2015 STAAR Questions & TEKS Review By: Randy Houchins
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2015STAARQuestions&TEKSReview
By:RandyHouchins
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TableofContents1 INTRODUCTION .............................................................................................................. 32 SUMMARY ........................................................................................................................ 33 STAAR 3RD GRADE MATH QUESTIONS ......................................................................... 54 STAAR 4TH GRADE MATH QUESTIONS ....................................................................... 185 STAAR 5TH GRADE MATH QUESTIONS ....................................................................... 246 STAAR 6TH GRADE MATH QUESTIONS ....................................................................... 377 STAAR 7TH GRADE MATH QUESTIONS ....................................................................... 478 STAAR 8TH GRADE MATH QUESTIONS ....................................................................... 56
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1 INTRODUCTION Thefollowingismyattempttodemonstratethefrustratingproblemsonthe3rdgradethrough8thgrade2015STAARassessmentsthataretestingprocessormethodologyinsteadoftestingknowledge.IhavealsoincludedtheContentandProcessStandardTEKSforeachtestquestionidentifiedandhighlightedthewordingintheTEKSthatcreatestheneedforthequestion.
2 SUMMARY BeforeIcompletedthistaskandtookallofthe20153rd-8thgradeSTAARassessments,IwasundertheimpressionthatthemainproblemwiththeTEKSwastheprocessstandardsinthe2012revision.AfterfurtherreviewoftheTEKS,Ihavefoundthatthecontentstandardsarecallingoutspecificmethodstobeusedinsolvingproblems.TheProcessStandardsforcemultiplemethodswiththeuseoftheword“Including”andtheuseof“And”insteadof“Or.”TheContentStandardsalsocalloutmultiplemethodsandneedtoberevisited.Anexampleofthisiswhenthecontentstandardcallsfortheuseof“objectsandpictorialmodels,includingnumberlines”,or“usingsymbols,words,objects,andpictorialmodels,”orlikein3rdgrade(TEK3.4K)“usingstrategiesbasedonobjects;pictorialmodels,includingarrays,areamodels,andequalgroups;propertiesofoperations;orrecalloffacts.”Manyofthesemethodswerealsointhe2014TEKS:4thgrade2014TEKScallfortheuseoftheareamodelandarrays.Pictorialmodelsarecalledoutinthe20141st,3rdand4thgrade.Inthe2012TEKStheuseofthesealternatemethodshasdramaticallyincreased.TheK-5ContentStandardscallfortheuseofareamodel(amethodofmultiplication)9timesandtheuseofpictorialmodels23times.Therearemanymoreexamplesofthese“process”or“methodology”questionsinthe2015releasedSTAARquestions(andtheyonlyreleasedabouthalfofthequestion).TheProcessStandardsinthe2012TEKS(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(C) selecttools,includingrealobjects,manipulatives,paperandpencil,andtechnologyasappropriate,andtechniques,includingmentalmath,estimation,andnumbersenseasappropriate,tosolveproblems;
(D) communicatemathematicalideas,reasoning,andtheirimplicationsusingmultiplerepresentations,includingsymbols,diagrams,graphs,andlanguageasappropriate;
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(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
(G) display,explain,andjustifymathematicalideasandargumentsusingprecisemathematicallanguageinwrittenororalcommunication.
WhyarethesemethodscalledupintheTEKS?Theshortansweris“ReformMath”expertsontheTEKSreview/re-writeaddedthiswordingintentionallytoensurethatthe“ConceptualUnderstanding”ofreformmatheducationwouldbetaught.Thethinkingwas,ifitisintheTEKSitwillshowupontheassessment—ifitshowsupontheassessmentitwillhavetobeaddedtothecurriculumandbetaught.Theargumentofteachingconceptualunderstandingorknowledgeandskillsisabogusdichotomyinmathematicseducation.Knowledgeandskillsshouldalwaysbetaughtwiththeinclusionofconceptualunderstanding.ThiswaswellstatedinH.Wu’sarticle“BasicSkillsVersusConceptualUnderstanding-ABogusDichotomyinMathematicsEducation.”Hereisalinktothearticlehttp://www.aft.org/sites/default/files/periodicals/wu.pdf.AnothergoodarticlethatdocumentsthisragingbattleinmathematicseducationisDavidKlein’s“ABriefHistoryofAmericanK-12MathematicsEducationinthe20thCentury.”Hereisalinktothearticlehttp://www.csun.edu/~vcmth00m/AHistory.html.Whatislostwhenusingreformmath(andhavingthesemultiplemethodscalledupinthecontentstandardsandthusreflectedintheSTAARassessment)isthefactthatittakesmuchlongertoteachALLofthemethods.Criticalconceptsgetpushedouttooldergradesandstudentsmissoutanimportantpartofmathinstruction–practiceusingthemostefficientmethod.Studentsthataretaughtwithreformmathtendtobeabouttwoyearsbehindthosestudentstaughtwithmoretraditionalapproachestomathbythetimetheyareinorexitinghighschool.ItputsCalculusoutofreachofmoststudentsinHighSchool.TheTEKSshouldnotforcemethodology.ItismyhopethatwecanremovethereformmathmethodologyfromtheTEKSandlettheteachersknowthatteachingeverymethodtoallstudentsisnolongerrequired.Ateachershouldbeabletodecidewhatmethodeachstudentwillunderstandthemosttoteachaconcept.Oncetheconceptisunderstoodandusedtodemonstratethemostefficientmethodforsolvingtheproblems,thestudentshouldnothavetodemonstratetheknowledgeofamethod.Belowareexamplesfromthe2015STAARassessments.
