teaching guide - oup.com.pk

1

T H I R D E D I T I O N

TEACHING GUIDE

viii1

Introduction iv

Curriculum 2 • StrandsoftheNationalCurriculum

• SyllabusMatchingGrid

Teaching Mathematics at Primary Level 8• TeachingtheStrands

• DevelopingPositiveAttitudetowardsMathematics

Features of the Teaching Guide 15

Unit Overview and Lesson Planning 18• SuggestedActivities

• ModelLessonPlan

Contents

iviv 1

Introduction

New Countdown 4istheseventhstageofaneightbookjourneyintomathsdesignedforthemathematicianoftoday’schallenging,fast-evolvingworld.Itincludesconceptsintroducedearlierinthejourney(place-value,thefouroperations,measurement,simplegeometryandfractions)toamoreadvancedlevelandintroducessomeexcitingnewideas;multiplesandfactors,primeandcompositenumbers,primefactorisation,testsofdivisibility,mixednumbersandimproperfractions,theknowledgeofgeometry,measuringandconstructingangles,learningmoreofthesecretsoftrianglesandquadrilaterals,andlinkingtheconceptoftherightanglewiththatofperpendicularlines.GraphworkbeguninNew Countdown 3isdevelopedinexcitingdirections.

New Countdown 4coversalltheconceptsrecommendedforClassFourlearnersbyallmajorsyllabuses.Italsoreachesbeyondtheminacarefulandsystematicway.Asintheprecedingbooksoftheseries,workedexamplesareprovidedforeachconceptintroduced,andarangeofpracticalactivitiesareincludedinanattempttoguaranteetheinvolvementofeverystudent.

New Countdown 4compriseseightunits,eachcontainingworkwhichcanbecoveredcomfortablyinthetimeavailableforeachterm.Irecommendthatyoufollowtheeightunitsinsequence,becauselaterportionsofthebooksrelatedirectlytoworkdoneorconceptsdiscussedinearlierportions.AsetofcomprehensivepracticesheetsandMathlabactivitieshavebeenincludedattheendofeachbook.

StartingfromBook3,theworkbookstylefollowedinjuniorbooksischangedtotextbookstyle.Thus,itisessentialthateachchildhasanotebooktowritein,ashe/sheworksthroughthebook.Greateruseoftheboardwillbenecessarytodemonstratenewideas.Tick-marks,stars,andsmileysgivestudentsconfidencethattheyaregettingtheirworkrightandhenceencourageswiftprogress.

ThemostimportantfeatureofthecurriculumisitscontinuedfocusonthecontentoftheMathematicsstandardsandthishasbeenaddedintheTeachingGuide.Thesestandardsnecessitatetheprovisionofmorecontinued,moresubstantive,morerigorousandmoresystematicinstructionforstudents.

Planningyourworkandthenimplementingyourplanarethebuildingblocksofteaching.Therefore,thisteachingguideprovidesdetailedlessonplans,includinglearningobjectives,learningcurves,learningactivities,andguidancetoimplementtextbookexercises.

vv1 Introduction

Useofresourcesareimportant,tomakethelessoninteresting,engagingandeasytounderstand.Teacherscanpreparetheirownmaterialoruseanyteachingorlearningaideasilyavailable,whenrequired.

ThejourneytillnowintheNewCountdownserieshasbeenveryusefulinexposingstudentstonewlearning.Apartfromhavinglearntnumbersandnewerstrategiesofworkingwiththem,thestudentsarenowabletograspnewtopics.Theycannowworkindependentlyandtheyarereadytoabsorbmore.

About the Teaching GuideTheTeachingGuideoffersextensiveteachingideaslinkedwithcurriculumandadaptableactivitiestodifferentsettings.ItprovidesthestrandsandbenchmarksoftheNationalCurriculum2006.Thestrandsofthecurriculumhavebeenexplainedinaneffectivewayasasupporttoteachers’teaching.Activitiesdesignedformaximumlearningintheclassroomanddailylifearementionedineachunit.Teachershavethelibertytouseanyoftheseortheonementionedinthemodellessonplan,oranyotheractivityoftheirchoicedependingontheinterestofthestudentsandthetimeavailable.

Asyllabusmatchinggridisalsogiventofacilitatetheteacherconnectingthestudentlearningobjectiveswiththetextinthebook.Theteachingguideemphasisesthedevelopmentofapositiveattitudetowardslearningmathsbyenhancingmemoryretention,buildingconcentration,andcreatingcuriosityformaths.Itcontainsamodellessonplanineachunittoimplementtimeappropriateeffectiveactivities.

Shamlu Dudeja

iv2 1

StrandsofNationalCurriculumforMathematics

MEASUREMENTS

HANDLING DATA

REASONING and LOGICAL THINKING

GEOMETRY

NUMBERS and OPERATIONS

Curriculum

v31 Curriculum

Syllabus Matching GridLeft columnof the followinggrid indicatesNational CurriculumSLOs,whereas therightcolumnindicatesthetextbookunits.

Unit 1: Numbers and Numbers OperationsTextbook

Reference

1.1 Numbers and Number Operationsi) Identifyplacevaluesofdigitsuptoonehundredmillion.ii) Readnumbersuptoonehundredmillion.iii) Writenumbersuptoonehundredmillion.iv) Recognisenumbersinwordsuptoonehundredmillion.v) Compareandordernumbersupto8digits.

Unit1

1.2 Additioni) Addnumbersupto6digits.ii) Solvereal-lifeproblemsinvolvingadditionofnumbersupto6digits.

1.3 Subtractioni) Subtractnumbersupto6digits.ii) Solvereal-lifeproblemsinvolvingsubtractionofnumbersupto6digits.

1.4 Multiplicationi) Multiplynumbersupto5digitsbynumbersupto3digits.ii) Solvereal-lifeproblemsinvolvingmultiplication.

1.5 Divisioni) Dividenumbersupto4digitsbynumbersupto2digits.ii) Solvereal-lifeproblemsinvolvingdivision.

1.6 Addition, Subtraction, Multiplication and Divisioni) Usemixedoperationsofaddition&subtractionandmultiplication

anddivision.ii) Solvereal-lifeproblems(usingPakistanicurrencyaswell)involving

addition,subtraction,multiplicationanddivision.

Unit 2: Factors and Multiples

2.1 Divisibility Testi) Identifydivisibilityrulesfor2,3,5and10.ii) Usedivisibilitytestsfor2,3,5and10onnumbersupto5digits.

Unit22.2 Prime and Composite Numbersi) Defineprimeandcompositenumbers.ii) Differentiatebetweenprimeandcompositenumbers.

iv4 1Curriculum

2.3 Factors and Multiplesi) Listfactorsofanumberupto50.ii) Listthefirsttwelvemultiplesofa1-digitnumber.iii) Differentiatebetweenfactorsandmultiples.

Unit2

2.4 Prime Factorisation Factoriseanumberbyusingprimefactors

2.5 Highest Common Factors (HCF)i) Determinecommonfactorsoftwoormore2-digitnumbers.ii) FindHCFoftwoormore2-digitnumbers,using: •Venndiagram •primefactorisationmethodiii) Solvereal-lifeproblemsinvolvingHCF.

2.6 Lowest Common Multiples (LCM)i) Determinecommonmultiplesoftwoormore2-digitnumbers.ii) FindLCMby• CommonMultiples• PrimeFactorisationMethod

iii) Solvereal-lifeproblemsinvolvingLCM.

Unit 3: Fractions

3.1 Fractionsi) Defineafraction.ii) Recogniselikeandunlikefractions.iii) Comparetwounlikefractionsbyconvertingthemtoequivalent

fractionswiththesamedenominator.iv) Arrangefractionsinascendinganddescendingorder.v) Verifythecommutativepropertyofadditionoffractionswithsame

denominators.vi) Verifytheassociativepropertyofadditionoffractionswithsame

denominators.vii) Subtractfractionswithunlikedenominators.

Unit3

3.4 Multiplication of Fractionsi) Multiplyfractionswithwholenumbers.ii) Multiplytwoormorefractions(proper,improperandmixedfractions).iii) Verifythecommutativepropertyofmultiplicationoffractions.iv) Verifytheassociativepropertyofmultiplicationoffractions.

v51 Curriculum

3.5 Division of Fractionsi) Divideafractionbyawholenumber.ii) Divideawholenumberbyafraction.iii) Divideafractionbyanotherfraction(proper,improperandmixed

fractions).iv) Solvereal-lifeproblemsinvolvingfractionsusingallfouroperations.

Unit 4: Decimals and Fractions

4.1 Decimalsi) Knowadecimalnumberasanalternatewayofwritingafraction.ii) Definedecimalasafractionwhosedenominatoris10orapowerof10.iii) Recognizetheplacesoccupiedbythedigits,afterthedecimalpoint,

asdecimalplaces.iv) Identifytheplacevalueofadigitindecimals.

Unit4

4.2 Conversion between Fractions and Decimalsi) Convertagivenfractiontoadecimalif:• denominatorofthefractionis10orapowerof10.• denominatorofthefractionisnotapowerof10butcanbe

convertedto.ii) Convertdecimals(uptothreedecimalplaces)tofractions.

4.3 Basic Operations of Decimalsi) Addandsubtractdecimals(uptotwodecimalplaces).ii) Multiplyadecimalby10,100and1000.iii) Multiplyadecimalbya2-digitnumber.iv) Divideadecimalbya1-digitnumber(quotientbeingadecimalup

totwodecimalplaces).Solvereal-lifeproblemsinvolvingdecimalsuptotwodecimalplaces.

