honors algebra pacing guide: 1 nine weeks...

HONORSALGEBRAPACINGGUIDE:1stNineWeeks

UNITONE:QuantitiesandModeling

Week Lesson Standards LearningTargetOther

Materials/Projects

ONE

GoalsExpectationsPre-Assessment

GREEN:MajorContentBLUE:SupportingContentYELLOW:AdditionalContent(+)orWCS:AdditionalContentperWCSHonorsRequirement

TWO

1.1-1.3:QuantitativeReasoning

A-REI.A.1:Explaineachstepinsolvingasimpleequationasfollowingfromtheequalityofnumbersassertedatthepreviousstep,startingfromtheassumptionthattheoriginalequationhasasolution.Constructaviableargumenttojustifyasolutionmethod.A-REI.B.3:Solvelinearequationsinonevariable.N-Q.A.1:Useunitsasawaytounderstandproblemsandtoguidethesolutionofmulti-stepproblems;chooseandinterpretthescaleandoriginingraphsanddatadisplays.N-Q.A.2:Defineappropriateunitsforthepurposeofdescriptivemodeling.N-Q.A.3:Choosealevelofaccuracyappropriatetolimitationsonmeasurementwhenreportingquantities.AlsoA-REI.B.3:Solvelinearequationsinonevariable.;Al.WCE.1:Evaluateexpressionsandsolveequationfluentlyusingsubstitutiontoverifysolutions;Al.WCE.3:Convertunitratesofmeasurementsinmultisteparithmeticproblems.;

ICAN:• justifystepsinsolvingmulti-stepequationsusingthe

propertiesofequality.• writemulti-stepequationsfromwordproblems.• usedimensionalanalysistocompareunitsandrates.

Ratioandproportionarealsointroducedinthislesson.

• usesignificantdigitstocalculateandreportvaluestoanappropriatelevelofprecision.

• givethesolutionofanequationusingthecorrectunits.

• usethescaletoreadthedatacorrectly.• defineappropriatequantities.• determinetheaccuracyofvaluesbasedontheir

limitationsinthecontextofthesituation.

THREE

2.1-2.2:AlgebraicModels

A-SSE.A.1a:Interpretexpressionsthatrepresentaquantityintermsofitscontext.a. Interpretpartsofanexpression,suchas

terms,factors,andcoefficients.A-CED.A.1:Createequationsandinequalitiesinonevariableandusethemtosolveproblems.Includeequationsarisingfromlinearandquadraticfunctions,andsimplerationalandexponentialfunctions.AlsoA-CED.A.3;A-REI.B.3;A-SSE.A.1b;N-Q.A.2

ICAN:• identifycoefficients,terms,variables,factors.• solvemulti-stepequationsincludingthosewith

variablesonbothsidesoftheequalsignandthoserequiringthedistributiveproperty.

• recognizeandexplainwhen1solution,nosolution,orinfinitesolutionsaretheresultofsolvinganequation.

• createlinearequationsandinequalitiesinonevariableandusetheminacontextualsituationtosolveproblems.


Materials/ProjectsFOUR

2.3-2.5:AlgebraicModels

A-CED.A.3:Representconstraintsbyequationsorinequalities,andbysystemsofequationsand/orinequalities,andinterpretsolutionsasviableornonviableoptionsinamodelingcontext.Forexample,representinequalitiesdescribingnutritionalandcostconstraintsoncombinationsofdifferentfoods.A-CED.A.4:Rearrangeformulastohighlightaquantityofinterest,usingthesamereasoningasinsolvingequations.Forexample,rearrangeOhm’slawV=IRtohighlightresistanceR.AlsoA-REI.B.3;Al.WCE.8:Translatearealworldsituationbywritingconstraintsforequationandinequalities.

ICAN:• isolateagivenvariableinliteralequationsand

formulas.• createandsolvemulti-stepinequalitiesincluding

whentherearevariablesonbothsidesoftheinequalitysymbol,andthoserequiringthedistributiveproperty.

• interpretthesolutioninthecontextoftheproblem.• solve,graph,andinterpretcompoundinequalitiesin

onevariable.• describethecalculationsneededtomodelafunction

betweentwoquantities.• writeequationstosolvecontextualproblemsthat

involvedistance/time/rate,mixture,consecutiveintegers,andcost.

• solvemulti-variableformulasorliteralequations,foraspecificvariable.

• writeanduseasystemofequationsand/orinequalitiestosolvearealworldproblem.

• representconstraintsbyequationsorinequalitiesandbysystemsofequationsand/orinequalities.

• interpretsolutionsasviableornonviableoptionsinamodelingcontext.

• solvesystemsofequationsandinequalitieswithandwithouttechnology.

UNITTWO:UnderstandingFunctions

Week Lesson Standards LearningTarget OtherMaterials/Projects

FIVE

3.1:Functionsand

Models

F-IF.B.4:Forafunctionthatmodelsarelationshipbetweentwoquantities,interpretkeyfeaturesofgraphsandtablesintermsofthequantities,andsketchgraphsshowingkeyfeaturesgivenaverbaldescriptionoftherelationship.Keyfeaturesinclude:intercepts;intervalswherethefunctionisincreasing,decreasing,positive,ornegative;relativemaximumsandminimums;symmetries;endbehavior;andperiodicity.