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3 STAAR 3RD GRADE MATH QUESTIONS Question6istestingastudent’sunderstandingofpictorialmodels…Pleasenotethattheuseofpictorialmodelisinthecontentstandard,nottheprocessstandard.ThisTEKrequiresthreemethods;objects,pictorialmodelsandnumberlines.Itdoesnottestacalculation.Theuseofthewordrepresentmeanstheyjusthavetorecognizetherepresentation;object,pictorialmodelsornumberline.TEK3.3Fstates: (ReadinessContentStandard)(3) Numberandoperations.Thestudentappliesmathematicalprocessstandardstorepresent
andexplainfractionalunits.Thestudentisexpectedto:(F) representequivalentfractionswithdenominatorsof2,3,4,6,and8usingavariety
ofobjectsandpictorialmodels,includingnumberlines;TEK3.1A,B,E&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolutionandevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Question7istestingequivalentfractions,butitdoesnottestifthestudentunderstandsthemathematicsbehindcomparingfractions.Itonlyteststhatthestudentcanrecognizethesamepointonanumberlineoranareamodel....Theuseoftheword“represent”meanstheyjusthavetorecognizetherepresentation;aremodel.TEK3.3Gstates: (SupportingContentStandard)(3) Numberandoperations.Thestudentappliesmathematicalprocessstandardstorepresent
andexplainfractionalunits.Thestudentisexpectedto:(G) explainthattwofractionsareequivalentifandonlyiftheyarebothrepresentedby
thesamepointonthenumberlineorrepresentthesameportionofasamesizewholeforanareamodel;and
TEK3.1B,E&Gstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolutionandevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(G) display,explain,andjustifymathematicalideasandargumentsusingprecisemathematicallanguageinwrittenororalcommunication.
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Question8issimilartoquestion7inthatthereisnomathbehindthequestioning,onlyunderstandingofmodels(symbols,words,objectsandpictorialmodels)…TheproblemwordinginthisTEKis“appliesmathematicalprocessstandardstorepresentandexplainfractionalunits”and“justifyingtheconclusionusingsymbols,words,objects,andpictorialmodels.”Thisquestioncouldhavealsoshownupwithpicturesandsymbols.TEK3.3Hstates: (ReadinessContentStandard)(3) Numberandoperations.Thestudentappliesmathematicalprocessstandardstorepresent
andexplainfractionalunits.Thestudentisexpectedto:(H) comparetwofractionshavingthesamenumeratorordenominatorinproblemsby
reasoningabouttheirsizesandjustifyingtheconclusionusingsymbols,words,objects,andpictorialmodels.
TEK3.1A,B,E&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolutionandevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Question11isagoodquestiontestingstraightforwardmath,butlookathowtheTEKisworded.Thereareactually7waysthisTEKcouldhavebeentested;pictorialmodels,arrays,areamodels,andequalgroups,propertiesofoperations,orrecalloffacts.Thisparticulartestquestionisgood,buttheotherfiveofsevenmethodsthatcouldhavebeentestedarenotgood…Propertiesofoperationsorrecalloffactsaretheonlytwomethodsherethatwillbenefitthestudentinuppergradelevels.TEK3.4Kstates: (ReadinessContentStandard)(4) Numberandoperations.Thestudentappliesmathematicalprocessstandardstodevelop
andusestrategiesandmethodsforwholenumbercomputationsinordertosolveproblemswithefficiencyandaccuracy.Thestudentisexpectedto:(K) solveone-stepandtwo-stepproblemsinvolvingmultiplicationanddivisionwithin
100usingstrategiesbasedonobjects;pictorialmodels,includingarrays,areamodels,andequalgroups;propertiesofoperations;orrecalloffacts.
