Karen Morrison Karen Press · 2020. 3. 19. · Singapore, São Paulo, Delhi, Mexico City Cambridge...

Mathematical Literacy

Karen Morrison • Karen Press

Study & Master

CAPS

Teacher’s Guide Grade

11SM_Mathslit_11_TG_CAPS_ENG.indd 1 2012/08/06 9:52 AM

MathematicalLiteracy

Study & Master

Karen Morrison • Karen Press

Grade 11Teacher’s Guide

Maths Lit Gr 11 TF.indd 1 2012/08/01 12:43 PM

cambridge university press

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Mexico City

Cambridge University PressThe Water Club, Beach Road, Granger Bay, Cape Town 8005, South Africa

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© Cambridge University Press 2012

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First published 2012

ISBN 978-1-107-38177-3

Editor: Clarice SmutsTypesetter: Anne Evans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Maths Lit Gr 11 TF.indd 2 2012/08/06 9:39 AM

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Section 1 Introduction 5

Section 2 PlanningSuggestedworkschedule 19ProgrammeofAssessment 22ActivitiesintheStudy & Master Learner’s Bookthatmaybeusedastests 23SuggestedassignmentsandinvestigationsintheLearner’sBook 25FormalAssessment:Examinations 26

Section 3 Unit-by-unitDealingwiththedifferentlevelsintheMathematicalLiteracyassessmenttaxonomy 29Workedanswers 41

Section 4 Resources 169A Multiplicationtables 169B Transparencies 172

Section 5 Documents 179

Contents


5S e c t i o n 1 • I n t r o d u c t I o n

IntroduCtIon

seCtIon 1

Study & Master Mathematical LiteracyGrade11isbasedontheCurriculumandAssessmentPolicyStatement(CAPS)issuedbytheDepartmentofBasicEducationinDecember2011.TheCAPSisanamendedversionoftheNationalCurriculumStatementGradesR–12,andreplacesthe2002NationalCurriculumStatementGradesR–9andthe2004NationalCurriculumStatementGrades10–12.

The general aims of the South African curriculum as stated in the CAPS:a) TheNationalCurriculumStatementGradesR–12givesexpressionto

whatareregardedtobeknowledge,skillsandvaluesworthlearning.Itwillensurethatlearnersacquireandapplyknowledgeandskillsinwaysthataremeaningfultotheirlives.Inthisregard,thecurriculumpromotestheideaofgroundingknowledgeinlocalcontexts,whilebeingsensitivetoglobalimperatives.

b) TheNationalCurriculumStatementGradesR–12servesthepurposesof:• equippinglearners,irrespectiveoftheirsocio-economicbackground,

gender,physicalabilityorintellectualability,withtheknowledge,skillsandvaluesnecessaryforself-fulfilment,andmeaningfulparticipationinsocietyascitizensofafreecountry

• providingaccesstohighereducation• facilitatingthetransitionoflearnersfromeducationinstitutionstothe

workplace• providingemployerswithasufficientprofileofalearner’s

competences.c) TheNationalCurriculumStatementGradesR–12isbasedonthe

followingprinciples:• socialtransformation:ensuringthattheeducationalimbalancesof

thepastareredressed,andthatequaleducationalopportunitiesareprovidedforallsectionsofourpopulation

• activeandcriticallearning:encouraginganactiveandcriticalapproachtolearning,ratherthanroteanduncriticallearningofgiventruths

• highknowledgeandhighskills:theminimumstandardsofknowledgeandskillstobeachievedateachgradearespecifiedandsethigh,achievablestandardsinallsubjects

• progression:contentandcontextofeachgradeshowprogressionfromsimpletocomplex

• humanrights,inclusivity,environmentalandsocialjustice:infusingtheprinciplesandpracticesofsocialandenvironmentaljusticeandhumanrightsasdefinedintheConstitutionoftheRepublicofSouthAfrica.

d) TheNationalCurriculumStatementGrades10–12(General)issensitivetoissuesofdiversitysuchaspoverty,inequality,race,gender,language,age,disabilityandotherfactors:• valuingindigenousknowledgesystems:acknowledgingtherich

historyandheritageofthiscountryasimportantcontributorstonurturingthevaluescontainedintheconstitution


6 S e c t i o n 1 • I n t r o d u c t I o n

• credibility,qualityandefficiency:providinganeducationthatiscomparableinquality,breadthanddepthtothoseofothercountries.

e) TheNationalCurriculumStatementGradesR–12aimstoproducelearnerswhoareableto:• identifyandsolveproblemsandmakedecisionsusingcriticaland

creativethinking• workeffectivelyasindividualsandwithothersasmembersofateam• organiseandmanagethemselvesandtheiractivitiesresponsiblyand

effectively• collect,analyse,organiseandcriticallyevaluateinformation• communicateeffectivelyusingvisual,symbolicand/orlanguageskills

invariousmodes• usescienceandtechnologyeffectivelyandcriticallyshowing

responsibilitytowardstheenvironmentandthehealthofothers• demonstrateanunderstandingoftheworldasasetofrelatedsystems

byrecognisingthatproblem-solvingcontextsdonotexistinisolation.f) Inclusivityshouldbecomeacentralpartoftheorganisation,planningand

teachingateachschool.Thiscanonlyhappenifallteachershaveasoundunderstandingofhowtorecogniseandaddressbarrierstolearning,andhowtoplanfordiversity.

time allocation: Grades 10–12TheinstructionaltimeallocationinGrades10–12isasfollows:

subject time allocation per week (hours)

I. HomeLanguage 4,5

II. FirstAdditionalLanguage 4,5

III. MathematicsandMathematicalLiteracy 4,5

IV. Lifeorientation 2

V.threeelectives 12(3×4h)

TheCAPSstatesthat‘theallocatedtimeperweekmaybeutilisedonlyfortheminimumrequiredNCSsubjectsasspecifiedabove,andmaynotbeusedforanyadditionalsubjectsaddedtothelistofminimumsubjects.Shouldalearnerwishtoofferadditionalsubjects,additionaltimemustbeallocatedfortheofferingofthesesubjects’.

What is Mathematical Literacy?Mathematicalliteracycanbedefinedas‘anindividual’scapacitytousemathematicsasafullyfunctioningmemberofasociety’(BallandStacey,UniversityofMelbourne).

TheCAPSdocumentidentifiesthefollowingfivekeyelementsofthesubjectMathematicalLiteracy:• theuseofelementarymathematicalcontent• real-lifecontexts• solvingfamiliarandunfamiliarproblems• decision-makingandcommunication• theuseofintegratedcontentand/orskillsinsolvingproblems.



Inotherwords,thesubjectMathematicalLiteracyaimstoproducelearnerswhohave:• asenseofself-worthandwhoareabletocontrolaspectsoftheirlife

relatedtomathematicalunderstanding• theskillsandunderstandingtoplayaresponsibleroleinoursociety• theabilitytocalculate,estimateandusemeasuringinstruments• developedstrategiesanddecision-makingskillsthatallowthemtobe

innovativeandflexibleintheirapproachtosolvingproblems• theabilitytocommunicateresultsandexplanationsandtheskillstowork

effectivelyandcollaborativelywithothers• theabilitytodrawsensibleconclusionsfrominformationpresented

graphicallyandapplyskillsindata-handlingandinterpretation.

What does it mean to be mathematically literate?Mathematicalliteracyismorethantheabilitytodobasicarithmetic.Italsoincludes:• workingconfidentlyandcompetentlywithnumbers,measuresand

diagramsinarangeofrealandrealisticcontexts• choosingandapplyingarangeoftechniquesandskills,includingtheuse

oftechnology(calculatorsandcomputers)• understandinghownumbersandmeasurementsarecollected,organised

anddisplayedintables,graphsandotherforms• developingandusingdecision-makingandproblem-solvingstrategiesthat

suitboththeproblemandthecontext• communicatingresultsandsolutionsinappropriateways.

Theflowdiagrambelowbreaksdownthestepsthatamathematicallynumeratepersonwillfollowanddetailswhatisinvolvedineachstep.

• dailylife– decisions– school– home

• community• finance

– money

• findinformation• interpret

information• actongiven

information• communicate

information

• number• shapeandspace• patterns• data• probability• measurement

• numbersandsymbols

• pictures• shapes• formulae• tables• graphs• maps• words/text

A mathematically literate person is able to …

Solve problems in real contexts

by deciding how to respond

to information involving

mathematical ideas

represented in different ways

Mathematics and Mathematical Literacy are not the sameMathematicsisanabstractsubjectthatisoftentheoreticalandthatrequiresspecificlanguage,skillsandmethodstodealwithsubject-specificproblems.

MathematicalLiteracytakesmathematicalknowledgeandskillsandappliesthemtoeverydaysituationsandproblems.MathematicalLiteracyiscontextualanduseful.Whenlearnerstakeprocessesandideasfrommathematicsandapplythemincontextsthatarespecifictotheirownlives,suchaschoosingacellphonecontract,theyaremathematicallyliterate.ThefollowingtableshowssomedifferencesbetweenMathematicsandMathematicalLiteracy.Italsoshowshowthecontentandcontextareinterconnectedwhenyouaredevelopingmathematicalliteracy.



Mathematical Literacy Mathematics

Task and context Content

doublingarecipe EquivalentfractionsMultiplyingandaddingfractions

readinginstrumentssuchasathermometer,raingaugeorbarometer

Measurementandunitsunderstandingascale

decidingwhichcellphonecontractisthemostaffordable

EquationsintwovariablesthatrepresentarelationshipSolvingsimultaneousequations(graphicallyoralgebraically)

Administeringmedicine readingatableofvaluestofindamountsthatcorrespondtogivenconditions(suchastheageormassofthepatient)ratioandcalculation

Mixingplaster(forbuilding) ratioandproportionMeasuringamountinunitsforvolumeandmass

Mixingsolutions(fertilisersorpesticides)

calculatingareaandusingratioandproportiontomixnecessaryamounts

Planningatrip time–distance–speedrelationshipsusingratioandproportionoralgebraBudgetingforpetrol,meals,accommodationandotherexpensescalculatingwithtime(non-decimalamounts)

Financial literacyFinancialliteracyisalargepartofmathematicalliteracyandithasbecomeincreasinglyimportantinmodernlife.Oursocietyneedscitizenswhoareabletounderstandthevalueofmoneyandmanagemoneyinappropriateandresponsibleways.Whenlearnersleaveschoolandentertheworldofwork,theywillhavetoengageactivelywithcomplexandspecialisedfinancialservicesjusttomanagetheirownmoneyaffairs.Inaddition,theywillneedtobeawareofconsumerissuesandmakeplansfortheirlonger-termfinancialwellbeing.

Inrecenttimestherehavebeenmanychangesinoursocietyincluding:• technologicaldevelopments(autobanking,internetbanking,chipandpin

cardservices)• increasedcompetitioninfinancialmarkets(morebankswantyourmoney)• ariseinquestionablefinancialpractices,includingunethicalloans,unfair

interestratesandHPtermsthatincludelarge‘balloon’payments• changesinpersonalfinances,includingrisinghouseholddebts• changesindemographics(morepoorerhouseholdswhomaynotuse

formalbankingsystems,moreyoungpeoplehavingtomakefinancialdecisionswithouttheguidanceofolderfamilymembers)

• increasedconsumerresponsibilityasyoungerpeoplehaveaccesstobankingservicesanddebitandcreditcards,whichinturnleadstoincreasedchanceofbeingavictimoffraud.

Theseandotherchangeswhicharelikelytooccurinthefuturemakeitevenmoreimportantthatweproducelearnerswhoarefinanciallyliterate.

our approach to teaching Mathematical LiteracyOurapproachisthatlearnersdevelopunderstandingbymakingconnectionsbetweenwhattheyarelearningandtheirownlives.



Hereisasummaryofthestepsinthisprocessandhowtheyaredevelopedinthecourse:Step1: Learningbasicskills(forexample,howtocarryoutoperationswith

fractions).Step2: Practisingwhatyouhavelearnt(forexample,namingfractionsofa

whole,addingsimplefractions).Step3: Usingandapplyinglearningineverydaycontexts(forexample,

dividinganamountofmoneyintodifferentfractions,drawingpiegraphsusingfractions).

Step4: Understandingthelargersocialandculturalusesofspecificmathematics(forexample,discussingthewaysinwhichdifferentsocietieshaveusedfractionsandhowEgyptianfractionsdifferfromthoseusedtoday).

Step5: Criticallyengagingwithwhatyouhavelearnt(forexample,examininghowfractionsandpercentagescanbeusedinthemediatomisleadconsumers).

Thiscourseoffersacarefullyplannedandcontextualisedapproachtothesubjectthatallowsteachersto:• helplearnersseehowmathematicscanbevaluableandusefulintheir

lives,developconfidenceandasenseofpersonalachievementandencourageongoinginterestandawillingnesstofindcreativesolutionstoproblems

• developskills,concepts,understandingsandattitudesthathelplearnersdealwiththemathematicalcontextstheyhavetomanageintheirlives

• ensurethelearnersdevelopandemployarangeofproblem-solvingmethodsandgrowtheirabilitytothinkandreasonlogicallyandsensibly

• makesurelearnershavethelevelsofmathematicalliteracytheyneedtocopeinanincreasinglytechnology-reliantandinformation-richsociety

• equiplearnerswiththetoolsandskillstheywillneedanduseastheyentertheworldofwork

• givelearnerstheskillsandconfidencetousetheirownlanguageandwaysofexpressingmathematicalideasandalsogrowtheirabilitytomakesenseofmathematicalideaspresentedtotheminvariousformatsandways.

Interpreting and communicating answers and calculationsStudy & Master Mathematical Literacyoffersacompletecoursethatprovideslearnerswiththetoolsandopportunitiesto:• constructtheirownknowledgeandunderstandingratherthanpassively

listeningtotheteacher(transmittedorreceivedknowledge)bysolvingreal-lifeproblems,usingrealdocumentsandinvestigatingrealissues,ontheirown,withapartnerandingroups

• integrateandconnecttheirlearning,includingconnectingtopics,content,proceduresandideas,aswellasactivelypromotingconnectionstotheirownlifeexperiencesandideasbyapplyingskillsindifferentcontexts,integratingwhattheyhavelearntinonecontextwithwhattheyaredoinginothers(throughmarginnotes)

• solveauthentic,real-life(ratherthancontrived)problems,whicharematchedtothecontentofthecoursebyusingrealdocuments,publishedcasestudiesandstatisticsfromtherealworld

• developmathematicalthinking,includingcommunicationandrepresentationofanswersandideas,andmovingtowardsmoreabstractandcreativethinkingbyworkingindifferentways,findingtheirownmethodsofrecordingtheirthinking,andusingtheirownlanguage



togetherwiththelanguageandnotationofmathematicswhereappropriatetomaketheircommunicationasclearandsimpleaspossible.

TheCAPStopicinterpretingandcommunicatinganswersandcalculationsisbuiltintothecourseandappliesacrossboththebasicskillsandapplicationtopics.Astheyworkthroughthematerial,learnerswillbeexpectedto:• makesenseoftheirownstrategiesandsolutions• sharetheirobservationsandsolutionsandunderstandotherlearners’

observationsandsolutions.

Making sense of their own strategies and solutionsThehabitofestimate–solve–checkisdevelopedandreinforcedthroughoutthecourse.Learnersareexpectedtoestimatebeforetheytrytofindsolutionsandchecktheirsolutionsagainsttheirestimatestomakesuretheyaresensibleandcorrect.Strategiesfordoingthisarepresentedintheexamplesandcasestudies,andarereinforcedaslearnersworkthroughtheapplicationtopicsinallfourterms.

Inaddition,learnersareexpectedtogiveexplanations,justifyandexplaintheirmethodsandcommunicatetheirfindingsandanswerstoothers,bothformallyandinformallyastheyworkthroughthecourse.

sharing observations and solutions and understanding others’ observations and solutionsThroughtakingpartinpair,groupandclassdiscussions,learnerswillfindthatthewaysinwhichtheyhavecommunicatedtheirworkingsandsolutionsarenotalwayscleartoothers.Discussionswithothers,andseeinganddiscussingmodelledsolutionsintheirbooks(andinthisteacher’sguide)willhelpthemseethatbetteruseofmathematicalconventionsandsymbols,aswellasmoresystematicpresentationofresults,willimprovetheircommunicationofideasandreduceambiguityandconfusion.Thiswillhelpthemtobetterunderstandsolutionsandideaspresentedtothembyothers.

Inaddition,Study & Master Mathematical Literacyaimstopointoutveryclearlytolearnersthatthereareseveralwaystoapproachmathematicalproblemsandencouragethemtobecreativewhentheyaredoingandusingmathematicsineverydaycontexts.

Your role as the teacherTeachingMathematicalLiteracyeffectivelymeansfocusingonprocessskillsincontextratherthanonstraightmathematicalcontent.Thismeansthatyourclassroompracticewillrevolvearound:• problem-solving,reasoninganddecision-making• communicatingandrepresentingideas• identifyingrelevanceandmakingconnections.

TeachingMathematicalLiteracyeffectivelymeansthatyoucannotjustusethetextbookandgetlearnerstomemorisefacts,learnrulesfordoingthingsandthenwriteformaltests.EffectiveteachersofMathematicalLiteracyneedtoapproachthesubjectfromareal-lifecontextualangle,wherethemathematicsisderivedfromactualsituationsorrealisticmodelsandlearnerscanworkthroughactivities,investigationsandproblemsintheirownways.



Making sure all learners are includedManylearnersfailtoreachtheirpotentialbecausetheydonotseehowmathematicalideasarerelevanttotheirlivesandbecausetheyarenotencouragedtoconnectwhattheyarelearningaboutmathematicstotheirexistingexperiences,skillsandknowledge.Thisisaparticularproblemforlearnerswhoseethecontextsinthetextbookasirrelevantorinappropriateintheirownsituations.

InMathematicalLiteracy,contextisthedriverforlearning.Whenreal-lifesituationsareused,thelearningbecomesrelevantandtheeducationalvalueoftheexperienceisincreased.However,contextsareuniqueandyoumayfindthatsomeofthecontextsofferedinthecoursearenotrelevantorappropriateforsomeofthelearners.Inthesecases,youmayneedtoadaptthegivenactivitiestobettersuityourownsituation.

TheCAPSdocumentdetailswhatthelearnersneedtolearnandsuggestscontextsforteaching.However,youcanadaptthistomeetspecificneedsbyaskingyourselfwhatthelearnersalreadydoorareinterestedin.Onceyouhaveestablishedthis,youcanworkoutwhattoteachthembyaskingwhatthelearnerhastoknowtobeabletodothethingtheyareinterestedin.

InGrade11thefocusisonhousehold,community,workplaceandsmallbusinesssituations,andontheproblemsthatindividualscouldhavetodealwithinanyofthesecontexts.LearnersbuildontheinformationandskillstheydevelopedinGrade10,andcontinuetoapplythesetohouseholdandcommunitysituationssuchasthefollowing,withsomeincreaseinthecomplexityoftheproblemstheymayhavetodealwith:• householdbudgetingandfinancialplanning• time-keepingatsportingevents• relatingspeedtopetrolconsumption• householdutilitybillsandsteppedtariffs• VATcalculations• compoundinterestonloansandinvestments• bankfeepackages• electronicbanking• currencyexchangecalculations• thebuyingpowerofdifferentcurrencies• budgetingforaschoolmealsprogramme• relatingbodymasstofoodmassandmedicinedosage• monitoringhouseholdwateruse• plantingschedulesrelatedtotemperature• interpretingdetailedmaps• plansforhousesandothersmallbuildings• small-scaleconstructionprojects• workingwithassemblydiagrams• understandingandusingprobabilitycalculations• critiquingpredictions• differentwaystopresentandinterpretstatistics.

Thenewfocusonworkplaceandsmallbusinesssituationsexposeslearnerstoplanning,problem-solvingandfinancialmonitoringinsightsandskillstheyneedtodeveloptodealwithreal-lifeexperiencessuchas:• readingquotationsfrombusinesses• budgetingbeforegivingquotationstocustomers



• preparinginvoicesandreceipts• calculatingcostpriceandsettingsellingprice• budgetingforprojectedexpenditure• budgetingforinflation• readingpayslips• travelallowanceclaims• understandingUIF.

ItisalsoexpectedthatinGrade11learnerswillactivelyresearchrelevantinformationtosolveproblemsusinglocallyavailabledataandresources–forexample,findingoutwhatbuildingsuppliesreallycostatlocalbuildingsuppliers’outlets;researchingthecurrentbankfees,loantermsandotheroptionsavailableatbanksthattheyandtheirfamiliesuse;usingtherealpricesoflocallyavailablegoodsandservicesasabasisforplanningaschoolmealsprogramme.

Youcanhelplearnerstoapplytheirmathematicalliteracyskillstoabroadrangeofcontextssimplybybringingnewspaperarticlesondiversetopicstoclassfordiscussionandanalysis.Learnersneedtobeabletoapplytheskillstheyaredevelopingintheclassroomtoageneralunderstandingofthesocial,economicandpoliticalinformationthatsurroundsthemineverydaylife.Theycangaintheconfidencetodothisbypayingdetailedattentiontoexamplesofdailynewsreportsthatincludegraphs,statisticsandfinancialinformation.Forexample,thegroupofmapsontheleftthatappearedinaSundaynewspaperinearly2012.Itcontainsinformationthatlearnerscouldfindinteresting,butthattheymightnotbothertoreadbecauseitispresentedin‘mathematical’language.Asklearnerstofindtheirownexamplesofsuchitemsinnewspapers,ontheinternetandfromothersources,andspendsomeclasstimeexploringanddiscussingtheinformationtheycontain.

YouwillfindothersuggestionsforalternativecontextsinthisTeacher’sGuideandintheCAPSdocumentitself.

Overcoming ‘maths anxiety’ManyofthelearnerswhooptedforMathematicalLiteracyinGrade10willhaveexperiencedsomeformof‘mathsanxiety’.Theymaybelievetheyarenotcapableofdoingmathsorthatitistoodifficultforthem.Or,theymayhaveexperiencedfailureinmathematicsclassesandthismightmakethemfeelanxiousaboutanythingtodowithmaths.Ortheymayjusthaveinternalisedattitudesandperceptionsaboutmathematicsthatmakeitdifficultforthemtoseehowtheywilleverbeabletosucceedatanythingmathematical–theseincludeperceptionssuchas‘girlscan’tdomaths’and‘myfatherwasnogoodatmathsandneitheramI’.

Central Region*

KwaZulu-Natal

Gauteng

Eastern Cape

Northern region**

Western Cape

64,6%of people in the province

report for treatment citing alcohol as their primary

substance of abuse

73,1%of young people (under

20 years) report for treatment citing alcohol

as their primarysubstance of abuse

73,1%

23,3%

44,4%

13,2%

44,1%

6,3%

35,7%

7,7%

29,8%

6,9%

total alcohol abuse rate alcohol abuse rateof people youngerthan 2010 percentage points

Alcohol is the most abused substance in themajority of privinces. The exception is theWestern Cape, where tik is the drug ofchoice and Mpumalanga and Limpopo, where cannabis is abused most frequently

Alcohol abuse in South Africa

*Free State, Northern Cape and North West** Mpumalanga and LimpopoSacendu data only reflect substance use among people who have managed to access available treatment services and is not representative of substance abuse trends in the general populationSource: 2010 Monitoring Alcohol and Drug Abuse Trends in South Africa report, compiled by the South African Community Epidemiology Network on Drug Use (Sacendu)



OneofyourrolesasateacherofMathematicalLiteracyislikelytobehelpingtoreducethelevelsofanxietythatlearnersfeelandencouragingthemtoseethattheyalreadycarryouttasksquiteeasilyineverydaylifethatrequirethemtoapplymathematicalthinking.Usingcontextrathercontentisoneofthefirststepstohelpinglearnersconsiderandtalkabouttheinformalmathematicstheyusewithoutreallythinkingaboutit,andthisinturncanempowerthemandboosttheirconfidenceandmotivation.

Therearesomethingsthatyoucansayandsomebehaviourthatyoucanencouragetohelplearnerstoovercomeanxietyaboutmathematics:• Don’tgiveupimmediatelyifyoudon’tunderstandsomething.• Itdoesnotmatterifyougetthewronganswer.• Youcanworkslowly–wearenotinarace.• Ifyougetstuckononepart,moveonandcomebacktoitlater.• Askanotherlearnerforhelp.• Don’timmediatelythinkyouarewrong.• Askforanotherexplanationifyoudon’tunderstandatfirst.• Workinagrouptosolvetheproblem.• Makesureyoucanexplainhowandwhyyougottheanswer.• Listentothequestionsthatotherlearnersaskbecauseitmightbeabout

somethingyoudon’tunderstandeither.• Makesureyouunderstandtheconceptyouareworkingonbeforeyou

moveon.• RefertothebasicskillssectionatthebackoftheStudy & Master

Learner’s Bookwhenyouforgethowtodosomething.

Using resources to enhance learningCalculatorsThecalculatorisanimportantlearningtoolthatlearnerscanusetodevelop,exploreandconsolidatenewideas.Calculatorsareveryusefulwhenyouwantlearnerstoinvestigateanddiscovernumberfactsandpatternsandmakegeneralisations.Usingacalculatorallowsthelearnerstofocusonfindingwaysofsolvingaproblemratherthanonroutinemechanicaloperationsthatcandetractfromtherealpointoftheproblem,particularlyinlearnerswhoarenotgoodatmathematicsandwholackconfidenceintheirownabilities.

Learnersshouldhaveaccesstoasimplecalculatorandbeencouragedtouseitforalltheactivitiesinthiscourse.

Measuring equipmentThereisnodoubtthattheuseofrealtoolsandapparatuscanhelplearnersdevelopandclarifytheirunderstandingsofmathematics,particularlyintheareasofmeasurement.Usingtoolsandmeasuringinstrumentsallowsthelearnerstodevelopabstractideasandformconceptsfrompracticalexperience.ThisisjustasimportantinGrade11asinlowergrades.

Navigating the textbookWehaveorganisedthecontentofthecoursetofollowthesequenceoftopicsectionssetoutintheCAPS‘SuggestedworkscheduleforGrade11’.Thefirstsectionofthecoursefocusesonthebasicskillstopicpatterns,relationshipsandrepresentations.Thereafter,thelearnersworktermbytermthroughsectionsoftheApplicationstopicsassequencedinthesuggestedworkschedule.



Tohelplearnerswhoarenotsureaboutthecalculationmethods,formulaeandothermathematicalmethodsthatwerecoveredinGrade10,thismaterialisincludedintheStudy & Master Learner’s BookGrade11asaskillsreferencesection.LearnersaredirectedtorelevantpartsofthissectioninshoulderboxesplacedthroughouttheapplicationssectionsoftheLearner’sBook,wheretheywillfindexplanationsandexamplesoftechniquestheyneedtouseinaspecificproblem-solvingcontext.

Theseconceptsyoulearntlastyeararecoveredonpages497to537intheBasicsskillssection.

Theexamplesusedinthebasicskillssectionareinterestingsourcesofinformationaboutcontextualtopicsofinteresttolearners,suchas:• smokinghabitsofsoccerplayersinanationalteam• bacteriainpotatosalad• thespreadofgossip.

3. DebbiewassecretlyinlovewithJabu.ShetoldherfriendMinkithisinconfidence.However,withinthree-quartersofanhourthewholeschoolknew.Minkiinsistedthatsheonlytoldtwopeople.DebbiedrewthisgraphtoshowMinkihowproblematicthatwas.a. Whatdoesthe

graphshow?b. Completethistableofvaluesbasedonthegraph.

time (minutes) 5 10 15 20 25 30 35 40 45

number of people

c. Whattypeofrelationshipisthis?d. Whatistheconstantratiobetweentheterms?e. Ifthenewscontinuedtospreadatthesamerate,howmany

peoplewouldknowDebbiewasinlovewithJabuafteranhour?

The spread of gossip

0

100

200

300

400

500

600

0 10 20 30 40 50Time (min.)

Num

ber o

f peo

ple

Therelevanceofthetopicswillencouragelearnerstoreadthe‘mathematical’aspectsofthegraphsandchartswithcloseattention,therebystrengtheningtheirskillsatinterpretingdatapresentedinthisform.Someofthecontentinthissection,suchasmethodsfordoingbreak-evenanalysisandcalculatingbodymassindex(BMI),isinvestigatedinmoredetailintheapplicationtopicsthatfollow.

Theapplicationtopicsusereal-lifeSouthAfricanaswellasinternationalexamplesasfaraspossible,toprovideappealingandinterestingcontextsthatwillinterestandengageGrade11learners.Informationispresentedinmanydifferentforms,sothatlearnersbecomefamiliarwiththemanywaysinwhichcontentthattheyneedtounderstandcanbestructured.YoushouldsupplementtheexamplesintheLearner’sBookwithasmanylocallyrelevantexamplesas



possible(suchasaccountsfromlocalshopsandyourlocalmunicipalityandmapsoftheregion,cityorneighbourhoodwhereyoulive).

ExamplesofinformationindifferentformsintheLearner’sBook:

Information in graphs and charts

Both employed

Who’s still got a job?

Both unemployed

0 20Percentage couples with dependants

40 60

Husband employedWife unemployed

Wife employedHusband unemployed

Information on diagrams

900 900 900610 730 850 970 1090 1210 1450

2090

2120

2111 94

4

No sill

Openinwards

Openoutwards

DH2090 DH2120 DH2111 WW610 WW730 WW850 WW970 WW1090 WW1210 WW1450

Information on documents

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UK R0,70 R0,60 R0,65 R0,60USA R0,70 R0,60 R0,65 R0,60Germany R1,30 R1,20 R1,00 R0,90France R0,90 R0,80 R0,90 R0,80Portugal R1,14 R1,04 R0,90 R0,80Zimbabwe R1,78 R1,68 R1,65 R1,55Pakistan R2,23 R2,13 R1,77 R1,66Israel R1,35 R1,25 R1,22 R1,12China R1,45 R1,35 R1,40 R1,30Australia R0,90 R0,80 R0,90 R0,80Canada R0,80 R0,70 R0,80 R0,70

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• Any transactions not in the electronic debit transaction bundle, will be charged according to Pay as you transact fees.

Student Achiever Pricing for 2011As a student, you live life to the full and need a bank account that matches your hectic lifestyle. That is why Standard Bank designed a transactional account specifically to meet the banking needs of senior scholars and full-time tertiary students between the ages of 16–26, making banking more flexible and more affordable for you!

What do you get for FREE per month?• Your first five electronic debit transactions2

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How does it help your lifestyle?Because you are an individual, it is importanto to have CHOICE, the choice to decide how much you transact a month and therefore how much you pay for banking per month. This is why on Student Achiever your electronicdebit transactions2 are grouped into bundles, based on how much you transact in any particular month.

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Number of electronic debit transactions2 per month0–5 Free6–15 R20

16–25 an additional R1026–35 an additional R1036 + Pay as you transact – personal

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Cross‑referencingAslearnersworkthroughthecourse,theyaredirectedtootherplacesinthebookbylinkboxesintheshoulder.Theselinkstellthelearnerswheretofindthemathsskilltheyneedtoapplytosolveaproblem.Theseboxeslinktothebasicskillsreferencesectionandtoplacesintheapplicationtopicswhereaparticularskillwastaughtorused.

representing dataGraphsareaveryusefulwaytorepresentdatabecausetheyallowyoutoseepatternsandtrendsinthedataataglance.

Lastyearyoudrewbargraphs,linegraphsandpiechartstorepresentsinglesetsofdata.InTerm1thisyearyouworkedwithdoublebarandlinegraphsthatshowtwosetsofdataatthesametime.Thistermyouwillalsolearnhowtodrawastackedbargraphandtodrawascattergraphanduseittoworkoutwhetherthereisaconnectionbetweentwosetsofdata.

Youshouldalreadyknowhowtodrawabargraph,linegraphandpiechart.Ifyouhaveforgottenhowtodothis,refertopages524and525.


19S e c t i o n 2 • P L A n n I n g

PLannInG

seCtIon 2

Suggested work scheduleBelowisaworkschedulethatoutlinesestimatedtimeallocationspertopicaswellasaparticularsequenceofteaching.ThisworkschedulefollowsexactlytherecommendationsgivenintheCAPSdocument.

term 1

Week CaPs topic unit Pages

1 Patterns,relationshipsandrepresentations

unit1Makingsenseofgraphsthattellastory

2–8


unit2Patternsandrelationships

9–12

unit3representingrelationshipsintables,equationsandgraphs

13–16


unit4Workingwithtworelationshipsatthesametime

17–24

4 Measurement(conversionsandtime)

unit5conversions 28–45

5 Measurement(conversionsandtime)

unit6Measuringtime 46–68

6 Finance(Financialdocuments;tariffsystems;Income,expenditure,profit/loss,income-and-expenditurestatementandbudgets;costpriceandsellingprice;Break-evenanalysis)

unit7Financialdocumentsathome

75–86

unit8Financialdocumentsatwork

87–107


unit8Financialdocumentsatwork(cont.)

87–107

unit9tariffs 108–126


unit10Income-and-expenditurestatementsandbudgets

127–151


20 S e c t i o n 2 • P L A n n I n g


unit11costpriceandsellingprice

152–167

unit12Break-evenanalysis 168–177

AssessmentAssignment/Investigationcontroltest(MeasurementandFinance,integratedwithnumbersandPatternsconcepts)

term 2


1 Finance(Interest;Banking;Inflation)

unit1Interestandinterestrates

185–202


unit2Banking 203–227


unit3Bankloansandinvestments

228–244


unit4Inflation 245–256

5 Measurement(Measuringlength,measuringweight,measuringvolume,measuringtemperature)

unit5Measuringlengthanddistance

261–273

unit6Measuringmass 274–292

6 Measurement(Measuringlength,measuringweight,measuringvolume,measuringtemperature)

unit7Measuringvolume 293–309

unit8Measuringtemperature 310–316

7 Maps,plansandotherrepresentationsoftheworld(ScaleandMapwork)

unit9Scale 322–326

unit10Maps 327–345

8 Maps,plansandotherrepresentationsoftheworld(ScaleandMapwork)

unit10Maps(cont.) 327–345

9 revision

AssessmentAssignment/InvestigationMid-yearexaminations(2papers;11_ 2hourseach;75markseach)(Finance;Measurement;andMaps;integratedwithnumbersandPatternsconcepts)



term 3


1 Measurement(Perimeter,areaandvolume)

unit1Perimeter,areaandvolume

350–375


unit1Perimeter,areaandvolume(cont.)

350–375


unit1Perimeter,areaandvolume(cont.)

350–375

4 Maps,plansandotherrepresentationsofthephysicalworld(ModelsandPlans)

unit2Plans(instructionsandassemblydiagrams)

379–384


unit3Floorandelevationplans 385–393


unit4usingmodelstoinvestigateshapeandspace

394–399

7 Finance(taxation) unit5taxation 404–413

8 Probability unit6Probability 416–434

9 Probability unit6Probability(cont.) 416–434

AssessmentAssignment/Investigationcontroltest(Measurement;ModelsandPlans;Finance;andProbability;integratedwithnumbersandPatternsconcepts)

term 4


1 Finance(Exchangerates) unit1Exchangerates 440–452

2 datahandling unit2datahandling 456–493

3 datahandling unit2datahandling(cont.) 456–493



6 revision

AssessmentAssignment/InvestigationEnd-of-yearexaminations(2papers;2hourseach;100markseach)(coveringalltopicsinthecurriculum)



Programme of AssessmentTheProgrammeofAssessmentforGrade11MathematicalLiteracyshouldconsistofeightformalassessmenttasksthatareassessedinternally.Sevenofthesetasksareundertakenandassessedduringtheschoolyear,andtheycomprise25%ofthetotalmarkforMathematicalLiteracy.Theeighthtaskistheend-of-yearexamination,whichcomprises75%ofthetotalmark.

TheProgrammeofAssessmentmustincludeassignments,investigationsandcontroltests,andtheseshouldbeplannedsothatalltopicsandsectionsoftheGrade11courseareaddressedthroughouttheyear.Itissuggestedthatlearnersundertakeatleastoneassignmentorinvestigationineachterm(so,fourintotal),controltestsinTerms1and3,anexaminationinTerm2,andthefinalexaminationinTerm4.

Activitiesthatcanbeusedbyteachersforcontroltests,assignmentsandinvestigationshavebeenincludedinStudy & Master Mathematical Literacy.

Control testsIncontroltests,learnersaregivenalltheinformationrequiredtocompleteatask.Thesetestsarecarriedoutunderexaminationconditions.Theywillhelppreparelearnersfortheirfinalexamination.TheStudy & Master Learner’s Bookincludesactivitiesthatrequirelearnerstoapplyamethodthatwastaughtinaunittoanewsetofinformation.Theseactivitiescanbeusedaspartofacontroltestorrepeatedforthetestwithnewinformationsuppliedbytheteacher.

ExampleActivity3.1inTerm2giveslearnerspracticeincalculatingthecostofaloan.

3.1 Practise calculating the real costs of a loan

1. WhatistherealcostofaloanofR6000atasimpleinterestrateof3,5%p.a.foreachperiodoftime?a. oneyearb. 18months

2. a. WhatistherealcostofaloanofR780atacompoundinterestrateof4,12%p.a.,repaidafterfouryears?

b. Whatistherealcostofthesameloan,ifhalftheloanisrepaidaftertwoyearsandthebalanceisrepaidafteranothertwoyears?

3. Whichloanhasthehigherrealcost:R2500borrowedat8,7%simpleinterestp.a.forthreeyears,orR2500borrowedat5,2%compoundinterestp.a.forthreeyears?

4. TonyborrowsR5800at4,25%compoundinterestp.a.andagreestorepaythemoneyattheendoffiveyears.Howmuchmoneywillhesaveifherepaystheloanafter36months?

Youcansetsimilarquestionsasatestusingnewamountsofmoneyandpercentagesofinterest.

ThetablethatfollowsindicateswhichLearner’sBookactivitiescanbeusedastestsinTerm1andTerm3.



Activities in Study & Master Learner’s Book that may be used as tests

Topic Section Activities that can be used or adapted for control tests

Learner’s Book page reference

Term 1

MeasurementandFinance,integratedwithnumbersandPatternsconcepts

readingtimeformats

term1:6.1readingdifferenttimeformats 48

time,speedanddistance

term1:6.8calculationswithtime,speedanddistance

67

tariffs term1:9.1readingandcalculatingtariffs 113

Income-and-expenditurestatements

term1:10.3calculatingandcomparingchangesinincome-and-expenditurestatements

135

Budgets term1:10.4calculationswithpersonalbudgets 147

Term 3

Measurement,ModelsandPlans,FinanceandProbability,integratedwithnumbersandPatternsconcepts

Interest term2:1.6usinggraphsofinterestgrowth 202

Inflation term2:4.1calculatinginflation-relatedpriceincreases

249

taxation term3:5.1VAtcalculationsterm3:5.2calculatinguIFcontributions

406412

Measurement:LengthMassVolumetemperature

term2:5.2readingodometersandtripmeters 263

term2:5.5calculatingcostofmaterials 272

term2:6.3calculatingquantitiesoffoodrelatedtobodymass

280

term2:7.1calculatingvolumesforpracticalprojects 297

term2:7.4calculatingpetrolconsumption 305

term2:8.1readingandconvertingtemperatureinformation

313

Perimeter,areaandvolume

term3:1.3usingformulaetocalculatetheperimeterandareaofcompositeshapes

357

term3:1.4usingformulaetocalculatesurfaceareaandvolume

363

Workingwithscale

term2:9.3usingrealdistancestocalculatemeasurementsonaplan

326

Plans term3:2.3readingandmakingsenseofinstructiondiagrams

382

term3:3.2Findingthesizeofitemsshownonaplan 386

Models term3:4.3Workingouthowmuchwoodyouneed 397

Probability term3:6.5calculatingexperimentalprobability 422

term3:6.10Interpretingpredictionsusedinthemedia

431



assignmentsAssignmentsarestructuredtasksthatgivelearnersclearguidelinesabouthowtocarryoutthetask,andwherethereisawell-definedsolutiontothetask.Thecontentandcontextofanassignmentshouldbebasedonworkalreadycoveredinthecourse,anditshouldallowlearnerstoapplyamethodorapproachthattheyhavealreadylearnedtouse.ThereareactivitiesthroughouttheStudy & Master Learner’s Bookthatcanbeusedasassignmentsforassessmentpurposes.Theyareindicatedinthetablethatfollows.

InvestigationsInvestigationsaretasksinwhichlearnersgothroughaseriesofstepsinvolvingguideddiscoverytoachieveanunderstandingofaconceptand/oramethod,andapplytheirmathematicalliteracyskillsinnewsituations.Animportantaspectofthistypeoftaskisthatlearnersshoulduseinsightandunderstandingofthecontexttomakeanappropriatedecisionbasedontheirinvestigativework.ThereareextendedinvestigativeactivitiesthroughouttheStudy & Master Learner’s Bookthatcanbeusedforassessmentpurposes.Theyareindicatedinthetablethatfollows.

