Mathematics Standards

Diocese of Baton Rouge

Mathematics Standards

Grade 7

Introduction

In Grade7,instructionaltimeshould focuson fourcriticalareas: (1)developingunderstanding of and applyingproportionalrelationships; (2) developing understanding ofoperationswith rationalnumbersandworkingwithexpressionsand linearequations; (3)solving problemsinvolving scaledrawings and informalgeometricconstructions,and working withtwo-andthree-dimensionalshapestosolveproblemsinvolvingarea,surfacearea,andvolume; and

(4)drawing inferencesaboutpopulationsbasedon samples.

(1)Studentsextendtheirunderstanding of ratiosanddevelop understandingofproportionalitytosolvesingle-andmulti-step problems.Studentsusetheirunderstanding of ratiosand proportionalitytosolveawidevarietyof percentproblems,including thoseinvolving discounts,interest,taxes,tips,and percentincreaseordecrease.Studentssolveproblemsaboutscaledrawingsbyrelatingcorresponding lengthsbetweentheobjectsor byusing thefact thatrelationshipsof lengthswithin an objectarepreservedin similarobjects.Studentsgraph proportionalrelationshipsandunderstand theunitrateinformallyas ameasureof thesteepnessoftherelatedline,calledtheslope.Theydistinguishproportionalrelationshipsfrom otherrelationships.

(2)Studentsdevelop a unified understanding ofnumber,recognizing fractions,decimals(thathavea finiteor arepeating decimalrepresentation),and percentsasdifferentrepresentationsof rationalnumbers.Studentsextendaddition,subtraction,multiplication,and divisionto allrationalnumbers, maintaining thepropertiesofoperationsandtherelationshipsbetweenaddition and subtraction,and multiplication and division.By applying theseproperties,andbyviewing negativenumbersin termsofeverydaycontexts(e.g.,amountsowedor temperaturesbelowzero),studentsexplain and interprettherules foradding,subtracting,multiplying,and dividingwith negativenumbers.Theyusethearithmeticof rationalnumbersasthey formulateexpressionsand equationsinonevariableand usetheseequationstosolveproblems.

(3)StudentscontinuetheirworkwithareafromGrade 6, solving problemsinvolving theareaand circumferenceofacircleand surfaceareaof three-dimensionalobjects.In preparation forworkoncongruenceand similarity in Grade8theyreason aboutrelationshipsamong two-dimensionalfiguresusing scaledrawingsand informalgeometricconstructions,and theygain familiarity with therelationshipsbetweenanglesformed byintersecting lines.Studentsworkwiththree-dimensionalfigures,relating them to two-dimensionalfiguresby examining cross-sections.Theysolvereal-world and mathematicalproblemsinvolving area,surfacearea,andvolumeof two- and three-dimensionalobjectscomposed oftriangles,quadrilaterals,polygons,cubesand rightprisms.

(4)Studentsbuildon theirpreviousworkwith single datadistributionstocomparetwodatadistributionsandaddressquestionsaboutdifferencesbetweenpopulations.Theybegin informalworkwithrandomsamplingtogeneratedatasetsand learn abouttheimportanceofrepresentativesamplesfordrawing inferences.

RatiosandProportionalRelationships DBR.7.RP

A.Analyze proportionalrelationshipsand use themto solvereal-world and mathematical problems.

1.Computeunitratesassociated with ratiosof fractions,including ratiosof lengths,areas,and otherquantitiesmeasured in likeordifferentunits.For example,if a personwalks½milein each¼hour,computetheunitrateasthecomplexfraction½/¼milesperhour,equivalently 2 milesper hour.

2.Recognizeand representproportionalrelationshipsbetween quantities.

a.Decidewhethertwoquantitiesarein a proportionalrelationship,e.g.,bytesting forequivalentratiosin atableorgraphing onacoordinateplaneandobserving whetherthegraph is a straightlinethroughtheorigin.

b.Identifytheconstantof proportionality (unitrate)in tables,graphs,equations,diagrams,andverbaldescriptionsofproportionalrelationships.

c.Representproportionalrelationshipsby equations.Forexample,iftotalcosttis proportional tothenumbern ofitemspurchasedata constantpricep,therelationship betweenthetotalcostandthenumberofitemscan beexpressed ast=pn.

d.Explain whata point(x,y)on thegraph ofa proportionalrelationship meansin termsofthesituation,withspecialattention tothepoints (0,0)and (1,r)whereristheunitrate.

3.Useproportionalrelationships tosolve multi-step ratioand percentproblemsofsimpleinterest,tax,markupsand markdowns,gratuitiesand commissions,fees,percentincreaseand decrease,and percenterror.

TheNumberSystem DBR.7.NS

A.Apply and extend previousunderstandingsofoperationswithfractions to add,subtract,multiply,and dividerationalnumbers.