Unit 5: Measurements

5.1 Lengthi) Convert:• kilometrestometres• metrestocentimetres• centimetrestomillimetres

ii) Addandsubtractexpressionsinvolvingsimilarunitsoflength.iii) Useappropriateunitstomeasurethelengthofdifferentobjects.iv) Solvereal-lifeproblemsinvolvingconversion,additionand

subtractionofunitsoflength.

Unit5

iv6 1Curriculum

5.2 Mass/Weighti) Convertkilogramstograms.ii) Addandsubtractexpressionsinvolvingsimilarunitsofmass/weight.iii) Useappropriateunitstomeasurethemass/weightofdifferent

objects.iv) Solvereal-lifeproblemsinvolvingconversion,additionand

subtractionofunitsofmass/weight.

Unit5

5.3 Volume/Capacityi) Convertlitrestomillilitres.ii) Addandsubtractexpressionsinvolvingunitsofvolume/capacity.iii) Useappropriateunitstomeasurethecapacity/volumeofdifferent

objects(utensilsetc).iv) Solvereal-lifeproblemsinvolvingconversion,additionand

subtractionofunitsofvolume/capacity.

5.4 Timei) Readtimeinhours,minutesandseconds.ii) Converthourstominutesandminutestoseconds.iii) Convertyearstomonths,monthstodaysandweekstodays.iv) Addandsubtractunitsoftimewithoutcarrying/borrowing.v) Solvesimplereal-lifeproblemsinvolvingconversion,additionand

subtractionofunitsoftime.

6 Geometry

6.1 Geometry Boxi) KnowinstrumentsofaGeometryBoxi.e.,pencil,ruler,compasses

(sometimescalledapairofcompasses),dividers(sometimescalledapairofdividers),setsquaresandprotractor.

ii) RecognisetheuseofpencilsofgradeHandHB.iii) DemonstratetheuseofHandHBpencilsbydrawingdifferentlines.

Unit66.2 Linesi) Measurethelengthofalineincentimetresandmillimetresusing

ruleranddividers.ii) Drawastraightlineofgivenlengthusingaruleranddividers.iii) Drawacurvedlineandmeasureitslengthusingthread/dividersand

ruler.iv) Recognisehorizontalandverticallines.v) Drawaverticallineonagivenhorizontallineusingsetsquares.vi) Recogniseparallelandnon-parallellines.

v71 Curriculum

vii) Recogniseparallelandnon-parallellines.viii)Identifyparallelandnon-parallellinesfromagivensetoflines.ix) Drawaparallellinetoagivenstraightlineusingsetsquares.x) Drawalinewhichpassesthroughagivenpointandisparalleltoa

givenline(usingsetsquares).

Unit6

6.3 Anglesi) Recogniseananglethroughnon-parallellines.ii) DrawanangleAOBwithvertex(0)andarms(OA,OB)torecognise

thenotation∠AOBforanangleAOB.iii) Recogniserightanglethroughhorizontalandverticallines.iv) Demonstrateacuteandobtuseanglesviatherightangle.v) Recognisethestandardunitformeasuringanglesasonedegree(1°)

whichisdefinedas1300 ofacompleterevolution.

vi) Measureanglesusingprotractorwhere:• upperscaleofprotractorreadsthemeasureofanglefromleftto

right• lowerscaleofprotractorreadsthemeasureofanglefromrightto

leftvii) Drawarightangleusingprotractor.viii)Drawacuteandobtuseanglesofdifferentmeasuresusingprotractor.ix) Drawanangle(usingprotractor):• equalinmeasureofagivenangle• twicethemeasureofagivenangleequalinmeasureofthesum

oftwogivenangles

6.4 Circlesi) Identifycentre,radius,diameterandcircumferenceofacircle.ii) Drawacircleofgivenradiususingcompassesandruler.

6.5 Quadrilateralsi) Constructsquaresandrectangleswithsidesofgivenmeasureusing

protractor,setsquaresandruler.ii) Identifycentre,radius,diameterandcircumferenceofacircle.

7. Information Handling

7.1 Bar GraphsReadandinterpretsimplebargraphgiveninhorizontalandverticalform.

Unit77.2 Line GraphsReadandinterpretsimplelinegraph.

Note: Unit6:PerimeterandArea:Basicknowledgeofthetopichasbeengiveningrade3.Thetopichasbeenfurtherenhancedinunit6.

iv8 1

TeachingMathematicsatPrimaryLevel

Teaching the StrandsFollowingarethefivestrandsofTheNationalCurriculum,

• Numberandoperations• Measurements• Geometry• Handlingdata• Reasoningandlogicalthinking

Thesignificanceandintegrationoftheabovefirst4strandsinteachingindividualunitsofNCDBook4arediscussedbelow,whereasthefifthstrandisintegratedinalltheunits.Specificallytalkingaboutthefifthstrand,studentsvalidateanswerswithlogicalreasonsbysolvingproblemsinvolvingnumbersanddata.Theyalsocommunicateandapplyanalyticalreasoningaboutgeometricalshapesandfigures.

Numbers and Number OperationsHelpyourstudentsgraspthepointthatnumbersofsixdigitsandaboveareorganisedinto‘periods’bygivingspaceaftereverythreedigitsfromtheleft.

Forexample:243101;8923102;52860459;731215821

Makegeneroususeoftheboard:forexample,drawtheplacevaluechartshownonpage2andputasuccessionof9-digitnumbersintoit.Provideplentyofpracticewith6-digit,7-digit,8-digitnumbersbeforemovingonto9-digitnumber.

Teamgamesarealsoanexcellentwayoftestingyourstudents’abilitytopresentbignumbersinexpandedform,arrangetheminascending/descendingorder,identifythepredecessororsuccessorofagivenbignumber,andskipcountaccurately(in5s,10s,20s,100s,etc.)

Thesectiononmultiplicationanddivisionincludesadiscussionon10anditsmultiples.Spendplentyoftimeonthequestionofwhathappenstonumberswhentheyaremultipliedordividedby10oritsmultiples.Thisprovidesanexcellentbasisfortheintroductionofdecimalfractionsanddecimalnotationlaterinthebook.Divisionworkreachesamoreadvancedlevelhere,featuring4-digitdividendsand2-digitdivisors.Plentyofpracticesumsareprovidedintherespectiveexercises,butyoumaywanttoprepareadditionalworksheets.Onceagain,emphasisetheimportanceofwritingthesumsneatlyandkeepingcolumnsstraight.

v91 TeachingMathematicsatPrimaryLevel

Factors And MultiplesHere,factorsandmultiplesarepresentedasentry-pointstothemarvelouspatternsandlinkagesintrinsictotheworldofmaths.Onpages35and41,asimpleVenndiagramisintroducedtohelpstudentsvisualisetheideaofcommonfactorsandmultiples.Itisstronglyrecommendedthatyoureproducethisexerciseontheboard,goingverycarefullystepbystep,usingcolouredchalktohighlightthecommonfactorsandmultiples.Encouragethestudentstomakediagramsoftheirown.

Factorsarewellintroducedbyhavingthestudentsarrangesimpleobjects(beads,nuts,straws,etc.)groupedindifferentmanners.Oncetheconceptof‘factor’isgrasped,studentsshouldbeabletodistinguishingprimenumbersfromcompositenumbers(pages23-26).Onpage32,primefactorisationispresentedintermsofatree,anideawhichyoumightliketodeveloponyourboard.Teamgameswillhelpyourclasslearnthevitaltestsofdivisibility.Forexample,youcandividetheclassinto4teams:TeamAfornumbersdivisibleby2,TeamBfornumbersdivisibleby3,andsoon.Fromalistofnumbers,youreadoutoneatrandom,andtheteamsdecidewhetherthenumberisdivisiblebythepre-setnumbersassignedtothem.Yourworkonmultiplesandfactorswillhaveprovidedanexcellentbasisforthesectiononfractions,whichincludestheideaofreducingfractionstotheirlowesttermsbyidentifyingcommonfactors(page34).

FractionsWhenintroducingtheconceptofimproperandmixedfractions,besuretoreproduceontheboardthesimplediagramsshownonpage60.Diagramsalsohelptoconveythepointthatimproperfractionscanbeexpressedasmixednumbers(andviceversa).Plentyofpracticesumsareprovidedfortheadditionandsubtractionofmixednumbers(withoutandwithregrouping),butyoumaywishtodevelopadditionalworksheetshere.

DecimalsHere,yourteachingfocusisondecimalfractionsandonhelpingstudentstounderstandthissimplepoint:thatdecimalnotationisanextensionofplacevalue(asusedforones,tens,hundreds,etc.)Thedecimalpointsimplymakesitclearwhereawholenumberendsandthedecimalfractionbegins.Tousedecimalfractionsconfidentlyandwell,yourstudentsmustunderstand,firstly,thenotationand,secondly,theequivalenceofdecimalfractionsandcommonfractions.BothideasareexplainedindetailinNew Countdown 4.

Whenintroducingthedecimalnotationforhundredths(page83),youmightfindithelpfultoprovideeachstudentwithahundred-squaregrid.Askthestudentstocounthowmanysquaresthereareineachgrid(100).Theycanthencolouroneofthesquaresandwritedownthefractionthathasbeencoloured.

1100

10100

= 110

iv10 1TeachingMathematicsatPrimaryLevel

Inthenextstage,askthemtocolouronewholecolumnofsquares,countthenumberofsquarescoloured(10),andthinkhowtheycanexpressthisasafractionofthewholegrid.Ifthestudentsthinkintermsof10smallsquares,theywillwritethefractionas 10

100.