Notethatanassignmentorinvestigationmaycovermorethanonetopicorsection,anditcanbeusedtoassessconceptsandmethodsthathavebeenlearntinboth/allthesesections.Forexample,aninvestigationthatinvolvescomparingcostsofdifferentcellphoneoptionscanbeusedtoassesslearners’understandingandskillsrelatingtoPatterns,relationshipsandrepresentations(workingwithtwoormorerelationships)andFinance(tariffsystems).



suggested assignments and investigations in the Learner’s Book

Topic Section Assessment type and name Learner Book page reference

Term 1

Patterns,relationshipsandrepresentations

representationsofrelationshipsintables,graphsandequations

4.4 Assignment:Makingdecisionsusinggraphs 24

Workingwithtwoormorerelationships

4.2 Investigation:comparingcostsofsolarandnuclearenergy

20

Finance tariffsystems 9.4 Investigation:Whichwatertariffisbetter? 125

Break-evenanalysis

12.3 Assignment:Break-evenanalysisforat-shirtbusiness

177

Measurement time 6.6 Assignment:readandinterpretatidetable 61

Term 2

Finance Interest 1.5 Investigation:compareinterestoptionsatdifferentbanks

199

Banking,loansandinvestments

2.3 Assignment:comparestudentfeepackagesofferedbydifferentbanks

218

Inflation 4.3 Investigation:Howdoesinflationaffectpropertyprices?

256

Measurement Measuringvolume

7.7 Assignment:calculatetotalwaterrun-offinasettlement

309

Term 3

Finance taxation 5.3 Assignment:Anemployer’sbudgetforuIFcontributions

413

Measurement Measuringmass(weight)

6.5 Investigation:collectbodymassdataanddetermineBMIweightstatus

288

Perimeter,areaandvolume

7.3 Assignment:calculateyourhousehold’sbasicwaterneeds

301

Maps,plansandotherrepresentationsofthephysicalworld

Plans,conversions,area,finance

4.2 Assignment:Makeacylindricalpackage 395

Models,surfacearea,volume

4.4 Investigation:Boxesandhowmuchtheyhold

397

Probability Allsections 6.4 Investigation:Howoftendoyouthrowadouble?

420

6.8 Investigation:Workingwithweatherpredictions

426

Term 4

datahandling Allsections 6.5 Investigation:collectbodymassdataanddetermineBMIweightstatus

288



Formal assessment: Examinations InGrade11,examinationpapersshouldbeset,markedandmoderatedinternallyunlessprovincialeducationdepartmentsinstructotherwise.

time and mark allocationGrade11examinationsshouldtakeplaceattheendofTerm2andtheendofTerm4.Foreachexamination,learnerswillwritetwopapers.Thepapersassessthesamecontentindifferentwaysandthecognitivedemandsofeachpaperdiffer(accordingtothelevelsoftheassessmenttaxonomy).Thetimeandmarkallocationsforeachpaperaregiveninthetable.

June examinationsend of term 2

Paper111_ 2hours75marks

Paper211_ 2hours75marks

november examinationsend of term 4

Paper12hours100marks

Paper22hours100marks

the main differences between the two papers

Paper 1 Paper 2

• Itassessesbasicskillsinfamiliarcontexts.

• Itassessestheabilitytoapplyconceptsinfamiliarandunfamiliarcontexts.

• Questionsaremainlyatlevels1and2(60%ofmarksatlevel1;35%atlevel2).

• Questionsaremainlyatlevels3and4(35%ofmarksatlevel3;40%ofmarksatlevel4).

• thereareasmallnumberofmulti-stepprocedures(level3,5%ofmarks).

• thereareasmallnumberofroutineprocedures(25%ofmarks)includedtohelplearnersmakesenseofthecontextsinwhichproblemsareset.

• contextsarelimitedtowhatisspecifiedinthecurriculumoutlinesectionofcAPS.

• contextsmaynotbefamiliartolearners,inotherwords,theyarenotlimitedtothosespecifiedinthecurriculumoutlinesectionofcAPS.

setting internal examinationsSettinganexaminationpaperisafairlydemandingtaskformostteachers.Forthisreason,teachersoftenchoosetoworktogethertosetdifferentquestions/sectionsofthepaper.Werecommendthatteacherstryasfaraspossibletoworkcooperativelytosetpapers.Wherethisisnotpossibleataschool,itmaybepossibletoworkwithotherteachersinthedistricttoproduceacollectionofquestionsthatcanbeusedinexaminationsatdifferentschools.

Whenyousetanexamination(ortest)question,youneedtokeeptrackof:• thetopicsbeingassessed• thecontent/skillsbeingassessed• theproportionofmarksallocatedtodifferentlevelsonthetaxonomy.

Atablesuchastheonebelowcanhelpyouorganiseandkeeptrackofallthedifferentthingsyouneedtoconsider.ThisisanexemplarforonequestionofaPaper1examination.



Question details Content/skills taxonomy level total

num

ber

Con

text

Part

Fin

ance

Mea

sure

men

t

Map

s an

d p

lan

s

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2 (3

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3 (5

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4 (0

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sub

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l

1 take-awaybusiness(familiar)

1.11.21.31.4

77 7 7

34

234

25364

18

100

Oncethetableiscompletedforallquestions,youcanaddupthemarkspertaxonomyleveltocheckthatyouhavemoreorlessthecorrectpercentageforeachlevel.Ifnot,youcanseefromthetablewhichlevelshavetoomanyortoofewmarksandyoucanadjustthequestionsaccordingly.

selecting contexts Whenyousetexaminations,youhavetodecideonacontextforthequestions.

ForPaper1,youcanselectdocuments,tables,graphsanddiagramsfromtheStudy & Master Learner’s Booktouseintheexaminations.Youcanthensetdifferentquestionsrelatedtoeachcontext.ThismaybeassimpleaschangingthevaluesusedintheLearner’sBooktomakeanewquestion.

ForPaper2questions,youneedtoincludesomecontextsthatarefamiliar(thesecanagainbedrawnfromtheStudy & Master Learner’s Book)andsomethatarenotfamiliar.Themediaisagoodsourceofnewcontexts.(Rememberthattrulymathematicallyliterateadultsareabletoreadandmakesenseofarticles,advertisements,graphsandothermathematicalinformationtheycomeacrossindailylife).Wesuggestthatteacherskeepafileofinterestingarticles,tablesofdata,graphsandothermathematicallyorientedmaterialstheyfindthroughtheyeartousewhensettingexaminationquestions.Forexample,duringeventssuchastheComradesMarathonandTwoOceansMarathon,theremaybedifferentmapsandstatisticspublishedinthenewspapers.Thesecanbeusedtosetquestionsbasedonfamiliarconcepts.Othersportingevents,suchastheCapeArgusCycleTour,thePSLSoccerFinalsandeventheOlympicGamescanbeusedasthecontextforquestionsthatarenotfamiliartothelearners.

Thisisasectionofthescheduleofeventsforthe2012LondonOlympics.

Date / time Sport Venue

25July16:00–20:45

Football MillenniumStadium,cardiff

Women’spreliminaries(2matches)

25July17:00–21:45

Football cityofcoventryStadium,coventry


25July17:00–21:45

Football HampdenPark,glasgow


26July12:00–16:45

Football HampdenPark,glasgow

Men’spreliminaries(2matches)



Date / time Sport Venue

26July14:30–19:15

Football StJames’Park,newcastle


26July17:00–22:00

Football oldtrafford,Manchester


26July19:45–21:45

Football MillenniumStadium,cardiff

Men’spreliminaries(1match)

26July19:45–21:45

Football cityofcoventryStadium,coventry

Men’spreliminaries(1match)

Youcouldusetheabovescheduletosetaquestionthatassessestheconceptsandskillsrelatedtotime,distancesbetweenplaces,travellingproblems,costsandevenprobabilityinanunfamiliarcontext.Youcouldalsocombineitwithmapsand/orplansofasoccerfieldtosetpartsofquestionsinwhichstudentsusethescaletodeterminedimensionsandthenanalysethelayoutofthevenueintermsofseating,access,locationofexitsandotherissues.Similarly,youcouldcombinethiswithgraphsshowingmedalsbycountryandaskthelearnerstoanswerquestionsandanalysethedataprovided.


29S e c t i o n 3 • u n I t - B y - u n I t •

unIt-BY-unIt

seCtIon 3

Dealing with different levels in the Mathematical Literacy assessment taxonomyCAPSprovidesanassessmenttaxonomyframeworktohelpteachersmakesuretheirassessmentmeetsdifferentlevelsofcognitivedemand.Sometasksandquestionsrequireonlytherecallofbasicfactsorsimplecalculationswhileothersrequirelearnerstoanalyseandmakesenseofunfamiliarcontextsandusevariedmethodsandskillstosolveproblems.

Thefourlevelsofcognitivedemandare:Level 1:KnowingLevel 2:ApplyingroutineproceduresinfamiliarcontextsLevel 3:Applyingmulti-stepproceduresinavarietyofcontextsLevel 4:Reasoningandreflecting.

Whenyoudesignassignments,investigations,testsandexaminations,youneedtoensurethatthenumberofmarksallocatedtoquestionsisroughlyinthefollowingproportions(about5%inoverallallocation).

taxonomy level Marks allocated to each level

Level1 30%

Level2 30%

Level3 20%

Level4 20%

Inexaminations,thefocusofthedifferentpapersmeansthatthepercentagemarksfordifferentlevelsvaryperpaper,buttheygivethesameoverallpercentageswhencombined(about5%varianceinallocations).Thesearegivenbelow.

taxonomy level Paper 1 allocation Paper 2 allocation overall allocation

Level1 60% – 30%

Level2 35% 25% 30%

Level3 5% 35% 20%

Level4 – 40% 20%

How the levels are built into the activities in the Study & Master Learner’s BookInordertopreparelearnersfortests,examinationsandotherformalassessmenttasks,theyneedtopractiseansweringquestionsatalllevelsonthetaxonomy.TheLearner’sBookprovidesexercisesandactivitiesineachtopicthatfallintoandacrossdifferentlevelsoftheMathematicalLiteracytaxonomy.

Thetablesthatfollowcontainexamplesofquestions,calculationsandexercisesfromeachterm’sworksortedbyleveltoshowthedifferencesbetweenthedemandsofquestionsatdifferentlevelsofthetaxonomy.

Notethatthesetablesdonotlistallthequestions/activitiesintheStudy & Master Learner’s Book,theyareintendedonlyageneralguidetohelpyouselectand/ordevelopsuitableassessmentquestionsofyourownandtoshowthatprovisionismadeforeachlevelinthecoursematerials.


30 S e c t i o n 3 • u n I t - B y - u n I t


31S e c t i o n 3 • u n I t - B y - u n I t

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now

ing

Le

vel 2

: Ap

ply

ing

ro

uti

ne

pro

ced

ure

s in

fam

iliar

co

nte

xts

Leve

l 3: A

pp

lyin

g m

ult

i-st

ep p

roce

du

res

in

a va

riet

y o

f co

nte

xts

Leve

l 4: R

easo

nin

g a

nd

re

flec

tin

g

Un

it 5

Co

nver

sio

ns

con

vert

bet

wee

nm

etric

un

its:

5.1

ques

tions

1a

nd2

con

vert

from

imp

eria

lto

met

ricu

nits

:5.

1qu

estio

n3

Mak

ea

scal

edd

raw

ing

and

enla

rge

itus

ing

ana

pp

rop

riate

con

vers

ion

fact

or:

5.4

ques

tion

2

des

ign

asi

gn,s

elec

ting

app

rop

riate

sca

lea

ndu

nits

:5.

4qu

estio

n3

Un

it 6

Mea

suri

ng

tim

e re

adv

alue

sfr

oma

clo

ck

face

:6.

1qu

estio

n1

reco

rda

ndc

alcu

late

tim

e:6.

4qu

estio

ns1

–5

Inte

rpre

ttim

eva

lues

on

atim

etab

lea

nd

answ

erq

uest

ions

rela

ted

toti

mes

:6.

5qu

estio

ns1

–3

Perf

orm

tim

eca

lcul

atio

nsa

nd

rela

teth

emto

oth

ertr

avel

re

sour

ces

ino

rder

top

lan

atr

ip:

6.8

ques

tion

3an

d4



term

1: F

inan

ce

Un

it

Leve

l 1: K

now

ing

Le

vel 2

: Ap

ply

ing

ro

uti

ne

pro

ced

ure

s in

fam

iliar

co

nte

xts

Leve

l 3: A

pp

lyin

g m

ult

i-st

ep

pro

ced

ure

s in

a v

arie

ty o

f co

nte

xts

Leve

l 4: R

easo

nin

g a

nd

refl

ecti

ng

Un

it 7

Fin

anci

al

do

cum

ents

at

ho

me

read

info

rmat

ion

from

hou

seho

ld

bill

s:7.

1qu

estio

n1

Show

how

the

tota

ldue

was

ca

lcul

ated

on

ana

ccou

nt:

7.1

ques

tion

3

cal

cula

ted

iffer

ence

sb

etw

een

bud

gete

dan

dac

tual

exp

endi

ture

in

aho

useh

old:

7.3

ques

tions

1a

nd2

Un

it 8

Fin

anci

al

do

cum

ents

at

wo

rk

read

info

rmat

ion

from

ap

aysl

ip:

8.3

ques

tion

1Sh

owh

owa

mou

nts

wer

eca

lcul

ated

:8.

3qu

estio

ns2

and

3

che

ckc

alcu

latio

nso

na

docu

men

tto

see

ifto

tali

sco

rrec

t:8.

1qu

estio

n1

rep

eatc

alcu

latio

nsto

pro

duce

a

new

bill

usi

ngd

iffer

entv

alue

s:8.

1qu

estio

n2

col

late

info

rmat

ion

from

diff

eren

tso

urce

sto

pre

par

ea

trav

elc

laim

:8.

5qu

estio

n2

Un

it 9

Tari

ffs

read

tab

les

ofd

iffer

entt

ariff

s:9.

1qu

estio

n1

cal

cula

tec

osts

and

tariff

sus

ing

give

nin

form

atio

n:9.

1qu

estio

ns2

and

3c

omp

lete

ata

ble

oft

ariff

sus

ing

give

nin

form

atio

n:9.

1qu

estio

n4

dra

wg

rap

hsto

rep

rese

nta

nd

com

par

edi

ffer

entt

ariff

s:9.

2qu

estio

n2

cho

ose

app

rop

riate

str

ateg

ies

(in

clud

ing

usin

gta

ble

and

dra

win

ggr

aphs

)to

com

par

eth

eco

sts

of

serv

ices

and

tariff

sin

diff

eren

tco

ntex

ts:

9.3

ques

tions

1–3

Un

it 1

0In

com

e-an

d-

exp

end

itu

re

stat

emen

ts

and

bu

dg

ets

cla

ssify

item

son

an

inco

me-

and-

exp

endi

ture

sta

tem

ent:

10.1

que

stio

n1

cal

cula

tep

rofit

and

loss

10.2

que

stio

ns1

–4

Prep

are

anin

com

e-an

dex

pen

ditu

re

stat

emen

t:10

.1q

uest

ion

4Pr

epar

ea

hous

ehol

db

udge

t:10

.5q

uest

ions

1a

nd2

con

stru

cta

two-

year

dra

ftb

udge

tfo

ras

mal

lbus

ines

s:10

.5q

uest

ion

3Pr

epar

ea

bud

getf

ora

sin

gle

even

t:10

.7q

uest

ions

1–4

Ana

lyse

ab

udge

tfor

as

choo

land

m

ake

reco

mm

enda

tions

toim

pro

ve

itsfi

nanc

es:

10.6

que

stio

ns1

–4

Un

it 1

1C

ost

pri

ce a

nd

se

llin

g p

rice

Find

the

cost

pric

eof

an

item

by

addi

nga

llth

eco

mp

onen

tcos

ts:

11.1

que

stio

ns1

–3

com

par

eco

sta

nds

ellin

gp

rice

and

calc

ulat

eth

em

ark

up:

11.3

que

stio

ns1

–411

.4q

uest

ions

1a

nd2

Inve

stig

ate

vario

usc

osts

and

dec

ide

ona

nap

pro

pria

tes

ellin

gp

rice:

11.2

que

stio

n1

cal

cula

tes

ellin

gp

rices

bas

edo

nva

rious

pro

fitle

vels

and

dec

ide

whi

chis

reas

onab

le:

11.5

que

stio

n1

con

duct

mar

ketr

esea

rch

and

use

the

resu

lts

tos

ugge

sta

ndd

efen

dth

ese

lling

pric

eof

an

item

:11

.2q

uest

ion

2

Un

it 1

2B

reak

-eve

n

anal

ysis

cal

cula

teb

reak

-eve

nva

lues

inth

eco

ntex

tofa

giv

enp

rob

lem

:12

.1q

uest

ions

1–3

read

val

ues

from

gra

phs

tofi

nd

the

bre

ak-e

ven

poi

nta

nda

nsw

er

ques

tions

ab

outi

t:12

.2q

uest

ion

2

dra

wg

rap

hsto

com

par

eop

tions

and

ta

riffs:

12.2

que

stio

n1

and

3



term

2: F

inan

ce

Un

it

Leve

l 1: K

now

ing

Le

vel 2

: Ap

ply

ing

ro

uti

ne

pro

ced

ure

s in

fam

iliar

co

nte

xts

Leve

l 3: A

pp

lyin

g m

ult

i-st

ep p

roce

du

res

in a

var

iety

of c

on

text

sLe

vel 4

: Rea

son

ing

an

d r

eflec

tin

g

Un

it 1

Inte

rest

an

d

inte

rest

rate

s

read

and

cal

cula

te

inte

rest

rate

s:1.

1qu

estio

n1

cal

cula

tes

imp

lein

tere

stra

tes

and

mon

thly

rep

aym

ents

:1.

1qu

estio

n3

Perf

orm

com

pou

ndin

tere

stc

alcu

latio

ns

over

mul

tiple

tim

ep

erio

ds:

1.2

ques

tions

1a

nd2

com

ple

tea

tab

leto

mod

eld

iffer

ent

optio

nsfo

rsav

ing

and

answ

erq

uest

ions

b

ased

on

the

resu

lt:

1.4

ques

tion

3

Inve

stig

ate

and

mod

elth

eeff

ecto

fch

angi

ngb

alan

ces

onp

aym

ents

and

to

talc

osto

floa

ns:

1.3

ques

tions

3a

nd4

Un

it 2

Ban

kin

g

Iden

tify

fees

and

cos

tso

nb

ank

docu

men

ts:

2.2

ques

tions

1a

nd2

cal

cula

teth

eco

sto

fala

tec

redi

tca

rdp

aym

ent:

2.4

ques

tions

1a

nd2

com

ple

tea

tab

les

how

ing

amou

nts

due

and

owin

gb

ased

on

give

nin

form

atio

n:2.

4qu

estio

n4

com

par

efe

eop

tions

and

inve

stig

ate

the

bes

tone

fory

ouro

wn

fam

ily:

2.1

ques

tion

3c

hoos

eth

eb

esti

nter

esto

ptio

nfo

ra

smal

lsoc

cerc

lub

and

just

ifyc

hoic

es:

2.5

ques

tion

2

Un

it 3

Ban

k lo

ans

and

in

vest

men

ts

Perf

orm

sim

ple

inte

rest

ca

lcul

atio

nsin

the

cont

exto

fhire

pur

chas

eag

reem

ents

:3.

2qu

estio

ns1

–4

cal

cula

teth

ere

alc

osto

fban

klo

ans:

3.1

ques

tions

1–4

M

ake

deci

sion

sre

gard

ing

inve

stm

ent

optio

nsfo

ras

mal

lbus

ines

sw

ithou

tsc

affol

ded

org

uide

dqu

estio

ns:

3.3

ques

tions

1–4

Un

it 4

Infl

atio

n

cal

cula

tep

rice

chan

ges

and

rate

sof

cha

nge:

4.2

ques

tion

1

Show

by

calc

ulat

ion

how

the

pric

eof

an

item

cha

nges

whe

nit

isa

ffec

ted

byin

flatio

n:4.

1qu

estio

ns2

and

3

Show

by

calc

ulat

ion

how

the

pric

eof

an

item

mig

htc

hang

eif

affec

ted

byin

flatio

nov

erm

ultip

leti

me

per

iods

:4.

2qu

estio

n2



term

2: M

easu

rem

ent

Un

it

Leve

l 1: K

now

ing

Le

vel 2

: Ap

ply

ing

ro

uti

ne

pro

ced

ure

s in

fam

iliar

co

nte

xts

Leve

l 3: A

pp

lyin

g m

ult

i-st

ep p

roce

du

res

in a

var

iety

of c

on

text

sLe

vel 4

: Rea

son

ing

an

d r

eflec

tin

g

Un

it 5

Mea

suri

ng

le

ng

th a

nd

d

ista

nce

read

mea

sure

men

tsfr

om

caro

dom

eter

san

dtr

ip

met

ers:

5.2

ques

tions

1a

nd2

Mea

sure

leng

ths

accu

rate

lyu

sing

ap

pro

pria

tein

stru

men

ts:

5.3

ques

tions

1–4

cal

cula

teu

sing

mea

sure

men

ts:

5.5

ques

tion

1c

alcu

late

ove

rall

cost

sus

ing

give

nm

easu

rem

ents

and

cos

ts:

5.4

ques

tions

1a

nd2

5.5

ques

tion

2

Un

it 6

Mea

suri

ng

mas

sM

easu

reth

em

ass

of

diff

eren

tite

ms:

6.1

ques

tion

3

cal

cula

teu

sing

mea

sure

dva

lues

an

dre

com

men

ded

amou

nts

per

m

ass:

6.3

ques

tions

1–3

cal

cula

tec

orre

ctd

osag

esfo

rmed

icin

es:

6.4

ques

tions

1a

nd2

Prep

are

ab

udge

tfor

ac

ater

ing

pro

ject

us

ing

mas

san

dco

sto

fing

redi

ents

:6.

6qu

estio

ns1

–3

Inve

stig

ate

and

com

par

eth

est

ated

an

dac

tual

mea

sure

men

tso

fpac

kage

dfo

ods

and

mak

ede

cisi

ons

bas

edo

nth

efin

ding

s:6.

2qu

estio

ns1

–3

Un

it 7

Mea

suri

ng

vo

lum

e

cal

cula

tev

olum

esfo

rpra

ctic

al

pur

pos

es:

7.1

ques

tions

1–3

cal

cula

tep

etro

lcon

sum

ptio

nra

tes,

al

coho

lcon

tent

and

wat

erru

n-off

ra

tes:

7.4

ques

tions

1a

nd2

7.5

ques

tions

1–4

7.6

ques

tion

1

cal

cula

teb

asic

wat

ern

eeds

usi

ngd

ata

from

gra

phi

cals

ourc

es:

7.3

ques

tions

1–3

use

mea

sure

dva

lues

inc

onju

nctio

nw

ith

othe

rski

llsto

com

ple

tea

nas

sign

men

ton

wat

erru

noff

ina

set

tlem

ent:

7.6

ques

tion

2

Inve

stig

ate

how

muc

hw

ater

ato

ilet

cist

ern

hold

san

dm

ake

deci

sion

sab

out

savi

ngw

ater

bas

edo

nfin

ding

s:6.

1qu

estio

n4

Un

it 8

Mea

suri

ng

te

mp

erat

ure

read

and

con

vert

te

mp

erat

ures

from

gr

aphs

:8.

1qu

estio

ns2

dra

wg

rap

hso

fave

rage

te

mp

erat

ures

and

com

par

ep

atte

rns:

8.1

ques

tion

7

com

pile

ap

lant

ing

cale

ndar

bas

edo

nte

mp

erat

ure

info

rmat

ion:

8.2

ques

tions

1a

nd2



term

2: M

aps,

pla

ns

and

oth

er re

pre

sent

atio

ns

of th

e w

orld

Un

it

Leve

l 1: K

now

ing

Le

vel 2

: Ap

ply

ing

ro

uti

ne

pro

ced

ure

s in

fam

iliar

co

nte

xts

Leve

l 3: A

pp

lyin

g m

ult

i-st

ep

pro

ced

ure

s in

a v

arie

ty o

f co

nte

xts

Leve

l 4: R

easo

nin

g a

nd

refl

ecti

ng

Un

it 9

Scal

e Ex

pla

inth

em

eani

ngo

fag

iven

sc

ale:

9.1

ques

tion

1

use

ag

iven

sca

leto

det

erm

ine

actu

alm

easu

rem

ents

:9.

1qu

estio

ns2

and

39.

2qu

estio

ns1

–3

use

ag

iven

sca

leto

geth

erw

ith

mea

sure

men

tso

na

pla

nto

de

term

ine

leng

tha

ndo

ther

di

men

sion

s:9.

3qu

estio

ns1

and

2

dec

ide

ona

nap

pro

pria

tes

cale

to

use

tod

raw

ap

lan

ofa

cla

ssro

om

blo

ck:

9.3

ques

tion

3

Un

it 1

0M

aps

des

crib

eth

ep

ositi

ono

fob

ject

son

a

map

:10

.1q

uest

ions

1–3

read

an

inde

xto

find

the

loca

tion

of

stre

ets:

10.2

que

stio

ns1

–3

Inte

rpre

tand

follo

wa

giv

ens

et

ofd

irect

ions

and

pro

vide

as

eto

fdi

rect

ions

bet

wee

ntw

op

lace

s:

10.3

que

stio

ns1

–3c

alcu

late

tim

e,d

ista

nce

and

spee

db

ased

on

map

s:10

.6q

uest

ions

1–5

use

as

tree

tmap

and

inde

xto

find

p

ossi

ble

rout

esb

etw

een

pla

ces:

10.4

que

stio

n4

Iden

tify

aro

ute

bet

wee

np

lace

son

a

map

,mea

sure

the

dist

ance

and

us

eth

esc

ale

toe

stim

ate

dist

ance

b

etw

een

pla

ces:

10.5

que

stio

ns1

–3

Mak

ede

cisi

ons

abou

tsto

pp

ing

poi

nts

ona

jour

ney

bas

edo

nin

form

atio

nav

aila

ble

:10

.7q

uest

ion

1dc

omp

are

two

mar

atho

nro

utes

us

ing

am

apa

nda

nel

evat

ion

map

an

dan

swer

que

stio

nsre

late

dto

the

rout

es:

10.8

que

stio

n2h

–j,3



term

3: M

easu

rem

ent

Un

it

Leve

l 1: K

now

ing

Le

vel 2

: Ap

ply

ing

ro

uti

ne

pro

ced

ure

s in

fam

iliar

co

nte

xts

Leve

l 3: A

pp

lyin

g m

ult

i-st

ep p

roce

du

res

in

a va

riet

y o

f co

nte

xts

Leve

l 4: R

easo

nin

g a

nd

refl

ecti

ng

Un

it 1

Peri

met

er,

area

an

d

volu

me

Know

that

are

ais

exp

ress

ed

ins

quar

eun

its:

1.1

ques

tions

5–7

Iden

tify

from

ag

iven

tab

le

whi

chfo

rmul

aar

ene

eded

for

diff

eren

tcal

cula

tions

:1.

2qu

estio

ns1

–10

cal

cula

tep

erim

eter

and

are

aby

su

bst

itutin

gva

lues

into

form

ulae

:1.

2qu

estio

ns1

–10

use

form

ulae

tofi

nds

urfa

cea

rea

and

volu

me:

1.4

ques

tions

1–3

Brea

kco

mp

osite

sha

pes

into

mor

efa

mili

ar

pie

ces

and

find

the

area

ofe

ach

ino

rder

to

find

the

area

oft

hew

hole

:1.

3qu

estio

ns1

–6W

ork

outt

hed

imen

sion

syo

une

edto

find

the

surf

ace

area

and

vol

ume

ofa

nirr

egul

ars

olid

an

dth

enu

seth

ese

tofi

ndth

esu

rfac

ear

ea

and

volu

me:

1.3

ques

tion

4

use

per

imet

er,a

rea

and

volu

me

calc

ulat

ions

toc

omp

lete

ala

rger

p

roje

ctw

ithou

tbei

ngto

ldw

hat

calc

ulat

ions

are

nee

ded:

Ass

ignm

ent1

p.3

64–3

70A

ssig

nmen

t2p

.371

–375

Un

it 2

Pla

ns

(in

stru

ctio

ns

and

ass

emb

ly

dia

gra

ms)

read

and

writ

ein

stru

ctio

ns:

2.1

ques

tions

1a

nd2

read

and

mak

ese

nse

of

diag

ram

s:2.

3qu

estio

ns1

and

2

Inte

rpre

tan

asse

mb

lyd

iagr

amto

id

entif

yw

hati

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eded

and

wha

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sto

be

done

:2.

5qu

estio

ns1

–3

crit

ical

lya

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seto

fpoo

rly

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ten

inst

ruct

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and

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rmul

ate

them

tob

ecl

eara

nds

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ble

:2.

2qu

estio

ns1

and

2

Un

it 3

Flo

or

and

el

evat

ion

p

lan

s

read

val

ues

and

dim

ensi

ons

from

ad

iagr

ama

nd/o

rdes

ign

draw

ing:

3.5

ques

tions

1a

nd2

3.6

ques

tions

1a

nd2

use

giv

enin

form

atio

nto

iden

tify

the

num

ber

sof

diff

eren

tfea

ture

son

a

pla

n:3.

1qu

estio

ns1

and

2

Mea

sure

dim

ensi

ons

ona

pla

nan

dus

eth

esc

ale

tod

eter

min

eac

tual

dim

ensi

ons:

3.2

ques

tion

1u

sep

lans

inc

onju

nctio

nw

itho

ther

in

form

atio

nto

det

erm

ine

mat

eria

lsn

eede

dan

d/or

cos

ts:

3.2

ques

tion

23.

3qu

estio

ns2

–4

des

crib

eite

ms

rep

rese

nted

on

ap

lan:

3.3

ques

tion

1d

ecid

eon

an

app

rop

riate

sca

le

inw

hich

tod

raw

ap

lan

and

then

dr

awit

:3.

4qu

estio

ns1

–4

Un

it 4

Usi

ng

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del

s to

inve

stig

ate

shap

e an

d

spac

e

Mea

sure

the

dim

ensi

ons

ofa

nite

mfo

rwhi

cha

m

odel

ofp

acka

ging

will

be

cons

truc

ted:

4.2

ques

tions

1a

nd2

Build

am

odel

ofa

cyl

indr

ical

p

acka

ge:

4.2

ques

tions

3–5

Build

am

odel

ofa

sim

ple

bui

ldin

ggi

ven

ane

tand

dim

ensi

ons:

4.5

ques

tions

1–4

Wor

kou

thow

muc

hw

ood

you

need

tob

uild

b

oxes

ofd

iffer

entd

imen

sion

s:4.

3qu

estio

ns1

–4Bu

ilda

mod

ela

ndu

seto

sol

vep

rob

lem

s:4.

4qu

estio

ns1

and

2

use

am

odel

toa

naly

seth

esp

ace

avai

lab

lea

ndm

ake

ade

cisi

ona

bou

tth

eb

estp

lace

men

tofi

tem

sto

m

axim

ise

avai

lab

les

pac

e:4.

6qu

estio

ns1

and

2



term

3: F

inan

ce

Un

it

Leve

l 1: K

now

ing

Le

vel 2

: Ap

ply

ing

ro

uti

ne

pro

ced

ure

s in

fam

iliar

co

nte

xts

Leve

l 3: A

pp

lyin

g m

ult

i-st

ep

pro

ced

ure

s in

a v

arie

ty o

f co

nte

xts

Leve

l 4: R

easo

nin

g a

nd

refl

ecti

ng

Un

it 5

Taxa

tio

nc

alcu

late

VAt

and

incl

usiv

ep

rices

:5.

1qu

estio

ns1

–3

cal

cula

teu

IFfo

rdiff

eren

ttim

ep

erio

ds:

5.2

ques

tions

1a

nd2

use

the

sala

ryb

illfr

oma

sm

allb

usin

ess

to

inve

stig

ate

the

effec

ttha

tas

alar

yin

crea

se

wou

ldh

ave

onu

IFc

ontr

ibut

ions

:5.

2qu

estio

ns3

and

4

term

3: P

rob

abili

ty

Un

it

Leve

l 1: K

now

ing

Le

vel 2

: Ap

ply

ing

ro

uti

ne

pro

ced

ure

s in

fam

iliar

co

nte

xts

Leve

l 3: A

pp

lyin

g m

ult

i-st

ep

pro

ced

ure

s in

a v

arie

ty o

f co

nte

xts

Leve

l 4: R

easo

nin

g a

nd

refl

ecti

ng

Un

it 6

Pro

bab

ility

u

sete

rms

asso

ciat

edw

ith

pro

bab

ility

cor

rect

ly:

6.1

ques

tions

1a

nd2

Iden

tify

allp

ossi

ble

out

com

es

fora

nev

entu

sing

atr

ee

diag

ram

:6.

11q

uest

ion

4

Exp

ress

pro

bab

ility

inp

erce

ntag

es

and

num

ber

s:6.

2qu

estio

ns1

–5d

oex

per

imen

tsa

ndre

cord

the

outc

omes

:6.

3qu

estio

ns1

–46.

4qu

estio

ns1

–5

Iden

tify

valu

esfr

oma

tab

lea

ndu

se

them

toe

xpre

ssth

ep

rob

abili

tyo

fce

rtai

nev

ents

:6.

5qu

estio

ns4

–6

use

ata

ble

ofr

ainf

alla

ndw

eath

er

pro

bab

ilitie

sto

mak

ean

das

sess

the

chan

ce

ofra

ina

tdiff

eren

ttim

es:

6.7

ques

tions

1–3

6.8

ques

tion

1c

ritic

ally

ass

ess

the

use

ofp

rob

abili

tyv

alue

sin

med

ias

ourc

esa

nda

dver

tisem

ents

for

pro

duct

ssu

cha

sp

regn

ancy

test

s:6.

8qu

estio

n2

6.9

ques

tions

1–5

6.10

que

stio

ns1

–3



term

4: F

inan

ce

Un

it

Leve

l 1: K

now

ing

Le

vel 2

: Ap

ply

ing

ro

uti

ne

pro

ced

ure

s in

fam

iliar

co

nte

xts

Leve

l 3: A

pp

lyin

g m

ult

i-st

ep

pro

ced

ure

s in

a v

arie

ty o

f co

nte

xts

Leve

l 4: R

easo

nin

g a

nd

refl

ecti

ng

Un

it 1

Exch

ang

e ra

tes

rank

cou

ntrie

sin

term

sof

the

give

nb

uyin

gp

ower

oft

heir

curr

enci

es:

1.3

ques

tion

1

use

giv

ene

xcha

nge

rate

sto

de

term

ine

the

valu

eof

one

cur

renc

yfo

rag

iven

val

ueo

fano

ther

:1.

1qu

estio

ns1

–4

Perf

orm

cur

renc

yco

nver

sion

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lcul

atio

nsre

late

dto

the

buy

ing

pow

ero

fthe

cur

renc

y:1.

3qu

estio

n2

Exp

lain

how

as

tron

gor

wea

kcu

rren

cya

ffec

tsp

rices

ind

iffer

ent

coun

trie

s:1.

2qu

estio

ns2

and

3c

omp

are

curr

enci

esu

sing

the

idea

of

buy

ing

pow

erfo

rdiff

eren

tite

ms:

1.3

ques

tions

3

term

4: d

ata

han

dlin

g

Un

it

Leve

l 1: K

now

ing

Le

vel 2

: Ap

ply

ing

ro

uti

ne

pro

ced

ure

s in

fam

iliar

co

nte

xts

Leve

l 3: A

pp

lyin

g m

ult

i-st

ep

pro

ced

ure

s in

a v

arie

ty o

f co

nte

xts

Leve

l 4: R

easo

nin

g a

nd

refl

ecti

ng

Un

it 2

Dat

a h

and

ling

re

adin

form

atio

nfr

oma

tab

leo

fre

sult

s:2.

1qu

estio

n1

read

dat

afr

oma

giv

enfr

eque

ncy

tab

le:

2.6

ques

tion

1W

ork

outt

hea

ngle

siz

efo

rsec

tors

of

ap

ieg

rap

h:2.

9qu

estio

n1

read

val

ues

dire

ctly

from

gra

phs

:2.

10q

uest

ion

1

dec

ide

whe

ther

as

amp

leis

re

pre

sent

ativ

eor

not

:2.

2qu

estio

n1

com

ple

tea

tab

leto

sum

mar

ise

data

co

llect

edd

urin

ga

surv

ey:

ques

tion

2c

alcu

late

the

mea

n,m

edia

n,m

ode

and

rang

e:2.

7qu

estio

ns1

–6d

raw

and

lab

elg

rap

hs:

2.9

ques

tions

1–5

2.11

que

stio

ns1

–32.

13q

uest

ions

1a

nd2

dec

ide

ona

pp

rop

riate

que

stio

nsto

in

clud

eon

aq

uest

ionn

aire

and

then

co

nduc

tthe

sur

vey:

2.4

ques

tions

1–8

use

raw

dat

ato

dra

wu

pa

gro

uped

fr

eque

ncy

tab

lea

nda

nsw

er

ques

tions

bas

edo

nth

eta

ble

:2.

6qu

estio

n2–

3c

hoos

eth

em

osta

pp

rop

riate

form

of

gra

ph

tore

pre

sent

diff

eren

tset

sof

dat

a,g

ivin

gre

ason

sfo

rcho

ices

:2.

16q

uest

ion

1

crit

ique

the

ques

tions

and

pos

ted

resu

lts

ofa

sur

vey:

2.2

ques

tion

3A

naly

sem

easu

res

ofs

pre

ad

and

cent

ralt

ende

ncy

tom

ake

dedu

ctio

nsa

bou

ttre

nds

inth

eda

ta:

2.8

ques

tions

2–6

Ana

lyse

gra

phs

and

mak

ede

duct

ions

ab

outt

rend

sin

the

data

an

dp

redi

ctio

nsfo

rthe

futu

re:

2.14

que

stio

n3

Inte

rpre

tand

crit

ical

lya

naly

sed

ata

pre

sent

edin

the

form

ofd

iffer

ent

grap

hs:

2.17

que

stio

ns1

–4


41t e r m 1 • u n I t 1

terM 1

Worked ansWers

Youmaywanttoreorganisethepagesinthisfilesothatthetableswithtaxonomylevelsforassessmentarenexttotheworkedsolutionsforeachterm.Rememberthoughthatthetablescontainexamplesofactivitiesthatfallintoeachlevelofthetaxonomyandittheydonotcontainadefinitiveorcompletelist.

Unit 1Making sense of graphs that tell a storyLearner’s Book pages 2–8

Teaching tips• LearnersworkedwithgraphsthattellastoryinGrade10.Thisunitaims

toexposethemtomoreexamplesofdifferenttypesofgraphtorevisewhattheyalreadyknowandbuildontheideathatinformationcanbepresentedinavarietyofdifferentways.

• Thetypesofgraphintroducedinthisunitwillbeusedandreusedaslearnersworkthroughthecoursesoitisimportantthatyoumakesuretheyunderstandhowtoreadandmakesenseofpictographs,piecharts,bargraphandlinegraphs.

• Learnersshouldalreadyknowthatgraphscanbemisleading(eitheraccidentallyoronpurpose).Theywilllookcriticallyattheinformationpresentedandhowitispresentedtoseehowgraphscangiveafairoramisleadingpicture.

Solutions1.1 Practise readingandmakingsenseofpictographsLearner’sBookpage2

1. a. ThegraphshowsthenumberoftouristsvisitingtheCradleofHumankindonamonthlybasisfromAugustthroughtoDecember.

b. OctoberandNovember.ApossiblereasonwouldbethatOctoberisthemonthwhenspring/summerbeginsandtheweatherisgood.

c. August;2000touristsvisitedtheCradleofHumankind. d. Thegraphwoulduseroundedofffiguresasapictographprovidesa

visualrepresentationofthedataanditisnotexact.2. a. Thegraphshowsthegrowthintheworld’spopulationfrom1650

to2070. b. Fromabout1930,theworld’spopulationhasgrownveryrapidly. c. 0,5billionpeople d. 7billionpeople e. Aprojectedpopulationisavaluethatiscalculatedusingthecurrent

trendintheworld’spopulationgrowth.So,thevaluegivenfortheworld’spopulationin2070isanestimatedvalue.

3. a. Thisgraphshowstheemployment/unemploymentrateforcoupleswithdependants.

b. Thereisnokeyasthereisascaleatthebottomofthepictograph. c. Usingthescaleyoucanworkoutthateachpicturerepresents5%.


42

d. No. e. Apictographiseasiertointerpretbyjustlookingatthepicturesandit

isalsomoreeye-catching.Abargraphwouldrequiremoreattentionfromthereadersiftheywishedtointerpretthedata.

1.2 Practise readingandmakingsenseofpiechartsLearner’sBookpage4

1. a. FavouritetypeofTVprogrammeamongGrade11learners b. Youcannottellhowmanylearnerswereinterviewedasthedatavalues

aregivenaspercentages. c. Comedy d. Realityandnature e. Youmightgetdifferentresultsifthesurveywereconductedamong

50maleGrade11learners.2. a. Thegraphshowsthesmokinghabitsofsoccerplayersinthenational

team. b. Thecirclewouldrepresentalltheplayersinthesurvey. c. Themajorityofplayersarenon-smokers. d. Numberofplayerswhosmokeeveryday=17___ 100×

15__ 1

=51__ 20

=211__ 20 Twoplayerssmokeeveryday.