ICAN:• interpretqualitativegraphsandsketchqualitativegraphs

givenawrittendescription.• givenalinearfunction,identifykeyfeaturesingraphsand

tablesincluding:intercepts,intervalswherethefunctionisincreasing,decreasing,positiveornegative;relativemaximumsandminimums;symmetries.

• usetheproblemsituationtoexplaintheendbehaviorofthefunction.

• writeafunctiontoexpressacontextualproblem.• describeasituationthatmatchesagraphbasedonitsshape.

SIX

3.2-3.4:FunctionsandModels

F-IF.A.1:Understandthatafunctionfromoneset(calledthedomain)toanotherset(calledtherange)assignstoeachelementofthedomainexactlyoneelementoftherange.Iffisafunctionandxisanelementofitsdomain,thenf(x)denotestheoutputoffcorrespondingtotheinputx.Thegraphoffisthegraphoftheequationy=f(x).F-IF.A.2:Usefunctionnotation,evaluatefunctionsforinputsintheirdomains,andinterpretstatementsthatusefunctionnotationintermsofacontext.AlsoF-IF.A.2,A-CED.A.2,F-IF.B.5:Relatethedomainofafunctiontoitsgraph,andtothecontextitdescribes.F-IF.C.7:Graphfunctionsexpressedsymbolicallyandshowkeyfeaturesofthegraphbyhand,usingtechnologyformorecomplexcases.

ICAN:• useinput-outputtablestographorderedpairsofafunction.

Thisincludeslinearandquadraticfunctions.• identifythedomainandtherangeandwillrepresenta

functiongraphically,onatable,andusingmapping.• identifyifarelationisorisnotafunctionandwillusethe

verticallinetest.• useandwriteequationsusingfunctionnotation.• identifyreasonablelimitationsonthefunction'sdomainand

range• knowthatthegraphofthefunction,f,isthegraphofthe

equation𝑦=𝑓(𝑥).• findfunctionvaluesforexpressionswritteninfunction

notation.• writeanalgebraicexpressionorequationtogeneralizethe

patterninatable.• determinewhetherornotarelationisafunctionanduse

thef(x)notation.• evaluatefunctionsforinputsintheirdomain.• interpretstatementsthatusefunctionnotationintermsof

thecontextinwhichtheyareused.• can(giventhegraph)choosethepracticaldomainofthe

functionasitrelatestothenumericalrelationshipitdescribes.

• explainwhenarelationisdeterminedtobeafunction,usef(x)notation.

• statetheappropriatedomainofafunctionthatrepresentsaproblemsituation,defendmychoice,andexplainwhyothernumbersmightbeexcludedfromthedomain.

• graphorwritetheequationofafunctionwhengivenatableofvalues.

• convertalistofnumbers(asequence)intoafunctionbymakingthewholenumbers(0,1,2,etc.)theinputsandtheelementsofthesequencetheoutputs.

SEVEN

4.1-4.2:PatternsandSequences

F-IF.A.3:Recognizethatsequencesarefunctions,sometimesdefinedrecursively,whosedomainisasubsetoftheintegers.Forexample,theFibonaccisequenceisdefinedrecursivelybyf(0)=f(1)=1,f(n+1)=f(n)+f(n-1)forn>1.F-LE.A.2:Constructlinearandexponentialfunctions,includingarithmeticandgeometricsequences,givenagraph,adescriptionofarelationship,ortwoinput-outputpairs(includereadingthesefromatable).F-BF.A.1a:Writeafunctionthatdescribesarelationshipbetweentwoquantities.a. Determineanexplicitexpression,a

recursiveprocess,orstepsforcalculationfromacontext.

AlsoF-IF.A.3,F-BF.A.2(+)

ICAN:• generatesequencesgivenanexplicitrule,andarecursive

rule.• graphsequencesonacoordinateplane.• explainthatarecursiveformulatellsmehowasequence

startsandtellsmehowtousethepreviousvalue(s)togeneratethenextelementofthesequence.

• explainthatanexplicitformulaallowsmetofindanyelementofasequencewithoutknowingtheelementbeforeit(e.g,IfIwanttoknowthe11thnumberonthelist,Iplugthenumber11intotheexplicitformulas.)

• distinguishbetweenexplicitandrecursiveformulasforsequencesandusethatknowledgetowriteequationsbasedonfunctions.

• determineexplicitandrecursiverulesforagivenarithmeticsequence.

• usecontextualexamplestocreatefunctionswithbothexplicitandrecursivesequences.

• createlinearandexponentialfunctions,fromasimplecontext,giventhefollowingsituations:arithmeticandgeometricsequences,agraph,adescriptionofarelationship,andtwopointswhichcanbereadfromatable.

• (fromcontext),identifypatternsandwriteanexplicitexpression.

• usetables,graphsandexpressionstomodelsituations.• definearecursiveprocess.• determineanexpressionbyinspectinganddefininga

pattern.

EIGH

T

4.3:PatternsandSequences

F-LE.A.2:Constructlinearandexponentialfunctions,includingarithmeticandgeometricsequences,givenagraph,adescriptionofarelationship,ortwoinput-outputpairs(includereadingthesefromatable).F-BF.A.1a:Writeafunctionthatdescribesarelationshipbetweentwoquantities.

a. Determineanexplicitexpression,arecursiveprocess,orstepsforcalculationfromacontext.