Butiftheythinkintermsofcolumns,theywillfindthereare10columnsaltogetherandthattheyhavecolouredoneofthem,or 1

10ofthegrid.Indecimals,thismeansthat

0.1ofthegridiscoloured.

Thefollowingequivalenceisnowestablished: 10100

= 110=0.1

Thirdly,askthestudentstocolour15squares:

Askthemhowtheycanexpressthesesquaresasafractionofthewholegrid.Theymayanswerinseveralways: 1

10 + 5

100,or 10

100 + 5

100,or 15

100or0.1+0.05.Whicheverwaythey

choose,theywillfindthat,inplacevalueterms,thereisnocolumntoaccommodate 15100

.Atthispoint,thehundredths(h)columncanbeintroduced,andthedecimalnotation, 0.15,discussed.Reinforcethepointthatthisdecimalfractioncanbewritten as:

0.15,or 110

+ 5100

,or 10100

+ 5100

,or 15100

Oncedecimalnotationisunderstoodasanextensionofplace-value,studentsshouldhavenodifficultyinhandlingthousandths(page86).Thediscussionofthemetricsystemreinforcesunderstandingbesidesprovidingplentyofopportunityforpracticalworkwithdecimals.

Measurement Studentsunderstandandusethefouroperationswithaccuracydealingwithlength,weight,andcapacityusingthemetricsystem. Thestudentshavealreadyworkedwithconceptsoflength,weight,andcapacityinthepreviousclasses.Inthischapter,theyareintroducedtothebasicunitsofmeasurement,forbiggerorsmallervalues.

Perimeter and AreaTointroducetheconceptofarea,avarietyofgeometricalgridsareshown.Askyourstudentswhichofthegridstheythinkistheeasiesttouse,inmostcasestheywillidentifythesquareasthemostconvenientmeasure.Half-squaresareintroduced,bringingthestudentsclosertotheproblemofestimatingtheareaofirregularshapes.Whenyoudiscussthetwoleavesshownagainstagridonpage139,examinewiththestudents,thefollowingmethodfordealingwithpartsofsquares covered:


1.Ifthepartcoveredislessthanhalfasquare,ignoreit.

2.Ifthepartcoveredisgreaterthanhalfasquare,countitasawholesquare.

Makesureallthestudentshaveaccesstosquaredpaperastheyworkthroughthissection.Ifagridofcentimetresquaresisprovided,theideaofasquarecentimetrecaneasilybeintroducedastheamountofspacecoveredbyoneofthesquares.

Bynowaccustomedtotheclock-faceanditsdivisions,yourstudentsshouldhavenodifficultyintellingthetimetotheexactminute(pages125-128).Makesuretheyhavealotofpracticeinhandling12-hourclocktimeand24-hourclocktime;onceagain,itisimportantthatstudentsmoveconfidentlybetweenthetwomethods.Whenintroducingtimetables,youneedtohavearealrailwayorflighttimetablewhichthestudentscanlookatanddiscuss.

Introductiontoa.m.andp.m.timeisgivenonpages126and127.

GeometryForthesectionongeometry,youmightfindithelpfultoprepareworksheetsoflarge-sizedangleswhichstudentscanmeasurewiththeirprotractors.Oncetheyhavegainedconfidenceinhandlingtheinstrument,thesmalleranglessetoutinNewCountdown4 willprovideamplepractice.

Information HandlingStudentslearntofindrelationshipsbetweengivensetsofdataquickly,usingbargraphsandlinegraphs.

Thestudentshaveworkedwithpictographsandblockgraphsearlier.Now,studentsarereadytolearnaboutbargraphsandlinegraphs.Itprovidesanopportunityforexcitingpracticalwork.Linegraphsareparticularlyusefulwhenwewanttomeasuresomethingwhichisgraduallychanging,forexample,arelationbetweencostandcommodity.Giveyourstudentsplentyofpracticeinreadingdatafromsimplelinegraphs,discussingwhysomegraphstaketheformofastraightlinewhileothersshowvariation.

Beforestudentsattempttheexercise,makesureyouhavethoroughlydiscussedhowtheaxesofthegraphshouldbepositionedandhowthesquaresofgraphpapershouldbeused.Followupthisexercisewithyourownvariants;forexample,packetsofpop-cornsoldatafun-fairoverthecourseofaday,orthenumberofstudentsenteringamuseumoneSundayafternoon.


Developing a Positive Attitude towards MathematicsTothispoint,theNewCountdownserieshasbeenveryusefulinexposingstudentstonewconcepts.Apartfromhavinglearntnumbersandnewerstrategiesforworkingwiththem,thestudentsarenowabletograspnewtopics.Theycannowworkindependentlyandtheirmindsarereadytoabsorbmore.NewCountdown4followsthesameactivity-based‘visual’formatofthepreviousbooksintheseries.

TheprimaryaimoftheNew Countdownseriesistoensurethateverychilddevelopsastrongaffinityformathematics,andforthis,thefollowingarenecessary:

• Atension-freeandfun-filledatmosphere• Concentrationbuilding• Logicalthinking• Aquestioningmind• Abilitytoanswerwithouthesitation• Aretentivememory• Asenseofdiscovery(ratherthan‘beingtaught’)• Lateralthinking

Tension-Free and Fun-Filled AtmosphereSuchalearningenvironmentestablishesgreaterbondingbetweenthestudentsandtheteacherandleadstohealthiermentalgrowth,greaterconfidenceandbetterlearning.Beinginacomfortable,familiar,andfriendlyenvironmentitself,buildsconfidence.

Themoreconfidentachildis,theeasieritisforhimorhertoabsorbnewconcepts,astheyearprogresses.Itisfirmlybelievedthatstudentsbegintogetmorejoybylearningnewconceptsthroughdiscovery.Ifthelessonsarebasedonsuchmores,thereisnoreasonwhythestudentwillnotgrowuptobeahappyandcaringchildwithabright,thinkingmind.

Concentration BuildingAstudentcannotperformwellintheclassroomifhe/sheisnotattentive,distracted,orfacingdifficultyinfocusingontheworkathand.Concentrationorattentionenhancesstudents’understandingandretention.Mostlystudentswillconcentrateonfunactivities,butitiscruciallyimportanttoconcentrateonallkindsoftasksdoneintheclassroomtoimprovelearningandbuildconfidence.Givenbelowaresomestrategiestoenhancetheconcentrationspanintheclassroom.

• Setanappropriateamountoftimetocompletethetask.Thismaybindastudenttofocusonthegiventasksothathe/shecouldcompleteitwithintimelimits.

• Dividebigtaskintoparts.Asshorteramountoftimeandonetaskatatimemaybecomeaneasierjobforthestudents.Abigtaskrequiresalongertimeandmoreconcentrationandfocusthatmaybecomeareasonfordistraction.

• Givethemenoughphysicalactivitytoavoidrestlessnessandmakeiteasiertofocusonthetask.

• Allowsomefreetimebeforebeginninganewtask.


• Reinforcepositivebehaviour.• Introducearewardsystembypraisingthestudentsorallowingthemtimetoread

theirfavouritebook.• Somegamesmaybehelpfultoincreaseconcentrationspan:• JustSit:Thisgameisplayedbychallengingthestudentstositintheirchairs

withoutmovingtoseehowlongtheycandoit.• Statue:Theteachersays‘statue’andeveryonewillbestillinwhateverposition

theyare,forafewminutes.Likeanyskill,concentrationcanbebuiltandimprovedwithconsistency.

Logical ThinkingEverypageinallthebooksinthisserieslaysstressonlogicalthinking.Themomentachildgetsinto‘logic’mode,thought,concentrationandretentivememorywillbethenaturaloutcomes.

A Questioning MindIfwewantourstudentstobeabove-averageachievers,weshouldencouragethemtoaskasmanyquestionsastheywishto.Aquestionfromonechildwillinvariablyleadtomorequestionsfromotherstudentsintheclass.Thisisaveryhealthyoutcome.Theremaybetimeswhentheteacherdoesnothaveanimmediateanswertoaquestion;thereisnoneedtobeashamedofthis,aslongasitisensuredthattheanswerisfoundwithinadayortwo.

Ability to Answer Questions without HesitationItisimportantforateachertogetintoquestion-answersessionswithstudents,asoftenaspossible.Themotherofawell-knownintellectualrecentlysaidthatthereasonforherson’sbrilliantperformanceinlifewasthathealwaysaskedtoomanyquestionsandofferedtogiveanswersevenwhenhewasnotspecificallyasked.Thehabitoftryingtoanswerasmanyquestionsaspossibleshouldalsobeinculcated.

A Retentive MemoryAnykindoflearningwhichisbasedonconcentration,logicalthinking,askingquestionsandfindinganswerswillautomaticallyleadtoretentivememory.Thepowerofretentivememoryasatoolforlearningatanystageinlifecanneverbeundermined.Rotelearningusestwosensesatthemost—listeningandseeing(reading),whereasactivity-basedlearning,involvestouching(doing)allthetime,andsmellingandtastingtoo,onafewoccasions,inadditiontolisteningandseeing.Thegreaterthenumberofsensesusedforalearningexercise,thebetterwillbetheconcentrationleadingtoimprovedspeedofunderstanding,retention,logic,andapplication.Itwouldbegreatfuniftheartandcraftclasses,offandon,incorporatemathematicalshapes,concepts,andlanguage.Thejoythatstudentsderiveoutofsuchalearningexperienceisanaddedbonus.


A Sense of DiscoveryDiscoveryisalwaysmorejoyousthanbeingtold.Ifamothertellshersonthathisteacherloveshim,thesonbelievesher,butifhediscoverstheteacher’slovethroughahugorapatontheback,imaginethejoy.ThesameappliestolearninginMathematics.