1.Applyand extend previousunderstandings of additionand subtraction toadd and subtractrationalnumbers;representaddition andsubtraction ona horizontalorverticalnumberlinediagram.

a.Describesituationsinwhich oppositequantitiescombineto make0. Forexample, a hydrogen atomhas0chargebecauseitstwoconstituentsareoppositelycharged.

b.Understand p+qasthenumberlocated a distance|q| fromp,in thepositiveornegativedirectiondepending on whetherq is positiveor negative.Showthata numberanditsoppositehaveasum of0 (areadditiveinverses).Interpretsumsofrationalnumbersbydescribing real-world contexts.

c.Understand subtractionofrationalnumbersasadding theadditiveinverse,p–q=p+(–q).Showthatthedistancebetween two rationalnumberson thenumberlineistheabsolutevalueoftheirdifference,andapplythisprinciplein real-world contexts.

d.Applypropertiesofoperationsasstrategiesto add and subtractrationalnumbers.

2.Applyand extend previousunderstandings ofmultiplication and division andof fractionsto multiplyand dividerationalnumbers.

a.Understand thatmultiplication isextended from fractionstorationalnumbersby requiring thatoperationscontinueto satisfythepropertiesofoperations,particularlythedistributiveproperty,leading toproductssuch as(–1)(–1)=1and therulesformultiplying signed numbers.Interpretproducts ofrationalnumbersbydescribing real-world contexts.

b.Understand thatintegers can bedivided,provided thatthedivisorisnotzero,and everyquotientofintegers(with non-zerodivisor)isarationalnumber.Ifp and qareintegers,then –(p/q) =(–p)/q=p/(–q).Interpretquotientsofrationalnumbersbydescribing real-world contexts.

c.Applypropertiesofoperationsasstrategiesto multiplyand dividerationalnumbers.

d.Convertarationalnumbertoadecimalusing long division; knowthatthedecimalform of a rationalnumberterminatesin0soreventuallyrepeats.

3.Solvereal-world andmathematicalproblemsinvolving thefouroperationswithrational numbers.1

ExpressionsandEquations DBR.7.EE

A.Use propertiesofoperationstogenerate equivalentexpressions.

1.Applypropertiesofoperationsasstrategiesto add,subtract,factor,and expand linearexpressionswithrationalcoefficientsto includemultiplegrouping symbols(e.g.,parentheses,brackets,and braces).

2.Understand thatrewritingan expression in differentformsin a problemcontextcan shed lighton theproblemand howthequantitiesin itarerelated.Forexample,a+0.05a=1.05ameans that“increaseby5%”isthesameas“multiplyby1.05.”

B.Solve real-lifeand mathematicalproblemsusingnumericaland algebraic expressionsand equations.

3.Solvemulti-step real-lifeand mathematicalproblemsposedwith positiveand negativerationalnumbersinanyform (wholenumbers,fractions,and decimals),usingtoolsstrategically.Applypropertiesofoperationstocalculatewith numbersinanyform;convertbetweenformsasappropriate; andassessthereasonablenessofanswersusingmentalcomputation and estimation strategies.Forexample: If a woman making$25an hourgetsa 10%raise,shewillmakean additional1/10ofher salaryan hour,or $2.50,fora newsalaryof$27.50.Ifyouwantto place atowelbar 93/4incheslong inthecenterof adoorthatis271/2incheswide,youwillneedtoplacethebarabout9inchesfromeachedge;thisestimatecan beused asacheckon theexactcomputation.

4.Usevariablesto representquantitiesin a real-worldormathematicalproblem,and constructsimpleequationsand inequalitiestosolveproblemsby reasoning aboutthequantities.

a.Solveword problemsleading to equationsoftheformpx+q=rand p(x+q)=r,wherep,q,andrarespecificrationalnumbers.Solveequationsoftheseformsfluently.Compareanalgebraicsolutionto anarithmeticsolution,identifying thesequenceoftheoperationsused in each approach.For example,theperimeter of arectangleis54cm.Itslength is6cm.Whatisitswidth?

b.Solveword problemsleading toinequalitiesof theformpx+qr,px+q≥r, px+qror px+q≤r,wherep,q,and rarespecificrationalnumbers.Graphthesolution setof theinequalityand interpretitin thecontextoftheproblem.Forexample: Asasalesperson,you are paid$50perweekplus$3per sale.Thisweekyou wantyourpay tobeatleast$100.Writeaninequalityforthenumber ofsalesyou need tomake,anddescribethesolutions.

1Computationswith rational numbersextend the rulesfor manipulatingfractionstocomplexfractions.

Geometry DBR.7.G

A.Draw, construct,and describe geometrical figures and describe therelationshipsbetween them.

1.Solveproblemsinvolving scaledrawingsof geometricfigures,such ascomputingactuallengthsand areasfrom ascaledrawing and reproducing a scaledrawing ata differentscale.