1.3 Practise readingandmakingsenseofbargraphsLearner’sBookpage6

1. a. ThegraphshowsaveragemonthlyrainfallforBloemfontein. b. Precipitationinmillimetres(mm) c. Thehorizontalscaleshowsthateachbarstandsfortheamountof

rainfallforeachmonthoftheyear d. January,FebruaryandMarch e. Approximately:68mm+71mm+70mm=209mm f. Winter2. a. ThegraphshowstheaveragemonthlyrainfallforSpringbok,

NorthernCape. b. Inbothgraphstheverticalscalerepresentsprecipitationinmillimetres

(mm).However,inthegraphthatshowstherainfallinBloemfontein,thescalegoesfrom0mmto80mm,whileonthegraphthatshowstherainfallinSpringbok,thescalegoesfrom0mmto30mmoverthesamedistanceontheverticalaxis.

c. Approximately27mmfellduringMay. d. Approximately3mmfellduringJanuary. e. TherainfallpatterninSpringbokshowsthatthemostrainfalls

duringwinterandtheleastrainfallsinsummer.ItistheoppositeofBloemfontein’srainfallpattern.

3. a. Thegraphsshowthemostfrequentlyuseddrugsandtherelativefrequencywithwhichtheyareused.

b. Alcoholfollowedbydagga c. Havingnoverticalscalemakesitdifficulttomakesenseofthegraphs

asyoudonotknowwhatthevaluesontheverticalaxisrepresent. d. Theverticalscalecouldpossiblyrepresentpercentagesofthegroup

whowereinterviewed.Ifyouaddallthetotalsofeachtypeofdrugitcomestoabout100%.

20

3


S e c t i o n 3 • W o r K E d A n S W E r S

43t e r m 1 • u n I t 2

1.4 Practise readingandmakingsenseoflinegraphsLearner’sBookpage7

1. a. ThegraphshowsthenumberoftomatoessoldatSalie’sVeggiesoveraperiodofoneweek.

b. WednesdayandSunday c. Salieshouldmakesurethathehasagoodstockoftomatoeson

WednesdaysandSaturdays.2. a. Thegraphshowsthenumberofburglariesinthesouthernsuburbs

fromJanuarytoMay. b. ThenumberofburglariesdecreasesteadilyfromJanuarythrough

toMay. c. Theverticalscalemuststartat0soanychangesandtrendscanbe

clearlyseen.3. Answerswilldiffer.4. a. Thegraphshowsthefrequencywithwhichwordsfromother

languagesareusedineverydayspeech. b. Eina c. Afrikaans d. Serious e. Answerswilldiffer.

Unit 2Patterns and relationshipsLearner’s Book pages 9–12

Teaching tips• LearnersworkedwithonlythreetypesofrelationshipinGrade10:fixed

(orconstantrelationships,relationshipswithaconstantdifferencebetweentermsandinverselyproportionalrelationships).Inthisunit,theywillbuildonthoseskillstounderstandanduserelationshipswithaconstantratiobetweenterms(compoundgrowth)andunpredictablerelationshipswherethereisnoconstantorpredictablepattern.

• Encouragelearnerstolookforpatternsineachexampleinthisunit.Oncetheycanseeapattern,itmeansthatarelationshipexists.Ifyoucandefinetherelationshipmathematically,youcanworkoutmissingvaluesandpredictwhatthepatternwilldo.

• Youmaywanttorefertothebasicskillssectionandrevisesomeoftheworkonproportionasyouworkthroughthisunit.

• Encouragelearnerstosuggestequivalentwaysofexpressingdifferentrelationships.Theaimisforthemtounderstandthatarelationshipcanbeexpressedasanequation,asatableofvaluesandagraph.ThisconceptiscoveredmoreformallyinUnit3.

Solutions2.1 Practise workingwithconstantratiosLearner’sBookpage11

1. Year 1 2 3 4 5

rent r3800,00 r4180,00 r4598,00 r5057,80 r5563,58


44 S e c t i o n 3 • W o r K E d A n S W E r S

2. Year 1 2 3 4 5 6

Value of car

r99000,00 r74250,00 r55687,50 r41765,63 r31324,22 r23493,16

3. Year 1 2 3

annual salary r184000,00 r191360,00 r199014,40

4. a. Adecreasingrelationship b. Population c. 49__ 50=0,98 d. Thepopulationin2015willbe112212. e. Classdiscussion.Possibleanswersinclude:migrationtothecitiesin

searchofemploymentandeffectsofHIV.

2.2 Practise workingwithrelationshipsinwhichthereisnoobvious patternLearner’sBookpage12

1. Client c A F B g E d

a. Height (m) 1,64 1,65 1,66 1,67 1,67 1,68 1,75

b. Mass (kg) 63 55 64 64 64 75 79

c. Thereisnorealpatterntothedatasoonecanconcludethatthereisnorelationshipbetweenheightandmass.

2. a. Client A B c d E F g

BMI 20,2 22,95 26,56 25,80 26,57 23,23 22,95

b. ClientsC,DandEareoverweight.3. a. Temperature b. Depth c. Thetemperatureoftheoceandecreaseswithincreasingdepth.

Temperaturedecreasesmostrapidlyuptoadepthof200m.Temperaturethendecreasesmoregraduallywithincreasingdepth.

d. depth (m) 0 100 200 300 400 500 600 700 800 900 1000

temperature (°C) 27 24 11 9 8 7 6,5 6 5,5 5,25 5

e. Thereisnorealpatternorrulethatlinksthedepthtothetemperature.

Unit 3representing relationships in tables, equations and graphsLearner’s Book pages 13–16

Teaching tips• Thisunitbuildsonandmakesexplicittheideathatinformation

(particularlyinformationaboutmathematicalrelationships)isnotalwayspresentedinthewaythatwewantorinwaysthatareusefulandeasytounderstand.

• Collecteverydayexamplesofpatternsandrelationshipsandasktheclasstorepresenttheseindifferentways.Forexample,youcouldfindagraph


45t e r m 1 • u n I t 3

inthenewspaperandaskthelearnerstodrawupatableofvaluesusingthegraph.Youcouldalsocollectexchangeratedataforaweek,giveninnumbersortablesandaskthelearnerstographthechangesinvalueoftherandoranothercurrency(thiswouldworkwithshareprices,dailytemperatures,numberoftimesaparticularpoliticianismentionedonthefrontpageandsoon.)

Solutions3.1 Practise representingdataindifferentwaysLearner’sBookpage15

1. a. ×1,005 b. Amountinmonth7=1,005×4101,00=R4121,51 Amountinmonth8=1,005×4121,51=R4142,12 c.

00 1 2 3 4

Months

Amou

nt in

savin

gs ac

coun

t (R)

5 6 7 8

1 000

2 000

3 000

4 000

5 000

2. a. Thegraphshowstherelationshipbetweenthepercentageofvisitorslostandthetimeawebpagetakestoload.

b. About68%–justunder70% c. At5seconds d. 30seconds e. 10% f. Ifawebpagetakestoolongtoload,visitorswillnotbepreparedto

waitandthepagewillnotreceivemanyvisitors.3. a. Thegraphshowstherelationshipbetweenthenumberofpeople

whoknowDebbie’ssecretandthetimeinminutesaftershefirsttoldMinki.

b. time (min.) 5 10 15 20 25 30 35 40 45

number of people 2 4 8 16 32 64 128 256 512

c. Thisisanexponentialrelationship.ThenumberofpeoplewhoknowDebbie’ssecretdoubleseveryfiveminutes.

d. Constantratio:×2 e. After50minutes:512×2=1024people After55minutes:1024×2=2048people After60minutes:2048×2=4096peoplewouldknowDebbiewas

inlovewithJabu.



Unit 4Working with two relationships at the same timeLearner’s Book pages 17–27

Teaching tips• InGrade10learnersworkedwithgraphsthatshowonlyonerelationship

atatime.Intherealworld,youareoftenexpectedtodealwithmorethanonerelationshipatthesametime.TheLearner’sBookgivesmanypracticalexamplestoshowwherethishappens,butyoushouldstressthatwheneveryoucomparetwosetsofdataonthesamegraph,youareworkingwithtwodifferentrelationships.Rememberthough,thatthelearnersonlyneedtodealwithtworelationshipsinGrade11,theywillhandlemultiplerelationshipsinGrade12.

• Theconceptofabreak-evenpointisintroducedinthisunit.Break-evenisthepointatwhichabusinessearnsasmuchmoneyasithasspent.Inotherwords,thecostsandtheincomeareexactlythesame.Whenyougraphthisrelationshipyougettwolines.Bothlinesnormallygoup(towardstherightonthegraphbecausethecostsincreaseovertimeandtheamountearnedalsoincreases).Pointouttolearnersthatthelinesmaynotstartatthesamepointandthattheydon’tusuallygoupatthesamerate.Whenthetwolinescross,thebusinesshasreacheditsbreak-evenpoint.Atthispoint,thecostsandincomeareexactlythesame(theyareatthesameplaceonthegraph).Workthroughthesimpleexamplewiththeclassandmakesuretheyunderstandtheconceptsbeforemovingon.ThistopicishandledagaininmoredetailinUnit12wherelearnersareexpectedtoapplythebasicskillsandunderstandingfromthisunittosolveproblemsandmakedecisionsincontext.

Solutions4.1 Practise interpretinggraphsthatshowtworelationshipsLearner’sBookpage19

1. a. Averagetimespentwatchingtelevisionandaveragetimespentdoinghomework

b. Asthelearnersmoveintohighergrades,theamountoftimetheyspendwatchingtelevisiondecreasesandtheamountoftimetheyspenddoinghomeworkincreases.

c. Theamountoftimespentonhomeworkincreases. d. 90minutesperday e. about44minutesperday2. a. ThegraphshowsthesalesofproductAandproductBoverfouryears. b. ThesalesofproductAincreasesteadilyforthefirstthreeyearsand

thenincreaseevenmoreduringthefourthyear. c. ThesalesofproductBdecreaseslightlyduringthefirstyearand

thereafterthesalesincreasesteadily. d. Duringthethirdandfourthyears e. ThecompanyearnedthesamefromproductAandproductBatthe

endofthesecondyear.Youcantellthisfromthefactthatthetwographsintersectatthatpoint.

f. AboutR1500


47t e r m 1 • u n I t 4

4.2 Investigation: comparingcostsofsolarandnuclearenergyLearner’sBookpage20

1. Thisgraphshowsthecomparativecostofnuclearenergyandsolarenergyfrom1998to2015.

2. AtthebottomoftheverticalaxisthecostisrepresentedbyasmallRandatthetopoftheverticalaxisthecostisrepresentedbyalargeR.Thisindicatesthatthecostincreasesasyougouptheaxis.

3. Asthereisnoactualscaleontheverticalaxisitisimpossibletogiveavalue.Allyoucansayisthatsolarenergywasconsiderablymoreexpensivethannuclearenergyin1998.

4. Thecostofnuclearenergyhasincreasedovertime.Apossiblereasoncouldbetheincreasedcostofbuildinganuclearpowerstationandalsotheincreasedcostofimplementingsafetyregulations.

5. Thecostofsolarenergyhasdecreasedovertime.Apossiblereasoncouldbethatthetechnologyhasimprovedinrecenttimesand,therefore,thesolarpowersystemsaremorecost-effective.

6. In20107. Thepersonwhodrewthisgraphwantedtoshowthepredictedcostsof

nuclearandsolarpowerin2015.Theywouldhavedrawnthegraphbasedoncurrenttrendsinthecostsofnuclearandsolarpower.

8. Asthereisnoscaleontheverticalaxis,itisimpossibletogiveavalue.Youcanhoweverseethatsolarenergywillbeconsiderablycheaperthannuclearenergyin2015.

4.3 Practise workingwithbreak-evenvaluesLearner’sBookpage22

1. a. number of cups 50 100 150 200 250 300 350 400

Cost (r) 267,50 355 442,50 530 617,50 705 792,50 880

Income (r) 100 200 300 400 500 600 700 800

b.

00 50 100 150 200 250 300 350 400 450 500

Number of cups sold per month

Amou

nt (R

)

550 600 650 700 750 800 850 900 950 1 000

100200300400500600700800900

1 0001 1001 2001 3001 4001 5001 6001 7001 800

c. R1440 d. 720cups e. Herprofitmarginwilldecrease.



2. Answerswilldiffer.Encouragelearnerstomotivatetheiranswers.3. a. Classdiscussion.Possibleanswersinclude:rent,utilityaccountsor

staffwages. b. R20 c. R20 d. thebreak-evenpoint e. Profit=revenue–cost=R40–R30=R10

4.4 Assignment: MakingdecisionsusinggraphsLearner’sBookpage24

1. a. MandyMinutes 20 40 60 80 100 120

Cost (cents per minute) 600 300 200 150 98 95

b. JamielaMinutes 20 40 60 80 100 120

Cost (cents per minute) 65 65 65 65 65 65

c.

020 40

Minutes

Cost

per m

inute

(cent

s)

Mandy

Jamiela

60 80 100 120

100

200

300

400

500

600

d. ThegraphshowsusthatJamielahasthecheaperoptionirrespectiveofhowmuchairtimeisused.

2. a.

01 2 3 4 5 6

Number of years7 8 9 10 11 12

Amou

nt (R

)

5 000

10 000

15 000

20 000

25 000

30 000

Make-a-Buck Bank

Gimme-Plenty Bank

b. FromthegraphwecanseethatMake-a-BuckBankgivesthebestreturnontheinvestmentoverthreeyears.Wecancheckthisbydoingacalculation.

Make-a-BuckBank:A=P(1+in)=15000(1+0,06×3)=R17700 Gimme-PlentyBank:A=P(1+i)n=15000(1+0,045)3=R17117,49


49t e r m 1 • u n I t 4

c. FromthegraphwecanseethatMake-a-BuckBankgivesthebestreturnontheinvestmentovertenyears.Wecancheckthisbydoingacalculation.

Make-a-BuckBank:A=P(1+ in)=15000(1+0,06×10)=R24000,00

Gimme-PlentyBank:A=P(1+i)n=15000(1+0,045)10=R23294,54

Revise and consolidate:Patterns,relationshipsandrepresentationsLearner’sBookpage26

1. a. Thiscompoundbargraphshowsthelevelsofemploymentcomparedtolevelofeducationforpeopleaged18to64years.

b. Forwhichcountryisthedata? Forwhichyearswasthedatacollected? Otheranswerscouldalsobecorrect.

2. a. number of learners 1 2 3 4 5

total cost (r) 313,50 332,00 350,50 369,00 387,50

b. ThecostincreasesbyR18,50foreachadditionallearner. c. C=cost N=numberoflearners C=R295+R18,50×N d. C=R295+R18,50×12

=R517 e. C=R295+R18,50N R443,00=R295+R18,50N R443,00–R295=R18,50N R148=R18,50N R148_____ R18,50=N \N=8 Eightlearnerswentonthetrip.

f. number of learners 1 2 3 4

total cost (r) 468,50 487,00 505,50 524,00

1 100

1 200

1 300

1 000

900

800

700

600

500

400

300

200

100

00 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Cost

(R)

Cost of visit for di�erent numbers of learners

Number of learners

(4; 524)

g. Thecostfor32learnersisR1042.



3. a. Thetopgraphshowsthecostofoveralllossesincurredbynaturaldisastersandthebottomgraphshowsthecostofinsuredlossesincurredbynaturaldisasters.

b. 1988 Thevalueofinsuredlosseswasabout$15billion. c. TheKobeearthquakein1995 d. Overalllossespeakin1995asaresultoftheKobeearthquake.

Overalllossesdroptobelow$100billionin1996,butincreaseagainfrom2007to2009.Overalllossesdropagainin2000andremainfairlylowuntillossesrisesteeplyin2005asaresultofHurricaneKatrinaandtheKashmirearthquake.

e. i. $150billion ii. $260billion4. a. Workoutthesize(indegrees)foreachsector. Floodsandlandslides:42___ 380×360°=68,21°

Storms:65___ 380×360°=61,58°

Earthquakes,tsunamisandvolcanoes:232___ 380×360°=219,79°

Other:11___ 380×360°=10,42°

Other

Earthquakes, tsunamis and volcanoes

Key

Storms

Floods and landslides

b. $380×6,20=R2356billion

Unit 5ConversionsLearner’s Book pages 28–45

Teaching tips• Learnersshouldalreadybefamiliarwithconversionsbetweenunitsin

themetricsystemastheydidextensiveworkonthisinGrade10.Theywillbrieflyrevisethebasicconceptsinthisunitandalsoreviseareaandvolumeconversionstoremindthemthattheseusepowersof10asaconversionfactor.

• Learnersshouldeasilybeabletoconvertbetweenunitsinthemetricsystem.Encouragethemtousetheconversiontablesonpages29to33asnecessary.Ifnecessary,maketransparenciesorpostersofthesetodisplayintheclassroom.

• Anewconceptinthisunitinvolvesconvertingbetweenmetricandimperialunits.TheImperialsystemofmeasurementisbasedonBritishunitsthatuseanon-decimalsystem(forexamplethereare12inchesin


51t e r m 1 • u n I t 5

onefootand16poundsinonestone).Thereareonlythreecountriesthatofficiallyretainthissystem:theUnitedStatesofAmerica,LiberiainWestAfricaandMyanmarinSouth-EastAsia.Allothercountrieshaveofficiallyadoptedthemetricsystem.However,inmanycountries,thereisstillatendencytousesomeImperialunits.Forexample,inSouthAfrica,surfersstilltalkaboutthesizeofwavesinfeet,intheUK,manydistancesarestillgiveninmilesandolderpeopleeverywhereusuallytalkaboutheightinfeetandinches(heissixfootfour)andsometimesmassinpounds(helostover30pounds).

• Itisimportanttoteachlearnerstoconvertbetweenthesesystems,particularlyastheymayusebooksandinstructionmanualsortechnicalguidelinesprintedintheUSA.Youwillfindatableofsensible(estimatedandroundedoff)conversionfactorstohelplearnersdotheseconversions.

• TheUSAandCanadaalsousetheFahrenheitscalefortemperature.ItiseasytoconvertbetweenFahrenheitandCelsiususingtheformulathatlearnersaregiveninthisunit.

• Lastly,learnerswillrevisethebasicconceptsofscale(youmaytoneedrevisethebasicskillssectiononratiosbeforeyoudothis).ThiswillberevisitedandreinforcedinTerm2whenlearnersworkwithmapsandplansinmoredetailedcontexts.

Solutions5.1 Practise conversionsLearner’sBookpage33

1. a. Closerto2m b. 2kgisbigger. c. 25rulers d. 40inches e. 2bagsofflour f. 1000plots g. 10plots h. 1,5ℓofpaintwillbeneeded.2. a. 12,78m=1278cm 1278cm×0,4=511,2inches b. 405m=0,405km 0,405km×0,6=0,24miles c. 0,125km=12500cm 12500cm×0,4=5000inches 5000inches÷12=416,67feet d. 304,5mm=0,3045m 0,3045m÷0,3=1,015feet(30cm=1foot) e. 79,4km=79400m 79400m×1,1=87304yards f. 3miles×1,6=4,8km=4800m g. 105g=0,105kg=105000mg h. 100,125kg=100125g=0,100125tonnes i. 12,1g=12100mg=0,0121kg j. 197520mg=197,520g=0,19752kg k. 0,09t=90kg=90000g l. 352,076kg=352076000mg=352076g m. 50ℓ=50000ml n. 124,05ml=0,12405ℓ o. 50000ml=50ℓ p. 202,3ℓ=0,2023kl q. 300ml=0,0003kl r. 0,6905kl=690,5ℓ s. 1200cm2=0,12m2

t. 0,78m2=7800cm2

u. 10,2km2=10200000m2

v. 350cm3=350000mm3

w. 98,4m3=984000000cm3

x. 350075mm3=350,075cm3



3. a. 2eggs 14,2gcastersugar 0,43ℓmilk(430mlmilk) 57gcakecrumbs 225gstoneddates 225gstonedraisins 57gfinelychoppedmixedpeel 1_ 4teaspoongroundnutmeg 450gcookingapples b. Adaptingtheaboverecipethatservessixpeople,toserve150people

meansthatthequantitiesmustbeincreasedbyafactorof25. 50eggs 10,75ℓmilk 1,43kgcakecrumbs 5,63kgstonesdates 5,63kgstonedraisins 1,43kgchoppedmixedpeel 61_ 4teaspoongroundnutmeg 11,25kgcookingapples

5.2 Practise calibratinghouseholdmeasuringequipmentLearner’sBookpage36

Answerswilldiffer.Discussanswersinclass.

5.3 Practise choosingappropriatemeasuringunitsLearner’sBookpage39

Answerswilldifferandshouldbediscussedinclass.

5.4 Practise convertingscalemeasurementsLearner’sBookpage45

1. a. i. 1cm ii. 1cm:2000cm 2000cm=0,02km b. i. 5mm ii. 1:55000000=5mm:275000000mm 275000000mm=275km c. i. 1cm ii. 1cm:2000000cm 2000000cm=20km d. i. 5mm ii. 1:110000=5mm:550000mm 550000mm=0,55km2, 3. Answerswilldiffer.4 a. Lengthofcarinphoto:82mm Scaleofphotograph:82mm:4750,or1:58 b. Answerswilldiffer.


53t e r m 1 • u n I t 6

Unit 6Measuring timeLearner’s Book pages 46–68

Teaching tips• Inthisunit,learnerswillbuildontheirpreviousskillsinworkingwith

timeandapplywhattheyknowtorecordtimesandusegiventimestoplantrips.Inplanningtrips,remindthemtothinkaboutreal-lifefactorssuchastraffic,actualtravellingspeed,stoppingtime(forbreaks,petrolandfood)andhowthesecanaffectthelengthofajourney.

• Timemeasurementcanbemorecomplicatedthanotherconversionsforlearnersbecausethereareanumberofdifferentconversionfactors(forexample,60forsecondstominutesandhours,but24forhourstodaysand52forweekstoyears).Timeisalsonon-decimal,so12minutesistwelve-sixtiethsofanhourandnot0,12hours.Similarly1,2hoursis1hourandtwo-tenthsofanhour(whichis12minutes,andnot2minutes).Makelearnersawareofthisastheyoftentrytousetheircalculatorstoconverttimemeasurementsforgettingthatthecalculatoronlyusesdecimalconversions.

• Sometimemeasurementsaregivenwithadecimalpointbecausethisishowthetimeisdisplayedonawatchorstopwatch.RemindlearnersthatinSouthAfricathistechnicallyshouldbewrittenwithadecimalpoint,butthatitoftenwon’tbeinthemedia.

Solutions6.1 Practise readingdifferenttimeformatsLearner’sBookpage48

1. Old-fashionedclock:11:54 Modernclock:8:55 Digitalwatch:7:292. Old-fashionedclock:11:54a.m.orp.m. Modernclock:8:55a.m.orp.m. Digitalwatch:7:29a.m.orp.m.3. Old-fashionedclock:11:54or23:54 Modernclock:8:55or20:55 Digitalwatch:07:29or19:294. a. i. 12/5/1945 ii. 5/12/1945 b. i. 31/1/2002 ii. 1/31/2002 c. i. 11/11/2011 ii. 11/11/2011 d. i. 1/6/1991 ii. 6/1/1991

6.2 Practise convertingtimefromoneunittoanotherLearner’sBookpage49

1. a. 5915s b. 21779,4s c. 4752min. d. 959460,3s e. 94,56min. f. 45172,09s g. 32598,03s h. 50808,48s i. Ifthereare3 leap yearsinthe10yearperiod: Totalnumberofdays=(3×365)+(7×365)+17=3670 Ifthereare2 leap yearsinthe10yearperiod: Totalnumberofdays=3669



2. a. 78hours;halfaweek;4days b. 15010s;24:13:10;3,5days;95:8:10 c. 4000min.;1week d. 11:23:0,99;12:3:1,55 e. 500days;18months;1,9years3. a. Itdependsontheconfigurationofthemoon. b. Easter–itchangesfromyeartoyearbecauseitalsodependson

configurationofthemoon.ItisalwaysfullmoonclosetoEaster. c. Learnersdiscusstheinformationtheyfoundaboutimportantfestivals

indifferentreligions.

6.3 Practise calculatingelapsedtimeLearner’sBookpage53

1. a. 05:13:03 b. 05:18:18 c. 07:48:30 d. 06:26:49 e. 05:10:59 f. 08:42:53 g. 05:44:30 h. 05:46:26 i. 09:09:11 j. 07:36:582. E A B G H D J C F I3. a. 11:35:54 b. 13:46:24 c. 14:27:39 d. 15:49:23 e. 11:45:30 f. 13:09:41 g. 12:26:57 h. 14:35:09 i. 14:09:44 j. 12:47:254. E A G J F B I H C D

6.4 Practise recordingandcalculatingelapsedtimeLearner’sBookpage53

Answerswilldiffer.

6.5 Practise readingandinterpretingtimetablesLearner’sBookpage60

1. a. Threeexams(Englishisnotwrittenduringthisweek.) b. No.TheGermanandPortugueseexamsarewrittenatthesametime

indicatingthatalearnercanstudyeitherGermanorPortuguese. c. No.TheGeographyandSportandExerciseScienceexamsareatthe

sametimeindicatingthatalearnercaneitherstudyGeographyorSportandExerciseScience.

d. EnglishHL–2hours Mathematics–3hours Music–3hours Tamil–21_ 2hours CivilTechnology–3hours Alearnerwillspend131_ 2hourswritingexams.


55t e r m 1 • u n I t 6

2. days of the week

Hours Monday 21/02

tuesday 22/12

Wednesday 23/02

thursday 24/02

Friday 25/02

9:00 EnglishHLandFALP1(2h)

geography(theory)P1(3h)

SportandExerciseScience

P1(2h)

isiZulu,isiXhosa,Siswati,

isindebeleHLandFALP1(2hrs)SAL(21_ 2h)

civiltechnology(3h)

MathematicsP1(3h)

MathematicalLiteracyP1(3h)

14:00 germanHLandSAL,Portuguese

HLandFALP3(21_ 2h)

Hindi,gujarati,urdu,tamil,

teleguHLandFALP3(21_ 2h)

geography(Mapwork)P2

(11_ 2h)

MusicP1theory(3h)

MusicP2comprehension

(11_ 2h)

6.6 Assignment: readandinterpretatidetableLearner’sBookpage61

1. 6:56a.m.,8:11p.m.,7:52a.m.,8:44p.m.,8:37a.m.,9:12p.m.,9:17a.m.,9:36p.m.,9:53a.m.,10:00p.m.,10:27a.m.,10:25p.m.,11:01a.m.

2. 1:42p.m.,1:01a.m.,2:20p.m.,1:54a.m.,2:32p.m.,2:40a.m.,3:22p.m.,3:23a.m.,3:50p.m.,4:02a.m.,4:17p.m.,4:40a.m.,4:38p.m.

3. tides 8 sep. 9 sep. 10 sep. 11 sep. 12 sep. 13 sep. 14 sep.

Low tide 1:01a.m. 1:54a.m. 2:40a.m. 3:23a.m. 4:02a.m. 4:40a.m.

High tide 6:56a.m. 7:52a.m. 8:37a.m. 9:17a.m. 9:53a.m. 10:27a.m. 11:01a.m.

Low tide 1:42p.m. 2:20p.m. 2:32p.m. 3:22p.m. 3:50p.m. 4:17p.m. 4:38p.m.

High tide 8:11p.m. 8:44p.m. 9:12p.m. 9:36p.m. 10:00p.m. 10:25p.m.

4. 8 sep. 9 sep. 10 sep. 11 sep. 12 sep. 13 sep. 14 sep.

Moonset 3:51a.m. 4:47a.m. 5:40a.m. 6:31a.m. 7:22a.m. 8:12a.m. 9:02a.m.

Moonrise 5:16p.m. 5:54p.m. 6:29p.m. 7:03p.m. 7:36p.m. 8:10p.m.

sunrise 7:13a.m. 7:13a.m. 7:14a.m. 7:14a.m. 7:14a.m. 7:15a.m. 7:15a.m.

sunset 7:49p.m. 7:39p.m. 7:38p.m. 7:37p.m. 7:36p.m. 7:35p.m. 7:34p.m.

5. Lowtideisat1:01a.m.,sothatwouldbeagoodtimetolaunchaboat.6. Hightideisat9:53a.m.and10:00p.m.Sosometimeroundabout

9:53a.m.wouldbeagoodtime(not10:00p.m.asitwouldbedark).

7. 8Sep. 9Sep. 10Sep. 11Sep. 12Sep. 13Sep. 14Sep.

time difference 12:36 12:26 12:24 12:23 12:22 12:20 12:19

8. Thesunisrisingslightlylatereachdayandsettingslightlyearliereachday.Thismeansthatthedaysarebecomingprogressivelyshorter,indicatingthattheseasonsarechangingandautumnorwinterisapproaching.



6.7 Practise drawingupatimetableLearner’sBookpage62

Answerswilldiffer.

6.8 Practise calculationswithtime,speedanddistanceLearner’sBookpage67

1. time=distance______ speed =580km______ 75km/h=7,73h

2. distance=speed×time=65km/h×0,5h=32,5km3. distance=speed×time=88km/h×24h=2112km4. distance=speed×time=3,8m/s×(12×60)s=2736m5. time=distance______ speed =

1,29m_____ 12m/h=0,1075h=6,45min.

6. speed=distance______ time 6:4:30,5

=90km_____ 6,075h =(6+4__ 60+30,5______ 60×60)h

=14,81km/h =6,075h

6.9 Practise usingtime,speedanddistancetoplanjourneysLearner’sBookpage67

1. Timerequired=distance______ speed =75km______ 60km/h=1,25h

Thedrivermustallowtimeforpickingupthechildrenanddroppingthemoffatschoolintimetogettotheirclassroomsby08:00.Hewouldprobablyneedtoleavethedepotat06:15orearlierallowinganextrahalfanhourforpickingupthechildrenanddroppingthemoffatschool.

2. truck number

Journey distance

departure time

number of rest stops

total length of rest stops

arrival time

5419 850km 09:30 1 0,5h 18:30

0617 1640km 10:15 3 1,5h 04:09thefollowing

day

8198 2200km 05:00 4 2h 05:00thefollowing

day

3319 930km 11:00 1 0,5h 20:48

2823 3175km 04:00 6 3h 14:45thefollowing

day

3. a. Iftheymakethejourneywithoutanystops, time=distance______ speed =

900km_______ 120km/h=7,5hours Theyshouldmakeaboutthreestops. b. Iftheaveragelengthofeachstopis30minutes,itwilladdanextra

1,5hourstotheirjourney,makingthejourney9hoursintotal. c. TheyshouldleavePolokwaneat6:00a.m.ifnotearlier. d. 3:00p.m.or15:004. Answerswilldiffer.5. Classdiscussion.


57t e r m 1 • u n I t 6

Revise and consolidate:Measurement–conversionsandtimeLearner’sBookpage70

1. a. i. 15miles ii. 15,70miles b. i. 0,4km ii. 0,39km c. i. 110yards ii. 109,36yards d. i. 1,8m ii. 1,83m e. i. 16000cm ii. 16093cm f. i. 4inches ii. 3,94inches g. i. 34884000mg ii. 34884000mg h. i. 0,23kg ii. 0,23kg i. i. 3136kg ii. 3149,44kg j. i. 125000ml ii. 125000ml k. i. 120015ml ii. 120015ml l. i. 0,255m2 ii. 0,255m2

m. i. 500cm2 ii. 500cm2

n. i. 5000m2 ii. 5000,15m2

o. i. 0,16km2 ii. 0,16km2

p. i. 49000mm2 ii. 49000mm2

q. i. 9120000000mm3 ii. 9120000000mm3

r. i. 1000ha ii. 999,97ha2. Answerswilldiffer.Learnersshouldgivereasonsfortheiranswers.3. Learnerscancheckeachother’senlargements.4. a. 1885min. b. 97818s c. 31092min. d. 12173h e. 1007,27s f. 847,12min. g. 8178,35s h. 931,31min. i. 5221days Therecouldbemorethanoneanswer.Thiswoulddependonhow

manyleapyearsareincludedinthe14yearsandthenumberofdaysinthethreemonths.

5. a. 36hours b. 220days c. 1,5days d. 2years6. a. 98years58days12hours b. 1:9,12 c. 57days4hours25minutes d. 4:51:457. a. Learnerscancomparetheiranswers(timetables). b. 11days12hours c. GujaratiFAL d. 20,5hoursor22,5hoursifyouarewritingMathsPaper3.8. a. t=199km______ 90km/h =2,21hours b. DistancefromAliwalNorthtoQueenstown =364–199 =165km Timetaken=1:09 =19__ 60h =1,15h Averagespeed=distance______ time =165___ 115 =143,48km/h



c. Time=distance______ speed WillemandMarianneFourie:Time=584___ 100=5,84hours Parents:Time=584___ 110=5,31hours

Arrivaltime:WillemandMarianneFourie: 5,84hours=5hours(84___ 100×60)minutes

=5hours40mins 7:45+5:40=13:25

Arrivaltime:Parents 5,31hours=5hours(31___ 100×60)minutes

=5hours19minutes 8:20+5:19=13:39

WillemandMarianneFouriearrivefirst. d. DistancefromEastLondontoQueenstown=220km Time=distance______ speed =

220___ 20=20hours. Theyshouldallowtwodaysforthejourney.

Unit 7Financial documents at homeLearner’s Book pages 75–86

Teaching tips• Therearenonewconceptsinthisunit.Learnerswillworkwithdifferent

versionsofthehouseholdaccountsandotherdocumentsthattheyworkedwithinGrade10.

• Remindthelearnersthatsomeofthedocumentsinthisunitmaylookdifferenttotheonesthattheyseeathomebecausedifferentprovincesormunicipalitiesanddifferentcompanieshavedifferentformatsandlayoutsfortheseaccounts.

• Itwillbeusefultocollectarangeofhouseholdaccountsforlearnerstolookat.Keeppeople’sprivacyinmindandblackoutanypersonaldetailsbeforeyoudistributetheseaccountstotheclass.Discussthiswiththelearnersasidentifytheftandfraudulentuseofbankdetailsisacommonproblemnowadays.

Solutions7.1 Practise readinghouseholdutilitybillsLearner’sBookpage78

1. A a. MrFRSmit b. 146893715 c. electricity d. R0,00 e. R148,49 f. R169,28 g. 9January2012 h. PaymentscanbemadeattheCityofCapeTowncashofficeor

BSA,Checkers,ShopriteorthePostOffice. B a. Yourname b. 0123456789123 c. telephonerentalandusage d. R0,00 e. R563,16(withdiscount) f. R642,01 g. 8July2012


59t e r m 1 • u n I t 7

h. Ifyoupayatacounter,thefullpagemustaccompanypayment.Alternatelyyoucouldpaybymail.

C a. MrMNMakgamathe b. A0795180 c. cellphoneusage d. R0,00 e. R236,25 f. R269,32 g. datenotgiven h. MTNSP’sbankaccount2. a. • Addressandcontactnumberoremailaddressofcompany • Dateofstatement • Openingbalance • Paymentreceived • Invoicenumberanddateforeachpurchaseintheperiodcoveredby

theaccount • Forhowlongamountsonunpaidaccountshavebeenowing • Bankdetailsforthecompanyorotherpaymentinstructions • Remittanceadvice(paymentslip) • Penaltiesforlatepaymentoftheamountowing3. a. TheamountofR1199,62owingwascalculatedasfollows: • Themonthlypropertyratesarecalculatedbasedonthemunicipal

valuationoftheproperty:R555,53 • Thechargeforwaterconsumptionforthemonth:R299,56 • AnamountofR75,44ischargedforrefuseremovalofthecontents

ofastandard240-ℓbin. • AseweragedisposalchargeofR199,41isalsoincluded. Thesumoftheabovefouramounts:R1199,62 b. On04/11/2011,thebalancebroughtforwardshowsanamountof

R167,50,ApaymentofR167,50wasmadeon30/11/2011.Thispaymentisindicatedby–R1267,50.From04/11/2011to03/12/2011,FredSmithranupanaccountofR254,29.Thisamountisnowowing.

c. ThepreviousaccountbalancewasR172,68.AnamountofR600,00waspaidintotheaccountleavingacreditbalanceofR427,32.ThelatestaccountforthecurrentmonthinvolvesanamountofR213,82owing.ThisamountofR213,82issubtractedfromthecreditbalanceofR427,32leavinganewcreditbalanceofR213,50.

7.2 Practise readinginvoices,receiptsandaccountstatementsLearner’sBookpage83

Discusslearners’answersinclass.

7.3 Practise calculationswithhouseholdfinancialdocumentsLearner’sBookpage86

Note:Theseanswersareestimates.Learners’answersmaydiffer.

1. Item estimate for april – June

rates r850

Electricity r1400

Food r7000

SchoolFees r2550

taxi/bus/trainfares r1800



2. Item actual amount spent april – June

difference from budgeted amount

Food r7395,05 r604,00 +7,56%overbudgeted

Petrol r2090,03 –r590,03 –39,34%underbudgeted

carrepairs r3101,20 –r2351,20 –313,41%underbudgeted

cellphone r861,00 r339,00 +28,25%overbudgeted

dVdrentals r145,00 r35,00 +19,44%overbudgeted

Booksandmagazines r410,50 r89,50 +17,9%overbudgeted

Medicalexpenses r7310,00 –r5810,00 –387,33underbudgeted

3. Theyneedtobudgetmuchmoreforpetrol,carrepairsandmedical. FromJanuarytoMarchtheyspentaboutR6000onfoodwhereasfrom

ApriltoJunetheyspentR7395,05.IfthistrendcontinuestheywillneedtobudgetaboutR9000forfoodfromJulytoSeptember.

Unit 8Financial documents at workLearner’s Book pages 87–107

Teaching tips• Thisunitfocusesondocumentsusedintheworkplace.Someofthese

documents(suchasinvoices,receiptsandstatements)arethesameasthoselearnersworkedwithinthecontextofhouseholdfinances,however,therearemanyworkplacedocumentsthatmaybenewtolearners.

• Youmightneedtoexplainthedifferencebetweenaninvoiceandastatement.Statementsareissuedtopeopleorcompanieswhohaveaccounts.Thestatementmaylistseveralinvoices.Youcanuseacompanycellphoneaccountasanexample.CompanyAmayhavetencellphonecontractsforitsworkers.EachmonththeserviceproviderwillsendcompanyAastatementofaccountshowinghowmuchtheyowe.Thestatementwilllistteninvoiceamounts,oneforeachcellphonecontract.

• Asyouworkthroughtheexamplesusingdifferentdocuments,focusonwhythesedocumentsareimportantandhowtheycanhelptheirbusinessownersmanagetheirfinancialaffairseffectively.

Solutions8.1 Practise readingquotationsLearner’sBookpage90

1. a. ThetotalamountisR1273,60.Thecontractorhasroundeduptothenearesthundred.

b. ThetotalcostisR411.00.ThesupplierhasunderquotedbyR15.2. Quotation

To:removeoldplantingsinfrontofhouse–R376,25replacewithnewfloweringplants–R800compostandmulchfor7m2–compostR94,50/m2

mulchR85,20/m2

prune5existingtrees@R64,50/treeplant4newtrees@R201,25/treeTotalcost:R3561,65


61t e r m 1 • u n I t 8

8.2 Practise workingwithinvoicesandreceiptsLearner’sBookpage94

1. HarliClothing:R250 PipePlumbers:R58,21 Rent:R1500

2. RECEIPTreceivedfor:2long-sleevedt-shirts1Skirt(velvetandlace)1WoollenJacket3WinterleggingsTotal

ABforLelanie’sdreamdresses

3May2012

r171,00r256,00r541,00

r102,57r1 071,07

3. a. Invoices28,32and36havenotbeenpaid. b. R235,49 c. R1224,64 d. Yes.Receipts307,309and316donotcorrespondtoanyof

theinvoices. e. Theownershouldchecktheinvoicesandreceiptsthatdonotreconcile.