Thesenseofjoyorpleasureatdiscoveringnewthings,whichismissinginrotelearning,isagreatacceleratorforlearning.Eachdiscoveryistheresultofapracticalactivity.

Lateral ThinkingBythistimestudentsknowseveralnumberfactsandarecomfortablewithaddition,subtraction,multiplication,anddivision.Conceptssuchasmultiplicationbeingaformofrepeatedaddition,anddivisionbeingaformofrepeatedsubtraction,areusedineverydaylifewithoutthenecessityofgoingbacktothebasics.Thisisanexampleoflateralthinking.

Verticallearningwouldbetolearn2stables,then3s,then4sandsoon.Lateralthinkingwouldentailunderstandingthefactsbehindthetablesandapplyingthesetosolveeverydayproblems.Intoday’stimes,morethaneverbefore,itisimportantthatstudentsthink,learntothinkandapplytheirknowledgelaterally,i.e.theyapplytheknowledgegainedfrombookstotheirsurroundings,throughouttheday.

v151 FeaturesoftheTeachingGuide

Features of the Teaching GuideTheTeachingGuidecontainsthefollowingfeatures.Theheadingsthroughwhichtheteacherswillbeledareexplainedasfollows:

Suggested Time FrameTimingisimportantineachofthelessonplans.Theguidewillprovideasuggestedtimeframe.However,everylessonisimportantinshapingthebehaviouralandlearningpatternsofthestudents.Theteacherhasthediscretiontoeitherextendorshortenthetimeframeasrequired.

Learning CurveItisimportanttohighlightanybackgroundknowledgeofthetopicinquestion.Theguidewillidentifyconceptstaughtearlieror,ineffect,revisethepriorknowledge.Revisionisessential,otherwisethestudentsmaynotunderstandthetopicfully.Theinitialquestionwhenplanningforatopicshouldbehowmuchdothestudentsalreadyknowaboutthetopic?Ifitisanintroductorylesson,thenaprecedingtopiccouldbetouchedupon,whichcouldleadontothenewtopic.Inthelessonplan,theteachercannotewhatpriorknowledgethestudentshaveofthecurrenttopic.

Eachtopicisexplainedindetailbytheauthorinthetextbooksupportedbyworkedexamples.Theguidewilldefineandhighlightthespecificlearningobjectivesofthetopic.Itwillalsooutlinethelearningoutcomesandobjectives.

Real-life ApplicationToday’sstudentsareveryproactive.Thestudyofanytopic,ifnotrelatedtopracticalreal-life,willnotexcitethem.Theirinterestcaneasilybestimulatedifwerelatethetopicathandtoreal-lifeexperiences.

?OOPS

!

Frequently Made MistakesItisimportanttobeawareofstudents’commonmisunderstandingsofcertainconcepts.Iftheteacherisawareofthesetheycanbeeasilyrectifiedduringthelessons.Suchtopicalmisconceptionsarementionedtosupportteachers.

Summary of Key FactsFactsandrulesmentionedinthetextarelistedforquickreference.

iv16 1FeaturesoftheTeachingGuide

Suggested ActivitiesThisteachingguideprovidesyouenoughhandsonactivitiesformakingyourlessonplanmoreinterestingandengaging.Theseactivitieswillhavemoreimpactonstudents’learning.

Lesson Plan Model Lesson PlanPlanningyourworkandthenimplementingyourplanarethebuildingblocksofteaching.Teachersadoptdifferentteachingmethods/approachestoatopic.

Amodellessonplanisprovidedineveryunitasapreliminarystructurethatcanbefollowed.Atopicisselectedandalessonplaniswrittenunderthefollowingheadings:

TopicThisisthemaintopic/sub-topic.

DurationThesuggestedtimedurationisthenumberofperiodsrequiredtocoverthetopic.Generally,classdynamicsvaryfromyeartoyear,soflexibilityisimportant.

Theteachershoulddrawhis/herownparameters,butcanadjusttheteachingtimedependingonthereceptivityoftheclasstothattopic.Notethatintroductiontoanewtopictakeslonger,butfamiliartopicstendtotakelesstime.

Specific Learning ObjectivesThisidentifiesthespecificlearningobjective/softhesub-topicbeingtaughtinthatparticularlesson.

Key VocabularyListofmathematicalwordsandtermsrelatedtothetopicthatmayneedtobepre-taught.

Resources: Teaching and Learning Aids (Optional)Thissectionincludeseverydayobjectsandmodels,exercisesgiveninthechapter,worksheets,assignments,andprojects.

StrategyStarter: EngagementActivity

Thelessoncanbeginwithsomethinginteresting,suchastellingastory,relatingareal-lifeexperienceoraneverydayeventwhichmayormaynotleadtothetopic;butisinterestingenoughtocapturetheattentionofthestudents.Involvingstudentsinadiscussiontofindouthowmuchknowledgetheyhaveofthetopicbeingtaughtisalsoagoodstrategy.Teacherscanusetheirowncreativitytocomeupwithideastocreateasenseoffun.

v171 FeaturesoftheTeachingGuide

Main Developmental ActivityLearningneedstostartwithpracticalactivities,thereforethemaindevelopmentalactivityisthefirststepthatleadstoactuallearning,whichinturnleadstotherequiredoutcomeofthelesson.Thisactivitycanbeplannedasindividualwork,pairorgroupworkasperrequirement.Workingindividuallycreatesself-confidencewherethechildenjoysasenseofself-achievement,whereaspairandgroupactivitiescreateasenseofdiscoveringandlearningtogether.

Theseactivitiesenhanceconcentrationandimproveretentionofmemory.Throughtheseactivitiestheteachercanbuildunderstandingofconceptsinafun-filledway.Itiseasierforstudentstograsptheconceptsandthenmovefromabstracttoconcrete.

Written AssignmentsFinally,writtenassignmentscanbegivenforpractice.Itshouldbenotedthatclassworkshouldcomprisesumsofalllevelsofdifficulty,andoncetheteacherissurethatstudentsarecapableofindependentwork,homeworkshouldbehandedout.Forcontinuity,alternatesumsfromtheexercisesmaybedoneasclassworkandhomework.

SupplementaryWork(Optional):Anactivityorassignmentcouldbegiven.Itcouldinvolvegroupworkorindividualresearchtocomplementandbuildonwhatstudentshavealreadylearntinclass.

Thestudentswilldotheworkathomeandmaypresenttheirfindingsinclass.

Wrap upAttheendofeachsub-topic,awrapupshouldbedoneusingvariousstrategies.Forexample,aquickquestionandanswersessioninvolvingthewholeclass,challengingstudentswithaquestiontochecktheirunderstandingoftheconcepttaught.

1

iv18 1

NumberandArithmeticOperations

1

Suggested Time Frame12-14periods

Learning CurveStudentshavealreadyworkedwithnumbersupto6digits.Here,theywilldealwithnumbersupto9digits.Previouslytheyhaveaddedandsubtractednumbersupto4digits,thiswillleadthemtoaddandsubtractnumbersupto6digits.Studentsarefamiliarwithmultiplicationanddivision(2digitnumberbya1digitnumber)nowtheywillbedealingwithmultiplicationanddivisionof4-digitnumbersby2-digitnumbers.Theywillbeabletoapplythisknowledgetosolvedailylifeproblemsinvolvingfouroperations.

Real-life Application

Wehavenumbersallaroundus.Weusethemindifferentways.

• Mathshelpsinbuildingthings.Forconstructingabuildingwefindtheareaofeachspaceandestimatetheexpenditure.

• Inthegrocerystorewepurchasethingsandusemathematicstopayforthem.• Whilebakinginthekitchenweusenumbersandoperationstomixthecorrect

amountsofingredients.• Ifweplanajourneyweneedtoestimatetheexpensesoftickets,

accommodation,andfood.• Savingmoneyalsoneedsmathematicaloperations.

?OOPS

!

Frequently Made Mistakes• Thestudentsmixinplacevalueswhiledealingwithbiggernumbers.• Theymakemistakesinwritingnumbersinthecorrectcolumnswhileaddingor

subtracting.• Theygetconfusedindistinguishingbetweenthedividendanddivisor.• Theymakemistakesinmultiplicationanddivisionsumsbecausetheyhavenot

learntthetimestables.

v191 NumberandArithmeticOperations 1

Summary of Key Facts• Comparingnumbersisthesameasknowingwhichnumberissmallerandwhich

numberisbigger.• Symbolically,asmallersignisdenotedas‘<‘andagreatersignisdenotedas‘>’.• Themultiplicandisthenumberorquantitytobemultiplied.Themultiplieristhe

numberorquantitybywhichthemultiplicandistobemultiplied.Theproductissimplytheendresultofthemultiplication.

• Thedividendisthenumberorquantitytobedivided.Thedivisoristhenumberorquantitybywhichthedividendistobedivided.Thequotientissimplytheanswerofthedivision.

• 'Remainder'isthequantitywhichisleftafterdivision.

Suggested ActivitiesIndividual/Pair Activity (10 mins)

Learning Outcome:Addnumbersupto6digits.

Resources:ActivityCards.

Instructions:

• Prepare the activity cards for each student.• Sampleoftheactivitycardgiven.• Studenthastoaddtherowshorizontallyandcolumnsverticallyandwritethe

answerinthegivenspace.• Gettheactivitycardspeerchecked.

Sample Activity Card

Completetheseadditionsquares.Addtherowsandcolumnstofindthetotals.

357890 29541

378201 268975

Individual/Pair Activity (10 mins )

Learning Outcome:Subtractnumbersupto6digits

Resources:ActivityCards

Instructions:

• Provideeachstudentwithanactivitycardwithsubtractionsumsofcomplexnumbers.