TEK3.1A,B&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolutionandevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Question12istestingtheunderstandingofequations,butdoesnottestthatthestudentcansolvetheequation.TheproblemwordinginthisTEKisagaintheuseofthewordrepresent;“representone-andtwo-stepproblemsinvolvingadditionandsubtractionofwholenumbersto1,000usingpictorialmodels,numberlines,andequations.”Thequestionshouldhavebeenwordedforthestudenttosolvenotrepresentandgetridofthemultiplemethods;pictorialmodels,numberlines,andequations.TEK3.5Astates: (ReadinessContentStandard)(5) Algebraicreasoning.Thestudentappliesmathematicalprocessstandardstoanalyzeand
createpatternsandrelationships.Thestudentisexpectedto:(A) representone-andtwo-stepproblemsinvolvingadditionandsubtractionofwhole
numbersto1,000usingpictorialmodels,numberlines,andequations;TEK3.1A,B,D&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolutionandevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(D) communicatemathematicalideas,reasoning,andtheirimplicationsusingmultiplerepresentations,includingsymbols,diagrams,graphs,andlanguageasappropriate;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Question13isonlytestingtheknowledgeofarraysandnotthemathematicalimportanceofthearray.TheTEKsaysrepresentandsolve,butthestudentonlyhadtorecognizethemodel,notsolvethemultiplication.Thisproblemcouldhavealsotestedknowledgeofstripdiagrams.TEK3.5Bstates: (ReadinessContentStandard)(5) Algebraicreasoning.Thestudentappliesmathematicalprocessstandardstoanalyzeand
createpatternsandrelationships.Thestudentisexpectedto:(B) representandsolveone-andtwo-stepmultiplicationanddivisionproblemswithin
100usingarrays,stripdiagrams,andequations;TEK3.1A,B,E&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolutionandevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Question20isonlytestingifthestudentknowsthedefinitionofcongruentandarea.Thequestionalreadystatesthattheshadedareasareboth¼anditisprettycleartherectanglesarethesamesize.TEK3.6Estates: (SupportingContentStandard)(6) Geometryandmeasurement.Thestudentappliesmathematicalprocessstandardsto
analyzeattributesoftwo-dimensionalgeometricfigurestodevelopgeneralizationsabouttheirproperties.Thestudentisexpectedto:(E) decomposetwocongruenttwo-dimensionalfiguresintopartswithequalareasand
expresstheareaofeachpartasaunitfractionofthewholeandrecognizethatequalsharesofidenticalwholesneednothavethesameshape.
TEK3.1B,E&Gstates (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolutionandevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(G) display,explain,andjustifymathematicalideasandargumentsusingprecisemathematicallanguageinwrittenororalcommunication.
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4 STAAR 4TH GRADE MATH QUESTIONS Problem8isanexampleofwheretheyaretestingtheknowledgeofapictorialmodelandnotifthestudentcansubtractfraction.Whatthestudentreallyneedstoknowatthispointisthefollowing:
𝟔𝟖−
𝟒𝟖 =
𝟐𝟖 =
𝟏𝟒
Theproblemwordingisagaintheuseof“represent”.ThisTEKatleastincludestheword“solve.’TEK4.3Estates: (ReadinessContentStandard)(3) Numberandoperations.Thestudentappliesmathematicalprocessstandardstorepresent
andgeneratefractionstosolveproblems.Thestudentisexpectedto:(E) representandsolveadditionandsubtractionoffractionswithequaldenominators
usingobjectsandpictorialmodelsthatbuildtothenumberlineandpropertiesofoperations;
TEK4.1A,B,E&Fstates (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem12isanexampleofanearlyintroductionintoAlgebra.Idon’tthinkmost4thgradersarereadyforthis,butatleasttheydon’taskthestudentstosolveforn.Theproblemistheuseoftheword“represent….usingstripdiagrams.”TEK4.5Astates: (ReadinessContentStandard)(5) Algebraicreasoning.Thestudentappliesmathematicalprocessstandardstodevelop
conceptsofexpressionsandequations.Thestudentisexpectedto:(A) representmulti-stepproblemsinvolvingthefouroperationswithwholenumbers
usingstripdiagramsandequationswithaletterstandingfortheunknownquantity;TEK4.1A,B,D&Fstates (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(D) communicatemathematicalideas,reasoning,andtheirimplicationsusingmultiplerepresentations,includingsymbols,diagrams,graphs,andlanguageasappropriate;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Question14isanexampleofwherealgebrahasbeenpusheddownto4thgrade.Thisisabovetheskilllevelofmost4thgraders.Doelementaryschoolteachershavethetrainingtoteachalgebra?NowhereinthisTEKdoesitsaythatthereshouldbeunknowns;infactitsayswheredimensionsarewholenumbers.Ifastudentmissesthisquestion,dotheynotunderstandperimeterordotheynotunderstandtheuseoftheunknown?TEK4.5Dstates: (ReadinessContentStandard)(5) Algebraicreasoning.Thestudentappliesmathematicalprocessstandardstodevelop
conceptsofexpressionsandequations.Thestudentisexpectedto:(D) solveproblemsrelatedtoperimeterandareaofrectangleswheredimensionsare
wholenumbers.TEK4.1A,B,C,E&Fstates (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(C) selecttools,includingrealobjects,manipulatives,paperandpencil,andtechnologyasappropriate,andtechniques,includingmentalmath,estimation,andnumbersenseasappropriate,tosolveproblems;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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5 STAAR 5TH GRADE MATH QUESTIONS Problem2istestingthatthestudentcandescribewhattheparenthesismeansinanorderofoperations.Ithinksolvingtheactualmathproblemdemonstratesthatthestudentunderstandsorderofoperations.Thisismuchmoreimportantthanbeingabletodescribeinwordswhattheparenthesismeans…Thisgetsbacktothequestionofwhatismoreimportant“knowledgeandskills”or“conceptualunderstanding.”Ithinkbothareimportant,butifyouhadhadtopickoneIwouldfallonthesideof“knowledgeandskills.”Someintheeducationcommunityviewalackof“conceptualunderstanding”aswhatiswrongwithmatheducationtoday.Thatisnotwhatiswrongwithmatheducationtoday.Studentspossessingaroteunderstandingofprocedurestheycannotperformisafargreaterproblem.IwouldbelessconcernedofastudentthatcanperformthecalculationbutnotexplainwhytheparenthesesaredonefirstthanIwouldofastudentthatcannotperformthecalculationbutcanexplaintheuseoftheparenthesis.TEK5.4Estates: (SupportingContentStandard)(4) Algebraicreasoning.Thestudentappliesmathematicalprocessstandardstodevelop
conceptsofexpressionsandequations.Thestudentisexpectedto:(E) describethemeaningofparenthesesandbracketsinanumericexpression;
TEK5.1B&Gstates (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(G) display,explain,andjustifymathematicalideasandargumentsusingprecisemathematicallanguageinwrittenororalcommunication.