8.3 Practise readingpayslipsLearner’sBookpage98

1. A a. NombuleloKrussers b. lineoperationsmanager c. 01/05/2011to01/06/2011 d. 40hours e. R33,48p/h f. 5hours g. R50,22 h. PAYE(14%):R222,64 B a. LanelleRiley b. cashier c. 09/01/2012to13/01/2012 d. 40hours e. R18,75p/h f. none g. notapplicable h. PAYE(25%):R187,50 C a. SharonMiller b. drilloperatorandstoremanager c. 23May2011 d. 8hours e. R18,75p/h f. none g. notapplicable h. none D a. GavinSteenkamp b. digitalanalyst c. 1October2011to1November2011 d. monthlywage(hoursnotgiven) e. notgiven f. overtime:3,5hours Sundays:4hours g. overtime:R500p/h Sundays:R750p/h h. PAYE:R57802. A (33,48×40)+(50,22×5) =1339,20+251,10 =R1590,30 B 18,75×40=R750,00 C 18,75×8=R150,00 D 15000+(500×3,5)+(750×8) =15000+1750+3000 =R19750



3. A R1590,30–R222,64=R1369,66 B R750,00–R187,50=R562,50 C nodeductions D R19750–R2768,00=R16982,00

8.4 Practise calculationswithpayslipsLearner’sBookpage101

a. R4608,00 b. R0 c. R4686,00d. R898,54 e. R3787,46 f. R527,00g. R100,00 h. R204,00 i. R68,00j. R0,00 k. R8,99 l. R85,27m. R813,73

8.5 Practise usingtravelallowanceclaimformsLearner’sBookpage104

1. a. 1030km b. 675km c. Fuelcost: 675×75,6c=R510,30 Maintenancecost: 675×32,3c=R218,03 Totalrefund: R728,33

2. a. date opening km Closing km total

21/522/525/525/525/5

4956849710499325004450189

4962149755499755007350197

53 45 43 29 8

total 178

b. Fuelcosts: 178×68c =R121,04 Maintenancecosts: 178×29,2c = R51,98 Totalrefund: R173,02

8.6 Practise readingbusinessbankdocumentsLearner’sBookpage106

1. a. HighHeelShoeRepairs b. currentaccount c. onemonth d. R26310,23credit e. cashdeposit,cashwithdrawal,staffsalariespaid(withdrawal),

interestcredited,debitorder,stoporder,cashwithdrawal,servicefeesdeducted

f. interestofR53,69earned g. R346,15(servicefee) h. R6645,25 i. R6296,19 j. R25961,17credit2. a. Safe-RideAirportShuttles b. savingsaccount c. onemonth d. R5000credit


63t e r m 1 • u n I t 9

e. cashdeposit,EFTdeposit,interestcreditedtoaccount,servicefeesdeducted

f. interestofR58,97earned;interestrate:5,5%p.a. g. R310,00(servicecharge) h. R310 i. R7923,97 j. R12614,07credit3. a. StefaniaSweetandSavoury b. 24-monthfixeddeposit c. threemonths d. R35000credit e. interestreinvested f. interestamountsofR1234,96;R124,40andR124,84earned;interest

rate:4,25%p.a.capitalisedmonthly g. Nobankfeescharged h. R0 i. R373,20 j. R35373,20credit

Unit 9tariffsLearner’s Book pages 108–126

Teaching tips• LearnersworkedwithtariffsinGrade10todeterminethebestoptionsfor

cellphonepackagesandotheroptions.• Tariffscanbeabitmorecomplicatedthannormalpricingbecausethey

areusuallystepped,whichmeansthatthetariffrate(theamountcharged)changesdependingonhowmuchorhowlittleyouuse.

• Theskillsdevelopedinthisunitareimportantbecausetheyequiplearnerstochoosetariffscriticallytosuittheirspecificneeds.Companiesoftentrytogetcustomerstotakethetariffoption(package)thatgivesthecompanythemostprofit,thesetariffsmaynotbethebestintermsofthecustomer’sneeds.

• Aswithpreviousunitsonfinancialdocuments,itwillbeusefultohavearangeofdifferentadvertisementsandbrochuresthatlisttariffssothatlearnerscanworkwiththemandbecomefamiliarwiththeoptionsandthewaysinwhichsmallprintispresented.

Solutions9.1 Practise readingandcalculatingtariffsLearner’sBookpage113

1. a. 1August b. Thefirstsetoftariffsgivethepeaktimetariffsforinternationalcalls.

Peaktimeisfrom08:00to20:00MondaytoFriday. Thesecondsetoftariffsgivestheoff-peaktimetariffsforinternational

calls.Off-peaktimeisfrom20:00to08:00thefollowingmorning,MondaytoFridayandfrom20:00Fridayto08:00thefollowingMonday.

c. 90s=1,5min. Tariff=R1,04×1,5=R1,56


64

2. a. For3September,thenewtariffsapply. Tariff=6×R1,35=R8,10assumingcallsmadeduringpeaktime;

3Septemberfallsintheweek. b. 230s=230___ 60min.=3,83min. Wewillusecurrenttariffatoff-peaktime. Tariff=3,83×R1,65=R6,32 c. Tariff=17,5×R1,66=R29,05 (Thecallisbefore08:00andafter1August,sowewillusenewtariff

atoff-peaktime.) d. Tariff=20,25×R0,6=R12,15 Wewillusethenewtariffatpeaktime.

3. Percentage decrease in peak time

Percentage decrease in off‑peak time

a. Germany 0,1___ 1,30×100___ 1 =7,69% 0,1

___ 1 ×100___ 1 =10%

b. usa 0,1___ 0,7×100___ 1 =14,29% 0,05

___ 0,65×100___ 1 =7,69%

c. australia 0,1___ 0,9×100___ 1 =11,11% 0,1

___ 0,9×100___ 1 =11,11%

4. stage departure point Fare Luggage Cost

stage 1 Pretoria r275 1piece Free

Midrand r275 2pieces r25

Johannesburg r275 3pieces r50

stage 2 Swinburne r225 4pieces r75

Pietermaritzburg r225

stage 3 Ixopo r175

Mzimkulu r175

Kokstad r175

stage 4 MountFrere r125

Qumbu r125

Mthatha r125

stage 5 Idutywa r75

Butterworth r75

5. a. name Connection fee

WeekenderWeekenderPlustalk100talk200talk500

r91,20r91,20r91,20r91,20r91,20

b. name Free minutes

WeekenderWeekenderplustalk100talk200talk500

100120100200500

c. R1,37perminute d. Mon–Fri:07h00–20h00 e. NotariffoffersfreeSMSes.


S e c t i o n 3 • W o r K E d A n S W E r S

65t e r m 1 • u n I t 9

f. Internationaloff-peakcostsR0,68+Telkomoff-peaktariff. So,acalltoChinausingTelkom’scurrenttariffswouldcost

R0,68+R1,40=R2,08perminute. g. Talk500hasthemostexpensivemonthlychargeofR570. h. Youget500minutespermonthfreecalltimethatyoucanuse

anytime.Also,yourpeakstandardrateisR1,37perminuteandyougetfreevoicemail.Theotherservicesofferedarestandard.

9.2 Practise usinggraphstofindtariffinformationLearner’sBookpage120

1. a. Shecanspeaktohimforjustover13minuteseachevening. b. 3hours=(3×60×60)s

=10800s/w(secondsperweek) EachdayoftheweekSiphokazicanspeakfor10800_____ 7 s

=1542,86s/d(secondsperday)

2. a. stage 1 2 3 4 5

Fare r275 r225 r175 r125 r50

01 2 3

Stage from which passenger departs

Fare

(R)

4 5

25

50

75

100

125

150

175

200

225

250

275

Pieces of luggage 1 2 3 4

Cost 0 r25 r50 r75

00 1 2

Pieces of luggage

Cost

(R)

3 4

25

50

75

100

3. a. 11% b. Percentagediscount=50%,whichmeansareductionofR490

c. Month toll charges paid discount not received

January r420 15%:15___ 100×r420=r63

February r656 26%:26___ 100×r656=r170,56

March r568 26%:26___ 100×r568=r147,68



april r795 37,5%:37,5___ 100×r795=r298,13

May r497 15%:15___ 100×r497=r74,55

June r870 45,9%:45,9___ 100×r870=r399,33

9.3 Practise comparingtariffsLearner’sBookpage125

1. Prepaidcellphonepackage1billspersecondandprepaidcellphonepackage2billsperminute.

0

3

6

9

R10,76

R8,07

R5,38

R2,69

12

30 60 90 120Time of call (s)

Package 2

Package 1

Graph comparing the cost of voice callsat peak time

Cost

(R)

150 180 210 240 0

3

6

9

R3,72

R4,96

R1,24R2,48

12

30 60 90 120Time of call (s)

Package 2

Package 1

Graph comparing the cost of voice callsat off-peak time

Cost

(R)

150 180 210 240

2. Package2seemstobebestoverall.Fromthegraphswecanseethatifyoumakeacalloflongerthan11_ 2minutesduringoff-peaktime,package2ischeaper.

9.4 Investigation: Whichwatertariffisbetter?Learner’sBookpage125

1. a. i. CityB ii. CityA b. Foraconsumptionof8klpermonth: CityA:5×R3,80+3×R5,75=R36,25 CityB:6×R0+2×R4,32=R8,64 CityBischeaper.

Forconsumptionof25klpermonth: CityA:(5×R3,80)+(10×R5,75)+(10×R6,25)=R139,00 CityB:(6×R0)+(4,5×R4,32)+(9,5×R9,22)+(5×R13,66)

=R175,33 CityAischeaper. c. PerfectionLaundryServicesincityA: Wateraccount=(5×R3,80)+(10×R5,75)+(15×R6,25)

+(20×R8,80)+(50×R9,95)+(20×R12,05) =R1084,75

PerfectionLaundryServiceincityB: Wateraccount=(6×R0)+(4,5×R4,32)+(9,5×R9,22)

+(15×R13,66)+(15×R16,87)+(10×R22,25) =R787,48 MrsDlaminishouldbudgetR1084,75forherlaundrybusinessin

cityAandLoyisoshouldbudgetR787,48forhislaundrybusinessincityB.

2. Learnersdiscusstheiranswers.


67t e r m 1 • u n I t 1 0

Unit 10Income‑and‑expenditure statements and budgetsLearner’s Book pages 127–151

Teaching tips• InGrade10,learnersworkedwithincome-and-expenditurestatements

andbudgetsinthecontextsofindividualandhouseholdfinances,planningforaholidayandpersonalprojects.Thisyeartheywillextendthisworktoincludebusinessandworkplacecontexts.

• Revisethebasicconceptswiththeclassandmakesuretheyunderstandthatanincome-and-expenditurestatementisadocumentthatrecordsactualfiguresforapastperiod.Abudgetisadocumentthatlistswhatyouexpecttoearnandspendforagivenperiodinthefuture.

• Remindthelearnersthatthenamesgiventovarioustypesofincomeandexpensesshouldnotbeappliedtoostrictly–theysometimesoverlap,forexample,abillforbuildingmaintenancecouldbeeitheravariableoroccasionalexpense.

• Givelearnerspracticeindrawingupbudgetsforvariousprojectsandeventsandrelatethesetotheworldofworkwherepossible.Remindthemthatbudgetingisanimportantelementofrunningabusinessbothintermsofmanagingexpenses,butalsoinmakingsureyoumakeaprofit.

Solutions10.1 Practise analysingandpreparingincome-and-expenditure statementsLearner’sBookpage132

1. a. Singhfamilyhouseholdincome-and-expenditure2012

Income (total for 2012) expenditure (total for 2012)

Fixed income Fixed expenditure

SalaryMSingh(net)WagesJSingh(net)

77200,0036000,00

rentJanuary–June 6×r3200rentJuly–december 6×r3575MedicalAidHouseholdandcarinsuranceAnnualAAmembership

19200,00

21450,0028800,0011424,00

780,00

Variable income Variable expenditure

commissionLSingh(net)Interestonbanksavings

19543,002986,00

telephoneElectricityFood,andsoonFixroofleakPetrol,carservice

6133,495381,30

28596,453297,60

14784,95

occasional income

cashsaleofoldwardrobe 1250,00

total income r136 979,50 total expenditure r139 847,74



b. Joe&Flora’sGardenServicesincome-and-expenditure2012


Fixed income Fixed expenditure

regularweeklygardenmaintenance for16clientsBankloantopurchasenewequipment

62400,00

12000,00

rentforpartofJoe’shouserepaymentforbakkie(hire purchaseagreement)InsuranceonplantsandequipmentBankcharges(12×r99)Interestonbankloan

6000,00

13200,005800,001188,001068,00

Variable income Variable expenditure

Plantingnewgardensfor15clientsclearingoldvegetationfor25clientsSaleofseedlings(about220trays permonth)

28950,0017360,00

5704,80

telephoneElectricitySeedlingsfromwholesalesupplierPetrol,carrepairsandsoonFertiliser,mulch,compostWagestopart-timeworkers(gross)*

3618,074951,183400,00

11788,454950,00

31200,00

occasional income occasional expenditure

Saleofthreeoldlawnmowers r900,00 newlawnmowers r99163,70

*thisisvariableastheyarepart-timestaff.

2. Joe & Flora’s Garden Services Running costs RentforpartofJoe’shouse Repaymentforbakkie(hirepurchaseagreement) Telephone Electricity Insuranceonplantsandequipment Petrol,carrepairsandsoon Wagestopart-timeworkers(gross) Bankcharges Interestonbankloan

Production costs Costofseedlingsfromwholesalesupplier Newlawnmowers Fertiliser,mulch,compost3. a. Mapetlahasacreditbalance–herexpenditureislessthanherincome.

b. Mapetla’s statement February–october

Income expenditure

BursaryWagesfromrestaurantcontributionfromdadBirthdaychequefromgran(Mapetlaonly receivesthisinFeb)Interestonsavings

10800,008550,007200,00

2000,00675,00

rentcellphoneBooksforcoursesStationeryclothes,shoesFoodandtoiletriesdentistcontributions tohousehold cleaningstuff

7875,002331,00

15126,752160,006411,005611,953114,00

1350,00


c. ThisextendedstatementisanestimatedstatementasithasbeencalculatedbasedonMapetla’sincomeandexpenditureforFebruary.


69t e r m 1 • u n I t 1 0

Someoftheitemswillbevariable.Forexample,itisunlikelythatshewillspendR1680,75onbookseverymonth.

d. Mapetla’soverallbalancefortheninemonthsshowsadebitbalanceasherexpenditureismorethanherincome,however,ifshehasboughtmostofhertextbooksinFebruary,shewillnotbespendingR1680,75fortheremainingeightmonths.Also,shewouldprobablynotspendR346,00atthedentisteverymonth.Ifwetakethesechangesintoaccount,herexpenditurewouldnotexceedherincome.

4. Joe & Flora’s Garden services (Branch 2) income‑and‑expenditure 2012


regularweekly gardenmaintenance

for24clientsPlantingnewgardens for5clientsclearingold vegetationfor

5clientsBankloantopurchase newequipmentSaleofseedlings (about110traysper

month)

93600,00

9650,00

3472,00

6000,00

2852,40

renttransportcosttelephoneElectricitySeedlingsfrom wholesalesuppliernewlawnmowersInsuranceonplants andequipmentFertiliser,mulch, compostWagestopart-time workers(gross)BankchargesInterestonbankloan

3000,0018000,00

1809,042475,59

1700,006000,00

2900,00

2475,00

15600,001188,00

534,00


10.2 Practise calculatingprofitandlossLearner’sBookpage135

1. Income–expenditure=R7843,00–R7911,45=–R68,45

Lou’sCyclerepairsmadealossofR68,45in2011.2. Income–expenditure=R2101–R1021

=R1080 DumileWalksYourDogmadeaprofitofR1080in2011.3. Income–expenditure=R28336,70–R29018,25

=–R681,55 FastBestCopyShopmadealossofR681,55in2011.4. Income–expenditure=R5539,20–R4921,85

=–R617,35 VegetableValuemadeaprofitofR617,35in2011.

10.3 Practise calculatingandcomparingchangesinincome-and- expenditurestatementsLearner’sBookpage135

1. a. Items of income that increased Items of income that decreased

SalaryJrobinson Mrobinsoninterestonbanksavings



b. Items of expenditure that increased

Items of expenditure that decreased

rates,water,refuseservicestelephoneElectricityFoodandgroceriesMedicalaidHouseholdandcarinsurancePetrol,carserviceSchoolandcollegefees

Bondrepaymentsonhouse

c. 2010endedwithacreditbalance–incomeexceededexpenditure. 2011endedwithadebitbalance–expenditureexceededincome. d. i. Electricityfor2011–electricityfor2010 =R5142,19–R4761,29 =R380,90 Percentageincrease:380,90______ 4761,29×

100___ 1 =8% ii. Homebondrepayments2011–homebondrepayments2010 =R47718–R48200 =–R482 Percentagedecrease: 482_____ 48200×

100___ 1 =1% iii. Telephone2011–telephone2010 =R5638,20–R5269,35 =R368,85 Percentageincrease:368,85______ 5269,35×

100___ 1 =7% iv. Foodandgroceries2011–foodandgroceries2011 =R35031,42–R32436,50 =R2594,92 Percentageincrease:2594,92_______ 32436,50×

100___ 1 =8% v. Wagesandsalaries2011–wagesandsalaries2010 =(R136032+R62890)–(R130800+R66200) =R1922 Percentageincrease: 1922_____________  (130800+66200)×

100___ 1 =0,98% Salary2011–salary2010=136032–130800

=5232 Percentageincrease: 5232______ 130800×

100___ 1 =4% Wages2011–wages2010=62890–66200

=–3310 Percentagedecrease:3310_____ 66200×

100___ 1 =5% vi. Incomefrombankinterest2011–incomefrombankinterest2010 =R1803,20–R1840 =–R36,80 Percentagedecrease:36,80____ 1840×

100___ 1 =2%


71t e r m 1 • u n I t 1 0

e. Income (total for 2012) expenditure (total for 2012)

SalaryJrobinson(net)WagesMrobinson(net)Interestonbanksavings

141473,0062890,00

1803,20

Bondrepaymentsonhouse(decr1%)rates,water,refuseservicestelephone(incrby8%)Electricity(incr8%)Foodandgroceries(incrby8%)MedicalaidHouseholdandcarinsuranceMonthlypaymentsonnewcarPetrol,carserviceSchoolandcollegefees

47240,828678,026032,875553,57

37833,9321388,50

9845,3315588,0017463,6043197,00


MRobinson’swageswillnotnecessarilydecreasein2012.Theyaremorelikelytostaythesameorincrease.Interestonbanksavingcouldincrease,decreaseorstaythesame,dependingontheinterestrate.Paymentsonthenewcararelikelytoremainthesame.Alltheotheritemsontheincome–and–expenditurestatementwillprobablyincrease.Ifthebondrepaymentsfollowthesametrendsasin2011,theywilldecreaseby1%.However,thiswilldependontheinterestrates.

f. Ascanbeseenfromtheincome-and-expenditurestatement,theRobinsonfamilyislikelytoend2012withadebitbalance.

2. a. In2011thebusinessshowedaprofit. In2012thebusinessshowedaloss. b. Income2012–income2011 =R141212,00–R144860,00 =–R3648,00 Percentagedecrease= 3648______ 144860×

100___ 1 =2,52% c. Productioncosts2011:R55050,00 Productioncosts2012:R59976,00 Productioncost2012–productioncost2011 =R59976,00–R55050,00 =R4926.00 Percentageincrease=4926_____ 55050×

100___ 1 =8,95% d. Runningcosts2011:R80300 Runningcosts2012:R83533,00 Runningcost2012–runningcost2011 =R83533,00–R80300,00 =R3233,00 Percentageincrease=3233_____ 80300×

100___ 1 =4,03% Theproductioncostwentupmuchmorethantherunningcosts.

e. Income (total for 2013) expenditure (total for 2013)

Photocopies(A4)PrintingA1plansforarchitectsPrintingfancystationery

7705,3527231,0431717,07

running costsWagesandsalariesrentElectricity,phoneofficeadministrationProduction costsPrinterrentalsPaperInk

50849,8616715,5411469,31

7864,67

30070,2022879,5012394,15




10.4 Practise calculationswithpersonalbudgetsLearner’sBookpage147

1. a. Nomonde’snetsalary=R63420–R5785=R57635p.a.

nomonde’s annual expenses

transportFood,groceriesandentertainmentPhoneandinternetclothes,books,stationery

r130×52=r6760r1200×12=r3890

r400×12=r4800r7220

total annual expenses r 37 070

Nomondeearnsenoughtocoverherannualexpenses. b. Hersavingperyear=R57635–R37070

=R20565 Hersavingpermonth=R20565______ 12 =R1713,75 c. Expensesnextyear=R37070+5,6%ofR37070

=R39145,92 NomondewouldneedtoearnR39145,92,whichwouldnotbea

problemevenifsheispaidthesamesalary.2. a. EachweekendNomandeearns:6×R55=R330,00 NumberofweekstosaveR24000=24000_____ 330 =72,73weeksofsaving Shewouldhavetosaveherearningsfor73weekends. b. Yes,sheisnotabletosaveR1713,75eachmouth. c. Amountshecanaffordtopayeachmonth=R1713,75+(4×R330)

=R3033,753. a. Ifweassumethattherearefourweeksinamonth, Brendan’smonthlysalary=R2750×4

=R11000net Savings=R11000–R5345

=R5655 Percentageofearningshecansaveeverymonth =5655_____ 11000×

100___ 1 =51,41% b. Totalcostofcomputer=R4500+1,5%ofR4500

=R4567,5 Monthlypayment=R4567,5______ 12 =R380,63 Brendancaneasilyaffordtomaketherepayments. c. Wearenotgivenanydetailsaboutthecomputerandalsowearenot

toldhowolditis.R4500soundsratherexpensiveforanoldcomputerandsinceBrendanhasthemoney,hewouldprobablybebetteroffpayingabitmoreandbuyinganewcomputer.

10.5 Practise preparingpersonal,householdandbusinessbudgetsLearner’sBookpage148

Learnersworkoutpersonalbudgets.


73t e r m 1 • u n I t 1 1

10.6 Practise changingabudgettosuitchangingcircumstancesLearner’sBookpage149

1. Grade 1 Costforonesetofallthetextbooks=R122,70 TotalcostforGrade1textbooks=R122,70×264

=R32392,80 Costoftheteachers’guides=4×3×49,95

=R599,40 TotalcostforGrade1=R32992,20 Grade 2 Costforonesetofallthetextbooks=R131,70 TotalcostforGrade2textbooks=R131,70×212

=R27920,40 Costofteachers’guides=4×3×R49,95

=R599,40 TotalcostforGrade2=R28519,80 Grade 3 Costforonesetofallthetextbooks=R137,70 TotalcostfortheGrade3textbooks=R137,70×280

=R38556,00 Costofteachers’guides=4×3×R49,95

=R599,40 TotalcostforGrade3=R39155,40 Totalcostforalltextbooks=R32992,20+R28519,80+R39155,40

=R100667,402. Yes,theschoolbudgethadenoughmoneytocoverthecostofthe

textbooks.

3. amended budget for textbooks for Grades 1, 2 and 3

Grade 1 Grade 2 Grade 3

Increasednumberoflearners 275 221 291

costofbooksbeforediscount 33742,50 29105,70 40208,40

costofbooksafterdiscount 32561,51 28087,00 38801,11

costofteachersguidesafterdiscount 578,42 578,42 578,42

total cost per grade r33 139,93 r28 665,42 r39 379,53

Revisedtotalfortextbooks=R33139,93+R28665,42+R39379,53=R101184,88

4. Theschoolwillhaveenoughfundstocoverthecostofthebooks.

10.7 Investigation: PrepareabudgetforasingleeventLearner’sBookpage151

Answerswilldiffer/classdiscussion.



Unit 11Cost price and selling priceLearner’s Book pages 152–168

Teaching tips• TheconceptsinthisunithavenotbeentaughtpreviouslyinMathematical

Literacyalthoughlearnersmayrememberthemfromearliergradesandworkwithpercentage,profitandloss.

• Somelearnersmaythinkcostpriceiswhatanitemcostswhenyoubuyitintheshop.Remindthemthatshopshavetobuyormakethethingstheysell.Thepricetheypayforanitemisthecostprice.Similarly,thetotalcostofmakinganitemisitscostprice.Shopsthenaddonanamounttocovertheirexpensesandmakeaprofitbeforesellinganitemtothecustomers.Thepriceanitemissoldforisthesellingprice.

• Inbasicterms,sellingprice–costprice=profitperitem.However,inrealterms,thisisnotthetotalprofitforthebusiness.AshopkeeperwhobuysthingsforRxandsellsthemforR10000xdoesnotactuallymakeR10000profit.Theshopkeeperstillneedstopaysalariesandrunningcostsbeforeheorshecanworkoutwhattheactualnetprofitis.Thisisanimportantconceptandlearnerswhohaveentrepreneurialexperiencewillunderstandthisandbeabletogiveexamplestoenrichthelessons.

• Youmayliketoinvitealocalsmall-businessownertoschooltotalktothelearnersaboutcostprices,sellingpricesandprofitingeneralterms.

Solutions11.1 Practise calculatingcostpricesLearner’sBookpage155

1. a. Numberofscarvesmadeannually=75×12=900 b. Costprice=(R980×12)+R3400=R7850=R23010p.a. c. Costpriceperscarf=23010_____ 900 =R25,572. Monthlyrunningandproductioncosts=(R420×4)+( R6950_____ 6 ) =R2833,33 Costpriceofasinglecrate=R2833,33_______ 40 =R70,963. Monthlycosts=R500+R340=R840 Costpriceperlearnerpermonth=R840____ 12 =R70

11.2 Practise identifyingreasonablesellingpriceLearner’sBookpage158

Answerswilldiffer.

11.3 Practise calculatingprofitandlosswithcostpriceandsellingpriceLearner’sBookpage163

1. a. Profit=sellingprice–costprice=R11,95–R1,72=R10,23

b. Profit=sellingprice–costprice=R59,00–R7,95=R51,05 c. Profit=sellingprice–costprice=R99,95–R129,40=–R29,45 AnegativeprofitshowsthatalossofR29,45hasbeenmade.


75t e r m 1 • u n I t 1 1

d. Profit=sellingprice–costprice=R149,50–R0,95=R148,55 e. Profit=sellingprice–costprice=R75,50–R285,00=–R209,50 AnegativeprofitshowsthatalossofR209,50hasbeenmade.2. CostpricepersingleA4copy=R150,00______ 500 =R0,30

=30c Tomakeaprofitof50cpercopy,theshopmustselleachsingleA4copy

for80c.3. Costpriceofonesliceofpizza=R35,00_____ 8 =R4,38 Profit=sellingprice–costprice=R9,50–R4,38=R5,124. a. Costpricepersetofgiftwrapandcard=2×R4,50+2×R1,25

=R11,50 Profit=sellingprice–costprice=R39,95–R11,50=R28,45 b. IfshesellsthesetsforR11,50each,shewilljustbreakeven.Ifshe

sellsthesetsforanamountgreaterthanR11,50,shewillmakeaprofit.

11.4 Practise calculatingpercentageprofitorlossLearner’sBookpage164

1. 1. a. Percentageprofit= profit_______ costprice×100___ 1

=10,23____ 1,72×100___ 1

=594,77% b. Percentageprofit=51,05____ 7,95×

100___ 1 =642,14% c. Percentageloss= loss_______ costprice×

100___ 1

=29,45_____ 129,40×100___ 1

=22,76% d. Percentageprofit=148,55_____ 0,95 ×

100___ 1 =15636,84%

e. Percentageloss=209,50_____ 285,00×100___ 1 =73,51%

2. Percentageprofit=50__ 30×100___ 1 =166,67%

3. Percentageprofit=5,12___ 4,38×100___ 1 =116,89%

4. Percentageprofit=28,45____ 11,50×100___ 1 =247,39%

2. a. Province Percentage mark‑up selling price of a pocket of potatoes in May

Limpopo 55 r6,30+55%ofr6,30=r9,77

Easterncape 35 r6,30+35%ofr6,30=r8,51

northerncape 14 r6,30+14%ofr6,30=r7,18

FreeState 23 r6,30+23%ofr6,30=r7,75

KZn 26 r6,30+26%ofr6,30=r7,94

b. Mark-uponpotatoesinLimpopoinJune:30% Sellingprice=R12,95 =100%ofcostprice+30%ofcostprice \12,95=130%ofcostprice 12,95=130___ 100×costprice

12,95×100___ 130=costprice Costprice:R9,96



c. Mark-uponpotatoesinKZNinMay=26% Mark-uponpotatoesinFreeStateinJuly=23,5% CostpriceofPotatoes=R6,30inMay(wearetoldthis). InKZN,sellingprice=R16,45 =100%ofcostprice×23,5%ofcostprice =123___ 100×costprice \R16,45×100____ 123,5=costprice=R13,32 ThecostpriceofthepotatoeswaslowerinMay(R6,30)andmore

thandoubleinJuly(R13,32) d. Answersmaydiffer.Apossibleanswersithatifpotatoesaregrown

locally,theywouldbecheaperastherewouldbenotransportcostsinvolved.

11.5 Practise budgetingtoachieveapercentageprofitLearner’sBookpage166

1. a. Item Cost price

selling price at 10% profit



sunglasses 12,40 13,64 14,63 16,74

sunglasses with mirror lenses

15,20 16,72 17,94 20,52

denim handbags 21,95 24,15 25,90 29,63

denim rucksacks 28,35 31,19 33,45 38,27

Leather handbags 45,50 50,05 53,69 61,43

Leather rucksacks 52,80 58,08 62,30 71,28

Cellphone pouches 3,95 4,35 4,66 5,33

b. Answerswilldiffer.2. a. Profit=income–expenditure

=R127314,80–R99163,70=R28151,10

b. Percentageprofit= profit_________ totalincome×

100___ 1

=28151,10________ 127314,80×100___ 1

=22,11% c. Profit=income–expenditure P=I–99163,70.......................... (1) Percentageprofit=profit_____ income×

100___ 1

\P__ I×100___ 1 =45%

\P__ I=0,45............... (2) SubstitutingP=I–99163,70into(2) I–99163,70_________ I =0,45 \I–99163,70=0,45I \I–0,45I=99163,70 \0,55I=99163,70 \I=99163,70_______ 0,55 =180297,64 Tomakeaprofitof45%,theywouldneedanincomeofR180297,64.


77t e r m 1 • u n I t 1 2

d. Expenditurefor2013:R99163,70+13,5%ofR99163,70 Expenditure2013–112550,80 Profit=income–112550,80 P=I–112550,80........................(1) Percentageprofit=P__ I×

100___ 1 =45%

\P__ I=0,45...............(2) Substituteequation1into(2). I–112550,80__________ I =0,45 \I–112550,80=0,45I \I–0,45I=112550,80 \0,55I=112550,80 \I=112550,80________ 0,55 =204637,82 Ifexpensesincreaseby13,5%andtheywanttomakeaprofitof45%,

theywouldneedanincomeofR180297,64.

Unit 12Break‑even analysisLearner’s Book pages 168–177

Teaching tips• Break-evenpointsongraphswerecoveredinUnit4.Remindthelearners

aboutthisbeforestartingtodiscusstheconceptsinthisunit.• Theunitstartswithanexampleofcostsandincomefromabusiness

venture,thenitcoversusingbreak-evenanalysistomakedecisionsandchoosebetweentwodifferentoptions.Pointouttolearnersthatagraphisamucheasierwaytoshowcomplexdataaboutsteppedtariffsanddrawyourowngraphsusingtwodifferenttariffoptionsfromarealbrochureasafurtherexample.

Solutions12.1 Practise break-evenanalysisusingequationsLearner’sBookpage176

1. LetnumberofdogsBettinamustwalkeveryweekinordertobreak-evenbex.

30x=360 \x=360___ 30 x=12 So,Bettinamustwalk12dogsperweekifshewantstobreak-even.2. LetthenumberofpagesAyandatranslatespermonthbex. 85x=4500 \x=4500____ 85 \x=52,94 Ayandamusttranslate53pagesinordertobreak-even.



12.2 Practise break-evenanalysisusinggraphsLearner’sBookpage177

1. Length of phone call standard optioncost

Closer optioncost

10 4,20 0

20 8,40 0

30 12,60 0

40 16,80 4,30

50 21,00 8,60

60 15,20 12,90

70 29,40 17,20

80 33,60 21,50

90 37,80 25,80

100 42,00 30,10

200 84,00 73,10

300 126,00 116,10

400 168,00 159,10

500 210,00 202,10

600 252,00 245,10

700 294,00 288,10

800 336,00 331,10

900 378,00 374,10

1000 420,00 417,10

1100 462,00 460,10

1200 504,00 503,10

1300 546,00 546,10

2. TheCloserrateischeaperforanycalllessthat1290minutes,whichis21,5hours.Sodespitethehighermonthlycharge,thiswillbethebetteroptionforthemajorityofpeople.Theaveragephonecallisgenerallylessthan30minuteswhichwouldbefreeonCloser.OntheStandardoption,acallof30minuteswouldcostR12,60.

300200100 500Length of phone call

Cost

(R)

Standard option

Closer option

400 800700 1 1001 000 1 4001 300600 900 1 2000

50100150200250300350400450500550600


79t e r m 1 • u n I t 1 2

12.3 Assignment: Break-evenanalysisforat-shirtbusinessLearner’sBookpage177

1. a. Totalcosts=R800+R7perT-shirt b. LetthenumberofT-shirtsMoeketsineedstosellinorderto

break-evenbex. ThenumberofT-shirtssold=R800+R7forhowevermanyT-shirts

hesells. 15x=800+7x \15x–7x=800 \8x=800 \x=800___ 8 =100 Moeketsimustsell100T-shirtsinordertobreak-even.2.

1000

200300400500600700800900

1 0001 1001 2001 3001 4001 5001 6001 7001 800

10 150

ABCD

xy

1401301201101009080706050403020Number of T-shirts

Cost

(R)

GraphAshowsincreaseincostasthenumberofT-shirtsincrease. GraphBshowsincreaseinincomeasthenumberofT-shirtssoldfor

R15perT-shirtincreases.3. GraphCshowstheincreaseinincomeasmoreT-shirtsaresoldfor

R20perT-shirt. Thebreak-evenpoint(x)isreachedwhen60T-shirtsaresold. GraphDshowstheincreaseinincomeasmoreT-shirtsaresoldfor

R25perT-shirt. Thebreak-evenpoint(y)isreachedwhen45T-shirtsaresold.

Revise and consolidate:FinanceLearner’sBookpage179

1. Answersmaydiffer.Discusslearners’answerswiththeclass.2. a. MsLWDlamini b. 366EndRoad,Newlands,7700 c. 137702816 d. rates,water,refuse,sewerage e. water:(1)6,9040litresfree;(2)5,1780kl@R2,9900;(3)10,9320kl

@R8,5100;(4)13,9880kl@R12,6100:R290,05 Learnerscandiscusstheothertariffs. f. January2011 g. R0,00



h. R1199,62 i. R1199,62 j. 14/02/20113. a. EliteStores b. DexterJordaan c. ID:8209031223013 Employeenumber:J02-D19 d. Shelfpacker e. 01/08/2012to31/08/2012 f. R1185,20 g. weekly h. R29,63perhour i. R1185,20 j. R59,20perhour k. R177,78 l. R1362,98 m. PAYE–R190,82 Union–R13,62 n. R1158,544. a. Option3 b. Onweekdays,Option1chargesR1,23percalluptoanhourlong

whilethereisnochargewithOption2. Atweekends,bothOption1and2arethesame. c. ThesubscriptionamountforOption3includesthecostofcallsmade

withinthemonthaccordingtotheguidelinessetout. d,e. Answerswilldiffer.

5. a. expenditure Income

twodaysinrecordingstudio@r2800/day

5600 300cd’s@r75/cd 22500

Soundengineerfortwo8-hourdays@r375/h

6000

designerfortenhours@r225/h

2250

300cdsatr200/75 800

Jewelcasesfor300cdsatr99/100

297

computerpaperandsoonatr3,50/cd

1050

total r15 997 r22 500

b. Mokokomakesaprofit. c. Percentageprofit:R22500–R15997_____________ R15997 ×100___ 1 =40,65%

d. 70%ofR15997=70___ 100×15997=11197,90 Totalincome=R15997+R11197,90

=R27194,90 CostperCD:27194,90_______ 300 =R90,65 e. Oldsellingprice:R75/CD Fixedproductioncosts:R13850 CostsperCD:R2,67+R0,99+R3,50=R7,16


81t e r m 1 • u n I t 1 2

number of Cds 1 2 10 20

Cost (r) 13857,16 13864,32 13921,00 13993,20

number of Cds 30 50 100 150 200 250

Cost (r) 14064,80 14208,00 14566,00 14924,00 15282,00 15640,00

number of Cds 300 350 400

Cost (r) 15998 16356 16714

number of Cds sold 10 20 50 100 150 200 250

Income (r) 750 1500 3750 7500 11250 15000 18750

Thebreak-evenpointliessomewherebetween200and250CDs. Thebreak-evenpointofcostsandincomeisat205CDs.

Income and cost at old price (R74/CD)

Number of CDs

Cost/

incom

e (R)

2 000

4 000

6 000

8 000

10 000

12 000

14 000

16 000

18 000

20 000

22 000

Cost

Income

0 50 100 150 200205 break-even point

250 300 350 400

Newsellingprice:R50foreachCD Thecostsdonotchangesoprevioustableapplies.

number of Cds sold 50 100 150 200 250 300 350 400

Income (r) 2500 5000 7500 10000 10500 15000 17500 20000

Thebreak-evenpointliessomewherebetween300and350CDs. Thebreak-evenpointofcostsandincomeisat321CDs.



Income and cost at old price (R74/CD)

Number of CDs

Cost/

incom

e (R

)

2 000

4 000

6 000

8 000

10 000

12 000

14 000

16 000

18 000

20 000

22 000

Cost

Income

0 50 100 150 200 321

break-even point250 300 350 400


83t e r m 2 • u n I t 1

terM 2

Worked ansWers

Unit 1Interest and interest ratesLearner’s Book pages 186–202

Teaching tips• Learnerswillneedtomakecalculationsusingpercentages.Ifnecessary,

revisethebasicskillsonpages497to537oftheLearner’sBookbeforeworkingthroughthisunit.Alsoworkthroughthetermsusedtotalkaboutinterestonpage185oftheLearner’sBooktorevisethese.

• InGrade10thelearnersworkedwithsimpleinterest.Inreallife,mostinterest(onbothloansandinvestments)iscompounded.Thatmeansitisworkedoutatsettimesandaddedtotheprincipalamount.So,ifyouhaveR100andinterestiscompoundedannuallyatarateof5%,youwillhaveR105afteroneyear.Thenextyear,theinterestisworkedoutonR105notontheoriginalR100,soyouearnslightlymore.Obviouslywhenyouowemoney,thismeansyoupaymoreinterestontheoutstandingbalance.

• Learnersdonotneedtolearnorusetheformulaforcompoundinterestatthislevel.Rathertheywilldoaseriesofperiodonperiodcalculationstoworkoutamountsandsolveproblems

• Comparingsimpleandcompoundinterestratesisanimportantlifeskillthatwillhelplearnersbecomecriticalandinformedconsumers.Theskillsthatthelearnersdevelopedinworkingwithbreak-evenvaluescanbeusedtographthistypeofcomparison.Whatisimportantisthatthelearnersrealisethatcompoundinterestisamuchbetteroptionthansimpleinterestforsavings,butthatitisalsoamuchmoreexpensiveoptionforloansandotherdebts.

Solutions1.1 Practise calculatingsimpleinterestLearner’sBookpage188

1. a. i. 10%ofR5000=R500 Simpleinterestoverthreeyears=3×R500

=R1500 ii. Totalamount=R5000+R1500

=6500 b. i. 8%ofR9000=R720 Simpleinterestover24months(2years)=2×R720


=R10440 c. i. 9,5%ofR12000=R1140 Simpleinterestovertwoyears=2×R1140

=R2280



ii. Totalamount=R12000+R2280=R14280

d. i. 11%ofR23000=R2530 Simpleinterestoverfiveyears=5×R2530


=R356502. a. i. 9%ofR10000=R900 Simpleinterestoverthreeyears=3×R900


=R12700 Monthlyrepayments=12700_____ 36

=R352,78 b. i. 9%ofR26000=R2340 Simpleinterestoverthreeyears=3×R2340


=R33020 Monthlyrepayments=33020_____ 36

=R917,22 c. i. 9%ofR4000=R360 Simpleinterestoverthreeyears=R×R360


=R5080 Monthlyrepayments=5080____ 36

=R141,113. a. i. Interest:R170 ii. Monthlyrepayments:R48,75 b. i. Interest:R357,00 ii. Monthlyrepayments:R48,81 c. i. Interest:R255,00 ii. Monthlyrepayments:R125,28 d. i. Interest:R433,50 ii. Monthlyrepayments:R59,26 e. i. Interest:R229,50 ii. Monthlyrepayments:R112,75 f. i. Interest:R187,00 ii. Monthlyrepayments:R53,63

1.2 Practise calculatingcompoundinterestLearner’sBookpage191

1. a. i. Year1:Amount=R200+2%ofR200=R200+R4=R204

Compoundinterest=R4 ii. Totalamount=R204 b. Year1:Amount=R200+2%ofR200

=R200+R4=R204


85t e r m 2 • u n I t 1

Year2:Amount=R204+2%ofR204=R204+R4,08=R208,08

Year3:Amount=R208,08+2%ofR208,08=R208,08+R4,16=R212,24


i. Compundinterest=R216,48–R200=R16,48

ii. Totalamount=R216,48 c. Year1:Amount=R750+1,25%ofR750

=R750+R9,38=R759,38

i. Compundinterest=R9,38 ii. Totalamount=R759,38 d. Year1:Amount=R8000+3,4%ofR8000

=R8000+R272=R8272


i. Compundinterest=R553,25 ii. Totalamount=R8553,25 e. Year1:Amount=R6340+10%ofR6340

=R6340+R634=R6974







i. Compundinterest=R6014,86 ii. Totalamount=R12354,86 f. Year1:Amount=R25000+12%of25000

=R25000+R3000=R28000

Year2:A=R28000+12%ofR28000=R28000+R3360=R31360



i. Compundinterest=R6360 ii. Totalamount=R313602. Usethesamemethodasshowninquestion1. a. Balance=R2460 b. Balance=R2584,54 c. Balance=R2924,173. a. Bank 1 Amount=R12630–12×R12,50(bankcharges)

=R12480(afteroneyear) Bank 2 Amount=R12612(afteroneyear) b. Bank 1 Amount=R15498,57–5×(12×R12,50)(bankcharges)

=R14748,57(afterfiveyears) Bank 2 Amount=R15388,45(afterfiveyear) Bank2willgiveLouiseabiggercreditbalanceafteroneyearand

afterfiveyears.