AlsoF-IF.A.3

ICAN:• createlinearandexponentialfunctions,fromasimple

context,giventhefollowingsituations:arithmeticandgeometricsequences,agraph,adescriptionofarelationship,andtwopointswhichcanbereadfromatable.

• usetables,graphsandexpressionstomodelsituations.

• definearecursiveprocess.

UNITTHREE:LinearFunctions,Equations,andInequalities


NINE

5.1-5.3:LinearFunctions

F-LE.A.1:Distinguishbetweensituationsthatarelinear/exponential.a. Provethatlinearfunctionsgrowbyequal

distancesoverequalintervals.b. Recognizesituationsinwhichonequantity

changesataconstantrateperunitintervalrelativetoanother.

F-IF.B.6:Calculateandinterprettheaveragerateofchangeofafunction(Presentedsymbolicallyorasatable)overaspecifiedinterval.Estimatetherateofchangefromagraph.F-IF.C.7a:Graphfunctionsexpressedsymbolicallyandshowkeyfeaturesofthegraph,byhandinsimplecasesandusingtechnologyformorecomplicatedcases.★a.Graphlinearandquadraticfunctionsandshowintercepts,maxima,andminima.AlsoF-LE.A.2,A-REI.D.10,F-LE.B.5,F-IF.B.4:Interpretkeyfeaturesofgraphsandtablesintermsofthequantities,andsketchgraphs.

ICAN:• determineifatableofvaluesrepresentsaconstant

rateofchange.• graphlinearfunctionsinstandardformusingan

input-outputtable.• appropriatelyconnectornotconnectpointsona

graph.• graphlinearfunctionsbyidentifyingxandy

intercepts.• findtheslopeofalineusingtheformula,acoordinate

plane,andatableofvalues.• describewhetheragivensituationinquestionhasa

linearpatternofchangeoranexponentialpatternofchange.

• showthatlinearfunctionschangeatthesamerateovertimeandthatexponentialfunctionschangebyequalfactorsovertime.

• describesituationswhereonequantitychangesataconstantrateperunitintervalascomparedtoanother.

• determinetheparentfunctionforthelinef(x)=x.• describealineasatranslationoftheparentfunctiony

=x.• identifyandcomparethedifferentformsoflinear

functions.(point-slope,standard,slope-intercept)• identifytheinterceptsofafunction.• comparethekeyfeaturesoftwolinearfunctions

representedindifferentways.• explaintheconnectionbetweenaveragerateof

changeandtheslopeformula.• calculatetheaveragerateofchangeoveraspecified

intervalofafunctionpresentedsymbolicallyorinatable.

• estimatetheaveragerateofchangeoveraspecifiedintervalofafunctionfromthefunction’sgraph.

• interpretthemeaningoftheaveragerateofchange(usingunits)asitrelatestoareal-worldproblem.

• comparetheratesofchangeoftwoormorefunctionswhenrepresentedwithfunctionnotation,withagraph,orwithatable.

HONORSALGEBRAPACINGGUIDE:2ndNineWeeks

UNITTHREE:LinearFunctions,Equations,andInequalities(continued)


Materials/Projects

ONE

6.1-6.5:FormsofLinearEquations

A-REI.D.10:Understandthatthegraphofanequationintwovariablesisthesetofallitssolutionsplottedinthecoordinateplane,oftenformingacurve(whichcouldbealine).A-CED.A.2:Createequationsintwovariablesormorevariablestorepresentrelationshipsbetweenquantities.F-BF.B.3:Identifytheeffectonthegraphofreplacingf(x)byf(x)+k,kf(x),f(kx),andf(x+k)forspecificvaluesofk(bothpositiveandnegative);findthevalueofkgiventhegraphs.Experimentwithcasesandillustrateanexplanationoftheeffectsonthegraphusingtechnology.Includerecognizingevenandoddfunctionsfromtheirgraphsandalgebraicexpressionsforthem.F-IF.C.7a:Graphfunctionsexpressedsymbolicallyandshowkeyfeaturesofthegraph,byhandinsimplecasesandusingtechnologyformorecomplicatedcases.★a.Graphlinearandquadraticfunctionsandshowintercepts,maxima,andminima.F-IF.C.9:Comparepropertiesoftwofunctionseachrepresentedinadifferentway(algebraically,graphically,numericallyintables,orbyverbaldescriptions).Forexample,givenagraphofonequadraticfunctionandanalgebraicexpressionforanother,saywhichhasthelargermaximum.AlsoF-LE.B.5;Al.WCE.9:Determinetheequationofalineand/orgraphalinearfunction;Al.WCE.10:Writetheequationofalineinpoint-slope,slope-intercept,andstandardform;Al.WCE.11;Describeandsolveproblemsusingtherelationshipbetweenparallelandperpendicularlines.

ICAN:• writelinearequationsinslope-interceptformgiven:a

slopeanday-int,2pointsanday-int,and2pointsontheline,oragraph.

• writelinearequationsinpoint-slopeformgiven:aslopeanday-int,2pointsanday-int,and2pointsontheline.oragraph.

• writelinearequationsinstandardformgiven:aslopeanday-int,2pointsanday-int,and2pointsontheline.oragraph.Studentswillalsotranslatebetweenforms.