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Problem4coversTEK5.3andisanexampleoftestingknowledgeofamethodofmultiplyingdecimals.Thismethodcannotbeusedinupperlevelmath.Itisfinetousethismethod/processasameanstoteachaconcept,butitshouldnotbetestedascontentknowledgebecauseitdoesn’thelpthestudentlongterminupperlevelmath.Trytousethismethodwhenthousandthsorless…Theuseofthewordrepresentiswhatmakesthisproblemaboutrecognizingthemodelinsteadofperformingthecalculation.Astudentthatcanperformthecalculationbutnotunderstandthemodelwouldlikelypick“A”astheanswerbecause80x40=3,200.Theywouldbepenalizedforbeingabletodoacalculationbutnotunderstandanareamodel.TEK5.3Dstates: (SupportingContentStandard)(3) Numberandoperations.Thestudentappliesmathematicalprocessstandardstodevelop
andusestrategiesandmethodsforpositiverationalnumbercomputationsinordertosolveproblemswithefficiencyandaccuracy.Thestudentisexpectedto:(D) representmultiplicationofdecimalswithproductstothehundredthsusingobjects
andpictorialmodels,includingareamodels;TEK5.1B,D&Fstates (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(D) communicatemathematicalideas,reasoning,andtheirimplicationsusingmultiplerepresentations,includingsymbols,diagrams,graphs,andlanguageasappropriate;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem6isanotherexampleoftestingtheunderstandingofpictorialmodels.Pictorialmodelsarefinetointroduceaconcept,buttheyarenotveryusefulonceyougetintoupperlevelmath.Thisproblemshouldhavejustaskedthestudenttodivide(asshownbelow)butasyoucansee,theTEKrequirestestingrepresentingquotientsofdecimalswithobjectsandpictorialmodels:
TEK5.3Fstates: (SupportingContentStandard)(3) Numberandoperations.Thestudentappliesmathematicalprocessstandardstodevelop
andusestrategiesandmethodsforpositiverationalnumbercomputationsinordertosolveproblemswithefficiencyandaccuracy.Thestudentisexpectedto:(F) representquotientsofdecimalstothehundredths,uptofour-digitdividendsand
two-digitwholenumberdivisors,usingobjectsandpictorialmodels,includingareamodels;
TEK5.1B,D&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(D) communicatemathematicalideas,reasoning,andtheirimplicationsusingmultiplerepresentations,includingsymbols,diagrams,graphs,andlanguageasappropriate;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem8isanotherproblemwheretheTEKrequirespictorialmodels.Theexpectationiscountinguptheshadedsquaresofthemodelandnotperformingthecalculationofaddingfractions.Theuseoftheword“represent”and“objectsandpictorialmodels”aretheprobleminthisTEK.TEK5.3Hstates: (SupportingContentStandard)(3) Numberandoperations.Thestudentappliesmathematicalprocessstandardstodevelop
andusestrategiesandmethodsforpositiverationalnumbercomputationsinordertosolveproblemswithefficiencyandaccuracy.Thestudentisexpectedto:(H) representandsolveadditionandsubtractionoffractionswithunequal
denominatorsreferringtothesamewholeusingobjectsandpictorialmodelsandpropertiesofoperations;
TEK5.1A,B,E&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem9isanotherexampleoftestingamethodorprocess(represent….usingobjectsandpictorialmodels).Theexpectationismarkingout4outof6ofthesquaresineachcolumnandcountingthemarkedoffsquaresofthemodelandnotperformingthecalculation…Theyshouldbetaughthowtoconvertthewholenumberintoafraction,simplifyandthenmultiplythefractionstosolve(asIhaveshownbelow).IbelievethatiswhatTEK5.3Lcovers(seenextexample,problem11).TEK5.3Istates: (SupportingContentStandard)(3) Numberandoperations.Thestudentappliesmathematicalprocessstandardstodevelop
andusestrategiesandmethodsforpositiverationalnumbercomputationsinordertosolveproblemswithefficiencyandaccuracy.Thestudentisexpectedto:(I) representandsolvemultiplicationofawholenumberandafractionthatrefersto
thesamewholeusingobjectsandpictorialmodels,includingareamodels;TEK5.1A,B,E&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem11coversTEK5.3Lwithoutallofthepicturesandmodels.Thisisanexampleofgoodstraightforwardproblem.TEK5.3Lstates: (ReadinessContentStandard)(3) Numberandoperations.Thestudentappliesmathematicalprocessstandardstodevelop
andusestrategiesandmethodsforpositiverationalnumbercomputationsinordertosolveproblemswithefficiencyandaccuracy.Thestudentisexpectedto:(L) dividewholenumbersbyunitfractionsandunitfractionsbywholenumbers.