1.3 Practise calculatingdailyandmonthlyinterestonaccountswith changingbalancesLearner’sBookpage196

1. a. Interestforoneday=2,5%ofR500× 1___ 365=0,0342…(keepthisvalueonyourcalculator)

Thereare30daysinJune,sointerestforJune=0,0342×30=R1,03

b. Thisinterestwillbecapitalisedon1JulysothebalanceintheaccountwillbeR500+R1,03=R501,03

c. ThebalanceinZodwa’saccounton2JulywillbeR501,03(interestisonlycapitalisedattheendofthemonth).

2. a. Interestforoneday=8%ofR3000× 1___ 365=0,6575…(keepthisvalueonyourcalculator)

Balanceinaccounton1April=R3000+16×0,6575=R3010,52

BalanceinaccountwillbeR3010,52on15April b. InterestforonedayinApril=8%ofR3010,52× 1___ 365

=R0,65984…(keepthisvalueonyourcalculator)

Whenhecloseshisaccounton16April,theclosingbalancewillbe:R3010,52+15×0,65984=R3020,42

3. a. Interestcalculation 1Jan. R1000+3,5%ofR1000× 1___ 365=R1000+0,09589

8Jan. R1220+3,5%ofR1220× 1___ 365=R1220+0,11698

15Jan. R1580+3,5%ofR1580× 1___ 365=R1580+0,1515

22Jan. R1855+3,5%ofR1855× 1___ 365=R1855+0,17787

29Jan. R2335+3,5%ofR2335× 1___ 365=R2335+0,2239 TotalinterestforJan. =(7×0,09589)+(7×0,11698)+(7×0,1515)+(7×0,17787)+(7×0,2239) =R4,47


87t e r m 2 • u n I t 1

b. Ifheropeningbalanceon1FebruarywereR1000,shewouldearnlessinterestthaninJanuaryasFebruaryhasfewerdaysthanJanuary.

Or IfshecapitalisestheinterestsheearnedinJanuary,givinghera

greateropeningbalance,shemightearnmoreinteresteventhoughtherearefewerdaysinFebruary.

4. a. i. Balanceafter3years:R16035,06 ii. Balanceafter3,5years:R16501,63 b. Balanceafter4years:R16981,77 BalanceafterwithdrawalofR1500=R16981,77–R1500

=R15481,77 Balanceafterfouryearsandonemonth:R15555,18.

1.4 Practise comparinginterestratesLearner’sBookpage198

1. Compoundinterestof3,75%p.a.

Years account balance

1 r350,00+3,75%ofr350,00=r363,13

2 r363,13+3,75%ofr363,13=r376,74

Simpleinterestof4,5%p.a.


1 r350,00+4,5%ofr350,00=r350,00+r15,75=r365,75

2 365,75+r15,75=r381,60

Janetshouldtakeherbrother’sloan.2. a. i. Interestafteroneyear=12%ofR3460,00

=R415,20 ii. Interestaftertwoyears=2×R415,20

=R830,40 b. i. Accountbalanceafteroneyear=R3460,00+R415,20–R18,00

=R3857,20 ii. Accountbalanceaftertwoyears=R3857,20+R415,20–R18,00

=R4254,40 c. i. Balanceafteroneyear=R3460,00+7,5%ofR3640,00

=R3719,50 ii. Balanceaftertwoyears=R3719,50+7,5%of3719,50

=R3998,46 d. Thebankthatoffers12%p.a.simpleinterest e. Balanceafterthreeyears=R3998,46+7,5%of3998,46

=R4298,35 Afterthreeyearshewillbeabletoinvestinthefixeddepositaccount.

1.5 Investigation: compareinterestoptionsatdifferentbanksLearner’sBookpage199

1. ThefamilyhaveR2500todepositrightnowsotheyqualifytoinvestatbankB.WecanimmediatelyexcludebankCasitpaysalowerinterestratethanbankB.



Bank a


1 r2500,00+r206,25=r2706,25

2 r2912,50

3 r3118,75

4 r3325,00

5 r3531,25

6 r3737,50

7 r3943,75

8 r4150,00

9 r4356,25

10 r4562,50

11 r4768,75

12 r4975,00

Andsoon

TheinvestmentwillgrowbyR206,25peryear.

Bank B


1 r2500,00+6,15%ofr2500,00=r2653,75

2 r2653,75+6,15%ofr2653,75=r2816,96

3 r2990,20

4 r3174,10

5 r3369,30

6 r3576,51

7 r3796,47

8 r4029,95

9 r4277,80

10 r4540,88

11 r4820,14

12 r5116,58

Andsoon

Eachyeartheaccountbalanceearnsinterestof6,15%.2. BankA:Itwilltake85yearsforthefamily’ssavingtoreachR20000. BankB:Itwilltake35yearsforthefamily’ssavingtoreachR20000.

1.6 Practise usinggraphsofinterestgrowthLearner’sBookpage202

1. a. i. Aftertwoyearsinvestment2isworthmore. ii. Aftersevenyearsinvestment2isworthmore. b. Aftersixyearsinvestment1hasearnedR270. c. Aftertwoyearsinvestment2hasearnedR555. d. Obviously,thebiggertheinitialinvestment,thebiggertheinterestyou

willearn.


89t e r m 2 • u n I t 2

2. a. R8606,42 b. R8907,65

01 2 3 4 5 6

2 000

4 000

6 000

8 000

10 000

1 000

3 000

5 000

7 000

9 000

Loan at 3,5% p.a. compound interest

Number of years

Amou

nt ow

ing (R

)3. Amountowingafterthreeyears:R8315,39–R5000,00=R3315,39 Amountowingafterfouryears:R3431,43 Amountowingafterfiveyears:R3551,53 Amountowingaftersixyears:R3675,834. a.

0 20Number of years

Bank A

Bank B

Acco

unt b

alanc

e (R)

30 35 40 50 60 70 80 90100

1 0002 000

2 5003 0004 0005 0006 0007 0008 0009 000

10 00011 00012 00013 00014 00015 00016 00017 00018 00019 00020 000

(10; 4562,50)(10; 4540,88)

b. Thetablesandgraphsforthefirst10yearsshowthatbankAgivesahigherbalance.ThereafterbankBgivesahigherbalance.EventhoughbankBoffersalowerinterestratethanbankA,bankB’sinterestiscompounded,sotheaccountbalancegrowsmorerapidly.AtbankAittakes85yearstoreachR20000,whilebankBtakes35years.InvestingatbankAisnotasensibleideaasitgivesaverypoorreturninthelongterm.IntheshorttermbankAisafairinvestment.

ThegraphforbankAisastraightlinethatindicatsthesameinterestthatisearnedeachmonth.ThegraphforbankBiscurvedindicatingthattheamountofinterestearnedincreaseseachyear.



Unit 2BankingLearner’s Book pages 203–227

Teaching tips• Learnersmayalreadyhaveopenedabankaccount.Iftheyhave,

encouragethemtobringinformationtoclassabouttheaccounttheyopened.Discouragethemfromsharingaccountdetailsthough.

• Today,mostemployersinsistthatworkershaveabankaccountasitistooriskytopaypeoplecash,andchequepaymentsareexpensiveandoutdated,somostcompaniesdon’tusethemanymore.Thisunitexploresdifferentaccountsandprovidesusefulguidancetohelplearnerschoosethemostsuitableaccountfortheirneeds.

• Aslearnersworkthroughthisunit,theywilldealwithrealbankdocumentsandfeestructuresandperformcalculationsanddrawgraphstocomparedifferentoptions.Rememberthoughthatthesechargeschangeeachyear,soitwillbeusefultocollectarangeofrealbankcharges.Youcangetbrochuresfrombranchesofdifferentbanksandaccessbankwebsitesanddownloadfeestructures.Youmayalsobeabletofindadvertisementsthatincludebankfees(CapitecBankforexampleisupfrontabouttheirfeesandprintstheseinadvertisementsinthenewspapers)andarticlesthatcomparethecostofaccountsfordifferentbanks.Itisimportantthatlearnersrealisethereisacostinvolvedinbankingandthattheycansaveconsiderableamountsofmoneybychoosingtherightoptionand/orbycomparingofferingsfromdifferentbanks.

Solutions2.1 Practise choosingasuitablebankaccountLearner’sBookpage206

Answerswilldiffer.Possibleanswersincludethefollowing.1. AcurrentaccountwithadebitcardwouldworkwellforMrMorofe.He

wouldnotneedtocarrylargeamountsofcashwithhimashecouldpayforhispurchaseswithhisdebitcard.Hecouldeasilywithdrawcashifheneededtodoso.Hewouldhavetowatchoutforbankcharges,butasapensionerhemightqualifyfordiscountedbankcharges.

2. MrsTshwetealreadyhasabankaccount,whichisprobablyacurrentaccount.Shecouldconsideropeningasavingsaccountsoshecouldearninterestonmoneysheisabletosave.Thiswouldhelpherachieveheraimofopeningahairsalon.

3. Theclubshouldopenasavingsaccountorevenafixeddepositaccountoversixmonths.Inthesewaystheywillbeabletoearninterestonmoneytheyarenotcurrentlyusing.

4. Dariencouldopenacurrentaccounttocaterforhisdailyexpensesandafixeddepositaccountforthebalanceofhisinheritance.Thiswouldgivehimabetterinterestrateandhelphimachievehisaimofstartinghisownbusinessmorequickly.


91t e r m 2 • u n I t 2

2.2 Practise estimatingandcalculatingfeespertransactionLearner’sBookpage214

1. a. Yes,thereisamonthlyfeeforallaccounts. b. Yes,withafewexceptionssuchaswhenyoumakeachequedepositat

anABSAATM. c. Thereisnocharge. d. 2×R1,05=R2,10 e. i. R3,75+8×R1,01=R11,83 ii. R20,00+8×R1,01=R28,80 iii. R9,75+8×R1,01=R17,83 f. Yes. g. Yes. h. R3,15 i. R3,75+10×R0,75=R11,25 j. Transaction Charge Total TwochequesdepositedatATM Nocharge CashwithdrawalfromATM R200 R3,75+2×R1,01 R500 R3,75+5×R1,01 R450 R3,75+5×R1,01 R47,03 R1500 R3,75+15×R1,01 R80 R3,75+1×R1,01 Electronicpayment(R864) R3,75+9×R1,01 R10,50 Prepaidtop-up Nocharge BalancerequestatATM(×2) R2,00 Fullaccountstatementatbranch R5,50 Stoporders: R1400(internal) R3,15 R650(internal) R3,15 Monthlyaccountfee(currentaccount):R21,00 Totalmonthlyfee:R92,332. Pricingoption2–RebateBankingwouldbethebestdealforthelistof

transactionsin1j,providedtheminimumbalanceismaintained. Ifmaintainingaminimumbalanceisaproblem,option4wouldbethe

nextbestdeal.3. Answerswilldiffer.

2.3 Assignment: comparestudentfeepackagesatdifferentbanksLearner’sBookpage218

1. Possibletransactionsacollegeoruniversitystudentmightneedtodo: • cashwithdrawals • cash/chequedeposit • debitcardpurchases • electroniclinkedaccountpayments. Obviously,differentstudentswillhavedifferentrequirementsdepending

onanumberoffactors.Forinstance,studentswholiveathomewiththeirfamilieswillhavedifferentrequirementsfromthosewhoisinaresidenceorinaflat.Ifyoudofiveorlesstransactionspermonth,theStudentAchieverPlanisagoodoption.

2–4. Answerswilldiffer.



2.4 Practise calculatingthecostoflatepaymentoncreditcardsLearner’sBookpage225

1. Minimumpayment=5%ofR5784,30=R289,22

2. JabuwillstartthemonthwithadebitbalanceofR5495,08.3. Interest=18,4%×1__ 12×R5495,08

=R84,26

4. Month opening balance

Credit card purchases

Interest on debit balance

Monthly debit balance

Minimum payment due (5% of debit balance)

Payment made into the account

Month1 r0,00 r1235,00 r0,00 r1235,00 r61,75 r61,75

Month2 –r1173,25 r988,40 r22,49 r2184,14 r109,21 r109,21

Month3 –r2074,93 r3560,00 r39,77 r5674,70 r283,73 r283,73

Month4 –r5390,97 r2298,35 r103,33 r7792,65 r389,63 r389,63

Month5 –r7403,02 r1049,20 r141,89 r8594,11 r429,71 r429,71

Month6 –r8164,40 r817,65 r156,48 r9138,53 r456,93 r456,93

Totals –r8681,60

2.5 Practise calculatinginterestondifferenttypesofbankaccountsafter thesameperiodoftimeandwiththesamestartingbalanceLearner’sBookpage227

1. a. b. c.three months six months twelve months

Current account r24,71 r49,71 r100,17

savings account r21,06 r42,23 r84,91

Fixed deposit account r59,87 r120,64

Credit card account r24,35 r48,84 r98,28

Calculationsforinterestearnedonacurrentaccount Month1: Simpleinterestperday=2,5%ofR4000× 1___ 365

=0,2739… Interestpermonth=30×0,2739

=R8,22 Month2: Capitalisethepreviousmonth’sinterest R4000+R8,22=R4008,22 Simpleinterestperday=2,5%ofR4008,22× 1___ 365


=R8,24 Month3: Capitalisethepreviousmonth’sinterest R4008,22+R8,24=R4016,46 Simpleinterestperday=2,5%ofR4016,46× 1___ 365


=R8,25 Capitalisetheinterest:accountbalance=R4016,46+R8,25

=R4024,71 Accountbalanceafterthreemonths=R4024,71


93t e r m 2 • u n I t 3

Interestearned:R24,71Usingthesamemethod,completethetable.Iftheanswersarenotexactlythesame,thedifferencecouldbearesultofroundingoffdifferences.

2. Thebestoptionwouldbetoinvestinafixeddepositaccount(interestof3%p.a.)andthenleavethemoneyinthecurrentaccountfortheremainingtwomonths.

3. a. Accordingtotheratesgiven,heshouldkeephismoneyinhiscurrentaccount.

b. AfterhehassavedR1000,whichwilltakehimfourmonths,hecouldtransferhismoneytoafixeddepositaccountthatwouldgivehimabetterinterestrate.

Unit 3Bank loans and investmentsLearner’s Book pages 228–244

Teaching tips• Thisunitbuildsonworkdoneonloansandsavingsinpreviousunitsand

itinvestigatesdifferentaspectsofloansandsavings.Learnerswillalsoapplywhattheyhavelearntaboutinterestratestoseehowtheseaffecttherealcostsofinvestingorborrowingmoneyindifferentcontexts.

• RememberthatmanySouthAfricanfamiliesmakeuseofinformalfinancialservices.TheSouthAfricanLabourandDevelopmentResearch Unit(SALDRU)andtheCentreforSocialStudiesResearch(CSSR) carriedoutayear-longinvestigationintohowfamiliesindifferentparts ofthecountryconducttheirfinances.Thefindingsfromthisstudycan befoundonline(www.financialdiaries.com).Thewebsitehasmany usefulgraphsandtablesthatyoucanusetodevelopthistopicfurther intheclassroom.Ifyoudonothaveinternetaccess,youcancontactthe SALDRUofficesat0216505696andtheymaybeabletopostyousome publications.

• AnimportantskillinthisunitisworkingouttherealcostofanHPagreement.ManylearnersmaynotrealisethatsomeHPoptions(suchasbuyingacarandpayingitover60monthswithnodeposit)maymeanthattheypaymorethandoublethepriceofthecarbecausetheywillpaysomuchinterestovertheperiod.Itwillbeusefultohaveclassdiscussionsaboutthis.Learnerscandocalculationstosubstantiatetheirarguments.

Solutions3.1 Practise calculatingtherealcostsofaloanLearner’sBookpage234

1. a. Realcost=loanamount+simpleinterestfor1year=R6000+3,5%ofR6000×1=R6000+R210=R6210

b. Realcost=loanamount+simpleinterestfor1,5years=R6000+3,5%ofR6000×1,5=R6000+R315=R6315



2. a. Year 1 2 3 4

amount of loan r812,14 r845,60 r880,43 r916,71

Therealcostoftheloan:R916,71

b. Year 1 2 3 4

amount of loan r812,14 r845,60–1_ 2(r780)=r455,60

r474,37 r493,91

Therealcostoftheloan=R390+R493,91=R883,91

3. R2500at8,7%simpleinterest

Year 1 2 3

amount owed r2717,50 r2935,00 r3152,50

R2500at5,2%compountinterest

Year 1 2 3

amount owed r2630,00 r2766,76 r2910,63

Theloanat8,7%simpleinterestwouldhaveahighercost.4. Totalamountowedafterfiveyears:R714,81 Totalamountowedafter36months:R6618,76 Amountsaved=R7141,81–R6618,76

=R523,05

3.2 Practise calculatingtherealcostsofahirepurchaseagreementLearner’sBookpage236

1. a. i. Realcost=15%ofR112500+R3985×36=R160335

ii. Differenceinprice=R160335–R112500=R47835

b. i. Realcost=10%ofR2119+R110×24=R2660,90

ii. Differenceinprice=R2859,90–R2119,00=R660,90

c. i. Realcost=20%ofR5999+R580×12=R8159,20

ii. Differenceinprice=R8159,20–R5999,00=R2160,20

2. a. Realcost=R121,30×12=R1455,60 b. Realcost=15%ofR1200+R105×12=R1440,00 OptionBhasthelowestrealcost.3. a. Realcost=R120,80×6=R724,80 b. Realcost=25%ofR700,00+6×R91,00=R721,00 OptionBhasthelowestrealcost.4. a. Realcost=R131,27×24=R3150,48 b. Realcost=10%ofR3000,00+R126,04×24=R3324,96 OptionAhasthelowestrealcost.


95t e r m 2 • u n I t 4

3.3 Practise comparinginvestmentoptionsLearner’sBookpage244

1. Option2orifthebusinesshasinternetbankingfacilities. Option3hasaslightlyhigherinterestrateoversixmonths.2. Overall,option3hasthehighestinterestrates.Themonthlysavingscould

beinvestedinoption1andoncetheyhaveaccumulatedalumpsumtheycouldtransferittooption3.

3. Option1wouldprobablyworkwellasyoucanaddtoyourinvestmenteachmonth.Oncethepensionerhasaccumulatedalumpsumshecouldtransferthemoneytooption2oroption3.

4. Forthemonthlysavings,option1wouldworkwell.Ifthebusinessusesoption2theywillhavetoopenanewfixeddepositaccounteachmonth.FortheamountofR35000overfiveyears,option2andoption3offerthesameinterestratesoeitheronewouldbeagoodchoice.

Unit 4InflationLearner’s Book pages 245–256

Teaching tips• Inflationisoftenmentionedinthemedia,bothinrelationtoprice

increasesandalsotoinflation-linkedwageincreases.Theconceptisexplainedinsimpletermsinthisunitandlearnersdoseveralpercentagecalculationstoworkouthowinflationaffectspricesandincomelevels.

• Collectarticlesandheadlinesthatrefertoinflationanddisplaythemintheclassroom.Discusswhattheymeaninrealterms.

Solutions4.1 Practise calculatinginflation-relatedpriceincreasesLearner’sBookpage249

1. Variawafamilybudgetadjustedfor8%inflationrate

a. Item January February March

rates r296,48 r273,89 r296,48

Electricity r465,15 r426,79 r514,32

Food r1692,31 r2025,32 r2229,66

Schoolfees r918,00 r918,00 r918,00

taxi/bus/trainfares r466,99 r677,92 r711,02

b. Item april

rates r303,89

Electricity r527,18

Food r2285,40

Schoolfees r918,00

taxi/bus/trainfares r728,80

(Schoolfeesusuallyremainthesamethroughouttheyear.)



2. Cookie’sCookieBakespricelist(adjustedfor7,4%inflationrate) R2,69/cookie R32,22/kgfudge R51,55/cheesecake Savourysnackplatters:R64,44(small),R80,55(medium),R96,66(large) Deliverycharges:R26,85per10-kmdistancefromthebakery. DeliveryfreeonordersoverR268,50.3. a. Theirexpenditurewillincreasebyabout4,5%.Ifsalariesandwages

donotincreasebyasimilarrate,theycouldendupwithadebitbalance.

b. Theirpurchasingpowerwillbelessin2012.Thismeanstheywillbeabletopurchaselessforthesameamountofmoney.

c. Theywouldneedtoincreasetheirincometokeeppacewithinflation.4. Ifthedemandfortheirservicesremainsthesame,theirproduction

requirementswillremainthesame,buttheirproductioncostsandrunningcostswillincreaseby6,85%.Theyneedtoincreasetheirincomeby6,85%sotheywillbeabletopaytheincreasedrunningandproductioncosts.Todothistheywillneedtoputtheirpricesupby6,85%.

4.2 Practise comparingratesofpriceincreaseanddecreaseLearner’sBookpage255

1. a. Pricechangeforcheddarcheese=R37,99–R34,99=R3,00

Percentageincrease=3,00____ 34,99×100___ 1 =8,57%

Pricechangeforgoudacheese=R28,55–R25,20=R3,35

Percentageincrease=3,35____ 25,50×100___ 1 =13,29%

Goudacheeseshowsthegreatestrateofpricechange. b. Pricechangefordishwashingsoap=R14,95–R14,20

=R0,75 Percentageincrease=0,75____ 14,20×

100___ 1 =5,28% Pricechangeforbodysoap=R8,50–R7,95

=R0,55 Percentageincrease=0,55___ 7,95×

100___ 1 =6,92% Bodysoapshowsthegreatestrateofpricechange. c. Pricechangeforpetrol=R8,75–R9,10

=–R0,35 Percentageincrease=0,35___ 9,10×

100___ 1 =3,85% Pricechangeforparaffin=R5,60–R5,75

=–R0,15 Percentagedecrease=0,15___ 5,75×

100___ 1 =2,61% Petrolshowsthegreatestrateofpricechange–inthiscase,therateof

changeinpriceisdecreased.2. Totalcosttopaintthehousein2010:R355,70 Costatendof2012:R389,54


97t e r m 2 • u n I t 4

4.3 Investigation: Howdoesinflationaffectpropertyprices?Learner’sBookpage256

1. a. Property Price increase/ decrease

% increase/ decrease

one-bedroomflat,nogarage,communalswimmingpoolinblock

r45000 5,81%increase

two-roomhouse,smallfrontyard,off-streetparking

r165000 25,38%increase

Five-roomhouse,threebathrooms,grannyflat,extensivegarden,doublegarage

–r130000 5,31%decrease

Penthouseflatinluxurycomplex,fouren-suitebedrooms,designerkitchenjacuzzi

–r185000 25,17%decrease

Atwo-roomhousewithsmallfrontyardandoff-streetparkingshowsthegreatestpercentageincrease.

b. Answerswilldiffer. c. Eachmonththepricewillincreaseatarateof4,25%.

Property Price in January

Price in February

Price in March

one-bedroomflat,nogarage,communalswimmingpoolinblock

r854850 r891,181 r929056

two-roomhouse,smallfrontyard,off-streetparking

r849638 r885747 r923391

Five-roomhouse,threebathrooms,grannyflat,extensivegarden,doublegarage

r2418600 r2521391 r2628550

Penthouseflatinluxurycomplex,fouren-suitebedrooms,designerkitchenjacuzzi

r5733750 r5977434 r6231475

2–4. Answerswilldiffer.Discusstheinformationlearnerscollectedwiththeclass.

Revise and consolidate:Finance–Interest,banking,loansandinvestments,inflationLearner’sBookpage258

1. Interest owing total amount owing

a. r1050 r4800

b. r5117,50 r14017,50

c. r164,24 r564,24

d. r3302,15 r18302,15

2. a. R7554,61 b. R8206,063. a. R191,13



b. Balanceon1June:R7836,43 Interestearned: 1–3June:7836,43×0,025____ 365×3=1,61

4–16June:6536,43×0,025____ 365×13=5,82

17–27June:5961,93×0,025____ 365×11=4,49

28–30June:5662,93×0,025____ 365×3=1,61 TotalinterestearnedinJune:R13,08

4. Year 0 1 2 3 4 5

a. Amount(r) 850 906,10 962,20 1018,30 1074,40 1130,50

b. Amount(r) 2500 2602,50 2709,20 2820,28 2935,91 3056,28

c. Amount(r) 10000 10380 10774,44 11183,87 11608,86 12049,99

d. Amount(r) 10000 10750 11500,00 12250,00 13000,00 13750,00

Graphs a.

Number of years

Amou

nt (R

)

500

750

850

1 000

1 250

(1; 906,10)(2; 962,20)

(3; 1 018,30)(4; 1 074,40)

(5; 1 130,50)

1 2 3 4 5

y

x

b.

Number of years

Amou

nt (R

)

1 000

500

1 500

2 000

2 500

3 000

3 500

(1; 2 602,50)(2; 2 709,20)

(3; 2 820,28)(4; 2 939,91)

(5; 3 056,28)

1 2 3 4 5

y

x


99t e r m 2 • u n I t 5

c. y

xNumber of years

Amou

nt (R

)

5 000

7 500

10 000

12 500

15 000

(1; 10 380) (2; 10 744,44) (3; 11 183,87)(4; 11 608,86)

(5; 12 049,99)

1 2 3 4 5

d. y

xNumber of years

Amou

nt (R

)

5 000

7 500

10 000

12 500

15 000

(1; 10 750)(2; 11 500)

(3; 12 250)

1 2 3 4 5

(4; 13 000)(5; 13 750)

5. a. 3,50+1,5%ofR2150,00=R35,75

FeewillbeR18,00–maximumamount b. R12,50 c. R12,50 d. R18,006. Option1:Amount=18000(1+0,05)=R18900 Option2:Amount=18000(1+0,075)4=R24038,44 Option3:Afteroneyear: Amount=18000(1+0,025)12

=R24208,00 Option1wouldappeartobethebestoptionbutJoycewouldneedto

repaytheloaninoneyear.Option2ismoreexpensivebutshewouldhavefouryearstorepaytheloan.DependingonJoyce’sfinancialsituation,option1oroption2wouldbethebetterchoices.

7 a. Realcost:R459,50×36=R16542 b. Realcost:R500+R620×24=R15380 c. Realcost:R675+R385,50×36=R145538. a. Totalexpenditureandincomewouldincreaseby7,8%. Totalexpenditurefor2013:R160288,66 Totalincomefor2013:R164911,66 b. Income:R119291,89 Thiswouldmeanthattheircurrentexpenditurewouldexceedtheir

income.Theywouldhavetocutbackontheirspending.9. a. Amount=415000(1+0,063)(1+0,078)

=R475554,31 b. Amount=675000(1+0,078)

=R727650 c. No.10. D(jacket);A(jeans);C(pants);B(trainers)



Unit 5Measuring length and distanceLearner’s Book pages 261–273

Teaching tips• Learnershaveestimatedandmeasuredlengthsanddistancessincethey

wereinFoundationPhase.Thisunitbuildsontheirexistingskills,butalsorequiresthemtomeasurewithincreasinglevelsofaccuracy.

• Makesureyouhavearangeofrulersandmeasuringtapesavailableforlearnerstouse.Askthemtobringinstrumentsfromhometoschoolasnecessary.Ifanyonehasaccesstoanelectronicmeasuringdevice,itwouldbegoodtoshowtheclasshowitworks.Theseinstrumentsuselaserbeams(theyareveryaccurate,butneedssomethingforthelasertobounceoff)orultrasonicwaves(theyarenotasaccurate)tocoveradistanceandgiveanelectronicreadingoftheexactdistance.Iflearnersareinterested,encouragethemtodoresearchintohowelectronicmeasuringdevicesareusedindifferentindustries.Alsodiscusswhypeople(especiallyolder,experiencedpeople)maystillprefertousetraditionaltapemeasuringdevices(reasonsincludecost,easeofuseandmistrustofchange).

• Oncelearnershaverevisedthebasicconceptstheywillapplytheirskillstocalculatingthecostofproductsthatuselengthasameasurement.

Solutions5.1 Practise comparingmeasuringinstrumentsLearner’sBookpage262

Answerswilldiffer.

5.2 Practise readingodometersandtripmetersLearner’sBookpage263

1. A:odometer:100187 B:odometer:528570 C:odometer:30516;tripmeter:26 D:tripmeter:872. a. A:odometer:100341 B:odometer:528724 C:odometer:30670;tripmeter:180 D:tripmeter:241 b. A:odometer:100108,6 B:odometer:528491,6 C:odometer:30437,6;tripmeter:0 D:tripmeter:8,63. a. Nababeep:477,6 Garies:596,6 Calvinia:740,6 b. 606km–30km=576km Sheshouldstartlookingforanexitwhenthetripmetershows:1011,6

5.3 Practise estimatinglengthsanddistancesLearner’sBookpage266

Answerswilldiffer.


101t e r m 2 • u n I t 6

5.4 Practise calculatingtravellingcostsLearner’sBookpage269

1. a. 12ℓ_____ 100km=xℓ_______ 3560km

\x= 12ℓ_____ 100km×3560km_______ 1

=427,2ℓ Costofpetrol=R8,17×427,2=R3490,22 b. PetrolcostsforJuly=R3490,22–2%ofR3490,22

=R3420,42 c. Numberofkilometrestravelled=279801,5–122458,4

=157343,1km Numberoflitresused: xℓ_________ 157343,1km=

12ℓ_____ 100km

\x= 12ℓ_____ 100km×157343,1 =18881,17ℓ Costofpetrolfortheyear=18881,17×R8,34

=R157468,97

2. travelling speed (km/h)

Petrol consump‑tion (km/ℓ)

Length of journey (km)

Petrol price (per litre)

Litres of petrol used for the journey

Cost of the journey

theyare 11,75 56 r8,30 56____ 11,75=4,77 r8,30×4,77=r39,59

50 12,2 56 r8,30 56___ 12,2=4,59 r33,10

60 12,8 56 r8,30 56___ 12,8=4,38 r36,35

70 12,9 56 r8,30 56___ 12,9=4,34 r36,02

80 12,9 56 r8,30 56___ 12,9=4,34 r36,02

90 12,2 56 r8,30 56___ 12,2=4,59 r33,10

100 12,0 56 r8,30 56__ 12=r4,67 r33,76

5.5 Practise calculatingcostsofmaterialsLearner’sBookpage272

1. Bookcaserequirestenlengthsforshelvesandtwolengthsfortheuprights. a. Pine Cost=12×2,4mlengths@R149,99/length=R1799,88 b. Chipboard Cost=12×2440mlength@R260,00/length=R3120,002. 105m+35,3m=140,5m 140,5÷3,8=50,17 51×R175=R8925



Unit 6Measuring massLearner’s Book pages 274–292

Teaching tips• Inthisunit,learnerswillrevisetheconceptsandskillstheyweretaught

lastyear.Remindthemthatmassisnotthesameasweightalthoughindailylife,thetermsareoftenusedinterchangeably.(Weightistheforceofgravityonanobject,oftenmeasuredinNewton(N).)Learnersarenotexpectedtoworkwithweightinthiscourse.

• Learnerslearnaboutandcalculateameasurementknownasbodymassindex(BMI).Thisisonewayofdeterminingwhetheryourmassisinahealthyrangeforyourheight,however,itisnotanabsoluteandsomeveryfitpeople(suchasOlympicweightliftersandboxers)haveaBMIthatisintheveryobeserangebecausetheyhavelotsofmusclemassandmuscleisheavierthanfat.Sportsscientistsanddieticiansalsouseabodyfatpercentagetohelpthemdecidewhetherapersonisoverweight.ItisimportantthatlearnersdonotgetstressediftheirBMIishigherorlowerthannormalasmanyyoungadultshavebodyimageissues.Donotexpectlearnerstosharethisinformationaboutthemselvesiftheyarenotcomfortabledoingso.

Solutions6.1 Practise estimating,calculatingandmeasuringquantitiesoffoodLearner’sBookpage275

1. Flourfor100scones:100___ 24×450g=1875g=1,875kg

a. 2×1kgbags b. 2×1kgbags2. (5×105g)+(2×210g)+(1×315g) =525+420+315

=1260g3. Answerswilldiffer.

6.2 Practise measuringthenetmassoffoodsLearner’sBookpage278

Answerswilldiffer.

6.3 Practise calculatingquantitiesoffoodrelatedtobodymassLearner’sBookpage280

1. Dry food: Acatwithabodymassof1kgwouldbegiven20g–25gofdryfood.Onceweknowthis,wecancalculatetheamountofdryfoodacatofanymasswouldreceivebysimplymultiplyingthisquantitybythecat’smassinkilograms.

Wet food:Acatwithamassof1kgwouldbegiven19,5gofwetfoodand8,75gofdryfood,or39gofwetfoodand3,75gofdryfood.(Youaregiventhefeedingscheduleforacatof4kgsotofindouthowmuchacatof1kgshouldbegiven,divideby4.)


103t e r m 2 • u n I t 6

i. ii.Body mass amount of dry food amount of dry and wet food

a. 3kg 40–55g 58,5gwetfoodand26,5gdryfoodor

117gwetfoodand11,25gdryfood

b. 1,8kg 28–37g 35,1gwetfoodand15,75gdryfoodor

70,2gwetfoodand6,75gdryfood

c. 7kg 70–105g 136,5gwetfoodand61,25gdryfoodor

273gwetfoodand26,25gdryfood

d. 800g(0,8kg) 16–20g 15,6gwetfoodand7gdryfoodor

31,2gwetfoodand3gdryfood

2. Mass as an adult dog

dry food dry food mixed with canned food

1pound=0,45kg 1cup=250ml250mlwaterhasamassof250g.Whatistheconversionforthedogfood?

upto4,5kg 62,5ml–187,5ml Halftheamountofdryfoodandsubstitutethesameamountwithcannedfood.

4,5kg–11,25kg 187,5ml–250ml Halftheamountofdryfoodandsubstitutethesameamountwithcannedfood.

11,25kg–22,5kg 250ml–500ml Halftheamountofdryfoodandsubstitutethesameamountwithcannedfood.

22,5kg–33,75kg 500ml–625ml Halftheamountofdryfoodandsubstitutethesameamountwithcannedfood.

over33,75kg 500ml–1000ml Halftheamountofdryfoodandsubstitutethesameamountwithcannedfood.

3. a. i. i.Cattle Grain recommended grain

intake (kg/month)recommended grain intake (kg/year)

drybeefcows(120)

Straw (2,0to4,0)×30×120=7200to144000

(2,0to4,0)×365×120=87600,0to175200

Suckledbeefcows(240)

Straw (3,0to6,0)×30×240=21600to43200

(3,0to6,0)×365×240=262800to525600

goodhay (0,0to4,0)×30×240=0to28800

(0,0to4,0)×365×240=0to350400

Bulls(4) Straw (3,0to5,0)×30×4=360to600

(3,0to5,0)×365×4=4380to7300

goodhay (1,5to3,0)×30×4=180to360

(1,5to3,0)×365×4=2190to438



b. Numberofdrybeefcows=120+34%of120=161 Numberofsuckledbeefcows=240+27%of240=305 Numberofbulls=4+100%of4=8

i. i.Cattle Grain recommended grain

intake (kg/month)recommended grain intake (kg/year)

drybeefcows(161)

Straw (2,0to4,0)×30×161=9660to19320

(2,0to4,0)×365×161=117530to235060

Suckledbeefcows(305)

Straw (3,0to6,0)×30×305=27450to54900

(3,0to6,0)×365×305=333975to667950

goodhay (0,0to4,0)×30×305=0to36600

(0,0to4,0)×365×305=0to445300

Bulls(8) Straw (3,0to5,0)×30×8=720to1200

(3,0to5,0)×365×8=8760to14600

goodhay (1,5to3,0)×30×8=360to720

(1,5to3,0)×365×8=4380to8760

6.4 Practise calculatingcorrectmedicinedosagesLearner’sBookpage284

1. Mass of child (kg) 1 1,5 2 2,5 3 3,5 4 4,5

Paracetamol dose (mg) 15 22,5 30 37,5 45,5 52,5 60 67,5

Mass (kg) 5 5,5 6 6,5 7 7,5 8 8,5

Paracetamol dose (mg) 75 82,5 90 97,5 105 112,5 120 127,5

0 1 2 3 4 5 6 7 8 9 10 11Paracetamol dose (mg)

Mas

s of c

hild (

kg)

0

15

30

45

60

75

90

105

120

135

150

2. a. Chestmeasurementof143cm:massof246kg 150kg–350kg:6ml–10ml 246kg–150kg=96kgand350kg–150kg=200kg Dose=6ml+96___ 200×4ml=7,92ml b. Chestmeasurementof156cm:massof306kg 306kg–150kg=156kg Dose=6ml+156___ 200×4ml=9,12ml c. Chestmeasurementof169cm:massof390kg Dose:about11ml Chestmeasurementof150cm:massof272kg 272kg–150kg=122kg Dose=6ml+122___ 200×4ml=8,44ml


105t e r m 2 • u n I t 7

Chestmeasurementof129cm:massof186kg 186kg–150kg=36kg Dose=6ml+36___ 200×4ml=6,72ml Chestmeasurementof119cm:massof146kg 146kg–150kg=96kg Dose=6ml+96___ 200×4ml=5,84ml

Total amount of medicine (2animals@390kg):11×2×2×30 1320ml 1animal@272kg:8,49×2×30 506,4ml 1animal@186kg:6,72×2×30 403,2ml 2animals@146kg:5,84×2×2×30 700,8ml Total medicine 2930,4ml

6.5 Investigation: collectbodymassdataanddetermineBMIweightstatusLearner’sBookpage288

1, 2. Answerswilldiffer.

6.6 Practise calculationswithcostandmassLearner’sBookpage292

Answerswilldiffer.

Unit 7Measuring volumeLearner’s Book pages 293–309

Teaching tips• Learnersoftenfindconvertingbetweenunitsofvolumeandcapacity

difficult,especiallythesolid-to-liquidconversionstheywilluseinthisunit.RevisetheworkonconversionsfromTerm1Unit5asnecessary,andremindthelearnerstousetheconversionfactortablesonpage29oftheLearner’sBooktohelpthemdotheseconversions.

• LearnersshouldbeawareofthedifferencebetweenvolumeandcapacityastheyhaveworkedwiththeseconceptssinceGrade4.Reiteratethisbyreadingthroughpage293withtheclassbutbearinmindthatthetermsvolumeandcapacityareoftenusedtomeanthesamethingindailylife.

• Thenewconceptinthisunitinvolvesusingformulaetocalculatevolumes.Learnerswillworkwithandsolveproblemsrelatedtopetrolconsumptionrates,alcoholcontentandwaterrun-offrates.Itmaybeusefultofindafewcartestarticlesfrommotoringmagazinesorthemotoringsectionofthenewspapertocomparethegivenpetrolconsumptionratesfordifferentcars.Youwillalsofindthealcoholcontentofvariousdrinksonthelabelsanditmaybeusefultocomparethese.Ifyoudonotwishtousealcoholcontentasacontextyoucouldusefruitdrinksandcomparethefruitjuicecontentpervolumeofvariousbrands.Thisinformationwillbegivenonthelabels.



Solutions7.1 Practise calculatingvolumesforpracticalprojectsLearner’sBookpage297

1. a. i. 14m2ofwallsurfacefortwocoats ii. One1-ℓtinwillbeneeded;14__ 15=0,93ℓ iii. Amountofpaintleftover:1ℓ–0,93ℓ=0,07ℓ b. i. 46m2ofwallsurfacefortwocoats ii. Numberoflitresofpaintneeded:46__ 15=3,07ℓ Four1-ℓtinswillbeneeded. iii. Amountofpaintleftover:4ℓ–3,07ℓ=0,93ℓ c. i. 95m2ofwallsurfacefortwocoats ii. Numberoflitresofpaint=95__ 15=6,33ℓ Two1-ℓtinsplus1×5ℓtinwillbeneeded. iii. Amountofpaintleftover:7ℓ–6,33ℓ=0,67ℓ d. i. 436m2ofwallsurfacefortwocoats ii. Numberoflitresofpaint=436___ 15=29,07ℓ Three10-ℓtinsplusone5-ℓtinwillbeneeded. iii. Amountofpaintleftover:30ℓ–29,07ℓ=0,93ℓ2. a. Thecapacityofthebucketwouldbeabout15ℓandacupis250ml.

Dilutefertiliser:125mlfertiliserto15ℓofwater b. 3buckets=3×15ℓ=45ℓ c. 7×6drops=42dropsperweek Usingthevaluegivenintheexampleonthepreviouspageof

25drops=10ml:42drops=42__ 25×10ml=16,8ml.

Ifwemakeenoughfertiliserforthreemonthswewillneed3×4×16,8mlofdilutedfertiliser.Thismeansthatwewillneedhalftheamountofconcentratedfertiliser.So,wewillneed:201,6ml______ 2 =100,8mlofconcentratedfertiliser.