• exploreandbeabletorecognizetransformationsperformedonlinearfunctionsincluding:Translations,stretches,shrinks,andreflections.

• comparefunctionsdomain,range,slope,andy-interceptgivenagraphandatable.

• explainthatallsolutionstoanequationintwovariablesarecontainedonthegraphofthatequation.

• createequationsintwoormorevariablestorepresentrelationshipsbetweenquantities.

• graphequationsintwovariablesonacoordinateplaneandlabeltheaxesandscales.

• decidewhichfunctionsarerelativelyeasytosketchaccuratelybyhandandwhichshouldbegraphedusingtechnology.

• comparepropertiesoftwofunctionsandshowtheirrelationshipusinggraphs,tablesandverbaldescriptions.

TWO

7.1-7.2:LinearEquationsandInequalities

A-CED.A.3:Representconstraintsbyequationsorinequalities,andbysystemsofequationsand/orinequalities,andinterpretsolutionsasviableornonviableoptionsinamodelingcontext.Forexample,representinequalitiesdescribingnutritionalandcostconstraintsoncombinationsofdifferentfoods.A-REI.D.11:Explainwhythex-coordinatesofthepointswherethegraphsoftheequationsy=f(x)andy=g(x)intersectarethesolutionsoftheequationf(x)=g(x);findthesolutionsapproximately,e.g.,usingtechnologytographthefunctions,maketablesofvalues,orfindsuccessiveapproximations.Includecaseswheref(x)and/org(x)arelinear,polynomial,rational,absolutevalue,exponential,andlogarithmicfunctions.AlsoS-ID.C.7;N-Q.A.1;N-Q.A.2

ICAN:• writeanduseasystemofequationsand/orinequalities

tosolvearealworldproblem.• representconstraintsbyequationsorinequalitiesand

bysystemsofequationsand/orinequalities.• interpretsolutionsasviableornonviableoptionsina

modelingcontext.• solvesystemsofequationsandinequalitieswithand

withouttechnology.• explainwhytheintersectionofy=f(x)andy=g(x)for

anylinearfunction.• findthesolutionsbyusingtechnologytographthe

equationsanddeterminetheirpointofintersection,usingtablesofvalues,orusingsuccessiveapproximationsthatbecomecloserandclosertotheactualvalue.

THREE

7.3:LinearEquationsandInequalities

A-REI.D.12:Graphthesolutionstoalinearinequalityintwovariablesasahalf-plane(excludingtheboundaryinthecaseofastrictinequality),andgraphthesolutionsettoasystemoflinearinequalitiesintwovariablesastheintersectionofthecorrespondinghalf-planes.AlsoA-CED.A.3

ICAN:• writelinearinequalitiesintwo-variablesinslope-interceptform,andbeabletographthesolutionmanuallyandwithtechnology.

UNITFOUR:StatisticalModels


FOUR

8.1-8.2:M

ulti-Variable

CategoricalData

S-ID.B.5:Summarizecategoricaldatafortwocategoriesintwo-wayfrequencytables.Interpretrelativefrequenciesinthecontextofthedata(includingjoint,marginal,andconditionalrelativefrequencies).Recognizepossibleassociationsandtrendsinthedata.

ICAN:• read,complete,andinterprettwowayfrequencytables.• analyzedifferenttypesoffrequenciesintwowaytables.

FIVE

9.1-9.4:One-VariableData

Distributions

S-ID.A.1:Representdatawithplotsontherealnumberline(dotplots,histograms,andboxplots).S-ID.A.2:Usestatisticsappropriatetotheshapeofthedatadistributiontocomparecenter(median,mean)andspread(interquartilerange,standarddeviation)oftwoormoredifferentdatasets.AlsoN-Q.A.1,S-ID.A.3

ICAN:• constructdotplots,histograms,andboxplotsfordata

onarealnumberline.• makepredictionsbasedongraphsanddatasets.• constructandinterpretvariousformsofdata

representations,(includinglinegraphs,bargraphs,circlegraphs,histograms,scatter-plots,box-and-whiskers,stem-and-leaf,andfrequencytables).*

• describeasituationusingcenterandspread.• usethecorrectmeasureofcenterandspreadto

describeadistributionthatissymmetricorskewed.• identifyoutliers(extremedatapoints)andtheireffects

ondatasets.• comparetwoormoredifferentdatasetsusingthe

centerandspreadofeach.

SIX

10.1-10.2:LinearM

odelingandRegression

S-ID.B.6b-c:Representdataontwoquantitativevariablesonascatterplot,anddescribehowthevariablesarerelated.b. Informallyassessthefitofafunction

byplottingandanalyzingresiduals.c. Fitalinearfunctionforascatterplot

thatsuggestsalinearassociation.AlsoS-ID.B.6a,S-ID.C.7,S-ID.C.8,S-ID.C.9,F-LE.B.5

ICAN:• determinewhenlinear,quadratic,andexponential

modelsshouldbeusedtorepresentadataset.• determinewhetherlinearandexponentialmodelsare

increasingordecreasing.• determinetherelationshipshowninascatterplot.• sketchthefunctionofbestfitonthescatterplot.• usetechnologytofindthefunctionofbestfitfora

scatterplot.• findtheequationforthelineofbestfitanduseitto

makepredictions.• computetheresiduals(observedvalueminuspredicted

value)forthesetofdataandthefunctionofbestfit.• constructascatterplotoftheresiduals.• analyzetheresidualplottodeterminewhetherthe

functionisanappropriatefit.• sketchalineofbestfitonascatterplotthatappears

linear.• writetheequationofthelineofbestfit(𝑦=𝑚𝑥+𝑏)using

technologyorbyusingtwopointsonthebestfitline.