• Timetheactivityandgettheactivitycardspeerchecked.

iv20 1NumberandArithmeticOperations1

• Sampleoftheactivitycardisgivenbelow.Activity Card

Workoutthedifferencebetweenthepairofnumbers:

123456543210

Individual Activity (20 mins )

Learning Outcome: Multiply/dividenumbersupto4digitsby2digits.

Resources: ActivityCards

Instructions:

• Provideeachstudentwithanactivitycardwithtwowordproblems.• Timetheactivityandgettheactivitypeerchecked.

(Sampleoftheactivitycardisgivenbelow).

cherrieseachday.Javeriahasabagof45cherriestoevenlysplitupintoher3schoollunchesfortheweek.Howmanycherrieswillshegettoeateachweek?

wordsinanhour.

Shahidstartedtypinghisstorybookovertheweekend.Hetypedfor3hoursandcompleted15pageswith240wordsoneachpage.Howmanywordsdidhetypeinanhour?

Group Activity (20 mins)

Learning Outcome:Read/Writenumbersuptoonehundredmillioninnumeralsandwords.

Resources:Whiteboards,markers,cardswith9-digignumbersinwords.

Instructions:

• Divideyourclassinto4groupsA,B,C,andD.• ThefirstcompetitionwillbebetweenAandB.• OnememberofgroupAwillpickacardandreadsthenumber.• AmemberofgroupBwillwritethatnumberinfiguresonthewhiteboardand

showittotheteacher.• Now,groupBwillpickacardandgroupAwillwritethenumberinfiguresonthe

whiteboard.

v211 NumberandArithmeticOperations 1

• Threecardwillbepickedbyeachgroup.• Teacherwilldecidethewinneraccordingtothenumberofcorrectanswers.• ThesameprocedurewillberepeatedbygroupsCandD.• Nowthetwowinnergroupswillcompeteagainsteachother.• Thistimetheteacherwillreadanumberandthegroupthatwritethecorrect

answerfirst,willbethewinner.

Lesson Plan Model Lesson PlanTopic

Introductionofnumbersupto9digits.

Duration80minutes

Specific Learning ObjectivesBytheendofthelessonstudentswillbeabletoidentifyplacevaluesofdigitsuptothehundredmillions.

Key Vocabularymillion,placevalue

ResourcesPlacevaluechartonsmallcards,abigplacevaluechart.

StrategyStarter: Engagement Activity (5 mins)

Writeanumberontheboard,forexample,909437.Askthestudentstheplacevalueofeachdigit.

Helpthestudentsifthereisanyambiguity.

Main Developmental Activity (20 mins)Distributeplacevaluechartcardstothestudentsandaskthemtopasteintheirnotebooks.

Millions Thousands OnesHM TM M HTh TTh Th H T U

Tellthemtowrite100000intheplacevaluechart.

iv22 1NumberandArithmeticOperations1

Askthestudentstoguessthebiggest6-digitnumberi.e.999999.

Tellthemthatthenextnumberwillbe10000000whichisa7-digitnumber.Askthemtoputthisnumberintheplacevaluechart.

Highlightthatthenumberofdigitsmovesonecolumntowardstheleftincreasingthevalueofthenumber.

Similarly,make8-digitand9-digitnumbers.Explainusingtheplacevaluechartthata7-digitnumberisamillion,8-digitnumberistenmillion,and9-digitnumberishundredmillion.

EmphasisetheabbreviationsHM,TM,andM.

Givethemseveralexamplesof7,8,and9digitnumbersbywritingontheboardemphasisingtheplacevalueofamillion,tenmillions,andhundredmillions.

Tellthemthatorderingandcomparingof9-digitnumbersfollowsthesameruleasfor6-digitnumbers.

Pair work (10 mins)

Writesome7,8,and9digitnumbersontheboardwitharinged/bolddigit.Askthestudentstoidentifytheirvaluebywritingthemintheprovidedplacevaluechart.Forexample:2952602;

238902185;69732415;980053465.

Written Assignments (40 mins)Ex1aQ(7,11,13,and14)

Wrap up (5 mins)Givethemthree9-digitnumbersinwordsontheboardandaskthemtowritetheminnumeralsintheplacevaluechartgiventothem.

v231

FactorsandMultiples2


Learning CurveThestudentsalreadyknowaboutmultiplesof10.Heretheyfindoutthemultiplesofothernumbersandthencommonmultiplesbetweentwoormorenumbers.Thereafter,theyfindtheLCM.

Next,thestudentslistthefactorsofanumberandidentifythecommonfactorsbetweenthetwonumbers.InthiswaytheyidentifytheHCF.TomakethecalculationofLCMandHCFeasy,studentsareintroducedtoco-primenumbers,primenumbers,compositenumbers,andprimefactors.

Real-life ApplicationHCFisusedto:

• splitthingsintosmallersections.• equallydistribute2ormoresetsofitemsintotheirlargestgrouping.• figureouthowmanypeoplecanbeaccommodatedinaplace.• arrangeobjectsintorowsorcolumns.

LCMisusedto:

• tellaboutaneventthatisorwillberepeatingoverandover.• purchaseorgetmultipleitemsinordertohaveenough.• figureoutwhensomethingwillhappenagainatthesametime.

?OOPS

!

Frequently Made Mistakes• Studentsgetconfusedinidentifyingfactorsandmultiples.• Errorsduetonotrememberingthetimestables.

iv24 1FactorsandMultiples2

Summary of Key Facts• Anynumberwith0,2,4,6,8attheunitplaceisdivisibleby2.• Ifthedigitsofanynumberadduptoanumberwhichisdivisibleby3,thenthe

originalnumberisalsodivisibleby3.• Anynumberwith0or5attheunitplaceisdivisibleby5.• Anynumberwith0attheunitplaceisdivisibleby10.• Aprimenumberhasonlytwofactorsthatis1andthenumberitself.• Compositenumbershavemorethantwofactors.• Factorsofanumberarelimited.• Multiplesofanumberareunlimited.• Everynumberisafactorofitself.• 1isafactorofeverynumber.• Compositenumberscanalwaysbearrangedinexactrectangles.

Suggested ActivitiesPair Activity (20 mins)

Learning Outcome:Usedivisibilitytestsfor2,3,5,and10tonumbersupto5digits.


Instructions:

• Revisethedivisibilityruleswiththeclass.• Provideeachpairwithanactivitycard(samplegivenbelow).• Timetheactivityandannouncethewinningpair.

Usethedivisibilityrulestocheckwhethereachgivennumberisdivisibleby2,3,5or10.WriteYesorNo.

Number Divisibleby2 Divisibleby3 Divisibleby5 Divisibleby10

18702 YES YES NO NO

24900

15672

87534

42207

59345

v251 FactorsandMultiples 2

Individual Activity (20 mins)

Learning Outcome:DifferentiatebetweenPrimeandCompositeNumbers.


Instructions:

Providestudentswiththeactivitycardsandallowthemsometimetothinkaboutprimenumbersandcompositenumbers.Usetheirknowledgetosolvethequestionontheactivitycard.

Activity Card

Identifytheprimenumbersandaddthemtogether

1 3 7 11 15 19 23 6 10 16 18 25

Isthetotalaprimenumber?

Completetheequationsandcircletheanswersthatareprime.

1. 7×5= 2. 15+14= 3. 10+11=

4. 12+2= 5. 60–29= 6. 4× 8 =


Learning Outcome:FindtheHCFoftwoormorenumbers.

Resources: Cardsheetinlightcolours,Printer,Scissors

Instructions:

• Makeplentyofcut-outsofmulticolourflowersandplacetheminabasket.• Makecut-outsoflargeflowerpotsaccordingtothenumberofstudents.• Oneachflowerpot,pastedifferentnumbersthatyouwantyourstudentstofind

thefactorsof.Ensurethenumbersareboldandclearlyvisible.• Writethesamenumbersontheboard,askthestudentstofindallthefactorsfor

eachofthenumbersandwritethemovertheflowers.Theflowerswillbeputbackintothebasket.Ensurethenumbersareboldandclearlyvisible.

• Now,giveoneflowerpottoeachstudentandhavethemsorttheflowersfromthebasketwithcorrectfactorsofthenumberswrittenontheflowerpot.Askthemtopastetheflowersontheirflowerpots.

• Youcanmaketheactivitymorechallengingbysettingatimelimit.

iv26 1FactorsandMultiples2

Individual Activity (10 mins) Learning Outcome:Listthefactorsofa2-digitnumber.Resources:Worksheet

Instructions:Tofindallpossiblefactorsofanumber.

Howmanydifferentnumberscanyouusetodivide12?Writethembelow:

Lesson Plan Model Lesson PlanTopic: HCF

Duration80minutes

Specific Learning ObjectivesBytheendofthelessonstudentswillbeabletofindHighestCommonFactors.

Key Vocabularyfactors,HighestCommonFactors

ResourcesWorksheets,cut-outs,gluestick.

StrategyStarter:EngagementActivity(5mins)

Askmultiplicationfactsrandomlyinvolvingthewholeclass.Forexample,whatisfourtimesfive,whatis8×4,orwhatisproductof3and2?Thisactivitywillreinforcethevocabularyrelatedtomutiplicationandhelpthestudentsrecallthemultiplesandfactors.

Main Developmental Activity (20 mins)Write3numbersontheboard.Asstudentsarealreadyfamiliarwithfindingfactors,askthemtofindthefactorsofthegivennumbersintheirnotebooks.

v271 FactorsandMultiples 2

Factorsof6=1,2,3,and6 Factorsof4=1,2,and4 Factorsof8=1,2,4,and8

Askthemtopointoutthefactorswhicharecommontoallthegivennumbers.Tellthemthatthecommonfactorsof6,4,and8are1and2.Thereforethehighestcommonfactoris2.