3. a. 500ml=0,5ℓ Thismeansthat50bottlesof500mleachwouldgiveusatotalof25ℓ. b. i. Dilutedfertilisermixture:0,5ℓfertiliserto10ℓwater Thiswillmakeupatotalof10,5ℓofdilutedfertiliser. Tomake120ℓofdilutedfertiliser: 0,5:10,5ℓ=x:120l 0,5___ 10,5×120=x \x=5,71ℓ Tomake120ℓofdilutedpoultryfertiliser:5,71ℓofthe

concentratedfertiliser. ii. Seaweed fertiliser Dilutedseaweedmixture:1_ 2cuptoabucketofwater

=125mlto15ℓ Thiswillmakeupatotalof15,125ℓofdilutedfertiliser. Tomake120ℓofdilutedfertiliser: 125ml:15ℓ=x:120ℓ 125ml_____ 15ℓ ×120ℓ=x \x=1000mlofcontratedfertiliser. iii. Comfrey fertiliser Dilutecomfreyfertiliser:50/50mix Tomake120ℓofdilutedfertiliser:1_ 2×120ℓ=60ℓof

concentratedcomfreyfertiliser.


107t e r m 2 • u n I t 7

4. Answerswilldiffer.

7.2 Practise monitoringyourwaterfootprintLearner’sBookpage300

1. 1gallon=8pints=(8×0,57ℓ)=4,56ℓ

Rise and shine Toilet: 6gallons/flush Low-flowtoilet: 1,3g/flush =27,36ℓ/flush =5,93ℓ/flush Shower:3,8g/minute Low-flowshower:2,3g/min. =17,33ℓ/min. =10,49ℓ/min. Faucet: 5g/min. Low-flowfaucet: 1,5g/min. =22,8ℓ/min. =6,84ℓ/min. Total:49gallons=223,44ℓ Total:25,8gallons=117,65ℓ Amountsaved:23,2gallons=105,79ℓ

Breakfast Coffee:37gallons=168,72ℓ Tea:9gallons=41,04ℓ Egg(two):36gallons/egg Cerealwithmilk:22gallons =164,16ℓ/egg =100,32ℓ Apple:18gallons=82,08ℓ Orange:13gallons=59,28ℓ Total:127gallons=579,12ℓ 44gallons=200,64ℓ Amountsaved:83gallons=378,48ℓ

Lunch Soda:33gallons=150,48ℓ Water:0,125gallons=0,57ℓ Hamburger:634gallons Salad(lettuce,tomatoandcarrot): =2891,04ℓ 31gallons=141,36ℓ Total:667gallons=3041,52ℓ 31,125gallons=141,93ℓ Amountsaved:635,875gallons=2899,59ℓ

Dinner Beef:1500gallons=6840ℓ Chicken:287gallons=1308,72ℓ Wine:31gallons=141,36ℓ Beer:20gallons=91,20ℓ Bread(2slices):11gallons/slice Bakedpotato:7gallons=31,92ℓ =50,16ℓ/slice Dishwashinginsink Dishwashinginmachine 20gallons=91,2ℓ 4gallons=18,24ℓ Total:1573gallons=7172,88ℓ 318gallons=1450,08ℓ Amountsaved:1255gallons=5722,8ℓ

Cleaning up Washingmachine: Secondwashingmachine: 40gallons=182,4ℓ 22gallons=100,32ℓ Toilet:69g/flush=27,36ℓ Low-flowtoilet:1,3g/flush

=5,93ℓ/flush Bath:35gallons=159,6ℓ Nobath Faucet(tap):5g/min. Low-flowfaucet:1,5g/min. =22,8ℓ/min. =6,84ℓ/min. Total:46gallons=209,76ℓ 2,8gallons=12,77ℓ Amountsaved:43,2gallons=196,99ℓ

Energy Nuclear:255g/day=1162,8ℓ/day Solar:24,5g/day=111,72ℓ/day Amountsaved:230,5gallons=1051,08ℓ2–5. Answerswilldiffer.



7.3 Assignment: calculateyourhousehold’sbasicwaterneedsLearner’sBookpage301

Answerswilldiffer.

7.4 Practise calculatingpetrolconsumptionLearner’sBookpage305

1. a. Petrolconsumption(ℓ/km)= 80ℓ_____ 830km=0,09638ℓ/km Consumptioninℓ/100km=0,09638×100

=9,638ℓ/100km=9,64ℓ/100km

b. Petrolconsumption(ℓ/100km)= 42ℓ_____ 465km×100=9,03ℓ/100km

c. Petrolconsumption(ℓ/100km)= 65ℓ_____ 710km×100=9,15ℓ/100km

2. a. Petrolconsumption(ℓ/100km)= 10ℓ_____ 120km×100=8,33ℓ/100km b. 8,33ℓ:100km=55ℓ:xkm 8,33ℓ_____ 100km=

55ℓ____ xkm

x=55×100___ 8,33 =660,20km3. a. 7ℓ:100km=xℓ:1200km x= 7___ 100×1200 x=84l b. 6ℓ:100km=x:3458km 6___ 100=

x ____ 3458

x= 6___ 100×3458 x=207,48ℓ c. Totalnumberoflitresofpetrol:84+207,48=291,48ℓ Tocalculatethemonthlypetrolcost,multiply291,48ℓbythecurrent

priceofpetrolperlitre. d. TheycouldusetheirJunetravelexpensesforthewholeyear,butit

wouldbefarfromaccurateaspetrolpricesaresubjecttofrequentchange.

e. Answerswilldiffer.5. Wecanseethattheoptimum(best)petrolconsumptionoccursatspeeds

between75km/hand100km/h.Petrolconsumptionincreasesatspeedsabove100km/h.Theownerwillinstructthedriverstomaintainspeedsofbetween75km/hand100km/handavoidtravellingatspeedsover100km/hunlessthereisaspecialneed.

6. Overall,thesmartcarshowsthelowestrateofpetrolconsumptionfollowedbytheHyundiaElantra.Obviouslywhenchoosingacar,anumberoffactorssuchasone’srequirementsandfinancialsituationneedtobeconsidered.Aspetrolisquiteexpensive,petrolconsumptionrateswouldbeanimportantfactortoconsider.


109t e r m 2 • u n I t 7

7.5 Practise calculatingalcoholcontentLearner’sBookpage307

1. Alcoholcontent A Onebeer(300ml):4,4%of300ml=13,2ml B Oneglassredwine(175ml):13,7%of175ml=23,98ml C Onebrandy(30ml):40%of30ml=12ml D Oneglasssparklingwine(200ml):11%of200ml=22ml E Onechocolateliqueur(50ml):35%of50ml=17,5ml Drinksrankedinorderfromleasttomostalcoholcontent: C Onebrandy(30ml) A Onebeer(300ml) E Onechocolateliqueur(50ml) D Oneglasssparklingwine(200ml) B Oneglassredwine(175ml)2. Alcoholcontent a. 1ℓ(1000ml)wine:14,2%of1000ml=142ml b. 5ℓ(5000ml)wine:10,7%of5000ml=535ml c. bottleofwhisky(750ml):25,4%of750ml=190,5ml d. sixbeers(1800ml):5,7%of1800ml=102,6ml3. Alcoholcontent fourbeers:4×13,2ml=52,80ml twoglassesofredwine:2×23,98ml=47,96ml oneglassofsparklingwine:1×22ml=22,00ml oneliqueur:1×17,5ml=17,50ml Totalamountofpurealcoholconsumed:140,26ml4. halfabottleofwine:375ml Amountofalcoholperhalfbottleofwine:12,2%×375ml=45,75ml Amountofalcoholconsumedinoneyear=365×45,75ml

=16698,75ml=16,70ℓ

7.6 Practise calculatingwaterrun-offLearner’sBookpage309

1. a. Run-off=R×A=564mm×38m2

=21432ℓ=21,432kl

b. Ifthehouseholdisgoingtostorethewater,theyshouldinstallawatertankwithacapacityof25000ℓ(25kl).Iftheyusedthewaterregularlytheycouldmanagewithatankof15klor20kl.

2. Month durban Cape townJanuary 130 20February 115 22March 122 23April 75 40May 65 60June 30 90July 35 80August 60 76September 75 40october 100 28november 110 20december 100 20total 1 017 519



a. Annualrun-offforCapeTown=R×A=519mm×338m2

=175422ℓ=175,422kl

Thetotalannualrun-offis175,422kl.AsCapeTownhasadrysummer,itwouldprobablybenecessarytostoreasmuchwateraspossibleduringthewetmonthssotherewouldbeenoughwaterduringsummer.Forthisreasonastoragetankof150klwouldbethebestoption.

b. Annualrun-offforDurban=R×A=1017mm×415m2

=422055ℓ=422,055kl

Thetotalannualrun-offforDurbanis422,055kl.Astoragetakwithacapacityof300klor350klwoudmostlikelybesufficienttostorethewaterastherainfallinDurbanisfairlysteadywiththelowestmonthlyrainfallbeing30mlinJune.

7.7 Assignment: calculatetotalwaterrun-offinasettlementLearner’sBookpage309

1. Run-off=R×A=980mm×40m2

=39200ℓ=39,2kl

2. Totalrun-off=240×39,2kl=9408kl

3, 4. Answerswilldiffer.

Unit 8 Measuring temperatureLearner’s Book pages 310–316

Teaching tips• Learnershavealreadydonesomebasictemperatureconversions.Thisunit

buildsonwhattheyalreadyknowandallowsthemtoapplytheirskillsindifferentcontexts.

• Remindlearnerstoreadthelabelsontheaxesoflinegraphsbeforetheyworkwiththeconversiongraphsinthisunit.

Solutions8.1 Practise readingandconvertingtemperatureinformationLearner’sBookpage313

1. 8°C=(1,8×8°C)+32°=46°F –5°C=(1,8×–5°C)+32=23°F 0°C=32°F Wemustlookforplaceswherethetemperaturerangeisbetween23°F

and46°F.Theminimumtemperaturemustbe32°Forlessiftheyarehopingforsnow.Citiesthatsatisfytheirrequirementsare:Amsterdam,ZurichandTokyo.


111t e r m 2 • u n I t 8

2. Answerswilldiffer.3. Foraccurateconversions,acalculationwouldbethebestoption.For

estimatedtemperaturesthatdonotneedtobeexact,aconversiongraphwouldbethequickestandeasiestwaytomakeconversions.

4. a. 2002and2003 b. Temperaturein°C:(58–32)÷1,8=14°C5. a. 1998 Temperaturein1998:58,1°F Temperaturein°C=(58,1–32)÷1,8=14,5°C6. Temperaturein2004:59°F=14,4°C Temperaturein1880:56,7°F=13,7°C Globalaverageannualtemperaturerise: temperature2004–temperature1880=14,4°C–13,7°C

=0,7°C7. Answerswilldiffer.

8.2 Practise compilingplantingcalendarsbasedontemperature informationLearner’sBookpage315

1. a,b. GroupC:avocados,bananas,citrus,figs,litchis,mangoes,pawpaws c. Inthesouth-westinJanuarytemperaturesrangefrom10–15°C.

Thistemperaturerangewouldbesuitableforapples,cherries,pears,quincesandraspberries(groupB)

andalsoapples,apricots,berries,citrus,figs,grapes,guavas,peaches,nectarines,pears,plums,quinces,strawberries(groupA).

d. FruitfromgroupA. e. FruitfromgroupC. f. FruitfrombothgroupsAandC

2.Vegetable

Planting times

Polokwane Bloemfontein east London Cape town Johannesburg durban

beans Feb.–Aug. Aug.–dec. oct.–dec. Sep.–Jan. Aug.–Jan. Feb.–Aug.

cabbage Feb.–Jun. nov.–Feb. Aug.–Apr. nov.–Apr. Feb.–Apr.Aug.–Sep.

Feb.–Jun.

carrots Feb.–Aug. Aug.–oct.Jan.–Mar.

Jul.–Apr. Aug.–nov.Jan.–Apr.

Aug.–oct.Jan.–Mar.

Feb.–Aug.

cucumbers Feb.–Sep. Sep.–dec. Jul.–Feb. Sep.–nov. Aug.–Jan. Feb.–Sep.

peas Mar.–Jun. Jul.–Aug. May–Jul. Apr.–Aug. Mar.,Jul.–Sep. Mar.–Jun.

peppers Jan.–Apr. Aug.–oct. Aug.–oct. Aug.–oct. Aug.–oct. Jan.–Apr.

potatoes Jan.–Aug. dec.–Jan.Aug.–nov.

oct.–dec.Jul.–oct.

nov.–oct.(Allyearround)

dec.–Feb.Jul.–nov.

Aug.–Feb.May.–Aug.

spinach Feb.–Jun. Aug.–Apr. Aug.–Sep. Mar.–May Aug.–Apr. Feb.–Jun.

sweetcorn Jul.–nov. Aug.–nov. Sep.–dec. Aug.–dec. Aug.–dec. Jul.–nov.

tomatoes Jan.–Jul. Aug.–nov. Aug.–oct. Jul.–Sep. Jul.–dec. Jan.–Jul.



Revise and consolidate:Measurement–Length,volume,temperatureLearner’sBookpage318


2. number of litres of petrol Cost

a. 26,60 r293,88

b. 6,50 r71,87

c. 174,81 r1931,59

3. a. 23m b. R205,85 c. Ifhebuys13ofthe1,8mstrips@R14,40itwillcostR187,20.4. Answerswilldiffer.5. a. 125bottlesofmixedspice b. 156bottlesofginger c. 104bottlesofpepper6. a. R0,17+1,15=R1,32 b. R1,39 c. R1,457. a. 190ml b. 1330ml c. 1440ml

8. BMI=bodymassinkg___________ (heightinm)2

Child Mass (kg) Height (m) BMI

gabeba 35,2 0,9 43,46

Jeremy 42,8 1,3 25,33

Seithlamo 44,3 1,2 30,76

Ingrid 38,4 1,3 22,72

Lebo 45,1 1,5 20,04

Vonani 43,6 1,6 17,03

Mzi 36,9 0,7 75,31

nolwazi 35,7 0,8 55,78

9. a. R15,75 b. R20,43 c. R0,16 d. R3,3610. a. 0,3ℓbleach(300mlbleach) b. A750mlbottleofbleachwillbeenoughfortwowashes. c. Amountofbleach=1_ 4×5,5ℓ

=1,38ℓ11. Highland:none Rivervalley:plumtree,walnuttree Coastalplain:sweetpotatoes,sweetbasil


113t e r m 2 • u n I t 9

Unit 9 scaleLearner’s Book pages 322–326

Teaching tips• Thisunithelpstoreviseandapplytheconceptsthatlearnersdevelopedin

Grade10andpractisedinTerm1Unit5.• Makesurethelearnersareabletomeasuredistancesonmapsandconvert

themtorealdistancesbeforeyouaskthemtoworkwithrealdistancesanddrawtheirownscaleddiagrams.

• Inordertomakeiteasytomanagethisunit,somereallengthsaregiven.However,itwillbemoreinterestingandengagingifyouletthelearnersmeasurerealdistancesatschoolandusethesemeasurementstodevelopscaleddiagramsofyouractualbuildings.Theycanworkingroupsandtheywillneedalongmeasuringtape(theindustrialkind).

Solutions9.1 Practise workingoutdistancesusingamapscaleLearner’sBookpage323

1. a. 6cm:10km \1cm:xkm 6cm_____ 10km=

1cm____ x

x=1cm×10km_____ 6cm x=1,67km So,1cmrepresents1,67km. c. 4cm:100km 1cm____ x = 4cm_____ 100km

x=1cm×100km_____ 4cm x=25km So,1cmrepresents25km.

b. 4cm:96km 1cm____ x =4cm_____ 96km

x=1cm×96km_____ 4cm x=24km So,1cmrepresents24km.

d. 4cm:400feet \1cm=100feet

2. a. 1:120=40mm:x 1___ 120=

40mm_____ x \x=40mm×120 =4800mm =4,8km b. 1____ 1200=

40mm_____ x \x=40mm×1200 =48000mm =48km c. 1_____ 12000=

40mm_____ x \x=40mm×12000 =480000mm =480km d. 4800km e. 48000km f. 480000km g. 4800000km



3. a. 1:18000=3cm:x \ 1_____ 18000=

3cm____ x \x=3cm×18000 =54000cm =540km b. Distanceonground=mapdistance×scale

=7,2cm×18000=129600cm=1296km

c. Distanceonground=mapdistance×scale=14mm×18000=252000mm=252km

d. Distanceonground=mapdistance×scale=2,45cm×18000=44100cm=44,1km

9.2 Practise measuringmapdistancesandworkingwithscaleLearner’sBookpage323

1. a. 33mmor3,3cm b. 17mmor1,7cm c. 5,3cmor53mm scale:2cm:300km \2cm:300km=5,3cm:x 2cm_____ 300km=

5,3cm_____ x

\x=5,3cm×300km_____ 2cm =795km d. 3,4cm 2cm:300km=3,4cm:x 2cm_____ 300km=

3,4cm_____ x

\x=3,4cm×300km_____ 2cm =510km

2, 3. From Pretoria to … Map distance (mm) real distance (km)

Johannesburg 4 60

Polokwane 17 226

Mafikeng 8 120

Mbombela 19 285

Kimberley 32 480

Bloemfontein 29 435

ulundi 30 450

Bhisho 55 825

capetown 92 1380


115t e r m 2 • u n I t 1 0

9.3 Practise usingrealdistancestocalculatemeasurementsonaplanLearner’sBookpage326

1. a. 1:50=1cm:50m=100cm:50m=80cm:40m=40cm:20m

Scalediagram:80cm×40cm b. 1m:500m=1000cm:500m x _____ 20cm=

100cm_____ 500m x ____ 40m=100cm_____ 500m

\x=100cm_____ 500m×20m \x=100cm_____ 500cm×40m =4cm =8cm Scalediagram:8cm×4cm c. 1m:1000m=100cm:1000m x _____ 20cm=

100cm______ 1000m x ____ 40m=100cm______ 1000m

\x=100cm______ 1000m×20m \x=100cm______ 1000m×40m =2cm =4cm Scalediagram:4cm×2cm2. Answerswilldiffer.3. First,wemustdecidewhatscaleweneedtouse.Thewidthofthepageis

about20cmandweneedtorepresentthewidthoftheclassroomblockwhichis25monthepage.

20cm:25m 20cm:2500cmor20:2500(divideby20) Scale:1:125 25m=20cmonplan Scaletheotherdimensions 8mor800cm x:800=1:125 \x= 1___ 125×800 x=6,4cm 7mor700cm x:700=1:125 \x= 1___ 125×700 x=5,6cm 3mor300cm x:300=1:125 \x= 1___ 125×300 x=2,4cm 1,8mor180cm x:180=1:125 \x= 1___ 125×180 x=1,44cm 1mor100cm x:100=1:125 \x= 1___ 125×100 x=0,8cm

Office Englishroom

BiologyLab

Geographyroom

20 cm0,8 cm 0,8 cm 0,8 cm 0,8 cm 0,8 cm

2,4 cm 5,6 cm 5,6 cm6,4 cm

6,4 cm



Unit 10MapsLearner’s Book pages 327–345

Teaching tips• Learnershaveworkedwithfloorplansandsimplemapsbefore.Inthis

unit,theywillworkwiththesamekindsofmapindifferentcontexts.Theywillalsolearnhowtoreadandinterpretstreetmapswithanindexandgridsystem,mapsthatshowlargerareas(mapsofSouthAfrica)andelevationmaps(alsocalledcrosssections).

• Itwillbeusefultohavefloorplansoflocalshoppingcentresavailable.Youwillfindtheseattheinformationkiosksinthecentres.Usethesetorevisethebasicskillsoflocatingplacesonamap.Workingwithmapsofplacesthatarefamiliartothelearnerscanhelpthemformalisetheirspatialandmappingabilities.

• Streetmapbooksofcitiesandtownsinyourprovincearealsoausefulclassroomresourceastheyhavemapsofsmallareasandalsocontainadetailedindextoplacenamesthatyoucanrefertoasyouworkthroughtheunit.Learnerscanmakeupactivitiesforeachothertocompleteusinglocalareamaps.

• Youshouldhaveanatlasavailableinclassforthelearnerstorefertoasnecessary.

• Themostcommonuseofroadmapsisprobablytofindyourwaywhiledriving.Makesurethelearnersunderstandhowtoreadthedistanceindicatorsgivenonthesemaps.Theymaybepresentedindifferentwaysbydifferentpublishers.

• IfanyonehasaccesstoaGPSsystem,useittoshowtheclasshowmapsandroutesappearonthis.ThedistancesgivenbytheGPSareexact,anditcouldbeafunactivitytocomparethesetotheonesmarkedonamap.(Usethemaponpage335forthis,oramapofyourlocalarea).

• Pointouttolearnersthataprofileorelevationmapislikealinegraphthatshowsdistance(inkm)onthehorizontalaxisandheight(inmetresusually)ontheverticalaxis.Theheight(oraltitude)isoftengivenonbothsidesofthegraphtomakeiteasiertoreadthevalues.

Solutions10.1 Practise describingthepositionofobjectsonamapLearner’sBookpage329

1. a. Edgarsisthetherightofentrance1orentrance1isjusttotheleftofEdgars.

b. Thetoiletsaretotheleftofentance3. c. TheATMisleftaroundthefirstcornerafterentrance4. d. Ifyouenterthemallatentrance1,walkpastthephonesandthe

escalator,theCNAisonyourleft. e. Walktotheleftasyouenterthemall(atentrance5),walkbetween

Woolworthsonyourleftandshops34,32and30onyourright,theATMisoutsideshop26.

f. WalkpastClicksandshops3,5and7andtheAMTonyourleft.GointoEdgars,theliftisinfrontofyou.

2. a. anescalator b. apublicphone,publictoilets,ababyroomandadisabledfacitily c. anescalatorandentrance1


117t e r m 2 • u n I t 1 0

d. acustomerservicescounter3. a. Edgars,WoolworthsandCheckers b. Edgars:entrance1isnearest Woolworths:entrance5isnearest Checkers:entrance3isnearest

10.2 Practise usingtheindextolocatestreetsLearner’sBookpage332

1. a. p.72 b. p.39 c. p.91 d. p.282. a. p.36DA118 b. p.41DE114 c. p.72DR139 d. p.35DC1183. a. p.36 b. p.53 c. p.28 d. p.39

10.3 Practise followingandgivingdirectionsusingastreetmapLearner’sBookpage334

1. a. MandelaHouse b. ReginaMundiChurch2. AsyouexittheChrisHaniBaragwanathHospitalinthedirectionof

Orlando,turnleft.Continueonthisroad.YouwillpasstheReginaMundiChurchonyourleft.Continuefollowingtheroad.WhenyoureachtheintersectionwiththeN12,donotgetontoit,butproceedacrosstheN12andLenasiawillbedirectlyaheadofyou.

3. a. Walkthroughtheparkingarea,themainarenaisstraightahead. b. Theparkingforgates4/5isjusttotherightofthetechnicalworkshop. c. Themonorailmakesashortcircuitthroughthecentreoftheexhibition

centregoingpastthemainexhibitionhallsasfarasterrace2andthencompletesitscircuitpasttheothermainhalls(5,6,7and8)andreturnstotheterminal.

d. Afterenteringthroughturnstile4/5,sheshouldturnleftandcontinuewalkingandpassthe4×4Track,turnrightandtaketheescalatortothenextfloor.Terrace2isontheleft.

10.4 Practise workingwithastreetmapLearner’sBookpage335

1. a. B3 b. A1 c. A1 d. B12. A1:NelsonMandelaDrive A3:RugbyStreet3. MafikengMuseum4. DirectionsfromWarren’sForttotheMafikengGameReserve: LeavingWarren’sFortturnleft.AtVryburgRoad,turnright.Continue

onVryburgRoad,crossingtherailwayline,whereafteritbecomesMainStreet.ContinuedownMainStreetuntilyoucometoaT-junctionatMandelaDrive.TurnrightintoMandelaDrive.Turnfirstleftaftercrossingtherailwayline.Whentheroadforks,taketherightforkandthatwilltakeyoutothereserve.

10.5 Practise workingoutroutesanddistancesusingamapLearner’sBookpage338

1. a. 42km b. 33km+30km=63km c. 35km+34km=96km



d. 35km+22km+62km+6km=125km2. a. DistancefromBethlehemtoSenekal:35km+22km=57km DistancefromSenekaltoVentersburg:55km (ThereappearstobearoadofftheR70–thiscouldbeanentrance,

butitsdistanceisnotgiven.) Distancecovered:109km b. Time=distance______ speed =

109___ 75=1,45hours. BreakatSenekal:45minutes=0,75hours Jeffwilltake1,45+0,75=2,2hoursor2hours12minutes.3. a. Sinidi’sjourney MaserutoTeyateyaneng:45km TeyateyanengtoPeka:20km FromtheturnofftoFicksburg:5km Totaldistance:45km+20km+19km+5km=89km b. Traveltime=distance______ speed =

89__ 70=1,27hours=1hour16min. TimeSinditakestocrosstheborder=30min. Totaltraveltime=1h16min.+30min.=1h46min. SindiwillarriveatFicksburgatabout5:00+1:46=6:46a.m. c. Mpho’sjourney MaserutoLadybrand:15km LadybrandtoFicksburg:35km+34km=69km Totaldistance:15km+69km=84km d. Travellingtime=distance______ speed =

18km______ 90km/h=0,93h=56min. Totaltime=56min.+35min.=91min.≈1,5h MphowillarriveinFicksburgat6:30a.m.

10.6 Practise workingoutdistance,timeandspeedusingastripmapLearner’sBookpage339

1. a. DistancebetweenPretoriaandtheVilliersturn-off: (39+20+8+6+30+11)km=114km b. DistancebetweenPretoriaandVredefort: (39+20+8+6+30+11+28+19+13)km=174km c. DistancebetweenBloemfonteinandOdendaalsrus: (4+18+80+9+43)km=154km d. DistancebetweenParysandtheKrugersdorpturn-off: (19+28+11+30+6)km=94km2. a. DistancebetweenPretoriaandSasolburg: (39+20+8+6+30+11+28)km=142km Time=d _ s =

142km_______ 100km/h=1,42h b. DistancebetweenPretoriaandKroonstad: (39+20+8+6+30+11+28+19+13+75+9)km=258km Time=d _ s =

258km_______ 100km/h=2,58h c. DistancebetweenPretoriaandBloemfontein: (39+20+8+6+30+11+28+19+13+75+9+50+43+9+80

+18+4)km=462km Time=d _ s =

462km_______ 100km/h=4,62h3. Answerswilldiffer.Answersmayinclude:thequalityoftheroadsurface,

whetheritisastraightroadorwindyroad,thevolumeofthetrafficontheroad–youcouldalsogetstuckbehindalargetruck,weather–motoristsgenerallytravelatlowerspeedswhentheroadsarewetoritisrainingheavily.Sometimesthereisfogormistontheroadwhichwillcausemotoriststodrivewithextremecaution.


119t e r m 2 • u n I t 1 0

4. a. Speed=distance______ time =59km_____ 1,5h=39,33km/h

b. At5p.m.thevolumeoftrafficeontheroadswouldbeveryhighresultinginmotoriststravellingatlowaveragespeeds.

5. a. Time=distance______ speed =60km_______ 160km/h=0,375hor0,375h×60=22,5min.

b. DistancefromPretoriatoJohannesburg:59km Timewithnostops=distance______ speed =

59km_______ 160km/h=0,369h or0,369×60=22,13min.≈22min. Timespentatstations:40–22=18min. c. Possibleanswersincludethetraincanmaintainaconstantspeedof

160km/h,itisnotdelayedbytrafficjams.

10.7 Practise workingwithnationalroadandrailmapsLearner’sBookpage341

1. mapscale:3,5cm:400km a. DistancefromPolokwanetoCapeTown:about15cmonthemap 15cm:x=3,5cm:400km 15__ x =

3,5___ 400

\x=15×400___ 3,5 =1714,29km =1175km b. Time=distance______ speed =

1715____ 100=17,5h

c. Time=distance______ speed =1715____ 80 =21,44h

d. Itisrecommendedthatthedrivertakesabreakof15minuteseverytwohoursorso.Workoutwhichtownswouldallowyoutostopforabreakeverytwohoursandfillupwithpetrolasnecessary.

2. a. DistancefromPolokwanetoCapeTown:roughly1715km Thenumberoflitresofpetrol:1715____ 10 =171,5ℓ b. Numberoftanksofpetrolneededforthetrip:171,5____ 55 =3,12tanks Youwouldneedaboutfourtanksofpetrol. c. Usingthisinformation(onetankofpetrolallowsyoutotravel

550km),youwouldplanyournextbreaktocoincidewithrefillingyourpetroltank.

d. Answerswilldiffer.3. Durban–Pietermaritzburg–Harrismith–Bloemfontein Distanceonmap:about7cm Actualdistance: 7cm____ xkm=

3,5cm_____ 400km

7cm×400km_____ 3,5cm=800km DistancefromDurbantoBloemfonteinbyrail:about800km4. DistanceonthemapfromPortElizabethtoEastLondonis±13cm. Actualdistance:3,5___ 400=

13__ x \x=13×400___ 3,5 =1485,71km5. a. DistanceonrailmapfromMthathatoCapeTown:about16cm Actualdistance:3,5___ 400=

16__ x \x=16×400___ 3,5 =1829km b. Costforfamily:4×R256=R1024,00



c. DistanceonroadmapfromMthathatoCapeTown:about11cm Actualdistance:3,5___ 400=

11__ x \x=11×400___ 3,5 =1257km Cost:1257×0,82=R1031(Adapttothecurrentpetrolprices.) Thecostfordrivingisvirtuallythesameastravellingbytrain. Yourdecisionwould,therefore,bebasedonfactorssuchasthelength

oftimeforthetrip;wearandtearonthecar.

10.8 Practise interpretinginformationonelevationmapsLearner’sBookpage344

1. a. FromHoutBaytherunupaverysteephilluptothehighestpointinthemarathonwhichis215matConstantiaNek.RunnersthenrundownashortslopeandthenupanothersmallhillandarriveatKirstenbosch.

b. Thefirst30kmoftheroutelookstheeasiestbecausethereareonlysmallhills.Therearenosteephillsuntilafter30kmoftheroute.

2. a. 87km b. 150km(atDurban) c. UmlaasRoad(±850m) d. FromPinetowntoBotha’sHill e. Runnershavecovered40kmofthemarathon. f. FromTumbleInntoUmlaasRoad g. Runnershavecovered17kmofthemarathon. h. FromDurbantoPietermaritzburgseemsmostdifficultbecauseofthe

uphills. i. Timefortheuprunwouldprobablybelongerthanforthedownrun,

becauserunnerscanrunfasterdownhillsthantheycanrunuphills.3. a. Timedifference=5h24min.49s

–5h20min.49s 4min. b. Yes. c. Theuprouteismoredifficultthanthedownrouteforthereasongiven

in2i.

Revise and consolidate:ScaleandmapLearner’sBookpage347

1. a. 85mm b. 20mm c. 35mm d. 70mm e. 55mm2. a. A 212,5km B 50km C 87,5km D 175km E 137,5km b. A 212,5km B 50km C 87,5km D 175km E 137,5km c. A 1062500mm B 250000mm C 437500mm D 875000mm E 687500mm d. A 27200000mm B 6400000mm C 11200000mm D 22400000mm E 17600000mm3. Scaleofmap35mm:150km a. i. 20mm:85,71km ii. 25mm:107,14km


121t e r m 2 • u n I t 1 0

b. Byroad,ThabazimbitoLephaleiscloser. Asthecrowflies,VaalwatertoMokopaneiscloser.4. a. Usingthescale35mm:150km Distance:58mm:248,57km

b. Speed=248,57km_______ 15_ 6h

=135,58km/h c. 31,07ℓ d. R365,715. a. Runningcost=6,62×11,77+17,18+8,98

=104c/km(cents/kilometre) b. R1,04/km c. R1,17/km d. 40mmonmap=171,43km Charge=171,43×R1,17

=R200,576. a. Anelevationmap b. Heightabovesea-level c. Distancefromwestcoastinkilometres d. ThePacificOcean e. 2000m(Althoughtheunitisnotgivenontheverticalaxis,itmakes

senseforittobemetres.) f. Answerswilldiffer.



terM 3

Worked ansWers

Unit 1Perimeter, area and volumeLearner’s Book pages 350–375

Teaching tips• Whenworkingwithperimeter,areaandvolume,thelearnersneedtobe

veryconfidentwithmeasuringlengthandconvertingunits.Remindthemthattheyworkedontheseskillsinearlierunitsandpayparticularattentiontoconvertingbetweenunitsofareaandvolumeaslearnerssometimesfindtheseconfusing.

• Userealexamplesasfaraspossibletodemonstrateconcepts.Wehaveincludedsomepracticaldirectmeasuringactivitiesinthisunitbecausephysicallymeasuringfamiliaritemshelpslearnerswhentheyhavetoworkwithmoreabstractconcepts.Theactivitiesarebestcarriedoutingroupssothatlearnerscancompareandcheckresults.

• Itmaybeusefultomakealargeposterwiththeformulaeforperimeter,areaandvolumeofdifferentshapesandobjectsfordisplayintheclassroom.Itisimportantthatlearnerscanseehowtheseformulaeworkandthattheycanusethem,changingthesubjectoftheformulaiftheyneedto,buttheydoNOTneedtomemorisethembecausetheCAPSdocumentspecifiesthattheseformulaemustbegiveninassessmenttasksandexams.

• Oncelearnershaveworkedthroughsomebasicactivitiesinvolvingtheconcepts,theywillworkthoughmoreinvolvedinvestigationindifferentcontextstocalculaterealquantities.Aspriceschangefromareatoareaandfromtimetotime,wewouldencouragethelearnerstodotheirownresearchandtofindthecostoflocallysolditems(suchaspaintandwood)ifatallpossibletocomparethosewiththecostsgiveninthisbook(correctin2011).

Solutions1.1 Practise directmeasurementmethodstofindperimeter,areaand volumeLearner’sBookpage351

Answerswilldiffer.

1.2 Practise calculatingperimeterandareawithgivenformulaeLearner’sBookpage353

1. a. P=2l+2b b. A=l×b =2(12,05cm)+2(2,1cm) =12,05cm×2,1cm =28,3cm =25,31cm2


123t e r m 3 • u n I t 1

2. a. P=2π r b. A=π r 2 =2×3,142×23,4cm =3,412×(23,5cm)2 =147,67cm =1735,17cm2

3. a. P=(14mm+9mm+32mm) =55mm b. A=1_ 2bh =0,8cm2

4. a. P=4s b. A=s2 =4×0,75m =(0,75m)2 =3m =0,56m2

5. a. P=1_ 4(2π r) b. A=1_ 2π r 2

=1_ 2(2×3,142×21,52cm) =1_ 2×3,142×(21,52cm)2

=67,62cm =727,55cm2

6. a. P=0,074m+0,08m+0,107m =0,261m =261mm b. A=1_ 2bh =2942,5mm2

7. a. P=3_ 4(2×3,412×84,5mm) b. A=3_ 4(3,412×84,5mm)2

=398,25mm =16825,00mm2

8. a. P=2(l×b) b. A=lb =2(1,5m×0,95m) =(1,5m)(0,95) =4,9m =1,43m2

9. a. P=1_ 2(2×3,412×33,5mm) b. A=P=1_ 2(3,412×33,5mm)2

=105,26mm =1763,01mm2

10. a. P=π d b. A=π r 2(r=1,08___ 2 =0,54) =3,142×1,08m =3,142×(0,54m)2 =3,39m =0,92m2

1.3 Practise usingformulaetocalculatetheperimeterandareaof compositeshapesLearner’sBookpage357

1. a. A=areaofsquare+areaofsemi-circle =s2+1_ 2π r 2 (r=4,4___ 2=2,2) =(4,4cm)2+1_ 2×3,412×(2,2cm)2 =26,96cm2

b. A=areaofsquare+areaoftriangle =s2+1_ 2bh =(25mm)2+1_ 2(25mm)(25mm) =625mm2+312,5mm2

=937,5mm2

c. A=areaofrectangle–areaoftriangle

2,4 m

4,5 m

2 m

=lb–1_ 2bh =2,4m×4,5m–1_ 2×2,4×2m =10,8m2–2,4m2

=8,4m2



2. a. Dividequadrilateralsintotwotriangles. A=area1+areaof2 (letthebaseofboths=17cm) =1_ 2bh+1_ 2bh

=1_ 2×17cm×8cm+1_ 2×17cm×5cm

=110,5cm2

b. Letthebaseofboths=18cm. A=1_ 2×18cm×9cm+

1_ 2×18cm×4cm =81cm2+36cm2

=117m2

3. a. Findthelengthofthemissingsides.