TEK5.1A,B,&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem17testsTEK5.9A.WhydoesaTEKgointosuchspecificitytorequireastudenttoknowhowtointerpretadotplotorstem-and-leafplot?Ihaveneverusedeitheroftheseinmycareerbutusebargraphsandlinegraphsallthetime.ItisinterestingthatonceCommonCorestartedshowingupsomeparentsnoticedthatwithinthesameweektherekidsacross3differentgradeswereintroducedtostem-and-leafplotswhentheyhadneverheardofthisformofgraphbefore(andwhywouldyou,sinceitisreallyaspecifictypeofchartforprobabilityandstatistics).IguessbecauseDavidColemanandJasonZimbadecidedallkidsinallgradesmustknowstem-and-leafthatiswhyitisshowinguponCommonCoreanSTAAR.TEK5.9Astates: (SupportingContentStandard)(9) Dataanalysis.Thestudentappliesmathematicalprocessstandardstosolveproblemsby
collecting,organizing,displaying,andinterpretingdata.Thestudentisexpectedto:(A) representcategoricaldatawithbargraphsorfrequencytablesandnumericaldata,
includingdatasetsofmeasurementsinfractionsordecimals,withdotplotsorstem-and-leafplots;
TEK5.1A,B,D&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(D) communicatemathematicalideas,reasoning,andtheirimplicationsusingmultiplerepresentations,includingsymbols,diagrams,graphs,andlanguageasappropriate;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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6 STAAR 6TH GRADE MATH QUESTIONS Problem1istestingTEK6.2AIhaveneverhadtouseorrememberthedefinitionofwhole,integerorrationalnumbers.Itismuchmoreimportanttoknowhowtousethesenumbersincalculations.Whyarewewastingtimememorizingclassificationsofnumbers?ItseemsthisquestionisdesignedmoretotestthatthestudentknowswhatisaVenndiagram…TEK6.2Astates: (SupportingContentStandard)(2) Numberandoperations.Thestudentappliesmathematicalprocessstandardstorepresent
anduserationalnumbersinavarietyofforms.Thestudentisexpectedto:(A) classifywholenumbers,integers,andrationalnumbersusingavisual
representationsuchasaVenndiagramtodescriberelationshipsbetweensetsofnumbers;
TEK6.1B,E&F (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem3istestingTEK6.2E.Thisproblemisjusttestingifthestudentunderstandsthatfractionsaredivisionproblemsandnotthatthestudentcanactuallyperformthecalculationorrecallthemathfact.ThisTEKisnotveryrelevantinshowingthestudentcanperformthemath.Itisbettertohavethestudentsolvedivisionproblemsineachoftheways.“Extendrepresentations”istheproblemwordinginthisTEK.TEK6.2Estates: (SupportingContentStandard)(2) Numberandoperations.Thestudentappliesmathematicalprocessstandardstorepresent
anduserationalnumbersinavarietyofforms.Thestudentisexpectedto:(E) extendrepresentationsfordivisiontoincludefractionnotationsuchasa/b
representsthesamenumberasa÷bwhereb≠0.TEK6.1B&F(ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem8istestingTEK6.3A.Thestudentdoesnothavetoperformthecalculation;theyonlyhavetorecognizetheprocess.Itwouldbebettertoshowtheyunderstandtheconceptbyactuallyworkingtheproblem.TheProcessStandardreallydoesn’tmeananythingifthestudentcannotperformthemath.TEK6.3Astates: (SupportingContentStandard)(3) Numberandoperations.Thestudentappliesmathematicalprocessstandardstorepresent
addition,subtraction,multiplication,anddivisionwhilesolvingproblemsandjustifyingsolutions.Thestudentisexpectedto:(A) recognizethatdividingbyarationalnumberandmultiplyingbyitsreciprocalresult
inequivalentvalues;TEK6.1B&F(ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem9istestingTEK6.3B.ThisTEKseemsoverlycomplicatedandredundantifyoujustsaythestudentmustbeabletomultiplefractions.Ifthestudentknowshowtoperformthecomputationofmultiplyingfractionsthisshouldbeenough.Whysay“withoutcomputation”thestudentisexpectedtodetermine?Theintenthereistohavethestudentvisuallylookatthefractionandseeifitisgreaterthanoneorlessthanone…Itistestingmentalmathandnotifastudentcanperformacalculation.Notallstudentswillbegoodatmentalmath,butiftheycanperformthecalculationshouldtheybepenalized?TEK6.3Bstates: (SupportingContentStandard)(3) Numberandoperations.Thestudentappliesmathematicalprocessstandardstorepresent
addition,subtraction,multiplication,anddivisionwhilesolvingproblemsandjustifyingsolutions.Thestudentisexpectedto:(B) determine,withandwithoutcomputation,whetheraquantityisincreasedor
decreasedwhenmultipliedbyafraction,includingvaluesgreaterthanorlessthanone;
TEK6.1B&F(ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem10isanotherexampleoftestingaprocessormethodinsteadofactuallyperformingthecalculation.Do6thgradersreallyneedtouseanumberlinetosolve?Whyistheemphasison“model”insteadofcalculation?TheuseofthewordrepresentistheproblemintheTEK.