Nowwritethree2-digitnumbersontheboardandaskthestudentstofindouttheHCFofthegivennumbers.Helpthemincalculatingthefactors.Thenaskthemtowritethehighestcommonfactoronthewhiteboardandshowittoyou.Foranywronganswerhelpthestudentinfindingthecorrectanswer.

Written Assignment (35 mins)Ex2e.Q(5and6).

Wrap up (10 mins)Askthestudents,whatwillbethecommonfactorofanythreeprimenumbers?

iv28 1

Fractions3


Learning CurveThestudentsalreadyknowhowtoaddandsubtract‘like’fractions.Theyhavelearntmixedfractions,equivalentfractions,orderingandcomparingoflikefractions.Here,studentswilldealwithunlikefractionsto:

• Identifyandcomparetwofractions.• arrangefractionsinascendinganddescendingorder.• simplifyfractionstothelowestform.• verifythecommutativeandassociativelawofadditionandmultiplicationoflike

fractions.Furthermore,theywillapplytheirknowledgetosolvereallifeproblemsinvolvingfractions.

Real-life ApplicationFractionplaysanimportantroleindailylife.

Fractionsareused:

• inbakingtotellhowmuchofaningredienttouse.• intellingtime;eachminuteisafractionofthehour.• todeterminediscountswhenthere’sasalegoingon.

Summary of Key Facts• Likefractionshavethesamedenominator.• Unlikefractionshavedifferentdenominators.• Equivalentfractionsareobtainedbymultiplyingordividingthenumeratorand

thedenominatorofafractionbythesamenumber(not0).• Afractionwiththenumerator1isknownasaunitfraction.

v291 Fractions 3

• Afractionhavingnumeratorsmallerthanthedenominatoriscalled aproperfraction.

• Afractionhavingnumeratorequaltoorgreaterthanthedenominator iscalledanimproperfraction.

• Amixedfractionismadeupofawholenumberandaproperfraction.• Fractionssatisfythecommutativeandassociativelawsofaddition.• Fractionssatisfythecommutativeandassociativelawsofmultiplication.• Whenafractionismultipliedbyitsreciprocal,theproductisalways1.• Twonumberswhoseproductis1arethereciprocalofeachother.• Dividingawholenumberbyafraction:changethedivisionsigntoa

multiplicationsignandtakethereciprocalofthefractionandsimplify.

Suggested ActivitiesIndividual Activity (15 mins)

Learning Outcome: Makingthefractions.

Resources:Worksheet

Instructions: Lookattheshapesandanswerthequestionsgivenbelow.

1. Howmanyshapesarethere?

2. Whatfractionoftheshapesaresquares?

3. Whatfractionoftheshapesarerectangles?

4. Whatfractionoftheshapesaretriangles?

5. Whatfractionoftheshapesisthecircle?

6. Whatfractionoftheshapesarenottriangles?

7. Whatfractiondothetrianglesandthecirclerepresentaltogether?

8. Whichshapehasthegreatestfraction?

9. Whichshapehasthesmallestfraction?

iv30 1Fractions3


Learning Outcome:Solvereallifeproblemsinvolvingfractions.

Resources:Worksheet

Instructions:Preparetheworksheetasgivenbelow.

Basimbuysanewcolouringbox.Hehasapictureof10pencils.Hecoloursthepencilsasgivenbelow:

First,hecolours1/10ofthepencils.(Colourthemred).

Then,hecolours1/3oftheremainingpencils.(Colourthemblue).

Lastly,hecolourshalfoftheremainingpencils.(Colourthemgreen).

Howmanypencilsareleftwithoutcolour?Writeyouranswerasafractionalso.


Learning Outcome:Add/Subtractfractionswithdifferentdenominators.

Resources:Worksheet/ActivityCards

Instructions:

• Reinforcetheconceptoffouroperationsinvolvingfractions.• Givethefollowingactivitycardtoeachstudent.

Activity Card

Manahillovesjam,andhasagreatjamrecipe.Sheuses¾kgofstrawberriesand12

kgofblueberriestomakeonebottleofjam.Howmanykilogramsdoessheneedaltogethertomakeonebottleofjam?Showyourworkingbelow:

Sabeenmade2316 litresoflemonadeforaparty.Attheendoftheparty,shehad

163

litresleft.Howmanylitresoflemonadewereconsumed?Showyourworkingbelow:

v311 Fractions 3


Learning Outcome:Multiply/dividefractionswithdifferentdenominators.

Resources:Worksheet/ActivityCards

Instructions:

• Reinforcetheconceptoffouroperationsonfractions.• Provideeachstudentwiththeactivitycardsgivenbelowandthengetitpeer

checkedintheend.

12½kgoftomatoesaredividedequallyinto4baskets.Howmanykilogramswillbefilledinonebasket?

Faiztravelled5¼kminoneday.Ifhetravelswiththesamespeed,howlongwillhetravelin8days?

Lesson Plan Model Lesson Plan

TopicFractions

Duration80(mins)

Specific Learning ObjectivesBytheendofthelesson,studentswillbeabletoarrangethegivenfractionsinascendingorder.

Key Vocabularyfraction,ascending,descending,order,like,andunlike

ResourcesWorksheet

StrategyStarter: Engagement Activity

Recall (5 mins)

Startyourlessonwitharecallofdifferenttypesoffractions.Discusstheruleofmakingequivalentfractions.Recallthatwhendenominatorsarethesame,thefractionwiththegreaternumeratorisgreater.

iv32 1Fractions3

Main Developmental Activity (20 mins)Reinforcetheconceptoflikeandunlikefractionsandreviserulesforcomparingunlikefractions.Writesomefractionsontheboard.Callafewstudentsonebyonetoconvertthemintoequivalentfractions.

Provideeachstudentwithoneoftheactivitycardsgivenbelow.Solvethefirstquestionontheboardinvolvingthestudents.Theywillsolvethesecondquestionontheirown.

Jasim’smothergavehimarecipeforcakemix,whichincluded58cupflour,13cup

peanuts,14cupalmonds,and

12cupraisins.Putthefractionsinorderfromsmallestto

greatestintheboxesbelow.

Smallest Greatest

Infifteenminutes,Ehsanwalked35km,Junaidwalked

34km,andKashifwalked

12km.

Comparethedistanceswalkedbyeachperson,writing‘more’or‘less’.

Ehsanwalked thanKashif.

Junaidwalked thanEhsan.

Kashifwalked thanJunaid

Whowalkedthefurthest,andwhowalkedtheshortestdistance?

walkedthemost. walkedtheleast.

Feedback (10 mins)

Worksheetswillbecheckedbypeers.Thenaskthestudentswhattheylearned?

Written Assignments (40 mins)Ex3aQ(6,7,and8).

Wrap up (5 mins)

Askthestudentswhichoneisthegreatestof13,16,and1

9.

1

v331

Decimals4


Learning CurveChildrenhaveusedthedecimalpointwhenworkingwithmoneyinClass3.Inthisbooktheylearnaboutdecimalplaces:tenths,hundredths,andthousandthsandcarryoutthefourbasicmathematicaloperationswithdecimalfractions.

Decimalshavelotsofimportanceinreallife,especiallywhenwepurchasecommoditiesordealwithinterestratesofcreditcardsorseetheaverageofanycricketer’sstrikingrateorrunrate.

?OOPS

!

Frequently Made Mistakes• Studentsdonotalignthedecimalpoint,whileaddingorsubtractingdecimals

numbers.• Theyforgettoputthedecimalpointwhileadding,subtracting,multiplying,or

dividingthenumbers.

Summary of Key Facts• Thedecimalpointisapointthatseparateswholenumbersfromdecimal

fractions.• Thenumberofdigitsafterthedecimalpointgivesthenumberofplacesina

decimalnumber.• Zerostotherightofadecimalpointafterthedigitshavenovalue.• Zerostotheleftofadecimalpointbeforethedigitshavenovalue.• Fractionscaneasilybeconvertedtodecimals,providedtheirdenominatorsare

multiplesof10or100.

iv34 1Decimals4

• Whenwechangeadecimalintoafraction,wemayneedtoreducethefractiontoitslowestterms.

• Whileaddingandsubtractingdecimalnumbers,keepthedecimalpointsinthesamecolumn.

• Whenwemultiplyadecimalnumberby10,100,1000,thevalueofthenumberincreasesby10times,100times,and1000times.

• Whenwedivideadecimalnumberby10,100,1000thevalueofthenumberdecreasesby10times,100times,and1000times.

Suggested Activities

Individual Activity (10 mins)Learning Outcome:Convertgivenfractionstodecimalsandviceversa.

Resources:Worksheet

Instruction:Preparethefollowingworksheetforthewholeclass.

Convertthefractionsintodecimalsanddecimalsintofractions.

Fraction Decimal

37100

0.0534710

1.4569100

12.2910

Pair Activity (20 mins)

Learning Outcome:Adddecimalsuptotwodecimalplaces.

Resources:Worksheet.

Instructions:

• Prepareworksheetslikethesamplegivenopposite.• Divideyourclassintopairs.• Giveeachpairaworksheettosolve.• Thepairtogetthemaximumcorrectanswerswins.• Thewinnerpairthendesignsaquestionorquestionsforthewholeclasstosolve

ontheirwhiteboards.

v351 Decimals 4

8.26+ 2.15

3.64+ 4.61

4.35+ 4.14

7.82+ 1.17

2.78+ 3.54

9.65+ 1.81

5.34+ 7.46

8.26+ 1.62

4.81+ 2.23


Learning Outcome:Convertfractionsintodecimals.