5,7 cm

1,1 cm

3,9 cm

(iii) 1,4 cm

(ii) 1,5 cm

(i) 2,2 cm

4,1 cm

2,5 cm

i 5,7cm–2,5cm=3,2cm ii 4,1cm–1,1cm–1,5cm=1,5cm iii 3,9cm–2,5cm=1,4cm P=3,9cm+4,1cm+5,7cm+1,1cm+3,2cm+1,5cm

+1,4cm+1,5cm =22,4cm A=(3,2×1,1)+(2,5×4,1)+(1,4×1,5)

=16,77cm2

b. P=2,9m+1,9m+1,5m+1,35m+6,1m+1,35m+1,7m+1,9m =18,7m A=(6,1×1,35m)+(1,9m×2,9m)

=13,75m2

c. P=7+5+9+3,9=24,9m 2,5 m

11,5 m

15 m

7 m 5 m

9 m 9 m

Heightoftriangle=11,5m–9m=2,5m A=areaofrectangle+areaoftriangle =l×b+1_ 2bh =(9m×15m)+(1_ 2×15m×2,5m) =144m2+18,7m2

=162,75m2

d. P=5,2+3,7+5+8,3+5=27,2m

5 m

8,3 m

2,4 m3,7 m5,2 m

A=areaofrectangle+areaoftriangle =l×b+1_ 2bh =(8,3m×5m)+(1_ 2×8,3×2,4m) =41,5m2+9,96m2

=51,46m2

e. P=324+562+435+440=1751cm A=areaofrectangle+areaoftriangle =(435cm×324cm)+(1_ 2×324m×127cm) =161514cm2

127 cm562 cm

435 cm

324 c

m

440 cm


125t e r m 3 • u n I t 1

f. A=areaofrectangle+areaof–areaofcutoutofrectangle =(460mm×300mm)+1_ 2(300mm×70mm)–

1_ 2(300mm×350mm) =96000mm2

350 m

m

300 mm

460 mm530 mm

70 mm

4. a. P=270cm+660cm+375cm+480cm+105cm+20cm+16cm+6cm+14cm+10cm+6cm=1962cm

=19,62m Areaofshadedpart: areaoftotalarea–[(0,06m×0,16m)+(0,14m×0,1m)] =22,84m2

b. 6,5 m

3 m

1,6 m3,3 m

1,8 m

0,8 m

2,3 m

0,8 m

3,2 m

4,6 m

Pofunshadedarea =4,6m+6,5m+3m+3,3m+1,6m+3,2m+2(0,8m+2,3m)

+2(1,8m+0,8m) =33,6m Aofunshadedarea =areaofunshadedarea–areaofshadedarea =(4,6m×3,2m)+(3m×3,3m)–(0,8m×2,3m)–(0,8m×1,8m) =21,34m2

5. a. P=54cm+60cm+60cm+1_ 2×circumferenceofcirclewithdiameterof54cm

=54cm+60cm+60cm+1_ 2πd =174cm+1_ 2×3,412×54cm =258,83cm A=areaofrectangle–areaofsemi-circle r=1_ 2d =lb–1_ 2π r 2 =1_ 2×54cm =60m×54m–1_ 2×3,142×(27cm)2 =27cm =2094,74cm2

b. Pofquartercircle=1_ 4(2π r) =1_ 4(2×3,142×2,8) =4,40cm



Aofquartercircle=1_ 4(π r 2) =1_ 4×3,142×(2,8)2

=6,16cm2

Pofshape=2,8m+5,6cm+5,6cm+2,8cm+4,4cm=21,2cm

Aofshape=areaofsquare–areaof1_ 4circle=(5,6)2–6,16cm2

=25,2cm2

c. Pofsemi-circle=1_ 2πd =1_ 2×3,142×620mm =974,02mm Aofsemi-circle=1_ 2π r 2

=1_ 2×3,142×(310mm)2

=150973,1mm2

Pofshape=3×620mm+974,02mm =2834,02mm Aofshape=areaofsquare+areaofsemi-circle =(620mm)2+150973,1mm2

=535373,1mm2

d. Circumferenceofsemi-circle=1_ 2πd =1_ 2×3,142×2,3m =3,61m Aofsemi-circle=1_ 2π r 2

=1_ 2×3,142×(1,15m)2

=2,08m2

Aoftriangle=1_ 2bh =1_ 2×1,3m×1m =0,65m2

P=2,3m+1,3m+3,61m+lengthofslantsidesoftriangle A=areaofrectangle+areaofsemi-circle+areaoftriangle =(1,3m×2,3m)+2,08m2+0,65m2

=5,72m2

e. Circumferenceofsemicircle=π×r=π×1,4=4,398cm(tothreedesimalplaces)

Poftwoshapesonthesidesofthetriangle(heightas1,4cm(radius)) =√ 

_________ 1,42+1,42

=√ ____ 3,92=1,98cm

=slantedsides(basesoftheshapesonthesides) Pofcompositeform=4,398+1,98+1,98=8,358cm Aoftriangle=1_ 2×2,8×1,4=1,96cm2

Aofsemicircle=1_ 2×π×r 2=1_ 2×π×1,42=3,079cm2(tothreedecimalplaces)

Therefore,areaofcompositeform=3,079–1,96=1,119cm2

f. P=circumferenceofsemi-circle+42cm+28cm+16cm+slantedsidesoftriangle

=1_ 2×3,142×28cm+42cm+28cm+16cm+sidesoftriangle

=43,99cm+42cm+28cm+16cm+15cm+15cm

=159,99cm

13 cm

15 cm15 cm

26 cm 16 cm

28 cm

42 cm


127t e r m 3 • u n I t 1

A=areaofsemi-circle+areaofrectangle–areaoftriangle =[1_ 2×3,142×(14cm)2]+(42cm×28cm)–(

1_ 2×26cm×13cm) =307,92cm2+1176cm2–169cm2

=1314,92cm2

6. a. i. A=l×b=5km×2,7km=13,5km2

ii. 100ha=1km2

13,5km2×100=13500ha b. i. A=l×b

=0,95km×8,76km=8,32km2

ii. 8,32km2×100=823ha c. i. A=l×b

=5km×0,1km=0,5km2

ii. 0,5km2×100=50ha d. i. A=areaofrectangle×areaoftriangle

=(5,54km×3,76km)+1_ 2(3,76km×3,09km)=20,83km2+5,81km2

=26,64km2

ii. 26,64km2×100=2664ha

1.4 Practise usingformulaetocalculatesurfaceareaandvolumeLearner’sBookpage363

1. a. SA=2(32cm×32cm)+4(32cm)×32cm=6144cm2

V=32cm×32cm×32cm=32768cm3

b. SA=2(5,7cm×2,5cm)+2(5,7cm×2,5cm)×8,9cm=174,46cm2

V=5,7cm×2,5cm×8,9cm=126,83cm3

c. SA=2(900mm×1200mm)+2(900mm×1200mm)×600mm=4680000mm2

V=900mm×1200mm×600mm=648000000mm3

2. a. SA=2π r 2+2πr×h=2×3,412×(10mm)2+2×3,142×10mm×12mm=1382,48mm2

V=π r 2h=3,142×(10mm)2×12mm=3770,4mm3

b. SA=2π r 2+2πrh=2×3,412×(3cm)2+2×3,142×2cm×45cm=590,70cm2

V=π r 2h=3,142×(2cm)2×45cm=565,56cm3

c. SA=2π r 2+2πrh=2×3,412×(0,65m)2+2×3,142×0,65m×10,4m=45,13m2



V=π r 2h=3,142×(0,65m)2×10,4m=13,81m3

3. a. SA=2×(26cm×19cm)+2(26cm×19cm)×31cm=3778cm2

V=26cm×19cm×31cm=15314m3

b. SA=2×(43cm×59cm)+2(43cm×59cm)×9cm=6910cm2

V=43cm×59cm×9cm=22833m3

c. SA=2×(5,7m×2,5m)+2(5,7m×2,5m)×8,9cm=174,46cm2

V=5,7m×2,5m×8,9cm=126,83m3

d. SA=2π r 2+2πrh=2×3,412×(9,25mm)2+2×3,142×9,25mm×13mm=1293,33mm2

V=π r 2h=3,142×(9,25mm)2×13mm=3494,89mm3

e. SA=2π r 2+2πrh=2×3,412×(0,45m)2+2×3,412×0,45m×8,05m=24,04m2

V=π r 2h=3,142×(0,45m)2×8,05m=5,12m3

f. SA=2π r 2+2πrh=2×3,412×(2cm)2+2×3,142×2cm×48,3cm=632,17cm2

V=π r 2h=3,142×(2cm)2×48,3cm=607,03cm3

4. SA=1433,98cm2

V=3179,8cm3

Assignment 1 AnurserywithanofficeshedLearner’sBookpage364

1. Scaledrawingsmaydiffer.2. a. Perimeter:2(18m+15m)=66m d. Youwillneed(66m–1,5m)offencing:64,5m e. Numberofpoles=64__ 2+1

=32+1=33poles

Youmightneedanothertwopolestosupportthegateateitherend.3. a. Areaofground=18m×15m=270m2

Volumeoftopsoil=270m2×0,75m=202,5m3

b. Topsoil:compost=3:1=202,5m3:x 3_ 1=

202,5____ x

\x=202,5×1_ 3 =67,5m3


129t e r m 3 • u n I t 1

Totalamountoftopsoil+compost=202,5+67,5=270m3

c. Topsoil:R55,00perm3orR199,00for5m3

=R199,00______ 5 =R39,80/m3

Buying5m3atatimeisthebestoption. Compost:R80,00perm3orR350for5m3

=R350____ 5 =R70/m3

Buying5m3atatimeisthebestoption. Topsoil:202,5m

3______ 5 =40(×5m3)+2,5m3

40×5m3=40×R199,00=R7960,00 2,8m3×R55=R137,5 Mosteconomical:40×5m3+2,51m3

Compost:67,5___ 5 =13(×5m3)+2,5m3

Moreeconomical:13×5m3+2,51m3

4. Learnerstoworkfromtheirownplans.5. Materialsforpergola: 8poles×3m=32m +4poles×1m= 4m

=36minlength Calculatethesurfaceareaofthepolethatneedstobevarnished–you

needtomeasurethediameterofthepolesyouareusing.6. Learnerstoworkfromtheirownplans.7. Answerswilldiffer.8. a. Volumeofcement=3m×2,4m×1,1m

=7,92m3

b–e. Answerswilldiffer.9–10. Answerswilldiffer.

Assignment 2 choosefittingsandfinishesforanewhouseLearner’sBookpage371

1. Answerswilldiffer.2. Usingascaleof1:100 a. Measurementonmap: 3,5cm×3cm: 10,5cm2

1,6cm×0,9cm: 1,44cm2

1,7cm×0,9cm: 1,53cm2

Totalareaonmap: 13,47cm2

Scaleof1:100or1cm:100cmor1cm:1m Areaofbedroom1plustheen-suitebathroom:13,47m2

b. Measurementonmap:1,7cm×2cm=3,4cm2

Areaofmainbathroom=3,4m2

c. Measurementonmap:1,5cm×1cm=1,5cm2

Areaofstoepoutsidekitchen:1,5m2

4. a. Classdiscussion–woulddependonpersonalpreferenceandwhatonecouldafford.

b. 1cm2onthemapis1m2ofareaofthehouse. c. • Bedroom1(excludingen-suite):10,5m2

Costofcarpets:10,5m2×R135=R1417,50 Costoftilesforbedroom1:12boxesrequired Cost:12×R89,95=R1079,40



• En-suite:2,97m2

4boxesoftilesrequired:Cost:4×R89,95=R359,80 • Mainbathroom:3,4m2

4boxesoftilesrequired:Cost:4×R89,95=R359,80 • Stoepoutsidekitchen:1,5m2

2boxesoftilesrequired:Cost:2×R89,95=R179,90 d. Answerswilldiffer.5. a. Sevendoorsandoneslidingdoor b. Learners’ownresearch.6. a–c. Answerswilldiffer. d. Learners’ownresearch. e. Main bedroom Floorarea:3,4m2

Areaoftiles:20cm×20cm=0,2m×0,2m=0,04m2

Numberoffloortiles: 3,4m2________ 0,04m2/tile=85tiles

Areaoftiles:30cm×30cm=0,3m×0,3m=0,09m2

Numberoffloortiles: 3,4m2________ 0,09m2/tile=38tiles

Perimeter=2(1,7m+2m)=7,4m Calculatewallareatobetiled: Perimeterofbathroom–widthofdoor=7,4m–0,9m=6,5m Wallareatobetiled=6,5m×1,2m=7,8m2

Numberofwalltilesrequired: 20cm×20cm: 7,8m2

________ 0,04m2/tile=195tiles

30cm×30cm: 7,8m2________ 0,09m2/tile=87tiles

Bothfloorandwalltilescanonlybeboughtinmultiplesof25. f. Cost of floor tiles 20cm×20cmfloortile:85tilesrequiredmeansfourboxesmustbe

purchased. Cost=4×R98,00=R392,00 30cm×30cmfloortile:38tilesrequiredmeanstwoboxesmustbe

purchased. Cost=2×R124,50=R249,00 Cost of wall tiles: 20cm×20cmwalltile: 195tilesrequiredmeanseightboxesmustbe

purchased. Cost=8×R74,00=R592,00 30cm×30cmwalltile: 87tilesrequiredmeansfourboxesmustbe

purchased. Cost=4×R109,00=R436,00 g. Fromtheresultsofquestion6fwecanseethe30cm×30cmtilesis

themosteconomical. Note:Accordingtotheplantheareaoftheerfis200m2.Ifweassume

thatthewidthof12,4miscorrect,thelengthwouldbe16,13m(thelengthonplanshouldbe16,13cmandthewidth12,4cm).

7. a. Perimeter=2(16,13+12,4)cm≈57cm Widthofdriveway=3m 54moffencingisrequired b–d. Learners’ownresearchandconclusion.8, 9. Answerswilldiffer.


131t e r m 3 • u n I t 2

Revise and consolidate:Measurement–Perimeter,areaandvolumeLearner’sBookpage376

1. a. i. 120m ii. 675m2

b. i. 109mm ii. 306mm2

c. i. 121,8m ii. 927,20m2

d. i. 80,38m ii. 514,46m2

e. i. 87,28m ii. 398,00m2

f. i. 514cm ii. 15700cm2

2. a. i. 18,84m+55=73,84m ii. 314,52m2

b. i. 258cm ii. 2144cm2

c. i. 436,9cm ii. 1553,38cm2

d. i. 418mm ii. 7248mm2

3. a. i. 82,93mm2 ii. 43,07m3

b. i. 16000+10080–3600=22480cm2

ii. 96000cm3

c. i. 0,38mm2 ii. 0,02m3

d. i. 7937,2cm2 ii. 28935cm2

4. a. 23,51m2

b. R899,90c. 109×R12=R1308d. 51,6me. Volumeoflivingroom:96,77m3

Volumeofmainbedroom:30,24m3

f. Wallareaofstudy:22,96m2

[email protected]:R372

Unit 2Plans (instructions and assembly diagrams)Learner’s Book pages 379–384

Teaching tips• Thisunitrevisesthebasicconceptsandskillsthatlearnersworkedwithin

Grade10toreadandmakesenseofinstructionsandassemblydiagrams.• Writteninstructionsareoftenmisreadormisinterpretedbecausepeople

don’treadthemproperlyorbecausetheydon’tfollowthemproperly.Itisusefultohavesomeinstructionmanualsinclassandtoasklearnerstofollowtheinstructions.Calculatormanuals,cellphoneinstructionbookletsandapplianceoperatinginstructionsarealleasytofind.Havelearnersworkinpairs,onetocarryouttheactions,theothertocheckwhethertheyaredoingitcorrectly.Youcandevelopandcarryoutsimilaractivitiesusingdiagramsandpictorialinstructions.

• Learnersshouldbeabletoidentifyinstructionsthatarenotclear.Thisis oftenthecaseforitemsmadeincountrieswherepeopledon’tusemuch English(particularlyChinaandKorea)orwherecountriesdon’thave thesamesafetystandardsasothercountries.Itwillbeinterestingtohave aclassdiscussionaboutinternationalsafetystandardsandtheroleof organisationssuchastheSouthAfricanBureauofStandards(www.sabs. co.za)inenforcingthosestandards.Itisalsointerestingtolookathow andwhylegalrequirementsleadtosomeseeminglysillyinstructions. ProductinstructionsfromtheEuropeanUnionareoftenover-specified



intermsofinstructionsandsafetyinformationsothatthemanufacturerscannotbesuedbyconsumers.Youcanfindlotsofexamplesofridiculousinstructionsonproductsifyoudoaninternetsearchandlearnerswillfindthesefunny.Localexamplesinclude:• Onaniron:Donotironclothesonbody.• Onababy’spram:Removeinfantbeforefoldingforstorage.• Onasupermancostume:Wearingofthisgarmentdoesnotenableyou

tofly.• Onahairdryer:Donotuseinshower.

Solutions2.1 Practise readingandwritinginstructionsLearner’sBookpage380

1. a. Turnthecameraon. b. c. Seepage71. d. Videoclipsfolder e. PresstheOK/ibutton f. PresstheCbutton2. Answerswilldiffer.

2.2 Practise writingclearinstructionsLearner’sBookpage381

1, 2. Answerswilldiffer.Discusslearners’answersinclass.

2.3 Practise readingandmakingsenseofinstructiondiagramsLearner’sBookpage382

1. a. Opentheflatcoveringtheslot. b. Thearrowsshowyouwheretoinsertthememorycard. c. Thiswillensurethatthememorycarddoesnotfalloutoftheslot. d. Removeitinexactlythesamewaythatyouinsertedthememorycard

butinreverse. e. Discusslearners’suggestions.2. A Keepawayfromliquids. B Storeinasafeandsecureplace. C Don’twriteontheobjectortouchitwithasharpobject. D Avoideyecontactwiththelaserbeam. E Donottouchthepowersocket. F Keepawayfromdraftsandextremetemperatures. G Donottouchtheprongsofthechargerwithmetalobjects. H Treatwithcare.Roughhandlingcoulddamagetheequipment. I Donotwrapelectricalcablesaroundtheequipment. J Useinasafeplace,awayfromotherobjects.

2.4 Practise readingandmakingsenseofinstructionswithwordsand diagramsLearner’sBookpage383

1. Matchingthecolours,connectthecomponent/progressivescanvideojacksontherecordertothecorrespondinginputjacksontheTVusingcableC.

2. Therearethreejacksoneitherendofthecable.


133t e r m 3 • u n I t 3

3. TheinputjacksarecolourmatchedtothesocketsontheTV.4. ConnectstheS-VideooutjackontherecordertotheS-videoinjackonthe

TVusingtheS-videocable(thecablelabelledSonthediagram).

2.5 Practise makingsenseofassemblydiagramsLearner’sBookpage384

Answerswilldiffer.Discusslearners’answerswiththeclass.

Unit 3Floor and elevation plansLearner’s Book pages 385–393

Teaching tips• LearnersworkedwitharangeofsimplefloorplansinGrade10.Theyalso

workedwithrealobjectstomodelandsolveproblemsrelatedtocontainersandpackaging.Thisyeartheywillextendthisworktoincludethefloorplansofmorecomplexstructures.Theywillalsolearntouseelevationplans(viewsofthestructurefromtheback,frontandsides).Oncelearnerscanreadandinterpretplans,theywillneedtoapplytheirskillsinUnit4tobuildscaled3-Dmodelsandthensolvespatialproblemsbymodellingandbycalculation.

• Makesurethelearnerscanworkwithlinescalesandratioscalesasthesewillbeusedthroughoutthisunit.IfnecessaryrevisetheconversionsinTerm1Unit5andTerm2Unit9beforeproceeding.

Solutions3.1 Practise describingitemsshownonaplanLearner’sBookpage385

1. a. rectangular b. 18×25=450squareunits c. three d. inwards e. fourchairs,workstation,roundtable,bookshelfandwaste-paperbin f. Waste-paperbin 4squareunits Workstation 97squareunits 4chairs: 4×9=36squareunits Table 21squareunits Bookshelf 12squareunits Total 170squareunits2. a. one b. outwards c. four d. eightcubicles e. Thereareeightwindows,fourinthefrontoftheofficeandtheother

fouronthebackwalloftheoffice. f. Inthestaffkitchen g. Therearetwotoilets–theyareatthebackoftheoffice.



3.2 Practise findingthesizeofitemsshownonaplanLearner’sBookpage386

1. a. 210cmor2,1m b. i. 240cm×50cm ii. Area=2,4m×0,5m=1,2m2

c. Area=2,2m×1,7m=3,74m2

d. Theentrancedoorsareeach80cmwide. e. Areaofmeetingroom:2,5m×3,1m=7,75m2

Areaofmanager’soffice:2,5m×3,1m=7,75m2

2. a. Totalareaofoffice:9m×10m=90m2

Totalmonthlyrental:90×R145,99=R13139,10 b. Newmonthlyrental:R13139,10+8%ofR13139,10

=R14190,23permonth

3.3 Practise makingsenseofelevationplansLearner’sBookpage387

1. a. rectangular b. Theroofwillslopedownfromfronttoback. c. trapezium d. No. e. Ithasastandardwidthfrontdoor. f. rectangular2. a.

0,8 mSide of shed

Side of shed

Front of shed

Back of shed

3,6 m

3,6 m

2,4 m

2,8 m

2,8 m

2,8 m

3,6 m

3,6 m

2,4 m

2,4 m

0,8 m

2,4 m

2,8 m

b. SAofside=areaofrect+areaoftriangle=0,8m×2,4m+1_ 2(0,8×0,4m)=2,08m2

SAoffront=3,6m×2,8m=10,08m2

SAofback=3,6m×2,4m=8,64m2

3. Doorframe:0,8m×2m

2 m

security gate

0,8 m

(80mm=0,08m0,08m×2=0,16m) Securitygate:(0,8m–0,16m)×(2,0m–0,16m)

=0,64m×1,84m4. a. length:9blocks width:4blocks sidesofeachblock:2,5mm lengthoffloor:9×2,5=22,5mm widthoffloor:4×2,5=10mm


135t e r m 3 • u n I t 3

Usingascalefactorof1:80: length:22,5mm×80=1800mm=1,8m width:10mm×80=800mm=0,8m b. A=1,8m×0,8m=1,44m2

c. cost:1,44×258,80=R372,67

3.4 Practise drawingscaledfloorandelevationplansLearner’sBookpage389

1. 2,8 cm

1,4 cmFront view Side view Back view

900 mm

2,5 cm

2,8 cm

2,5 cm

1 cm

2,5 m

2 090

mm

2. a. 900mm b. Outwards–allowsmorespaceforstorageinside(ifthedooropens

inwards,thereneedstoberoomforthedoortoopen). d. WW610,WW730willfitcomfortably. WW850willjustfit. e. WW6103. Shedfloor:2,8m×1,4m

1,4 cm

Scale: 1 : 1002,8 cm

900 mm610 mm 610 mm

4. a. floorareaforbookshelf:40cm×80cm=3200cm2=0,32m2

floorareaforbin:2×3,412×25cm2=4265cm2=0,43m2

floorareaforlawnmower:60cm×70cm=4200cm2=0,42m2

floorareaforwheelbarrow:90cm×50cm=4500cm2=0,45m2

b. Answerswilldiffer.

3.5 Practise answeringquestionsaboutcompassdirectionsin constructionLearner’sBookpage392

1. Theroomreceivesfullsuninmid-winteratanglea.2. Theangleincreasesfromwintertospring.Fromspringtosummerit

continuestoincrease.Fromsummertoautumntheanglewillstarttodecrease.

3. Theanglebetweentheroofandthesun’slightissolargethatthesunlightmissesthewindow.

4. Itiscoolinsummer;easytokeepcleanandhard-wearing.5. South-facingroomsgetalmostnosunlightinwinterasthesunshines

fromthenorth.6. a. Thebestplacetoplaceasolarpanelwouldbeonthenorth-facing

sectionoftheroof. b. Theywillreceivethemaximumexposuretosunlight.



3.6 Practise workingwithdesigndrawingsLearner’sBookpage393

1. 120cm×30cm=3600cm2

Or:1,2m×0,3m=0,36m2

2. 700mmor70cm3. V=1,2m×0,3m×0,03m=0,0108m3

V=120cm×30cm×3cm=10800cm3

4. a. Costoftheyellowwood:0,0108m3

=0,0108m3×R19000=R205,20

b. Costwith15%markup:R205,20+15%ofR205,20=R235,985. Learnersdiscussanswers.

Unit 4using models to investigate shape and spaceLearner’s Book pages 394–399

Teaching tips• Mathematicalmodellingisaveryusefullifeskill.Atabasiclevel,people

maydrawdiagramsofaroomandusescaledversionsoffurnituretoseehowtoarrangeit(learnersdidthislastyearandalsoinUnit3).Peoplemayalsomakeamodelorprototypeofanitem(scaledorlifesize)toseehowitwillworkandwhatitwilllooklike.Forexample,architectsoftenbuildscaledmodelsofhousingand/orofficedevelopmentstoshowprospectivebuyerswhattheywillget.Engineeringfirmsoftenmakeoneversionofanitemandthenusethatasatemplatetomanufacturelotsmore.Jewellersmakesingleitemsorcarvemodelsoutofwaxtousetomakeorcastmanymoreidenticalitems.

• Learnerswillneedtoconstructmodelsinthisunit.Makesureyouhaveasupplyofcardboard(oldpackagingcontainersorfilecoversareuseful),scissorsand/orcraftknives,adhesivetapeand/orglueforlearnerstouse.

Solutions4.1 Practise describingandsketchingshapesLearner’sBookpage395

1. Learnerswillchoosedifferentcontainers.Examplesaregivenbelow. a,b. dogfoodandpencilholderontheright:cylinder tissues(A):cube Tomtomcontainer,headacheliquidcapsules,boxwithtransparentlid,

boxofchocolates:rectangularprism pencilcase(leftfront):triangularprism c. Learnersdescribecylinders,cubes,rectangularprismsandtriangular

prismsandthensketcheachone.

4.2 Assignment: MakeacylindricalpackageLearner’sBookpage395

Answerswilldiffer.


137t e r m 3 • u n I t 4

4.3 Practise workingouthowmuchwoodyouneedLearner’sBookpage397

1. V=lbh=40cm×20cm×80cm=64000cm3

2. V=lbh=120cm×50cm×75cm=450000cm3

3. V=lbh=1,3m×0,7m×1m=0,91m3

4. V=lbh=880mm×500mm×920mm=404800000mm3

4.4 Investigation: BoxesandhowmuchtheyholdLearner’sBookpage397

1. a. Eachlearnermustdrawthescalednetsforeachboxusingthetemplateprovided.Ascaleof1:10isgiven.

ModelAwouldhavethefollowingmeasurements.

6 cm6 cm

6 cm

6 cm6 c

m

6 cm

6 cm

Allsidesofthecubeare60cm,sousingascaleof1:10givesalengthforeachsideinthescaledrawingof6cm.

ModelBandmodelCaredrawninthesameway.

3 cm

6 cm

6 cm

3 cm

3 cm

6 cm

3 cm

Model B

6 cm

1 cm 6 cm

6 cm

1 cm

1 cm

6 cm

6 cm

1 cm

Model C



b. ModelA:5×6cm×6cm=180cm2

ModelB:(6cm×6cm)+4(6cm×3cm)=108cm2

ModelC:(6cm×6cm)+4(6cm+1cm)=60cm2

c. Scaleoflength:1:10 Scaleofarea:1:100 ModelA:180cm2×100=18000cm2

=1,8m2

ModelB:108cm2×100=10800cm2

=1,08m2

ModelC:60cm2×100=6000cm2

=0,6m2

c. VolumemodelA=lbh =60cm×60cm60cm =216000cm3

=0,216m3

VolumemodelB=lbh =60cm×60cm×30cm =108000cm3

=0,108m3

VolumemodelC=lbh =60cm×60cm×10cm =36000cm3

=0,036m3

4.5 Practise makingandusingamodelofabuildingLearner’sBookpage398

1–3. Accuratescaleplans4. Elevationplansaregluedtothemodel.

4.6 Practise usingamodeltodecideontheplacementoffurnitureLearner’sBookpage399

Answerswilldiffer.

Revise and consolidate:ModelsandplansLearner’sBookpage401

1. a. two b. six c. Itisaslidingdoor. d. Atoiletandawashingbasin e. Thestudyandguesttoiletareonyourleft. Ontherightyoulookintotheopen-planlivingarea. Afterthestudyandguesttoiletthekitchenisontheleft. Thefrontdoorisdirectlyinlinewithentrancestobedrooms1and2.2. a. Jabumustsetthesysteminprogrammingstatus. b. 51*1209# c. Hewillhearadoublebeep. d. Nohecannot.Thepasswordmustbefourdigits.3. Answerswilldiffer.4. 23,51m2

5. R899,906. 109m2×R12___ m2=R13087. Learnersdiscusstheiranswers.Theyneedtouseallavailableinformation.8. Answerswilldiffer.


139t e r m 3 • u n I t 5

Unit 5taxationLearner’s Book pages 404–413

Teaching tips• Learnersneedtobeveryconfidentaboutdoingpercentagecalculations

inthisunit.Theywillhavehadsomepracticeinearlierunits,butifyoufeeltheystillstruggleinthisarearevisethebasicskillssectionsintheLearner’sBookbeforeproceeding.

• VATwasdealtwithinGrade10.RemindthelearnersthatVATismostlyalreadyaddedtothepriceofgoodswebuy.However,businessesandtouristscanclaimbackVAT(oroffsetagainsttheVATtheyhavechargedinthecaseofbusinesses)thattheypayonitemstheybuy.Inthecaseofatourist,thiscanresultinamassivesaving.UsetheexampleofbuyingacameraforR5000(includingVAT).Whenthetouristleavesthecountry,theycanberefundedtheVATontheirpurchase.ThisisR700.Alsoremindlearnersthatsomebasicfoodstuffsarezero-ratedforVAT.Theaimofthisistohelpthepoor.ThereisamovementinSouthAfricatolobbygovernmenttomakeeducationalbookszero-rated.Youcoulddiscussinclasswhatthebenefitsofthiswouldbeforlearnersandotherconsumers.

• UIFisacompulsorytaxleviedonallformalemployees.Employeesaretaxed1%oftheirearnings(uptoamaximumsetbySARS)andtheiremployerspayanadditional1%.ThisallowspeoplewholosetheirjobsandwomenonmaternityleavetoclaimunemploymentmoneyfromtheUIF.ThetermsandconditionsofUIFareoutlinedintheLearner’sBook.YoucanfindoutmoreaboutUIFfromyourlocalSARSofficeifnecessary,theyhavepublications(printedandonline)thatyoucantaketoclassforreference.

Solutions5.1 Practise VAtcalculationsLearner’sBookpage406

1. a. Priceexcluding:R144,50 VAT=R144,50×14___ 100=R20,23 Priceinclusive=R164,73 b. Priceexcluding=R750,00×100___ 114=R657,89 VAT=R750,00×14___ 114=R92,11 Priceinclusive=R750,00 c. Priceexcluding=R98,30 VAT=R98,30×14___ 100=R13,76 Priceinclusive=R112,06 d. Priceexcluding=R23,40×100___ 14=R167,14 VAT=R23,40 Priceinclusive=R190,54



2. Income (total for 2011) expenditure (total for 2011)

SalaryJrobinson(net) 136032,00 Bondrepaymentsonhouse 47718,00

WagesMrobinson(net) 62890,00 rates,water,refuseservice+VAt 9160,13

Inheritedfromgran 10000,00 telephone+VAt 6427,59

Interestonbanksavings 1803,20 Electricity+VAt 5862,10

Foodandgroceries+VAt 39935,82

MedicalAid 20370,00

Householdandcarinsurance+VAt

10689,21

Monthlypaymentsonnewcar+VAt

17770,32

Petrol,carservices+VAt 18960,48

Schoolandcollegefees 39270,00


3. a. VATcanbeclaimedbackonthefollowingitemsin2011: Electricityandphone:VAT=10500,00×14___ 114 1289,47 Officeadministration:VAT=7200,00×14___ 114 884,21 Printerrentals:VAT=27600×14___ 114 3389,47 Paper:VAT=18000,00×14___ 114 2210,53 Ink:VAT=9450,00×14___ 114 1160,53 Total amount that can be claimed for 2011 8 934,21 VATcanbeclaimedbackonthefollowingitemsin2012: Electricityandphone:VAT=11025×14___ 114 1353,95 Officeadministration:VAT=7560,00×14___ 114 928,42 Printerrentals:VAT=27600×14___ 114 3389,47 Paper:VAT=21000,00×14___ 114 2578,95 Ink:VAT=11376,00×14___ 114 1397,05 Total amount which can be claimed for 2012 9 647,84 b. VATmustbepaidbacktothegovernmentforthe

followingitemsin2011: Photocopies:VAT=81200,00×14___ 114 9971,93 PrintingA1plans:VAT=35800,00×14___ 114 4396,49 Printingfancystationery:VAT=27860,00×14___ 114 3421,40 Total amount to be paid 17 789,82 VATmustbepaidbacktothegovernmentforthe

followingitemsin2012: Photocopies:VAT=80740,00×14___ 114 9915,44 PrintingA1plans:VAT=27935,00×14___ 114 3430,61 Printingfancystationary:VAT32537,00×14___ 114 3995,77 Total amount to be paid 17 341,82

5.2 Practise calculatinguIFcontributionsLearner’sBookpage412

1. a. i. Hecontributed1%ofR1850=R18,50perweek. ii. Hiscontributionperyear=R18,50×52=R962,00


141t e r m 3 • u n I t 6

2. a. ContributionstoUIFfromsupermarketjob =1%ofR1250 =R12,50perweek ContributionstoUIFfromrestaurantkitchenjob =1%of(R90×5) =1%ofR450 =R4,50 b. Increasedwagesatsupermarket=R1250+5%ofR1250

=R1312,50 UIFcontribution:R13,13 weeklycontributionswillbeincreasedbyR13,13–R12,50=R0,63 c. ShesellsgoodsonacommissionbasisanddoesnotpayUIF. HerUIFcontributionwillbeR13,13perweekfromhersupermarket

job.(Shelostherjobattherestaurant.)

5.3 Assignment: Anemployer’sbudgetforuIFcontributionsLearner’sBookpage413

1. total salary paid for the year uIF

Ayanda r51900 r519,00

coco r14670 r146,70

Fezile r51345 r513,45

Hendrik r27300 r273,00

James r51900 r519,00

Total annual UIF contributions: R1 971,15

2. UIFcontributionwillalsoincreaseby3,5%. AnnualUIFcontribution=R1971,15+3,5%ofR1971,15

=R2040,14

Revise and consolidate:Finance–taxationLearner’sBookpage415

1. a. R3,64 b. R15743 c. R23,21 d. R1,592. a. R13,55 b. R254,30 c. R442,98 d. R30,703. a. R285 b. R3876 c. R250794,30 d. R1936,864. a. i. R8,55 ii. R8,55 b. i. R174,30 ii. R174,30 c. i. R890 ii. R8905. a. R214,50 b. R227,806. Maximumamountthatcanbepaidis58%ofwhatwasearnedperday. a. R448perweek b. R696perweek



Unit 6ProbabilityLearner’s Book pages 416–434

Teaching tips• Inthisunit,learnerswillcontinuetoworkwithgamesthatmakeuse

ofcoinsanddiceandweatherpredictionstoreviseandconsolidatetheconceptsandterminologythatwereintroducedlastyear.Theywillalsocontinuetousetwo-waytablesandtreediagramstorepresentthesamplespaceandoutcomesofdifferentevents.Rememberthoughthattheydonotneedtocalculateprobabilityfromtreediagrams;theyonlyusethemtorepresentallthepossibleoutcomesofoneormoreevents.

• Thisyearwealsointroducearangeofcontextswherethereisachanceofgettinganincorrectresult.Learnersshouldbefamiliarwithadvertisementsthatmakestatisticalclaims–forexample,80%ofteenagerswhousethisfacewashreportedfewerpimples.Encouragelearnerstomakeacollectionofthistypeofclaimfromprintmediaanddiscusstheclaimsinclass.

• Othertestswherethereisachanceofawrongresultarealsoincluded.Wedealspecificallywithpregnancytests(locallyavailableonesclaimtobe99%ormoreaccurate)andrandomdrugtests(whichlearnersmayhaveheardaboutinconnectionwithsportsevents).Remindlearnersthat1%seemslikeasmallmarginoferror,butthattheactualnumbersofwrongresultswillbegreater,themorepeoplewhodothetest.Showthemhowthisworksusinganexampleliketheonebelow.

How many people get wrong results if a test is 99% accurate?

number of people taking the test 10 100 1000 10000 100000 1000000 10000000

Correct results 9 99 990 9900 99000 990000 9900000

Incorrect results <1 1 10 100 1000 10000 100000

• Theexampleofanonlinepregnancytestdiscussedinthisunitisarealone–suchtestsexist.Itisimportantthatyoupointouttolearnersthattheyshouldnotrelyonresultsfromtestslikethisoneandencouragethemtobereallycriticalofsuchtests.Theexampleofaboyusingitandgettingahigherthan50%probabilityofbeingpregnantmayseemsilly,butitmakesthepointthatthetestisfundamentallyflawed(itdoesnotaskifyouarefemaleanditdoesn’taskifyouhavehadsex).

Solutions6.1 Practise expressingprobabilityineverydaytermsLearner’sBookpage416

1. a. Likely b. Unlikely(unlessthisyearisaleapyear) c. Unlikely d. Impossible e. Unlikely2. Answerswilldifferbutpossibleanswersincludethefollowing. a. Summerfollowsspring. b. IfItossacoin,Ihavea50–50chanceofgettingheads. c. IftodayisMonday,tomorrowwillbeSunday.3. Answerswilldiffer.Discussanswersinclass.


143t e r m 3 • u n I t 6

6.2 Practise expressingprobabilityinpercentagesandnumbersLearner’sBookpage417

1. a. Nadirahasa78%chanceoffallingpregnant. b. Nadirahasa5%chanceofbeinginfertile. c. Probabilitythatshewillnotgetpregnant:100%–78%=22% d. Probabilitythatshewillbefertile:100%–5%=95%2. Atabout333. a. Animpossibleoutcomehasaprobabilityof0. b. Acertainoutcomehasaprobabilityof1. c. Answerswilldiffer.Reasonsmustbegiven.4. Answerswilldiffer.5. Theprobabilityofawomanwhois15yearsto19yearsbeinginfertileis

lessthan3%.

6.3 Practise doingatrialandrecordingtheoutcomesLearner’sBookpage420

Answerswilldiffer.

6.4 Investigation: Howoftenyouthrowadouble?Learner’sBookpage420

Answerswilldiffer.

6.5 Practise calculatingexperimentalprobabilityLearner’sBookpage422

1. Experimentalprobability:35__ 60=7__ 12

2. Experimentalprobability/relativefrequency:175___ 200=7_ 8

3. Experimentalprobability:58___ 290=1_ 5

4. a. Relativefrequency:11__ 80

b. Relativefrequency:27__ 805. No.Asampleofsize80istoosmalltoberepresentativeofmost

customersinSouthAfrica.6. a. Generic:Needtoknownow:1:3 x :381=1:3 Numberofcustomerswhochoosethegenerictest: x=1_ 3×381 =127

b. Brand number sold relative frequency

needtoknownow? 381 381___ 508=3_ 4=75%

generic 127 127___ 508=1_ 4=25%

total 508 100%

c. i. P(Needtoknownow?)=75% ii. P(generic)=25%

6.6 Practise calculatingtheoreticalprobabilityLearner’sBookpage423

1. a. P(5)=1_ 6=16,67% b. P(even)=3_ 6=1_ 2=50%

c. P(prime)=3_ 6=1_ 2=50% d. P(number>3)=3_ 6=

1_ 2=50%



2. a. P(appleflower)=5_ 9=55,56% b. P(blackberryflavour)=4_ 9=44,44% c. P(neitherappleorblackberryflavour)=0 d. P(appleorblackberryflavour)=1=100%3. ABCDEFGHIJK a. P(vowel)=3__ 11 b. P(consonant)=8__ 11 c. P(D)=1__ 11 d. P(M)=04. a. P(M)=2__ 11=18,18% b. P(vowel)=4__ 11=36,36% c. P(consonant)=7__ 11=63,64% d. P(Y)=0 e. P(CorS)=2__ 11=18,18%5. Coin 1 Coin 2 Coin 3 H H H H H T H T H H T T T T T T H T T T H T H H a. P(3heads)=1_ 8=12,5% P(3heads)=1_ 2×

1_ 2×1_ 2=

1_ 8 b. P(atleastonehead)=1–P(alltails) =1–1_ 8=

7_ 8=87,5% c. P(twotails)=3_ 8=37,5%6. Theresultsoftheexamsarenotrandombutdependonthelearners’

performance,sotheprobabilityofapassorfailisnot50%.

6.7 Practise understandingpredictionsLearner’sBookpage425

1. a. 11days b. Thisyeartherecouldbelessrainsotherecouldconsequentlymore

sunnydays.2. a. Yes.Therelativefrequencyofrainydayswouldbe2__ 28=7,14%. Therelativefrequencyofrainydaysforthepreviousyear

was8__ 28=28,6%. b. Weatherpatternsarenotcertain.3. Weatherforecastsareonlyanestimatebasedonpresentconditions.There

isagoodchancethattheweatherforecastcouldbefairlyaccuratebuttheforecastsarenever100%certain.

4. a. Relativefrequencyofrain:13__ 30=43,33%

b. Weather Wins relative frequency (%)

Sunnyanddry 4_ 7 4_ 7×100=57,14%

cloudyandhumid 3_ 7 3_ 7×100=42,86%

rainy 3__ 13 3__ 13×100=23,08%

Fromthevaluesitwouldappearthattheyhaveabetterchanceofwinningifitissunny.


145t e r m 3 • u n I t 6

c. Fromtheaboveresults,GreyCollegehasagreaterchanceoflosingthetournamentwhenitisrainy.ThismeansthatLuhlazawouldhaveagreaterchanceofwinningwhenitisrainy.

d. Outof30tournaments,GreyCollegedrewsixmatches. P(draw)=6__ 30=

1_ 5=20%

6.8 Investigation: WorkwithweatherpredictionsLearner’sBookpage426

1. a. Probabilitythatweatherforecastiscorrect =7__ 10 =70% b. Probabilitythatweatherforecastiswrong =3__ 10 =30% c. Learnerstodiscuss.2. a. Wyoming,ColoradoandUtah b. WyomingandColoradohavea70%chance,whereasUtahhasan

about10%chance. c. ItismostlikelytosnowontheborderbetweenColoradoand

Wyoming,andinnorthernWyoming. d. ItwoulddependonwhichpartofColoradotheylivedin.IfSarah

livesinthesouthernpartofColorado,accordingtotheforecasttherewillbenosnow.

6.9 Practise consideringresultsthatmaybeinaccurateLearner’sBookpage429

1. a. Providedtheinstructionsarecorrectly,includingwaitingthetimespecified,97outof100testsareaccurate.

b. Notfollowinginstructionsproperlyornotwaitingthespecifiedtimewouldmakethetestlessaccurate.

c. 3% d. 97%2. a. Onlywomencanbecomepregnant. b. Thesymptomsmentionedinthetestareverygeneral–therecouldbe

otherreasonswhysomeonewouldpresentsomeofthesesymptoms. c. Classdiscussion

3. a. status test positive (fail drug test)

test negative (pass drug test)

total

Athleteswhoareusingillegalsubstances

9 1 10

Athleteswhoarenotusingillegalsubstances

99 891 990

total 108 892 1000

b. 99___ 990=10% c. No.Thetesthasbeenshowntobeonly90%accurate.4. a. 1_ 2of1%=

1_ 2×1___ 100=

1___ 200=0,005 b. Classdiscussion. (Theschoolcouldagreetore-testanyonewhotestspositiveinthe

test.)



c. Numberoflearnerswhocouldbeincorrectlyaccusedofbeingdrug-users:

1___ 200×3831937 =19160learners5. a. Thetableshowsthefindingsofextensivedrugtestingresearch. b. Non-users Totalnumberofnon-users:9025+475=9500 Percentageofnon-userswhotestednegativefordrugs: 9025____ 9500×

100___ 1 =95% Users Totalnumberofusers:475+25=500 Percentageofuserswhotestedpositivefordrugs:475___ 500×

100___ 1 =95% So,overall,thedrugtestswere95%accurate. c. Chancethatnon-userswouldtestpositivefordrugs:475____ 9500×

100___ 1 =5% d. Theaccuracyofthistestamongactualdruguserswas95%. e. Theaccuracyofthedrugtestwasthesameforusersandnon-users.

6.10 Practise interpretingpredictionsusedinthemediaLearner’sBookpage431

1. a. Classdiscussion b. Thereductionsinwrinkleswouldprobablybemeasuredbyobserving

theappearanceofthewomeninvolvedinthetest. c. Yes.Thesampleofwomenusedintheclinicaltestwasverysmall. d. Classdiscussion2. a. Yes. b. Tendentistscouldhavebeenaskedfortheirpreferenceandgiventhe

toothpastebrandinvolvedinthesurvey.Iftheyhadincludedmoredentistsinthestudy,theresultsmayhavebeendifferent.

3. a. Recommended by pharmacistsimpliesthatpharmacistsrecommendthisproductoversimilarproducts.

b. Itmeansthatifyouweretoaskapharmacisttorecommendavitamin,thisproductwouldbeoneofmanyproductstheymightrecommend.

c. Foradvertisingpurposes,itwouldbepossibletomakethisclaim.