𝟑×−𝟒 = 𝟏𝟐TEK6.3Cstates: (SupportingContentStandard)(3) Numberandoperations.Thestudentappliesmathematicalprocessstandardstorepresent
addition,subtraction,multiplication,anddivisionwhilesolvingproblemsandjustifyingsolutions.Thestudentisexpectedto:(C) representintegeroperationswithconcretemodelsandconnecttheactionswiththe
modelstostandardizedalgorithms;TEK6.1B,D&F (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(D) communicatemathematicalideas,reasoning,andtheirimplicationsusingmultiplerepresentations,includingsymbols,diagrams,graphs,andlanguageasappropriate;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem14istestingTEK6.5B.Itisanokayproblem,buttheTEKcallsforsolvingproportionalrelationshipsusing“concreteandpictorialmodels,”sothisproblemcouldhavebeenworse...TEK6.5Bstates: (ReadinessContentStandard)(5) Proportionality.Thestudentappliesmathematicalprocessstandardstosolveproblems
involvingproportionalrelationships.Thestudentisexpectedto:(B) solvereal-worldproblemstofindthewholegivenapartandthepercent,tofindthe
partgiventhewholeandthepercent,andtofindthepercentgiventhepartandthewhole,includingtheuseofconcreteandpictorialmodels;and
TEK6.1A,B&F (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem17istestingTEK6.9B.Numberlines?In6thgrade?Thereisamuchmoreefficientmethodofcommunicatingmathematicalsolutions.WhatiswrongwithequationsandinequalitiesasIhaveshownbelow?TheproblemwordinginthisTEKistheuseof“representsolutions…onnumberlines.”TEK6.9Bstates: (SupportingContentStandard)(9) Expressions,equations,andrelationships.Thestudentappliesmathematicalprocess
standardstouseequationsandinequalitiestorepresentsituations.Thestudentisexpectedto:(B) representsolutionsforone-variable,one-stepequationsandinequalitiesonnumber
lines;and
TEK6.1A,B,D&F (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(D) communicatemathematicalideas,reasoning,andtheirimplicationsusingmultiplerepresentations,includingsymbols,diagrams,graphs,andlanguageasappropriate;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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7 STAAR 7TH GRADE MATH QUESTIONS Problem1istestingTEK7.2A.IhavethesamecomplaintaboutthesequestionsasIdidfor6thgrade.Ibelievethisquestionistestingtheprocessstandardto“userepresentationstoorganize,record,andcommunicatemathematicalideas.”Theuseofnumbersincalculationsismoreimportantthanusingvisualrepresentationstodescriberelationships…Thisisanotherexamplewhere“conceptualunderstanding”ofnumbersseemstobemoreimportantthandemonstrating“knowledgeandskills”byperformingcalculationswiththosenumbers…TEK7.2Astates: (SupportingContentStandard)(2) Numberandoperations.Thestudentappliesmathematicalprocessstandardstorepresent
anduserationalnumbersinavarietyofforms.Thestudentisexpectedtoextendpreviousknowledgeofsetsandsubsetsusingavisualrepresentationtodescriberelationshipsbetweensetsofrationalnumbers.
TEK7.1B,E&Gstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(G) display,explain,andjustifymathematicalideasandargumentsusingprecisemathematicallanguageinwrittenororalcommunication.