UNITFIVE:LINEARSYSTEMSANDPIECEWISE-DEFINEDFUNCTIONS

SEVEN

11.1-11.4:SolvingSystemsof

LinearFunctions

A-REI.C.5:Provethat,givenasystemoftwoequationsintwovariables,replacingoneequationbythesumofthatequationandamultipleoftheotherproducesasystemwiththesamesolutions.A-REI.C.6:Solvesystemsoflinearequationsexactlyandapproximately(e.g.,withgraphs),focusingonpairsoflinearequationsintwovariables.

ICAN:• solvepairsoflinearequationsintwovariablesusing

substitutionandelimination.• choosethebestmethodforsolvingalinearsystem,and

Icanjustifymymethod.• graphasystemofequationsanddetermineitssolution.• usetechnologytosolvealinearsystemgraphically.• solveasystemoflinearequationsintwovariables

graphicallyandsymbolically.• determinethenumberofsolutionstothesystemof

equations.

EIGH

T

12.1-12.3:ModelingwithLinearSystems

A-CED.A.3:Representconstraintsbyequationsorinequalities,andbysystemsofequationsand/orinequalities,andinterpretsolutionsasviableornonviableoptionsinamodelingcontext.Forexample,representinequalitiesdescribingnutritionalandcostconstraintsoncombinationsofdifferentfoods.A-REI.D.12:Graphthesolutionstoalinearinequalityintwovariablesasahalf-plane(excludingtheboundaryinthecaseofastrictinequality),andgraphthesolutionsettoasystemoflinearinequalitiesintwovariablesastheintersectionofthecorrespondinghalf-planes.AlsoF-LE.B.5,F.IF.C.7d(+):Graphsquareroot,cuberoot,andpiecewise-definedfunctions,includingstepfunctionsandabsolutevaluefunctions.

ICAN:• graphsquareroot,cuberoot,andpiecewisefunctions

includingstepandabsolutevalue.• graphlinearinequalitiesonthecoordinateplaneand

describethemeaningofthesolutionset.• graphthesolutionstoalinearinequalityintwo

variablesasahalf-plane,excludingtheboundaryfornon-inclusiveinequalities

• graphthesolutionsettoasystemoflinearinequalitiesintwovariablesastheintersectionoftheircorrespondinghalf-planes.

NINE

ReviewAssessRemediate/Enrich

HONORSALGEBRAPACINGGUIDE:3rdNineWeeks

UNITFIVE:LinearSystemsandPiecewiseFunctions(cont.)


Materials/Projects

ONE

13.1-13.2:Piecewise-

DefinedFunctions F-IF.C.7b:Graphfunctionsexpressed

symbolicallyandshowkeyfeaturesofthegraph,byhandinsimplecasesandusingtechnologyformorecomplicatedcases.a. Graphsquareroot,cuberoot,and

piecewise-definedfunctions,includingstepfunctionsandabsolutevaluefunctions.

AlsoF-BF.A.1b,F-BF.B.3

ICAN:• determinetheparentfunctionforthelinef(x)=x.• identifyandcomparethedifferentformsoflinear


representedindifferentways.• describealineasatranslationoftheparentfunctiony=

x.

TWO

13.3-13.4:Piecewise-

DefinedFunctions

A-REI.B.3:Solvelinearequationsandinequalitiesinonevariable,includingequationswithcoefficientsrepresentedbyletters.AlsoA-REI.D.11,A-CED.A.1

ICAN:• solvelinearequationsinonevariable,includingthose

withcoefficientsrepresentedbyletters.• solvelinearinequalitiesinonevariable,includingthose

withcoefficientsrepresentedbyletters.• solvecompoundinequalitiesandgraphthesolutionsona

numberline.(ACT)• solveinequalitiesinonevariableandusethemina

contextualsituationtosolveproblems• matchinequalitieswiththeirgraphs.(*ACT)

UNITSIX:ExponentialRelationships


THREE

14.1-14.2:Rational

ExponentsandRadicals

N-RN.A.1(+)N-RN.A.2(+)AlsoN-RN.B.3,A-SSE.A.1b;Al.WCE.20:Operate(add,subtract,multiply,divide,simplify,powers)withradicalsandradicalexpressionsincludingradicandsinvolvingrationalnumbersandalgebraicexpressions.

ICAN• operatewithpositive,negativeandfractionalexponents.

Studentswillalsotranslatebetweenradicalformandexponentialform.

• identifywhichsumsandproductsarerationalorirrational.AnunderstandingoftheRealNumbersystemisassumed.

FOUR

15.1-15.3:Geometric

SequencesandExponential

Functions

F-LE.A.2:Constructlinearandexponentialfunctions,includingarithmeticandgeometricsequences,givenagraph,adescriptionofarelationship,ortwoinput-outputpairs(includereadingthesefromatable).F-BF.A.1a:Writeafunctionthatdescribesarelationshipbetweentwoquantities.a. Determineanexplicitexpression,a

recursiveprocess,orstepsforcalculationfromacontext.

