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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.
Week Lesson Standards LearningTargetOther
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
Week Lesson Standards LearningTarget OtherMaterials/Projects
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)
Week Lesson Standards LearningTargetOther
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
Week Lesson Standards LearningTarget OtherMaterials/Projects
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.)
Week Lesson Standards LearningTargetOther
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
functions.(point-slope,standard,slope-intercept)• identifytheinterceptsofafunction.• comparethekeyfeaturesoftwolinearfunctions
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
Week Lesson Standards LearningTarget OtherMaterials/Projects
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.
• showthatlinearfunctionschangeatthesamerateovertimeandthatexponentialfunctionschangebyequalfactorsovertime.
• describesituationswhereonequantitychangesataconstantrateperunitintervalascomparedtoanother.
• describesituationswhereaquantitygrowsordecaysataconstantpercentrateperunitintervalascomparedtoanother.
UNITSEVEN:POLYNOMIALOPERATIONS
Week Lesson Standards LearningTarget OtherMaterials/Projects
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
Week Lesson Standards LearningTargetOther
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
Week Lesson Standards LearningTargetOther
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.
• showthatlinearfunctionschangeatthesamerateovertimeandthatexponentialfunctionschangebyequalfactorsovertime.
• describesituationswhereonequantitychangesataconstantrateperunitintervalascomparedtoanother.
UNITTEN:InverseRelationships
Week Lesson Standards LearningTarget OtherMaterials/Projects
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
functions.(point-slope,standard,slope-intercept)• identifytheinterceptsofafunction.• comparethekeyfeaturesoftwolinearfunctions
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