Resources:Worksheet.

Instructions:

• Makefractionnumbercardswithdenominators10,100,and1000.• Makerespectivedecimalnumbercards.• Putthefractionnumbercardsupsidedownonthetable.• Placethedecimalnumbercardsopenonthetable.• Askthestudentstotakeouttheirwhiteboards.• Callonestudentandtellhim/hertoturnuponecardandshowittotheclass.• Askhim/hertopickthedecimalnumbercardmatchingwiththefractionbutdoes

notshowtootherstudents.• Askrestofthestudentstowritetherespectivedecimalnumberontheir

whiteboardinthirtysecondsandholdthemuptoshowyou.• Thestudentwhopickedupthecardwillalsoshowhiscardtoyou.Youcanseeall

therightandwronganswersandprovideguidance.Samplecards:

Fractionnumbercard Decimalnumbercard

12100 0.12

iv36 1Decimals4


Learning Outcome:Convertdecimalstofractions

Resources:Worksheet

Instructions:

Eachdecimalontheleftisequaltooneofthefractionsontheright.Writetheletterofthefractiononthelinenexttothecorrespondingdecimal.

0.33 _______

0.25 _______

0.75 _______

0.15 _______

0.80 _______

0.66 _______

0.50 _______

0.45 _______

0.60 _______

0.85 _______

0.35 _______

0.48 _______

0.95 _______

0.88 _______

0.20 _______

0.70 _______

0.65 _______

0.55 _______

A. 1/2

B. 7/20

C. 7/10

D. 1/3

E. 1/5

F. 13/20

G. 1/4

H. 12/25

I. 9/20

J. 3/4

K. 22/25

L. 3/5

M. 3/20

N. 11/20

O. 4/5

P. 2/3

Q. 17/20

R. 19/20

v371 Decimals 4


TopicAdditionofdecimalsinvolvingreallifesituations.

Duration80minutes

Specific Learning ObjectivesBytheendofthelessonstudentswillbeablesolvereallifeproblemsinvolvingdecimalsuptotwodecimalplaces.

Key VocabularyDecimals

ResourcesActivityworksheet,gardeningtools(toys).

StrategyStarter: Engagement Activity (5 mins)

Askthestudentswheretheyfinddecimalsinreal-life?Startjottingdowntheirresponsesontheboard.Recallingtheirpreviousknowledge,proceedtothefollowingactivity.Theyhavedoneadditionsubtraction,andmultiplicationofdecimals.

Main Developmental Activity (20 mins)Youshouldhavealreadycollectedthetoygardeningtoolsasmentionedbelow.Tieawashinglineintheclassroomandhangthetoolswithpricetagsonthem.

Dividetheclassintogroupsof5.Providetheactivitysheettoeachgroupandaskthemtocheckthepriceonwashinglineandsolvethequestionsonthesheet.Ensureequalparticipationamongthestudents.

Getthesheetspeercheckedintheend.

1. PriceTagswillbeasfollows:

Rs9455.75 Rs60.70 Rs100.40 Rs350.23 Rs420.38 Rs420.38

Lawnmower

Grassseeds LargePot Spade HedgeTrimmer

Fork

iv38 1Decimals4

Lookatthepricetagsanswerthefollowingquestions.

1. Whatisthecostofaspade,aforkandsomegrassseeds?

2. HowmuchchangefromRs.1000wouldtherebeifyouboughtaspade?

3. Whatisthecostoftwopotsandahedgetrimmer?

4. Whatwouldbethetotalcostof5packetsofgrassseeds?WhatchangewouldtherebefromRs500?

5. Whatisthedifferenceinpricebetweenthelawnmowerandhedgetrimmer?

Feedback (10 mins)

Askeachgrouptosharethefindingsoftheiractivityworksheet.

Written Assignments (40 mins)Pg.103wordproblemQ.5,6,7,and8

Wrap up (5 mins)AskthestudentstoseethepriceoftheirMathsbookanddivideitby100.Whatwouldbetheresult?

1

v391

Measurements5

Suggested Time Frame

16-18periods

Learning CurveIntheirpreviousclassstudentshavealreadyworkedwithunitsoflength,mass/weight,andvolume/capacity.Theyarewellawareofaddition,subtractionandconversionofunitsoflength,massandcapacityinvolvingthesameunits.Thiswillleadthemtoadditionandsubtractionofdifferentunitsofmeasure.

Theyalsohaveknowledgeofhowtousea.m.andp.m.torecordtimeinanalogueanddigitalclocks.Thepreviousknowledgeofconversionofunitsoftimewillhelpthemtomakeconversionswithyears,months,weeks,days.Thisknowledgewillenablethemtosolvereallifeproblemsincludinglength,weight,capacity,andtime.

Real-life ApplicationTimeisaveryimportantfactorandwefinditinevitableinourdailylife,forexample,travelling,workingandotheractivitiesinvolvetime.

Length,weight,andcapacityareimportantindaytodaylife.Thelongandshortdistances(kmandm),weighinggrocery(kgandg),measuringliquid(landml)areunitsofmeasurementsusedinourdailylife.Theschedules,events,programmes,appointments,andmeetingsetc.involvetimeasthebasicfactor.

?OOPS

!

Frequently Made MistakesStudentsmakemistakeswhentheyaddorsubtracttheunitsofmeasures.Theyneedtobecarefultowritethesameunitsinonecolumnwhileaddingorsubtracting.

Summary of Key Facts• Thesystemofmeasurementbasedonmultiplesof10iscalledthemetricsystem.• Thestandardunitsofweightarekilograms(kg)andgrams(g).

iv40 1Measurements5

• Thestandardunitofvolume/capacityislitres(l)andmillilitres(ml). 1km=1000m

1kg=1000g

1l=1000ml


Pair Activity (30 mins)Learning Outcome:convertgramstokilograms.

Resources:worksheet

Instructions: TherearetwotrucksAandBwhichcaneachcarryatotalofthreecrates.Thetotalweightofthecratesmustbeexactly200kg.Theweightofindividualcrateisgivenbelow.

Thesetruckscaneachcarryatotalofthreecrates.Thetotalweightofthecratesmustbeexactly200kg.

Crate1:80590gm= kg

Crate2:60590gm= kg

Crate3:85170gm= kg

Crate4:62570gm= kg

Crate5:76840gm= kg

Crate6:34240gm= kg

Whichcratesdoeseachtrucktake?

Truck : A

kg+ kg+ kg=200kg

Truck : B

kg+ kg+ kg=200kg


Learning Outcome:Convertlitrestomillilitres.

Resources:Worksheet

Instructions:

Takethestudentsoutoftheclassroom.Arrange2bucketsofcapacity3litresandajugofcapacity300millilitres.Fillonebucketwithwater.Dividetheclassintotwogroups.Callonegroupandaskthemtofilltheemptybucketbytakingwaterfromthefilledbucketusingthejug.Instructthemtocountthenumberofjugstheytransferfromonebuckettotheother.

v411 Measurements 5

Nowrepeatthesameactivitywiththeothergroup.

Askthemhowmanyjugsofwaterwereusedtofilltheotherbucket.

Explaintothemthatten300mljugwillmake3litres.Givethemthefollowingworksheettosolveindividually.

Afullbucketholds3.8liters.Ajugholds200ml.Howmanyjugswillfillthebucket?

3.8litres=____________________ml

Numberofjugsneededtofillthebucket=___________

Individual Activity (20 mins)Learning Outcome:Toconvertunitsoftime.

Resources:Paper/Whiteboard,Pencil/Marker

Instructions:

Askeachstudenttowritetheiragein(theycanusepaperorwhiteboard).

• Years • Months• Weeks • Days

Individual/Pair Activity (20 mins)Learning Outcome:Addunitsoftime.

Resources:ActivitySheet

iv42 1Measurements5

Instructions:

Rabiawantstogotoheraunt’shouse.Sheistiminghowlongittakeshertoreachthere.Writethetimeintheboxastimepasses.

Telling Time Through Tick Tock

Rabiastartsherjourneyat 11.30 am .

Whattimeisitnow?

Ticktock5minuteshavepassed.

Ticktock8moreminuteshavegoneby.

Ticktock11moreminuteshavegoneby.



Ticktock17minuteshavegoneby.

Ticktock21moreminuteshavepassed.

Howmuchtimedidshetaketoreachheraunt'shouse?

______________hours______________minutes.


TopicConversionofunitsoflength

Duration80minutes

Specific Learning ObjectivesBytheendofthelessonstudentswillbeabletoconvertdifferentunitsoflength.

Key Vocabularyunitsoflengths,stairdiagram,km,m,cm,mm

ResourcesWorksheet

v431 Measurements 5

Strategy (5 mins)Starter: EngagementActivityAskthestudents:Whataretheunitsofmeasurementforlength?

Isitpossibletoconvertunitsofmeasurementoflength?Likekmintomormintokm.

Main Developmental ActivityTeacher’s Exposition (10 mins)Askthestudentsthefactorsofconversionfromkmtom,mtocm,andcmtomm.Reinforcethemultiplicationanddivisionofnumbersbypowersoftens,thenwriteafewconversionsumsontheboardandwritetheanswers,takingstudents’feedback.

Nowgivethemthefollowingactivitysheettoworkinpairsorindependently.

Individual Activity (25 mins)Instructions:

Jawad,Taha,andJibranwerecompetingtoseehowfartheycouldrunin10minutes.Theydidnotrecordtheirdistanceinthesameunits.Converttheunitsintootherunitsasasked.