AlsoF-LE.A.3,F-BF.A.2(+),F-IF.A.2

ICAN:• createlinearandexponentialfunctions,fromasimple

context,giventhefollowingsituations:arithmeticandgeometricsequences,agraph,adescriptionofarelationship,andtwopointswhichcanbereadfromatable.

• writeanexplicitexpression,definearecursiveprocess,ordescribethecalculationsneededtomodelafunctionbetweentwoquantities.

FIVE

15.4-15.5:Geometric

SequencesandExponential

Functions

F-BF.B.3:Identifytheeffectonthegraphofreplacingf(x)byf(x)+k,kf(x),f(kx),andf(x+k)forspecificvaluesofk(bothpositiveandnegative);findthevalueofkgiventhegraphs.Experimentwithcasesandillustrateanexplanationoftheeffectsonthegraphusingtechnology.Includerecognizingevenandoddfunctionsfromtheirgraphsandalgebraicexpressionsforthem.AlsoF-IF.C.7e(+),F-IF.C.8b,F-IF.C.9,F-BF.A.1b

ICAN:• transformavarietyoffunctionsincludinglinear,

quadraticandlogarithmic.• usetechnologytoexperimentwiththegraphsofvarious

functionswhentransformingtheequationsusingdifferentvaluesofk.

• formconjecturesbasedonmyexperimentswithsubstitutingdifferentvaluesintothegeneral(parent)functions.

SIX

16.1-16.4:ExponentialEquationsandModels

A-CED.A.1:Createequationsandinequalitiesinonevariableandusethemtosolveproblems.Includeequationsarisingfromlinearandquadraticfunctions,andsimplerationalandexponentialfunctions.S-ID.B.6aRepresentdataontwoquantitativevariablesonascatterplot,anddescribehowthevariablesarerelated.b. Fitafunctiontothedata;usefunctions

fittedtodatatosolveproblemsinthecontextofthedata.Usegivenfunctionsorchooseafunctionsuggestedbythecontext.Emphasizelinear,quadratic,andexponentialmodels.

F-LE.A.1cAlsoA-SSE.B.3c,A-REI.D.11,F-BF.A.1a-c,F-LE.A.2,F-LE.A.3,F-IF.B.5,S-ID.B.6b,A-CED.A.2,F-IF.C.7e(+)

ICAN:• describewhetheragivensituationinquestionhasa

linearpatternofchangeoranexponentialpatternofchange.



• describesituationswhereaquantitygrowsordecaysataconstantpercentrateperunitintervalascomparedtoanother.

UNITSEVEN:POLYNOMIALOPERATIONS


SEVEN

17.1-17.3:Addingand

SubtractingPolynomials A-SSE.A.1a:Interpretexpressionsthat

representaquantityintermsofitscontext.a. Interpretpartsofanexpression,suchas

terms,factors,andcoefficients.A-APR.A.1:Understandthatpolynomialsformasystemanalogoustotheintegers,namely,theyareclosedundertheoperationsofaddition,subtraction,andmultiplication;add,subtract,andmultiplypolynomials.AlsoA-SSE.A.1b,A-SSE.A.2,A-CED.A.1

ICAN:• decomposepolynomialexpressionsandmakesenseof

multiplefactorsandtermsbyexplainingthemeaningoftheindividualpartsfocusingonquadraticandexponentialexpressions.

• applythedefinitionofanintegertoexplainwhyaddingorsubtractingtwointegersalwaysproducesaninteger.

• addandsubtractpolynomials.• understandhowclosureappliesunderadditionand

subtraction.(*ACT)

EIGH

T

18.1-18.3:MultiplyingPolynomials

A-APR.A.1:Understandthatpolynomialsformasystemanalogoustotheintegers,namely,theyareclosedundertheoperationsofaddition,subtraction,andmultiplication;add,subtract,andmultiplypolynomials.AlsoA-SSE.A.1,A-CED.A.1;A-APR.D.6(+):Rewritesimplerationalexpressionsindifferentforms;writea(x)/b(x)intheformq(x)+r(x)/b(x),wherea(x),b(x),q(x),andr(x)arepolynomialswiththedegreeofr(x)lessthanthedegreeofb(x),usinginspection,longdivision,or,forthemorecomplicatedexamples,acomputeralgebrasystem;A.APR.D.7(+):Understandthatrationalexpressionsformasystemanalogoustotherationalnumbers,closedunderaddition,subtraction,multiplication,anddivisionbyanonzerorationalexpression;add,subtract,multiply,anddividerationalexpressions.

ICAN:• applythedefinitionofanintegertoexplainwhy

multiplyingtwointegersalwaysproducesaninteger.• multiplypolynomials.• understandhowclosureappliesundermultiplication.