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Problem2,3and4areallproblemstestingprobabilityandstatistics.Thisisskillthathasbeenmoveddownintomiddleschool.Previously“ProbabilityandStatistics”hasbeenacollegelevelcourserequiredforspecificdegreeplans.Problem4isagoodexampleofthecomplexityofprobability.TEK7.6Istates: (ReadinessContentStandard)(6) Proportionality.Thestudentappliesmathematicalprocessstandardstouseprobability
andstatisticstodescribeorsolveproblemsinvolvingproportionalrelationships.Thestudentisexpectedto:(I) determineexperimentalandtheoreticalprobabilitiesrelatedtosimpleand
compoundeventsusingdataandsamplespaces.TEK7.1A,B&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem5isanexampleofagoodtwostepquestion.Withtheexceptionofstating“Thestudentappliesmathematicalprocessstandards”and“justifyingsolutions”theTEKisgood(althoughIdonotseetheneedtohavethis“B”intheTEKwhen“A”coversthesamething...TEK7.3Bstates: (ReadinessContentStandard)(3) Numberandoperations.Thestudentappliesmathematicalprocessstandardstoadd,
subtract,multiply,anddividewhilesolvingproblemsandjustifyingsolutions.Thestudentisexpectedto:(B) applyandextendpreviousunderstandingsofoperationstosolveproblemsusing
addition,subtraction,multiplication,anddivisionofrationalnumbers.TEK7.1A,B&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem10istestingTEK7.10B.Do7thgradestudentsreallyneedtobeusingnumberlines?Thisisnottheclearestwaytoexpressinequalities,butitisstressingwhatisintheProcessStandards…Thewordinginthecontentstandardthatisproblematicis“representsolutions…onnumberlines.”TEK7.10Bstates: (SupportingContentStandard)(10) Expressions,equations,andrelationships.Thestudentappliesmathematicalprocess
standardstouseone-variableequationsandinequalitiestorepresentsituations.Thestudentisexpectedto:(B) representsolutionsforone-variable,two-stepequationsandinequalitiesonnumber
lines;andTEK7.1B,D&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(D) communicatemathematicalideas,reasoning,andtheirimplicationsusingmultiplerepresentations,includingsymbols,diagrams,graphs,andlanguageasappropriate;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem11istestingaprocess(model)andnotcontentknowledge.Thesetypesofmodelsarefinetoteachaconcept,butstudentsbythisgradeshouldbeabletousethestandardalgorithmtoquicklysolvethisproblem.Thatiswhatshouldbetested,notthatthattheycanrecognizeamodel.ThecontentstandardTEKcallsfor“model”and“solve.”IthinkthemodelportionofthisTEKshouldberemovedsothatitisnottested.TEK7.11Astates: (ReadinessContentStandard)(11) Expressions,equations,andrelationships.Thestudentappliesmathematicalprocess
standardstosolveone-variableequationsandinequalities.Thestudentisexpectedto:(A) modelandsolveone-variable,two-stepequationsandinequalities;
TEK7.1B,E&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem15istestingTEK7.5C.Thisseemstobeaveryspecificexampleofaworkplaceproblem,buttheunderlyingmathematicsismultistepmultiplicationanddivisionoffractions…WhydotheTEKSneedtogetthisspecific?Understandingscaledrawingsisaskillneededforarchitectureanddrafting.TEK7.5Cstates: (ReadinessContentStandard)(5) Proportionality.Thestudentappliesmathematicalprocessstandardstousegeometryto
describeorsolveproblemsinvolvingproportionalrelationships.Thestudentisexpectedto:(C) solvemathematicalandreal-worldproblemsinvolvingsimilarshapeandscale
drawings.TEK7.1A,B&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem22istestingTEK7.12A,orasIsay,doesthestudentknowwhatadotplotis?ThisTEKistoospecificandnotveryuseful.TEK7.12Astates: (ReadinessContentStandard)(12) Measurementanddata.Thestudentappliesmathematicalprocessstandardstouse
statisticalrepresentationstoanalyzedata.Thestudentisexpectedto:(A) comparetwogroupsofnumericdatausingcomparativedotplotsorboxplotsby
comparingtheirshapes,centers,andspreads;TEK7.1A,B,E&Gstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(G) display,explain,andjustifymathematicalideasandargumentsusingprecisemathematicallanguageinwrittenororalcommunication.
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8 STAAR 8TH GRADE MATH QUESTIONS Problem1istestingTEK8.2A.ThisisanotherexampleofaTEKthatisjustnotallthatusefulintherealworld.EverysingleSTAARpracticeteststartedwiththisveryquestionofVenndiagramsanddefinition/classificationofnumbers.EverystudentIgaveittoowasimmediatelydiscouraged.Whoremembersthedefinitionofreal,integer,whole,counting(thisisanewcategorytheyaddedsinceIwenttoschool),imaginary,rational,irrationalandnatural?Cananyoneofthemathexpertsgivemearealwordexampleoftheuseorneedtoknowthedefinitionofthesenumbers?TheproblemwordinginthisTEKis“usingavisualrepresentation.”Thisissupposedtogivethestudent“conceptualunderstanding,”butitdoesn’treallyhelptheminperformingcalculations.TEK8.2Astates: (SupportingContentStandard)(2) Numberandoperations.Thestudentappliesmathematicalprocessstandardstorepresent
anduserealnumbersinavarietyofforms.Thestudentisexpectedto:(A) extendpreviousknowledgeofsetsandsubsetsusingavisualrepresentationto
describerelationshipsbetweensetsofrealnumbers;
TEK8.1B,E&Gstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(G) display,explain,andjustifymathematicalideasandargumentsusingprecisemathematicallanguageinwrittenororalcommunication.
