationsinwhichone quantity changesata constantrate perunitintervalasopposedtothosein whicha quantitychangesby constantpercentrateperunitinterval.
A2.FLQE.1b
Recognizesituationsinwhicha quantitygrowsordecaysbyaconstantpercentrateperunitintervalrelativetoanother.
A2.FLQE.5*
Interprettheparametersinalinearorexponentialfunctionintermsofthecontext.
Time Frame
(# of days, weeks) / Performance Indicators:
(skills/learning objectives/ content focus) / Suggested Activities / Resources / Assessment
(Performance task, portfolio, teacher observation with anecdotal notes, etc.)
2 weeks / A2.ASE.1,A2.FBF.1b,A2.FIF.8b,A2.FLQE.1b,A2.FLQE.5
Writeandevaluateexponentialexpressionstomodelgrowthand decaysituations.
Classifyanexponentialfunctionasrepresentinga growthora decay.
Calculatethegrowthofinvestmentsundervariousconditions usingexponentialandnaturalexponentialfunctions. / Activity–SheddingLightontheSubject
Activity–SpreadingRumors
Worksheet–WordProblemsFindingOtherVariable
UsingLogs
Worksheet–MoreWordProblems
Worksheet–CompoundInterestandExp.Functions
Worksheet–GrowthDecay–SolveforNewVariable / -Holt McDougal
Teacher Resources
-USA testprep
-Khan Academy
- Bing lesson plans / Tests, Quizzes, Projects, & Exams
A2.FIF.6
Calculateandinterpretthe averagerateofchangeofexponential functionsovera specificinterval
A2.FIF.7
Graphexponentialfunctionsusingtransformations.
Findthedomainandrange(in intervalnotation),intercepts,end behavior,andtheequationofthe horizontalasymptoteforan exponentialfunction / Worksheet–ExponentialGraphs
Worksheet–ExponentialEquationswithLikeBases
.A2.ACE.2
Rewriteexponentialequationsaslogarithmicequationsandvice versa.
Simplifyandevaluateexpressionsinvolvinglogarithmsusingthe propertiesoflogarithms. / Worksheet–PracticewithLogPropertiesand Solving
LogEquations
A2.F.IF.7
Graphtheinverseoftheexponentialfunctionanddefinethe logarithmicfunction. / Worksheet–IntrotoLogs
A2.FIF.5,A2.FIF.4
Findthedomainandrange(inintervalnotation),intercepts,end behavior,andtheequationofthe verticalasymptotefora
logarithmicfunction.
A2.ACE.1,A2.ASE.3c,A2.FLQE.1,A2.FLQE.1b
Usethedefinitionsofexponentialandlogarithmicfunctionsto solveequations.
Solveequationsinvolvinglogarithmsalgebraicallyand graphically.
Solveexponentialequationsusingcommonlogsalgebraicallyand graphically. / Review–1stHalfThroughLogProperties
Worksheet–BasicLogEquationswithNoCalculator
Worksheet–Logs
Worksheet–MoreonLogs
Review–LogEquationsandExponentialEquations usingLogs
Worksheet–ExponentialEquationswithUnlikeBases

Grade/Course: 11 / Algebra 2 Second Half of Semester Unit Title:Sequences and Series

Standard(s): / A2.ACE.2*
Createequationsintwoor morevariablestorepresentrelationshipsbetweenquantities.Graphtheequationsoncoordinateaxesusing appropriatelabels,units,andscales.
A2.FBF.1a
Writea functionthatmodelsa relationshipbetweentwoquantitiesusingbothexplicitexpressionsanda recursiveprocessbycombiningstandard formsusingaddition,subtraction,multiplicationanddivisiontobuild newfunctions.
A2.FBF.2*
Writearithmeticandgeometricsequencesbothrecursivelyandwithanexplicitformula,usethemtomodelsituations,andtranslatebetweenthe twoforms.
A2.FIF.3*
Definefunctionsrecursivelyandrecognizethatsequencesarefunctions,sometimesdefinedrecursively,whosedomainisa subsetoftheintegers.
A2.FLQE.1*
Distinguishbetweensituationsthatcanbemodeledwithlinearfunctionsorexponentialfunctionsby recognizingsituationsinwhichone quantitychangesata constantrate perunitintervalasopposedtothosein whicha quantitychangesby constantpercentrateperunitinterval.
A2.FLQE.2*
Createsymbolicrepresentationsoflinearandexponentialfunctions,includingarithmeticandgeometricsequences,givengraphs,verbaldescriptions,andtables.
Time Frame
(# of days, weeks) / Performance Indicators:
(skills/learning objectives/ content focus) / Suggested Activities / Resources / Assessment
(Performance task, portfolio, teacher observation with anecdotal notes, etc.)
2 weeks / A2.ACE.2,A2.FBF.1a,A2.FLQE.2
Recognize,write,and findthenthtermofarithmeticsequences.
Findthepartialsumofanarithmeticseries. / IntroductiontoSequences
ArithmeticSequences
SequencesandSeriesRealityProject
SequencesandSeriesArtProject / -Holt McDougal
Teacher Resources
-USA testprep
-Khan Academy
- Bing lesson plans / Tests, Quizzes, Projects, & Exams
A2.FBF.1a,A2.FBF.2,A2.FIF.3
Recognize,write,and findthenthtermofgeometricsequences.
Findpartialsumsofgeometricsequences. / ArithmeticSeries
Worksheet–ArithmeticSequencesandSeries
A2.FLQE.1
Usesigmanotationtorepresentarithmeticandgeometricseries / ReviewofArithmeticandGeometric Means
GeometricSequences

JCSD 2015-16

Updated 9-15-2015