(*ACT)

NINE

ReviewAssessRemediate/Enrich

HONORSALGEBRAPACINGGUIDE:4thNineWeeks

UNITEIGHT:QuadraticFunctions


Materials/Projects

ONE

19.1-19.3:GraphingQuadraticFunctions

F-BF.B.3:Identifytheeffectonthegraphofreplacingf(x)byf(x)+k,kf(x),f(kx),andf(x+k)forspecificvaluesofk(bothpositiveandnegative);findthevalueofkgiventhegraphs.Experimentwithcasesandillustrateanexplanationoftheeffectsonthegraphusingtechnology.Includerecognizingevenandoddfunctionsfromtheirgraphsandalgebraicexpressionsforthem.F-IF.B.4:Forafunctionthatmodelsarelationshipbetweentwoquantities,interpretkeyfeaturesofgraphsandtablesintermsofthequantities,andsketchgraphsshowingkeyfeaturesgivenaverbaldescriptionoftherelationship.Keyfeaturesinclude:intercepts;intervalswherethefunctionisincreasing,decreasing,positive,ornegative;relativemaximumsandminimums;symmetries;endbehavior;andperiodicity.Also.F-IF.A.2,F-IF.C.7a,F-IF.C.8,F-BF.A.1,F-BF.B.4(+)

ICAN:• transformavarietyoffunctionsincludinglinear,

quadraticandlogarithmic.• usetechnologytoexperimentwiththegraphsofvarious

functionswhentransformingtheequationsusingdifferentvaluesofk.

• formconjecturesbasedonmyexperimentswithsubstitutingdifferentvaluesintothegeneral(parent)functions.

• (givenalinearfunction)identifykeyfeaturesingraphsandtablesincluding:intercepts,intervalswherethefunctionisincreasing,decreasing,positiveornegative;relativemaximumsandminimums;symmetries.

• interpretandexplainfeaturesofthegraphofthefunctionintermsofthecontextoftheproblem.

• sketchagraphifgiventhekeyfeaturesofafunction.

TWO

20.1-20.3:ConnectingIntercepts,Zeros,andFactors

F-IF.C.7a:Graphfunctionsexpressedsymbolicallyandshowkeyfeaturesofthegraph,byhandinsimplecasesandusingtechnologyformorecomplicatedcases.a. Graphlinearandquadraticfunctionsand

showintercepts,maxima,andminima.A-APR.B.3:Identifyzerosofpolynomialswhensuitablefactorizationsareavailable,andusethezerostoconstructaroughgraphofthefunctiondefinedbythepolynomial.A-REI.B.4:Solvequadraticequationsinonevariable.a. Usethemethodofcompletingthesquare

totransformanyquadraticequationinxintoanequationoftheform(x–p)2=qthathasthesamesolutions.Derivethequadraticformulafromthisform.

b. Solvequadraticequationsbyinspection(e.g.,forx2=49),takingsquareroots,completingthesquare,thequadraticformulaandfactoring,asappropriatetotheinitialformoftheequation.Recognizewhenthequadraticformulagivescomplexsolutionsandwritethemasa±biforrealnumbersaandb.

AlsoA-REI.D.11,A-APR.A.1,A-SSE.A.2,A-SSE.B.3

ICAN:• graphquadraticfunctionsandshowintercepts,maxima,

andminima.• findthezerosofapolynomialwhenthepolynomialis

factored.• usethezerosofafunctiontosketchthegraphofthe

function.• transformaquadraticequationwritteninstandardform

toanequationinvertexform(x–p)2=qbycompletingthesquare.

• derivethequadraticformulabycompletingthesquareonthestandardformofaquadraticequation.

• solvequadraticequationsinonevariablebysimpleinspection,takingthesquareroot,factoring,andcompletingthesquare.(*ACT)

• understandwhytakingthesquarerootofbothsidesofanequationyieldstwosolutions.

• usethequadraticformulatosolveanyquadraticequation,recognizingtheformulaproducesallcomplexsolutions.

• writeacomplexsolutionasa+biforrealnumbersaandb.

• solvequadraticequationsbytakingsquareroots.• solvequadraticequationsbycompletingthesquare.solvequadraticequationsbyfactoring.

UNITNINE:QuadraticEquationsandModels


Materials/Projects

THREE

21.1-21.3:UsingFactorstoSolveQuadratic

Equations

A-SSE.B.3aChooseandproduceanequivalentformofanexpressiontorevealandexplainpropertiesofthequantityrepresentedbytheexpression.a. Factoraquadraticexpressiontoreveal

thezerosofthefunctionitdefines.A-REI.B.4bSolvequadraticequationsinonevariable.b. Solvequadraticequationsbyinspection

(e.g.,forx2=49),takingsquareroots,completingthesquare,thequadraticformulaandfactoring,asappropriatetotheinitialformoftheequation.Recognizewhenthequadraticformulagivescomplexsolutionsandwritethemasa±biforrealnumbersaandb.

AlsoA-SSE.A.2,A-SSE.B.3a

ICAN:• defineanexponentialfunctions,𝑓(𝑥)=𝑎𝑏𝑥.• rewriteexponentialfunctionsusingthepropertiesof

exponents.• usepropertiesofexponents,includingrationalexponents

(suchaspowerofapower,productofpowers,powerofaproduct,andrationalexponents,etc…)towriteanequivalentformofanexponentialfunctiontorevealandexplainspecificinformationaboutitsapproximaterateofgrowthordecay.(includingnegativeandzeroexponents).(*ACT)

• writeexponentialfunctionstorepresentgrowth,decayandcompoundinterest.