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Problem6istestingTEK8.5G.Thisproblemisanexampleofthedeeper“conceptualunderstanding”thatthenewTEKSaretryingtoprovide,butcananyonetellmewhatisthepracticalapplicationoftheanswerofthisproblem?Thisproblemistestingifthestudentcanunderstandthedefinitionofafunctioninadiagramformat;eachinput(alsoknownasdomain)canonlyhaveoneoutput(alsoknownascodomainorrange).TEK8.5Gstates: (ReadinessContentStandard)(5) Proportionality.Thestudentappliesmathematicalprocessstandardstouseproportional
andnon-proportionalrelationshipstodevelopfoundationalconceptsoffunctions.Thestudentisexpectedto:(G) identifyfunctionsusingsetsoforderedpairs,tables,mappings,andgraphs;
TEK8.1B,E&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem9istestingTEK8.8B.ThisTEKisnotrequired.Thestudentshouldbeabletosolvethewordproblemanddemonstratetheunderstanding.ThewaythisTEKiswrittenthestudentdoesn’tevenhavetosolvefortheunknown.Thewordproblemshouldbesolvedasfollows:
𝟑𝟒𝟎+ 𝟓𝒙 = 𝟔𝟓𝟎− 𝟖𝒙
𝟏𝟑𝒙 = 𝟑𝟏𝟎
𝒙 =𝟑𝟏𝟎𝟏𝟑 = 𝟐𝟑.𝟖𝟒𝟕
Doesmakingthestudentwriteawordproblemgivethem“conceptualunderstanding?”TEK8.8Bstates: (SupportingContentStandard)(8) Expressions,equations,andrelationships.Thestudentappliesmathematicalprocess
standardstouseone-variableequationsorinequalitiesinproblemsituations.Thestudentisexpectedto:(B) writeacorrespondingreal-worldproblemwhengivenaone-variableequationor
inequalitywithvariablesonbothsidesoftheequalsignusingrationalnumbercoefficientsandconstants;
TEK8.1A,B,D&Gstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(A) applymathematicstoproblemsarisingineverydaylife,society,andtheworkplace;(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(D) communicatemathematicalideas,reasoning,andtheirimplicationsusingmultiplerepresentations,includingsymbols,diagrams,graphs,andlanguageasappropriate;
(G) display,explain,andjustifymathematicalideasandargumentsusingprecisemathematicallanguageinwrittenororalcommunication.
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Problem10istestingTEKS8.8C.Unlikeproblem9above,thisproblemisstraightforward.ButwhydoestheTEKsay“model”atall?Thisproblemcouldhavebeenonethatwasnotstraightforwardbecauseoftheuseofthewordmodel.TEK8.8Cstates: (ReadinessContentStandard)(8) Expressions,equations,andrelationships.Thestudentappliesmathematicalprocess
standardstouseone-variableequationsorinequalitiesinproblemsituations.Thestudentisexpectedto:(C) modelandsolveone-variableequationswithvariablesonbothsidesoftheequal
signthatrepresentmathematicalandreal-worldproblemsusingrationalnumbercoefficientsandconstants;and
TEK8.1B&Fstates:(ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem11istestingTEKS8.9A.Thisreallydoesn’tneedtobean8thgradeTEK.TheconceptoftwoequationshavingthesamesolutionisanAlgebraIconcept,soifwearelookingtostreamlineandreducethenumberofTEKSwecouldstrikethisone.TEK8.9Astates: (SupportingContentStandard)(9) Expressions,equations,andrelationships.Thestudentappliesmathematicalprocess
standardstousemultiplerepresentationstodevelopfoundationalconceptsofsimultaneouslinearequations.Thestudentisexpectedtoidentifyandverifythevaluesofxandythatsimultaneouslysatisfytwolinearequationsintheformy=mx+bfromtheintersectionsofthegraphedequations.
TEK8.1B,E&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(E) createanduserepresentationstoorganize,record,andcommunicatemathematicalideas;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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Problem16issupposedtobetestingtheuseofthePythagoreanTheorem,butthisproblemdoesn’trequiretheuseofthePythagoreanTheoremtosolvebecause4+6=10.Themeasurementscouldnotrepresentatrianglemuchlessarighttriangle…TEK8.7Cstates: (ReadinessContentStandard)(7) Expressions,equations,andrelationships.Thestudentappliesmathematicalprocess
standardstousegeometrytosolveproblems.Thestudentisexpectedto:(C) usethePythagoreanTheoremanditsconversetosolveproblems;and
TEK8.1B,C&Fstates: (ProcessStandard)(1) Mathematicalprocessstandards.Thestudentusesmathematicalprocessestoacquireand
demonstratemathematicalunderstanding.Thestudentisexpectedto:(B) useaproblem-solvingmodelthatincorporatesanalyzinggiveninformation,
formulatingaplanorstrategy,determiningasolution,justifyingthesolution,andevaluatingtheproblem-solvingprocessandthereasonablenessofthesolution;
(C) selecttools,includingrealobjects,manipulatives,paperandpencil,andtechnologyasappropriate,andtechniques,includingmentalmath,estimation,andnumbersenseasappropriate,tosolveproblems;
(F) analyzemathematicalrelationshipstoconnectandcommunicatemathematicalideas;and
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