6.11 Practise representingsamplespacesforcompoundeventsLearner’sBookpage433

1. a. MMMFFMFF b. HHH HHT HTH HTT THH TTH THT TTT c. CHAT HCAT AHCT TCHA CHTA HCTA AHTC TCAH CAHT HACT ATHC THCA CTHA HTCA ACHT TACH CATH HTAC ATCH TAHC CTAH HACT ACTH THAC 24Possibleoutcomes d. AMR ARM MRA MAR RAM RMA

2. a. 1 2 3 4 5 6

Heads H1 H2 H3 H4 H5 H6

tails t1 t2 t3 t4 t5 t6


147t e r m 3 • u n I t 6

b. 1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

c. r1 r5

r1 r1r1 r1r5

r5 r5r1 r5r5

d. a B C d e

1 1A 1B 1c 1d 1E

2 2A 2B 2c 2d 2E

3 3A 3B 3c 3d 3E

4 4A 4B 4c 4d 4E

5 5A 5B 5c 4d 4E

6 6A 6B 6c 6d 6E

e. Brown eyes Green eyes Blue eyes

Black hair Blackhair/browneyes Blackhair/greeneyes Blackhair/blueeyes

Brown hair Brownhair/browneyes Brownhair/greeneyes Brownhair/blueeyes

red hair redhair/browneyes redhair/greeneyes redhair/blueeyes

Blond hair Blondhair/browneyes Blondhair/greeneyes Blondhair/blueeyes

3. a. pink

pink red

blue

pink

redred

blue

pink

red

blue

green

b. HH

Heads

Tails

T

HT

T

HH

T

HT

T



c. A

1

2

3

B

CA

B

CA

B

C

d. net

missnet

First player Second player

net

missmiss

e. red

red

white

black

white

blue

Box BBox A

red

white

bluered

white

blue

4. Coldandraining Coldandnotraining Notcoldandraining Notcoldandnotraining5. a. Yes. b. No. c. Yes. d. Youcouldchoosefrom12meals.6. a. positive

negativenon-drug users

positive

negativedrug users

b. Yes,thatispossible.Asweshowearlier;drugtestsareonly95%accurate.

Revise and consolidate:ProbabilityLearner’sBookpage436

1. a. Thechanceofaneventhappeningiscalledtheprobability. b. Ifitisimpossible,aneventneverhappen. c. Aneventiswhensomethinghappens,forexample,whenyoutossa

coinanditlandsheadup. d. Atrialwhensomethingistriedoutandtheresultsarerecorded,

forexample,tossingacoinorrollingdice. e. Anoutcomeistheresultofanevent. f. Outcomesareequallylikelywhentheprobabilityoftheoutcomeofan

eventarethesame.Forexample,whenwetossacoin,aheadoratailisequallylikely.


149t e r m 3 • u n I t 6

2. a. 1_ 2 b. 1_ 6

c. 1_ 9 d. 1_ 23. Multiplesof2:6;24;18;12 Multiplesof3:6;24;9;15;18;12 a. Itisnotafairgameastherearemoremultiplesof3thanof2. b. 6_ 8=

3_ 44. a. H H H T T H T T

b. set of coins number of tosses

number of times we got two heads

running total of two heads

Percentage of two heads (running total)

two10ccoins 25 6 6 6__ 25×100=24

two50ccoins 25 8 14 14__ 50×100=28

twor1coins 25 5 19 19__ 75×100=25,3

twor2coins 25 7 26 26___ 100=26

twor5coins 25 9 35 35___ 125×100=28

c. Theprobabilityofgettingtwoheadswhentossingtwocoinsatthesametime

d. 28% e. No.Iftheycarriedoutanothersetoftrials,itispossibletheycouldget

adifferentresult.Thisresultdoesnotagreewitheitherprediction.5. a. Thegraphshowstheaveragenumberoftimesofgettingtwoheadsin

100throws. b. Theyellowlineonthegraphisataprobabilityof25%. c. Theprobabilitychangesaftereachtrial;andsothepercentage

changes. d. Asthenumberoftossesincreases,theprobabilityofgettingtwoheads

getscloserto25%. e. Theprobabilityofgettingtwoheadstendsto25%asthenumberof

tossesincreases.6. a. i. 80% ii. 10% iii. Itiscertainthatitwillrain. b. Theprobabilityofrainis10%sothereisaslightchanceofrain.A

sensibleoptionwouldbeforKgomotsototakearainjacketincaseitrains.

c. ItishighlyunlikelythatitrainedinJohannesburginthisperiod.(Weatherforecastsdohoweversometimesgetitwrong.)




terM 4

Worked ansWers

Unit 1exchange ratesLearner’s Book pages 440–452

Teaching tips• Althoughtheconceptofexchangeratesisnewtothelearners,theyhave

alreadyworkedwithrates(comparingoneunittoanother).• Thefocusonthisunitisonunderstandingwhatexchangeratesmean

andtheinfluencetheyhaveonthebuyingpowerofaconsumerwhoistravellingorforabusinessthatimportsand/orexportsgoods.Thefocusisthereforeonestimatedvaluesratherthanformalmathematicalcalculations.

• Collectup-to-dateexchangeratetablesfromnationalnewspaperstouseintheclassroom.(Thenewspapersprintexchangeratesinthebusinesssection.)Alsoencourageanylearnerswhomayhavesamplesofforeigncurrenciestakethismoneytoclasstoshowtheothers.Ifyouhaveinternetaccess,youcannormallydownloadpicturesofdifferentcurrencies.

• Theinternetalsooffersmanyon-linecurrencycalculatorsthatwillperformcalculationsusingthemostrecentvaluesofcurrencies.These sitesnormallyoffergraphsthatshowhowthevaluesofdifferentmajor currenciesgoupanddownovertime.Oneofthesiteswerecommend (www.xe.com)alsooffersfreeapplicationsforsmartphonesandiPads. Learnerscandownloadtheseandusetheircellphonestofindupdated currencyconversionfactors.XEalsoofferscurrencyeducationthat includesanonlineencyclopaediathatgiveslotsofcurrentandhistorical datafordifferentcountries,includingSouthAfrica.Thisiswellworth usingifyouhaveaccesstotheinternet.

Solutions1.1 Practise estimatingcurrencyconversionvaluesLearner’sBookpage444

1. a. R227,02b. INR15,39c. €1000=R100,20

£1000=R83,35d. ¥18135e. HKD150=R153,69

INR35=R207,30NZ$900=R142,74TheNewZealandpriceisthecheapest.

f. ¥354700(roundedofftonearest100)2– 4. Learnersownresearch.


151t e r m 4 • u n I t 1

1.2 Practise identifyingthestrongerandweakercurrencyLearner’sBookpage448

1. a. Randstrengthened b. Randweakened c. Randstrengthened d. Randweakened2. a. Therandweakenedinrelationtothepound. b. Good.Whenthedollarsareconvertedintorand,themineswillget

morevalueintherandforeachdollar.3. a. i. EndofApril2011 ii. BeginningofAugust2011 b. A c. Whentherandwasatitsstrongest d. Whentherandwasatitsweakest

1.3 Practise comparingbuyingpowerLearner’sBookpage451

1. a. C Lima A Helsinki B Copenhagen b. A Johannesburg C RiodeJaneiro B Berlin c. B NewYork A Nairobi C Istanbul2. Convertallvaluestorand. €7,59=10,14×7,59=R76,96 P105=1,06×105=R111,30 France’smoneyhasthegreatestbuyingpower.3. a. Rankedfromhighesttolowest i. KualaLumpur ii. KualaLumpur Nairobi Nairobi Beijing Beijing Dubai Dubai Amsterdam Chicago London London Chicago Amsterdam Tokyo Tokyo b. i. Costofwomen’sclothinginTokyo:1050×9,40=R9870,00 Costofmen’sclothinginTokyo:1320×9,40=R12408,00 ii. Costofwomen’sclothinginKualaLumpur:

170×9,40=R1598,00 Costofmen’sclothinginKualaLumpur:250×9,40=R2350,00 c. Learners’research. d. Answerswilldiffer.

Revise and consolidate:Finance–ExchangeratesLearner’sBookpage453

1. a. R79 b. 500 c. Australiandollar d. R350 e. SixnightsinRiodeJaneiroand11nightsinBuenosAires



2. USprice:$12,85×7,8579=R100,97 UKprice:£7,99×12,459=R99,55 TheBritishwebsiteoffersaslightlybetterdeal.3. a. Therandwasgettingstronger. 16December:$0,119392=R1 17January:$0,12346=R1 ThevalueoftherandagainsttheUSdollarincreased. b. Justbefore15February,therandweakenedstronglyanddroppedtoa

lowonthatdate(15February).Thereafter,therandstrengthened.4. Therandbecamestronger. 17November:about6,2rupees=R1 15March:about6,6rupees=R15. a. Delhi b. Geneva c. 16,21% d. 10% e. HongKong:Itcost3,32%ofhissalarytopurchasethebasketof

goods. Bangkok:Itcost2,89%ofhissalarytopurchasethebasketofgoods. HeshouldchoosetogotoBangkok.

Unit 2data handlingLearner’s Book pages 456–493

Teaching tips• Thisunitrevisesthestepsinastatisticalinvestigation.Referlearnersto

theflowdiagramonpage456intheLearner’sBookanddiscusshowthestepsfittogether–theyshouldrememberthisfromearliergrades.Makesurelearnersunderstandthattheprocessiscyclical:inreality,theinvestigationdoesnotstopaftertheresultshavebeeninterpretedandanalysedbecausetheconclusionsoftenleadtonewquestions.

• Akeyskillinstatisticsistheabilitytoposetherightquestions.Learnersneedpracticeinbeingveryspecificinthewaytheyframearesearchquestion.Youcouldgivethemimaginaryresearchquestionsandaskthemtoexplainhowthequestionsmightbeunclearorinappropriate.

• Thetoolsthatlearnerschoosetousetocollectdatashouldfitthetypeofdatatheyarecollectingandthequestiontheyareasking.Surveysandquestionnairesneedtobeplannedcarefullyanddesignediftheyaretobeuseful.Spendasmuchtimeasnecessarylookingatexamplesofquestionnaires(printedonesandthosedesignedbylearners),criticallydiscussthesetodeterminewhichelementsareclearandusefulandwhicharenot.

• Learnersneedtobeabletoorganisethedatatheycollectinordertomakeiteasytouse.Usethenationalcensuscarriedoutin2011asanexampletoillustratehowaninvestigationmightresultinmassesofdata.(Forexample,thecensuscollectedtheagesofmorethan50millionSouthAfricans).Organisingthedataintofrequencytablesandrepresentingitongraphshelpsresearchersmakesenseofandanalysethedata.

• Summarystatisticsshouldbeveryfamiliartothelearnersbynow.Makesuretheyareabletocalculatetheseforgroupeddataasmostoftheexamplestheyworkwithfromnowonarelikelytoinvolvegroupeddata.


153t e r m 4 • u n I t 2

• Learnersshouldbecomfortableworkingwithpiecharts,bargraphsandlinegraphs.Iftheyarenot,revisethebasicskillscoveredinTerm1beforeproceeding.

• Thisyearlearnersbegantoworkwithtwosetsofdataatthesametimesotheyneedtousegraphsthatcanshowtwosetsofdata.Learnershavealreadyworkedwithdoublelinegraphs.Nowtheywillworkwithdoublebargraphsandcompositebargraphstoshowtwosetsofdataforcomparison.

• Scatterplotgraphsareusedtoshowbivariatedata(twosetsofdatacollectedinpairsatthesametime;forexample,theheightandfootsizeoflearners).Thepurposeofascatterdiagramistoshowwhetherthereisarelationshipbetweenthesetsofdata.Learnersneedtorecognisethethreemainrelationships–positive,negativeandnorelationshipbasedonthepatternsofdots.

• Usethesummarytableonpages488and489tohighlighttheadvantagesanddisadvantagesofdifferentkindsofgraphandencouragelearnerstousethistohelpthemdecidewhichtypeofgraphisbestsuitedfordifferentsetsofdatathattheycollectand/orworkwith.

• Learnersneedtointerpretandanalysedatathattheycollect,buttheyalsoneedtobeabletointerpretdatathatispresentedbyotherpeoplecritically.Oneoftheaimsoftheworkinthisunitistohelplearnersrealisethatdatacanbemanipulatedtogiveamisleadingimpression.

• Learnersneedtobecomecriticalconsumersandinformedcitizensandoneelementofthisisbeingcriticalofstatistics.Businessesoftenusestatisticsformarketingpurposeswhentryingtoselltheirproductsandtheytrytopresenttheirproductsinwaysthatwillconvinceasmanycustomersaspossibletobuythem.Thisisnottosayorganisationsaredishonest,itisjusttopointoutthatthewayyoupresentsomethingcanaffecthowpeopleseeit.Youmaywanttorefertosomeoftheclaimsusedintheprobabilitysectiontoillustratethis,buthereisanotherexample:

Amattresscompanyadvertisementpublishedinlocalnewspapersin2011madethefollowingclaims:• Theworld’sfastestgrowingbeddingbrand• Clinicalstudyprovesyou’llsleepbetter:

– 29%improvedsleepquality– 34%reducedbackpain– 96%reducedbackstiffness

• ResearchresultsweredocumentedintwoseparatescientificstudiesconductedbytheDirectoroftheExercisePhysiologyandHumanPerformanceLaboratoryatXYZUniversity

• TheonlymattresstobeendorsedbytheABCchiropractorsassociation

Pointouttolearnersthattheclaimsareinterestingbecausetheysoundverymathematicalandscientific.However,whatdotheyactuallymean?Howdoyoumeasure,forexample,thatyouarethefastestgrowingbeddingbrand“intheworld”?Also,whatdoesthatmean–ifyourcompetitorsincreasedtheirsalesby1%toearnonemilliondollarsandyouincreasedyoursalesby100%toearn$20000whichisthefastergrowth?Also,askquestionssuchas,whyisittheonlymattresstobeendorsed?Didthemattresscompanypayfortheendorsement?Didtheysponsortheresearch?Incidentally,aninternetsearchshowstheresearchwascarriedoutin1993(20yearsago)andthatitinvestigatedspinalzonetechnologyandnotspecificmattresses.Theseareallimportantpieces



ofinformationthatcanhelpyouavoidbeingsuckedintomeaninglessstatisticalclaims.

• Theinvestigationsthatlearnerschoosecanbekeptfairlysimple,buttheymustproducedatathatcanbeorganised,graphedandanalysed.Youcaneithersuggestthatthewholeclassinvestigatethesamequestion(togetalargerpicture)orthatdifferentgroupstakedifferentquestionsandthenfeedbacktotheclassontheirfindings.

Solutions2.1 Practise interpretingandorganisingdataLearner’sBookpage459

1. a. 67;69;70 b. 54;74;97 c. Boys’league–Altem;Bona;Fidelitas;Meadowlands Girls’league–Altem;Bona;Fidelitas;Meadowlands d. AltemandMeadowlands Meadowlandswonby9points. e. BonaandFidelitas Fidelitaswonby16points. f. Notreally.Thehighvalueof97scoredbythegirls’school

Meadowlandswasexceptionallyhighanddoesnotfollowageneraltrend.Itcouldbeaonce-offhighscoreratherthanthenorm.

2. Points scored Girls’ teams Boys’ teams

0–10

11–20

21–30

31–40

41–50

51–60

61–70

71–80

81–90

91–100

2.2 Practise identifyingrepresentativesamplesLearner’sBookpage460

1. a. Biasedsample;itshouldsurveyhouseholdsinarangeofsuburbs. b. Biasedsample;Amiraisfocusingonhowwelltheboysdoatrugby

afterschool.Theycouldhaveachievedinotherareas. c–e. Representativesamples.2. Answerswilldiffer/classdiscussion.3. A Agree.Intermsofthenumberofsoccersupporternationally,the

numberofSMSesisverysmall. B Agree C Agree D Agree E Agree


155t e r m 4 • u n I t 2

2.3 Practise planninganinvestigationandselectingasampleLearner’sBookpage462

1–2. Answerswilldiffer.3. a. Reef93 b. Meanpriceofpetrolin1990=sumofpetrolpricefor1990___________________ 12 =1648____ 12 =137,33c/ℓ =R1,37/ℓ c. Learnersneedtoresearchthecurrentpetrolprice. d. Percentageincreaseinthepetrolpricesince1990:(Unleaded93)

(percentageincrease) 10,43____ 1,37=761% Usethisanswerasoriginalpetrolpricewasgivenfor93. So,whilethepetrolpricehasincreasedquitesubstantiallysince1990,

theincreaseisfarlessthan2000%.

2.4 Practise designingandusingaquestionnaireLearner’sBookpage463

Answerswilldiffer.

2.5 Practise usingaquestionnairetocollectdataLearner’sBookpage464

Answerswilldiffer.

2.6 Practise workingwithfrequencytablesLearner’sBookpage467

1. a. Once,agirls’teamscored97. b. 41–50points c. 41–50points d. 0–10and11–20forbothboys’andgirls’teams. e. Notverywell,itcouldhelpyoutomakeapredictionbutthiswould

onlybeanestimate.

2. Points scored Boys’ and girls’ teams combined

0–10 0

11–20 0

21–30 7

31–40 14

41–50 23

51–60 7

61–70 7

71–80 1

81–90 0

91–100 1

total 60



3. a. number of siblings tally Frequency

0–1 5

2–3 14

4–5 18

6–7 3

total 40

b. 4–5 c. 6–7(7siblings) d. i. 6siblings ii. 5siblings iii. 6–7siblings iv. morethan7siblings

2.7 Practise calculatingsummarystatisticsLearner’sBookpage472

1. a. 2;3;4;4;5;5;6;6;7;7;8;9;9;12 mean: total____________  numberofscores=

87__ 14=6,21 median:6 modes:4;5;6;7;9Therearefivemodes. range:12–2=10 b. 21;22;25;28;29;32;36;37;47;54;65;65;67;69;78;83;94;95 mean: total____________  numberofscores=

947___ 18=52,61

median:47+54______ 2 =50,5 mode:65 range:95–21=74 c. 1;1;2;2;3;4;4;4;5;5;5;5;6;7;7;7;8;8;8;9;9 mean: total____________  numberofscores=

110___ 21=5,24 median:5 mode:5 range:9–1=8 d. 8;13;15;16;17;18;20;21;21;22;24;26;26;26;26 mean: total____________  numberofscores=

299___ 15=19,93 median:21 mode:26 range:26–8=18 e. R15;R16;R16;R16;R17;R17;R18;R19;R20;R21 mean: total____________  numberofscores=

175___ 10=R17,50 median:R17 mode:R16 range:R21–R15=R6 f. 3,4;4,3;4,8;5,5;6,5;6,5;7,6;7,9;8,6;9,8 mean: total____________  numberofscores=

64,9___ 10=6,49

median:6,5 mode:6,5 range:9,8–3,4=6,4 g. 4,8;4,9;5,2;5,8;5,9;6,7;6,9;7,2;7,3;7,7;7,7;7,8;8,1;8,1;8,2;9,1;

9,3;9,6 mean: total____________  numberofscores=

130,3____ 18 =7,24


157t e r m 4 • u n I t 2

median:7,7 mode:7,7and8,1 range:9,6–4,8=4,8 h. R11,40;R12,60;R12,80;R12,80;R13,50;R14,20;R15,60;R16,80;

R17,20;R18,50 mean: total____________  numberofscores=

R145,40______ 10 =R14,54

median:R13,50+R14,20____________ 2 =R27,70_____ 2 =R13,35 mode:R12,80 range:R18,50–R11,40=R7,10 i. 15kg;15kg;15kg;19kg;23kg;24kg;25kg;26kg;27kg;27kg;

27kg;28kg;35kg;35kg mean: total____________  numberofscores=

341___ 14=24,36kg median:25,5kg mode:15kg range:35kg–15kg=20kg j. 161cm;162cm;165cm;166cm;172cm;175cm;176cm;176cm;

180cm mean: total____________  numberofscores=

1533____ 9 =170,33kg median:172cm mode:176cm range:180cm–161cm=19cm2. a. 3and5 b. 12×1=12 mean=268___ 80 14×2=28 =3,35 15×3=45 12×4=48 15×5=75 12×6=60 totalfrequency:80 268 c. Medianscoreliesbetween40thand41stvalue. median:33. Letageoffifthlearnerbex. Totalageofthefivelearners=19×5=95 \14+17+18+20+x=95 \x=95–14–17–18–20 x=264. Totalnumberofpointsforthetengames:29×10=290points missingscore:290–37–29–11–42–38–33–36–38–20=65. a. mean:904___ 6 =150,67teabags b. modalnumberofteabags:152 c. moreorless d. themean e. No.Thelablesaysthattheaverageis150bagsperpackand

MrsKunene’spacketisoneteabagbelowaverage.6. a. 5cm3

2cm3×4= 8 3cm3×7= 21 4cm3×9= 36 5cm3×12=60 6cm3×10=60 7cm3×8= 56 Total: 241cm3

Totalfrequencyofmeasurements>50



b. mean:241___ 50=4,82cm3

c. Themedianliesbetweenthe25thandthe26thmeasurement. median:5cm2

d. range:7cm3–2cm3=5cm3

2.8 Practise interpretingandanalysingaveragesLearner’sBookpage475

1. a. mode:25 b. range:41–1=40 c. Ifwearrangethedatainorder: 0;1;10;12;12;19;19;20;24;25;25;25;25;27;30;36;39;41 Thespreadofthedataisfairlyconsistent. Considerthevalues0and1asoutliersandignoredthem;therange:

41–10=31. d. Therangeisfairlylarge,sothemeanwouldnotbethattypicalofthis

dataset. e. Themedianvalueis24,5,whichismoretypicalofthedata.2. a. Todeterminewhichlearner’sperformancehasimprovedthemost,

lookatbyhowmuchthenumberofsit-upsforeachlearnerhasincreasedaftertraining.

Karen’sperformanceimprovedthemost.Herperformanceimprovedby39sit-upsperminute.

b. i. rangebeforetraining:42–19=23 ii. rangeaftertraining:73–45=28 c. i. mean(beforetraining):328___ 10=32,8sit-upsperminute

ii. mean(aftertraining):615___ 10=61,5sit-upsperminute d. Ifyoufindthedifferencebetweenthetwomeans,youcanfindthe

averageimprovement,whichequals28,7sit-upsperminute. e. Yes. f. Yes. g. Themodeshowsthemostcommondata,butthiscouldbefarfromthe

meanvalue.

3. a. aasvoëls goals Frequency arende goals Frequency

0× 2 0 0× 1 0

1× 0 0 1× 4 4

2× 3 6 2× 5 15

3× 5 15 3× 5 15

4× 4 16 4× 2 8

5× 2 10 5× 6 30

total 47 goals total 63 goals

Mean= totalgoals____________  sumoffrequency Mean= totalgoals

____________  sumoffrequency

=47__ 16 =63__ 21 =2,94goalspermatch =3goalspermatch b. Aasvoëls Themediannumberofgoalspermatchwillbebetweenthe8thand

the9thscore. median:3goalspermatch


159t e r m 4 • u n I t 2

Arende Themediannumberofgoalspermatchwillbethe11thscore. median:3goalspermatch c. Aasvoëls modalnumberofgoals:3goalspermatch Arende Modalnumberofgoals:5goalspermatch4. a. TheArendedidbetter. b. TheArendedidbetter. c. Bothteamsdidthesame.5. IfyouusedthemodalscorefortheArende,youcouldgivetheimpression

thattheyscoredfivegoalspermatch,whereasthemeanofthreegoalspermatchismorerepresentativeoftherealsituation.

6. a. Sparky b. Powersurgewouldbethebestchoicebecausewhileitdoesnothave

thehighestmean,ithasthelowestrange.Thismeansthatyouwouldbemorelikelytogetcloseto41hoursfromthebattery.Sparkywithameanof45hourshasarangeof10hours,soyoucouldgetbatteriesthatlastmanyhoursfewerthan45hours.

7. a. number of slices Frequency fx10 2 20

11 9 99

12 8 96

13 5 65

14 5 70

15 5 75

total 34 425

b. range:15–10=5slicesperpack c. mean:425___ 34=12,5slicesperpack d. 11slicesperpack e. Medianin213thpostion median:12slicesperpack f. Theywillusethemodalnumberofslicesperpack.8. a. mode b. mode c. mean d. mean e. mean f. mode g. mean h. mean

2.9 Practise revisingbasicgraphsLearner’sBookpage477

1. a. Sixties:15___ 150×360°=36°

Seventies:25___ 150×360°=60°

Eighties:45___ 150×360°=108°

Nineties:37___ 150×360°=88,8°

Two-thousands:28___ 150×360°=67,2°



b.

Two-thousands

Nineties

Eighties

Seventies

Sixties

c. Themusicoftheninetiesandtwo-thousandswouldprobablybemorepopularaslearnerswouldbemorefamiliarwiththismusic.Themusicoftheeightiesmightbealittlelesspopular.

3. a. Week 1 2 3 4 5 6 7 8

Height (cm) 3 7 15 32 46 58 66 91

01 2 3 4

Week

Avera

ge he

ight (

cm)

Average height of plants per week

5 6 7 8

10

20

30

40

50

60

70

80

90

100

b. Answerswilldiffer.4. a. Percentageofherearningsthatshesaves = 750_____ 14500×

100___ 1 =5,17% b. Amountshespends:2100+1000=R3100 c. Classdiscussion d. Apiechartwouldbeasuitablegraphtoshowthisdataasitshows

howmuchofhersalaryshespendsonthevariouscategories.Ataglance,youcanseethatthelargestpositionisherrent.

Rent:3600_____ 14500×360___ 1 =89°

Householdaccounts:1850_____ 14500×360___ 1 =46°

Carpaymentandpetrol:60° Food:52° Clothing:44,7° Entertainment:24,8° Savings:18,6° Other:24,8°


161t e r m 4 • u n I t 2

Other

Savings

Entertainment

Clothing

Food

Car payment and petrol

Household accounts

Rent

5. a.

0 10 20 30 40 50Frequency

Point

s sco

red

Points scored by girls’ team

60 70 80 90 100

2

4

6

8

10

12

b.

0 10 20 30 40 50Frequency

Point

s sco

red

Points scored by boys’ team

60 70 80 90 100

2

4

6

8

10

12

2.10 Practise interpretingdoublebargraphsLearner’sBookpage479

1. a. TrueIQ b. DatalinkandGau-commerce c. TrueIQ d. Gau-commerce e. Gau-commerce f. Speedlink g. Keepgoodfinancialrecordsofcostsandincomeinordertodetermine

yournetprofitaccurately.2. a. 74%ofhouseholdshadaradioin2001.Thepercentageroseslightly

to78%in2007. b. About25%ofhouseholdshadalandlinein2001.Thisdroppedto

20%in2007.Areasonforthisdeclinewouldbethefactthatmorepeoplewereusingcellphonesandnolongerneededalandline.

c. Internetfacilitiesathome d. Thegreatestincreasewasinthepercentageofhouseholdswith

cellphones.Areasoncouldbethatcellphonesbecamecheaper.3. a. Numberofhouseholdswithalandlinetelephone:

20%of246618=49323,6



b. Numberofhouseholdswithaccesstotheinternet:10%of246618=24661,8

c. Numberofhouseholdswithacellphone:75%of246618=184963,5

2.11 Practise drawingdoublebar-graphsLearner’sBookpage480

1. a.

0Jan. Feb. Mar. Apr.

Units

sold

(thou

sand

s)

Number of cellphones sold by Super Cell and Cell-U-R

1

2

3

4

5

6

7

8

9

10

11

12

13

Super Cell

Key

Cell-U-R

b. ThenumberofcellphonessoldbySuperCelldeclinedforthethreemonthsandthenincreasedsignificantly.Cell-U-R’ssaleshavenotchangedsignificantlyoverthefourmonthsalthoughtheyalsosoldalargernumberofcellphonesinApril.

2. a.

0Flushtoilet

Chemicaltoilet

Pitlatrine

Bucketsystem

No toiletfacility

2001

Key

2007

Num

ber o

f hou

seho

lds

Bar graph showing toilet facilities available to 800 houses

100

200

300

400

b. Moreflushtoiletswereusedin2007thanin2001andthenumberofpeoplewhohadnotoiletfacility,chemicaltoiletsandthebucketsystemdecreased.Thenumberofusersofpitlatrinesremainedaboutthesame.


2.12 Practise interpretingstackedbargraphsLearner’sBookpage482

1. a. (125+230+185+220)kl=760kl b. (25+15+75+90)kl=205kl


163t e r m 4 • u n I t 2

c. Volume of water used month 1

cele 45

Malema 55

Kunune 25

d. Inmonths1and2,theKunene’swaterconsumptionisverylow.Inmonth3theconsumptionincreasessteeplyto75klandthenincreasesagainto90klinmonth4.

e. theCelehousehold f. Approximately75kl/month g. ItwouldappearthattheMalemahouseholdhadaleakingpipein

month3.Thisissuggestedbythefactthatthehouseholdconsumed140klofwaterinthatmonth.

2. a. Youareonlyabletoworkouteachcompany’stotalsalesifyouaregiventheactualtotalnumbers.Asthisinformationhasnotbeenprovided,youarenotabletoworkoutthecompany’stotalsalesfromthisgraph.

b. CompanyB c. CompanyD d. CompanyC e. 12,5%ofcompanyA’ssalesaredoneovertheinternet.This

represents1_ 8ofthesales.

f. Breakdown of company d’s sales

directfromshop 15%

Internetsales 15%

cataloguemailorder 40%

throughagent 30%

2.13 Practise drawingastackedbargraphLearner’sBookpage483

1.

0 Alana Ben Charl Dumile

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

Super-saver

Elite

Cellphone packages sold by four salespeople




2.14 Practise workingwithdoublelinegraphsLearner’sBookpage483

1. a.

0Jan. Feb. Mar. Apr. May Jun.

Month

Minimum and maximum monthly temperatures for Sutherland

Tem

perat

ure (

°C)

Jul. Aug. Sep. Oct. Nov. Dec.

3

6

9

12

15

18

21

24

27

30

33

36

Maximum

Minimum

b. Thetemperaturesareaveragemonthlytemperatures.Fortheaverageforamonthtobebelowzero,minimumtemperatureswouldhavetobebelowformostofthemonth.

2. a.

02005 2006 2007 2008

Year2009

Price

(R)

2010 2011

1

2

3

4

5

6

7

8

9

10

11

Diesel Petrol

Price of petrol and diesel (R)

b. Startingin2005thepriceofbothpetrolanddieselincreasesharplyuntil2008.Thereisasharpdropinbothpricesin2009,thenamoresteadyincreaseto2010andthereafterasteepincreasein2011.

c. 2006;2008 d. In2009.Thegraphslopesdownfromlefttorightshowingthatprices

aredecreasing. e. Classdiscussion3. a. Nathi’scardepreciates. b. Thepriceofanewcarincreasesfromyeartoyear. c. From2005to2006,thevalueofNathi’scardecreasedbyR15000. d. Priceofanewcarin2006:R60000 Priceofanewcarin2011:R105000 Difference:R45000 Percentageincrease:45000_____ 60000×

100___ 1 =75%


165t e r m 4 • u n I t 2

e. ValueofNathi’scarin2005:R60000 ValueofNathi’scarin2011:R25000 Difference:R35000 Percentagedecrease:35000_____ 60000×

100___ 1 =58,33% f. DifferenceNathiwillhavetopay:R105000–R25000=R80000 g. Factorscouldincludetheconditionofthecarandthemileage.

2.15 Practise drawingandinterpretingscatterplotsLearner’sBookpage487

1. a.

0

Predic

ted te

mpe

ratur

e (°C

)

25

23 24 25 26 27Actual temperature (°C)

Forecast and actual maximum temperatures

28 29 30 31 32

26

27

28

29

30

31

32

b. Thereisapositiverelationship.Asonevalueincreasestheothervaluealsoincreases.

c. Seegraph. d. Thepredictedtemperaturesarefairlyclosetotheactualtemperatures.2. a. Thelearnerwhoisabout1,5mtallandwearsasize8shoeisan

outlier. b. Thescatterplotsuggeststhatthereisapositiverelationshipbetween

heightandshoesize. c. Heorshewouldwearasize5. d. Tallerthan1,7m(about1,74m)3. a. Thecoldertheweather,themorecupsofhotchocolatearesold.So,

thereisanegativerelationshipbetweentheweatherandthenumberofcupsofhotchocolatesold.

b. About17cups. c. About5°C4.

Increasing temperature

Sale of ice-cold drinks compared to temperature in summer

Num

ber o

f ice c

old dr

inks



5. a. treatment relationship between hair growth and amount of treatment used

a nonoticeablerelationship.Hairgrowthwasrecorded,butdidnotdependontheamountoftreatmentused.

B thereisnonoticeablerelationship.therewasnotmuchhairgrowthrecordirrespectiveofhowmuchtreatmentwasused.

C thereisapositiverelationship.themoretreatmentthatwasused,themorehairgrowthwasrecorded.

b. TreatmentCshowsconclusivelythatitiseffectiveinpromotinghairgrowthwhiletheresultsfortheothertwoproductsareratherinconclusive.

c. i. Thestatementisnotentirelytrue.Somecustomersexperiencedminimalhairgrowth.

ii. Thestatementisnottrueatall.

2.16 Practise choosingthemostappropriategraphLearner’sBookpage490

1. Scatterplotgraph–itshowsaconnectionbetweentwosetsofdata.2. Bargraph–itmakesiteasytocomparetheaveragerainfallforthetowns.3. Linegraph–continuousdataandwillshowmaximumandminimum

valuesclearly.4. Doublebargraph–itallowsyoutocomparehowoftenboysandgirls

exercise.5. Stackedbargraph–therecanbeonebarforwins,oneforlossesandone

fordraws.6. Linegraph–whenworkingwithcontinuousnumericaldatathisisaclear

waytorepresentpatternsandrelationships.7. Linegraph–itshowspatternsandrelationshipsclearly.8. Dualbargraph–itclearlyshowsdifferencesbetweencostsandincome.9. Piechart–itclearlyshowswhatpercentageofthewholebudgetisspent

ondifferentitems.10. Piechart–itshowsclearlywhatproportionofthewholecommunityhas

eachtypeoftoiletfacility.

2.17 Practise interpretingandanalysingdatacriticallyLearner’sBookpage491

1. a. Theuseoftrainshasdecreasedquitedrastically. b. Cartransport c. Theproportionofpeoplewhousethebushasdecreased,butnottothe

sameextentastrainusehasdecreased.2. a. Theinformationhelpsyouinterpretthedatagivenin1980and2000

differently. b. No.The1980samplewasnotaskedthesamequestionasthe2000

sample.Sothesituationsweredifferent.Ifwewishedtofollowtrendsofhowtransporthaschangedovertime,wewouldhavetousesamplesinasimilarcontextandaskrespondentsthesamequestion.

3. a. Thegraphshavedifferentscalesontheirverticalaxes. b. Thefirstgraph


167t e r m 4 • u n I t 2

c. Telkommaypossiblyfindthesecondgraphuseful.Itmightimplythatalthoughthenumberofcellphonesubscribersincreasedinthelasttenyears,theincreaseisnotverybigandplentyofpeoplearestillusinglandlines.

4. a. CityC b. CityE c. Ingeneral,peopleearnmoreinurbanareas.Ifonelookedatliving

costsasaproportionorpercentageoftotalincome,cityAmightberelativelycheaperthancityEoranyofthecitiesthatappeartobecheaperasrepresentedinthisbargraph.

2.18 Investigation: choose,collectandreportondataLearner’sBookpage492

Investigationswilldiffer.

Revise and consolidate:datahandlingLearner’sBookpage495

1. a. median b. doublebargraph c. asample d. numericaldata2. Answerswilldiffer.3. a. Thequestionhasnotbeenwordedinsuchawaythatitsoundsneutral

–“sothatpeoplewhohavetoworkallweekhavetimetodotheirshopping”encouragespeopletoanswerthequestionpositively.

b. ShouldshopscloseonSundaysothattheshopassistantswhoworkallweekhaveadayofftospendwiththeirfamilies?

c. ShouldshopsremainopenonSundays?4. a. MrSmithasrepresentedthenumberofnewclientsasthetotalnumber

ofclients. b. No.Thegraphsuggeststhatthenumberofnewclientsincreaseseach

yearwhereasthenumberofnewclientsdecreaseseachyear. c. y

x

Num

ber o

f new

vehic

les

Num

ber o

f new

clien

ts

Operations of Sunny Medical

0

1

2

3

4

5

6

20

40

60

80

100

120

7

2008 2009 2010 2011 2012

Number of new vehicles Number of new clients

d. Classdiscussion



5. a. Answerswilldiffer.Learnersshouldmotivatetheiranswers. b. No,thesectorforproductAlooksmuchbiggerthanthesectorfor

productD. c. Theperspectiveskewstheappearanceofthe3-Dpiechart.6. a. 105 b. y

x

Num

ber o

f learn

ers

Bar graph showing where learners normally do their homework

0

2

6

10

14

18

4

8

12

16

20

Kitchen Lounge Dining room Bedroom Other

Male

Female

c. Theydotheirhomeworkinthelounge–thebarsarehighestforthatroom.

d. y

x

Num

ber o

f learn

ers

Stacked bar graph showing where learners normally do their homework

0

10

20

30

40

Kitchen Lounge Dining room Bedroom Other

Male

Female

7. a. Discrete;thedistanceflownduringeachflightstandsalone. b. Brick:10,45m FlyingArrow:10,88m Bullet:2,95m c. 10,9m d. 3,1m e. Brick:9,1m FlyingArrow:1,9m Bullet:0,4m f. BrickfliesthefurthestdistancebutFlyingArrowismoreconsistentas

shownbyitsthesmallrange.


169S e c t i o n 4 • r E S o u r c E S

resourCes

seCtIon 4

a Multiplication tables

the 1 times table

1×1=1 2×1=2 3×1=3 4×1=4 5×1=5 6×1=6 7×1=7 8×1=8 9×1=9 10×1=10 11×1=11 12×1=12

the 2 times table

1×2=2 2×2=4 3×2=6 4×2=8 5×2=10 6×2=12 7×2=14 8×2=16 9×2=18 10×2=20 11×2=22 12×2=24

the 3 times table

1×3=3 2×3=6 3×3=9 4×3=12 5×3=15 6×3=18 7×3=21 8×3=24 9×3=27 10×3=30 11×3=33 12×3=36

the 4 times table

1×4=4 2×4=8 3×4=12 4×4=16 5×4=20 6×4=24 7×4=28 8×4=32 9×4=36 10×4=40 11×4=44 12×4=48

the 5 times table

1×5=5 2×5=10 3×5=15 4×5=20 5×5=25 6×5=30 7×5=35 8×5=40 9×5=45 10×5=50 11×5=55 12×5=60

the 6 times table

1×6=6 2×6=12 3×6=18 4×6=24 5×6=30 6×6=36 7×6=42 8×6=48 9×6=54 10×6=60 11×6=66 12×6=72


170 S e c t i o n 4 • r E S o u r c E S

the 7 times table

1×7=7 2×7=14 3×7=21 4×7=28 5×7=35 6×7=42 7×7=49 8×7=56 9×7=63 10×7=70 11×7=77 12×7=84

the 8 times table

1×8=8 2×8=16 3×8=24 4×8=32 5×8=40 6×8=48 7×8=56 8×8=64 9×8=72 10×8=80 11×8=88 12×8=96

the 9 times table

1×9=9 2×9=18 3×9=27 4×9=36 5×9=45 6×9=54 7×9=63 8×9=72 9×9=81 10×9=90 11×9=99 12×9=108

the 10 times table

1×10=10 2×10=20 3×10=30 4×10=40 5×10=50 6×10=60 7×10=70 8×10=80 9×10=9010×10=10011×10=11012×10=120

the 11 times table

1×11=11 2×11=22 3×11=33 4×11=44 5×11=55 6×11=66 7×11=77 8×11=88 9×11=9910×11=11011×11=12112×11=132

the 12 times table

1×12=12 2×12=24 3×12=36 4×12=48 5×12=60 6×12=72 7×12=84 8×12=96 9×12=10810×12=12011×12=13212×12=144



tIMes taBLes Quick reference chart

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12 0 12 24 36 48 60 72 84 96 108 120 132 144



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8070

6050

4030

2010

0


179S e c t i o n 5 • d o c u M E n t S

doCuMents

seCtIon 5

Insertyourownnotesanddocuments,forexampletheCAPSdocumentforMathematicalLiteracyinthissection.


Mathematical Literacy

Study & Master Mathematical Literacy Grade 11 has been especially developed by an experienced author team according to the Curriculum and Assessment Policy Statement (CAPS). This new and easy-to-use course helps learners to master essential content and skills in Mathematical Literacy.

The comprehensive Learner’s Book includes:

a reference section of the basic skills topics to revise the knowledge, skills and concepts in Mathematical Literacy

margin notes to assist learners with new concepts

ample examples with a strong visual input to connect Mathematical Literacy to everyday life

a summary checklist and revision exercises at the end of each topic.

The Teacher’s Guide includes:

a weekly teaching schedule, divided into the four terms, to guide the teacher on what to teach

exemplar papers and memorandums

solutions to all the activities in the Learner’s Book.

11Grade

www.cup.co.za

Study & Master

SM_Mathslit_11_TG_CAPS_ENG.indd 2 2012/08/06 9:52 AM

Karen Morrison Karen Press · 2020. 3. 19. · Singapore, São Paulo, Delhi, Mexico City Cambridge...

Documents

Transcript of Karen Morrison Karen Press · 2020. 3. 19. · Singapore, São Paulo, Delhi, Mexico City Cambridge...