FOUR

22.1-22.3:UsingSquareRootstoSolveQuadraticEquations A-REI.B.4a-b

Solvequadraticequationsinonevariable.a. Usethemethodofcompletingthesquare

totransformanyquadraticequationinxintoanequationoftheform(x–p)2=qthathasthesamesolutions.Derivethequadraticformulafromthisform.

b. Solvequadraticequationsbyinspection(e.g.,forx2=49),takingsquareroots,completingthesquare,thequadraticformulaandfactoring,asappropriatetotheinitialformoftheequation.Recognizewhenthequadraticformulagivescomplexsolutionsandwritethemasa±biforrealnumbersaandb.

A-SSE.B.3b:Chooseandproduceanequivalentformofanexpressiontorevealandexplainpropertiesofthequantityrepresentedbytheexpression.b. Completethesquareinaquadratic

expressiontorevealthemaximumorminimumvalueofthefunctionitdefines.

AlsoA-SSE.A.2,A-SSE.B.3a,F-IF.C.8a

ICAN:• defineanexponentialfunctions,𝑓(𝑥)=𝑎𝑏𝑥.• rewriteexponentialfunctionsusingthepropertiesof

exponents.• usepropertiesofexponents,includingrationalexponents

(suchaspowerofapower,productofpowers,powerofaproduct,andrationalexponents,etc…)towriteanequivalentformofanexponentialfunctiontorevealandexplainspecificinformationaboutitsapproximaterateofgrowthordecay.(includingnegativeandzeroexponents).(*ACT)

• writeexponentialfunctionstorepresentgrowth,decayandcompoundinterest.

• recognizetheconnectionamongfactors,solutions(roots),zerosofrelatedfunctions,andx-interceptsinquadraticfunctions.

• identifyandfactorperfect-squaretrinomials.• completethesquaretorewriteaquadraticexpression

(𝑎𝑥2+𝑏𝑥+𝑐)withtheform𝑎(𝑥−ℎ)2+𝑘.predictwhetheraquadraticwillhaveaminimumoramaximumbasedonthevalueofa.

FIVE

22.4-22.5:UsingSquare

RootstoSolveQuadratic

Equations

A-REI.B.4b:Solvequadraticequationsinonevariable.b. Solvequadraticequationsbyinspection

(e.g.,forx2=49),takingsquareroots,completingthesquare,thequadraticformulaandfactoring,asappropriatetotheinitialformoftheequation.Recognizewhenthequadraticformulagivescomplexsolutionsandwritethemasa±biforrealnumbersaandb.

A-REI.C.7(+)

ICAN:• solvequadraticequationsusingavarietyofstrategies

(factoring,completingthesquare,graphing,takingthesquarerootofbothsidesofanequation,usingthequadraticformula).

• simplifyaradicalthatrepresentsanimaginarynumber.• writeacomplexsolutionasa±biforrealnumbersaand

b.

SIX

23.1-23.2:Linear,Exponential,and

QuadraticModels

A-CED.A.2:Createequationsintwoormorevariablestorepresentrelationshipsbetweenquantities;graphequationsoncoordinateaxeswithlabelsandscales.F-LE.A.1b:Distinguishbetweensituationsthatcanbemodeledwithlinearfunctionsandwithexponentialfunctions.b. Recognizesituationsinwhichone

quantitychangesataconstantrateperunitintervalrelativetoanother.

AlsoF-IF.B.4,F-IF.B.5,F-IF.B.6,F-LE.A.1,F-LE.A.3

ICAN:• createequationsintwoormorevariablestorepresent

relationshipsbetweenquantities.• graphequationsintwovariablesonacoordinateplane

andlabeltheaxesandscales.• decidewhichfunctionsarerelativelyeasytosketch

accuratelybyhandandwhichshouldbegraphedusingtechnology.describewhetheragivensituationinquestionhasalinearpatternofchangeoranexponentialpatternofchange.



UNITTEN:InverseRelationships


SEVEN

24.1-24.4:Functionsand

Inverses

F-IF.C.7b:Graphfunctionsexpressedsymbolicallyandshowkeyfeaturesofthegraph,byhandinsimplecasesandusingtechnologyformorecomplicatedcases.b. Graphsquareroot,cuberoot,and

piecewise-definedfunctions,includingstepfunctionsandabsolutevaluefunctions.

F-IF.C.7c(+)F-BF.B.4a(+)AlsoF-BF.B.3,F-BF.B.4c-d(+),A-CED.A.4,F-IF.B.5,

ICAN:• determinetheparentfunctionforthelinef(x)=x.• identifyandcomparethedifferentformsoflinear


representedindifferentways.• describealineasatranslationoftheparentfunctiony=

x.

EIGH

T

WCS:M

atrix Al.WCE.15(+):Representasystemoflinear

equationsasasinglematrixequationinavectorvariableAl.WCE.16(+):Findtheinverseofamatrixanduseittosolvesystemsoflinearequations(usetechnologyfor3x3andgreater)

ICAN:• performmatrixoperations(add,subtract,scalar

multiplicationandmatrixmultiplication)withandwithouttechnology

• findtheinverseofamatrixwithandwithouttechnology• solvesystemsofequationsusingmatrices

NINE

Finalassessmentsandyear-endingactivities

honors algebra pacing guide: 1 nine weeks...

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