2.Draw(freehand,with rulerand protractor,orwithtechnology)geometricshapeswith given conditions.(Focusison trianglesfrom threemeasuresof anglesorsides,noticingwhen theconditionsdetermineoneand only onetriangle,morethanonetriangle, or no triangle.)

3.Describethetwo-dimensionalfiguresthatresultfrom slicing three-dimensionalfigures,asin planesectionsofrightrectangularprismsand rightrectangularpyramids.

B.Solve real-lifeand mathematicalproblems involvinganglemeasure,area,surface area,andvolume.

4.Knowtheformulasforthe areaand circumferenceofa circleand solveproblems;givean informalderivation oftherelationship between thecircumferenceand areaof acircle.

5.Usefactsaboutsupplementary,complementary,vertical,and adjacentanglesina multi-step problemto writeand usethem to solvesimpleequationsforan unknown anglein a figure.

6.Solvereal-world andmathematicalproblemsinvolving area,volumeand surfaceareaof two-and three-dimensionalobjectscomposed oftriangles,quadrilaterals,polygons,cubes,and rightprisms.(Pyramidslimitedtosurfaceareaonly.)

StatisticsandProbability DBR.7.SP

A.Use randomsamplingto drawinferencesabout apopulation.

1.Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

2.Usedatafromarandomsampletodrawinferencesabouta population withan unknown characteristicofinterest.Generatemultiplesamples(orsimulatedsamples) ofthesamesizetogaugethevariation in estimatesor predictions.Forexample,estimatethemean word length in a bookbyrandomlysampling wordsfromthebook;predictthewinner ofa schoolelection based onrandomlysampled surveydata.Gaugehowfar offtheestimateor predictionmightbe.

B.Draw informal comparativeinferencesabout twopopulations.

3.Informallyassessthedegreeofvisualoverlapoftwonumericaldatadistributionswith similarvariabilitiesusingquantitativemeasures ofcenter(median and/ormean)and variability(interquartilerangeand/ormean absolutedeviation),aswellasdescribing any overall pattern and anystriking deviationsfromtheoverallpattern with referencetothecontextinwhich thedataweregathered.

4.Usemeasuresof centerand measuresofvariability fornumericaldatafromrandom samplesto drawinformalcomparativeinferencesabouttwo populations.For example,decidewhetherthewordsin a chapterof aseventh-gradesciencebookaregenerallylongerthanthewordsin a chapterof afourth-gradesciencebook.

C.Investigatechance processesand develop,use,and evaluate probability models.

5.Understand thattheprobabilityofa chanceeventis anumberbetween0and 1 thatexpressesthelikelihoodoftheeventoccurring.Largernumbersindicategreaterlikelihood. A

probabilitynear 0indicatesan unlikely event,a probability around½indicatesan eventthatisneitherunlikely norlikely,and aprobabilitynear 1 indicatesalikely event.

6.Approximatetheprobabilityofa chanceeventby collecting dataonthechanceprocessthatproducesitandobserving itslong-run relativefrequency,and predicttheapproximaterelativefrequencygiven theprobability.Forexample,when rollinga numbercube600 times,predictthata3or6 would berolledroughly200 times,butprobablynotexactly200 times.

7.Develop a probability modeland useittofind probabilitiesof events.Compareprobabilitiesfromamodeltoobserved frequencies;iftheagreementisnotgood,explain possiblesourcesof thediscrepancy.

a.Develop a uniformprobability modelby assigning equalprobability toalloutcomes,and usethemodeltodetermineprobabilitiesofevents.For example,if astudentisselected atrandomfroma class,find theprobabilitythatJanewillbeselected andtheprobabilitythata girlwillbeselected.

b.Develop a probability model(whichmaynotbeuniform)by observing frequenciesin datagenerated fromachanceprocess.Forexample,find theapproximateprobabilitythata spinning pennywilllandheadsup orthata tossed paper cup willlandopen-end down. Dotheoutcomesfor thespinning pennyappearto beequallylikelybased ontheobserved frequencies?

8.Find probabilitiesof compoundeventsusing organizedlists,tables,treediagrams,and simulation.

a.Understand that,justaswith simpleevents,theprobabilityofa compound eventisthefractionofoutcomesinthesamplespaceforwhichthecompound eventoccurs.

b.Representsamplespacesforcompound eventsusingmethodssuchasorganized lists,tablesand treediagrams. Foran eventdescribed in everydaylanguage(e.g.,“rolling doublesixes”),identify theoutcomesin thesamplespacethatcomposetheevent.

c.Design and usea simulation togeneratefrequenciesforcompound events.For example,userandomdigitsasa simulationtool to approximatetheanswer to the question:If40%ofdonorshavetypeAblood,whatistheprobabilitythatitwilltakeatleast4donorsto find onewithtype A blood?

Diocese of Baton Rouge Mathematics Standards: Grade 7 July, 2017 Page 1