Jawadran2kilometres= metres= centimetres.

Taharan3500metres= centimetresand millimetres.

Jibranran250000centimetres= millimetresand kilometres.

Intotal,togethertheyran kilometres= metres=centimetres

and millimetres.

Whoranthefarthest?____________________________________________

Written Assignments (30 mins)Ex5aQ.7and8

Wrap up (10 mins)Giveaquickrecapofthelessontotheclassanddiscussthefollowingtwoquestions

1. Whichisthebiggestunitoflengthandwhichisthesmallestunitoflength?

2. Wheredoweseetheseunitsoflengthinourdailylives?

iv44 1

6 PerimeterandArea


8-10periods

Learning CurveInpreviousclasses,studentshavecalculatedperimeterofasquareandarectangle(byusingtheformula).Now,theywillcalculatetheareaofsomesimpleshapesi.e.squareandrectangle.Theywillfurthermoveontocalculateareasofsomecompositeshapesalso.

Real-life ApplicationAreaandperimeterplayanimportantroleinourdailylives.Wheneverwewanttocoveraroom’sfloorwithtilesorcarpet,weneedtocalculatetheareaofthefloor.Similarly,inconstructionofanybuildingoranyinfrastructureweneedtoknowitsperimeterandarea.

?OOPS

!

Frequently Made MistakesStudentsoftenconfuseareawithperimeter.Areaandperimeterdealwith2-Dshapes,butsometimesstudentsassociateareaandperimeterwith3Dshapes,whichisnotcorrect.

Summary of Key Facts• Perimeteristheboundaryofaclosedshape.• Tofindtheperimeterofashape,startfromapointandaddallsidesclockwiseor

anticlock-wiseuntilyoureachthepointfromwhereyoustarted.• Theamountofsurfaceashapecoversiscalleditsarea.

v451 PerimeterandArea 6


Learning Outcome:Calculateareaandperimeterofasquare.

Resources:centimetregrid

Instructions:

• Eachstudentisprovidedwithacentimetergridandaskedtodrawasquare.(Usinganymeasurementsoftheirchoice).

• Studentsnowcalculatetheareaandperimeteroftheirdrawnsquares.• Compareyourresultwiththatofyourclassmates.• Findoutwhosesquarehasthelargestarea.

Group Activity (20 mins)Learning Outcome:Findtheareaandperimeterofcompositeshapes.

Resources:Colouredtape/maskingtape,measuringrulers,activitysheets.

Instructions:

• Makedifferentcompositeshapesonyourclassroom’sfloorusingtapeandmarkthemA,B,Candsoon.(Makeasmanyshapesasthenumberofgroupsinyourclass).

• Dividetheclassintogroupsof4.• WriteA,B,Cetc.onchits,foldthemandaskeachgrouptopickonechit.• Eachgroupwillcalculatetheareaandperimeterofthecompositeshape

mentionedontheirchit.• Twogroupscanbegiventhesameshapeaswellsothattheycancomparetheir

answersintheend.

Individual Activity (20 mins)Learning Outcome:Calculateareaandperimeterofarectangle

Resources:Worksheet

Instructions:

Yourschool'sfootballAssociationjustbuiltanewpracticefieldthatis100metreslongand67metreswide.Whatistheareaandperimeterofthenewfield?

Area=

Perimeter=

iv46 1PerimeterandArea6


TopicAreaandperimeter

Duration80minutes

Specific Learning ObjectivesBytheendofthelessonstudentswillbeabletocalculateareaandperimeterofarectangle.Theywillalsofindtheunknownlengthorbreadthoftherectangle.

Key VocabularyArea,perimeter,rectangle,length,andbreadth

Resources Whiteboards,rulers,measuringtape,andactivitysheets.

StrategyStarter: Engagement Activity (5 mins)Recall: Writedownthefollowingquestionsontheboard.

1. Whatistheformulafortheareaofasquareandarectangle?

2. Whatistheformulafortheperimeterofasquareandarectangle?

Studentswillwritetheanswersoftheabovequestionsonthewhiteboards.Askstudentstoraisetheirwhiteboardsothatyoucanseetheirwork.

Main Developmental ActivityPair Activity (20 mins)Instructions:• Divideyourclassintopairsandaskthemtowalkaroundintheclassandfindone

rectangularobject.• Itcanbetheirwhiteboard,classdoor,thesoftboard,theirlunchbox,class

windowetc.• Eachpairwillthenmeasurethesidesoftheirchosenrectangularobjectand

calculateitsareaandperimeterinthegivenactivitysheet.

v471 PerimeterandArea 6

Activity sheet:

Shape l=length b=breadth perimeter(P) area(A)

Nowtellthestudentsthattheycanfindtheunknownlengthorbreadthofarectanglebyusingtheformula.Tellthemthatifareaandlengthisgiven,breadthcanbefoundbydividingtheareabythelength.Similarly,lengthcanbefoundbydividingtheareabythebreadth.

Givethemsomeexamplesontheboard.

Feedback (10 mins)

Takefeedbackfromeachpairabouttheirfindingsandsharewiththewholeclass.

Written Assignments (40 mins)Ex6Q14,15and18

Wrap up (5 mins)Haveashortdiscussionontheimportanceofareaandperimeterofsimpleshapes(squareandrectangle)inpracticallife.

iv48 1

7 Geometry


10-12periods

Learning CurveStudentsalreadyknow2Dand3Dshapes.Theyhavedealtwithtrianglesandquadrilaterals.Theyknowwhatparallellinesareandtheyhavealsoworkedwithlinesegments.Here,theylearnhowtodrawdifferenttypesoflineswhichincludestraight,curved,vertical,andparallellines.Theywilllearntodrawanglesusingprotractor.Theywillconstructsquaresandrectangleswithsidesofgivenmeasures.Theywilllearncentre,radius,diameter,andcircumferenceofacifcle.

Real-life Application• Theglobalpositioningsystemusesgeometricalprinciplestolocateaposition,

navigatefromonelocationtoanother,andtrackingobjectsorpersonalmovements.

• Geometryhelpsintheaccuratecalculationofphysicaldistances.• Geometryisusedbyastronomerstomapthedistancebetweenplanetsandstars.• Geometryalsohelpsincomputeraideddesigns;itentailslines,curves,and

angles.• Geometryisusedindesigningbuildings,walls,anddoors.• Videogamesalsoincludetheconceptsofgeometry.

?OOPS

!

Frequently Made Mistakes

Studentsusuallymakemistakeswhentheymeasureangleswithaprotractor.

Summary of Key Facts• Alineisasetofpoints,placedtogether.• Alinesegmentistheshortestdistancebetweentwopoints.

v491 Geometry 7

• Arayhasoneendpointonly,andgoesonandon,inthedirectionofthearrow.• Thereare5typesofangles:

Rightangle

Acuteangle

Obtuseangle

Straightangle

Reflexangle

• Acirclehasacompleteturnof360º.• Halfofacircleiscalledasemi-circle.• Thelinejoiningtwopointsonthecircumferenceandpassingthroughthecentre

ofacircleiscalledthediameter.• Halfofthediameteriscalledtheradius.• Therearemanyspecialkindsofquadrilaterals,forexample,asquare,arectangle,

aparallelogram,atrapezium,andarhombus.


Learning Outcome:Identifydifferentkindsofangles,linesegments,parallelandnon-parallellines.


Instructions:

• Distributetheactivitysheettoeachstudent.• Haveashortdiscussionabouttheanglesandlineswiththewholeclass.• Askthemtosolvetheworksheet.

Lookatthehouseandanswerthequestions.

1. IdentifyalinesegmentinthegivenfigureandmarkitAB.

2. Howmanyrayscanyoufindinthepicturegivenabove?

3. FindapairofparallellinesandmarkthemCDandEF.

4. Findapairofnon-parallellinesandmarkthem GHandIJ.

5. Calculatethemeasureofthefollowingangles:

∠ X =

∠Y=

∠ Z =

x y

z

iv50 1Geometry7

Individual Activity (20 mins)Learning Outcome:Drawingangles.Resources:Protractor,ActivitySheets,MysteryBox,GeometryBox,Paperchits.

Instructions:

• Distributeblankpaperchitstoallstudents.• Askthestudentstowriteonemeasureoftheirchoiceforeach,anacuteandan

obtuseangle,onthepapergiventothem.(Thiswillhelptheteachertoassessifthestudentsknowwhatacuteandobtuseanglesare).

• Nowaskthestudentstofoldthechitsandputthemintheemptymysterybox.• Shufflethechitsanddistributeemptyactivitysheetstoallstudents.• Askeachstudenttodrawachitfromthemysterybox.• Eachstudentwilldrawanacuteandanobtuseangleobtainedfromthemystery

box,intheiractivitysheets.• Spotcheckthemeasuresoftheanglesforaccuracy.

Individual Activity (25 mins)Learning Outcome:Constructasquareandarectanglewithsidesgiven,usingprotractorandsetsquares.Resources:Protractor,setsquares,mysterybox,questionchits,activitysheet.Instructions:• Makeamysteryboxandputchitsinitwithquestionswrittenonthemsuchas: Drawasquarewithsidesoflength4.5cm Drawarectanglewithawidthof2cmandalengthof6cmetc.• Alloweachstudenttodrawachitfromtheboxandperformthetaskonthe

givenactivitysheet.• Studentscanlaterpeerchecktheactivitysheetsunderteacher’ssupervision.

Individual Activity (15 mins)Learning Outcome:Identifycentre,radii,anddiametersofagivencircle.

Resources:ActivitySheetsInstructions:• Haveashortdiscussionaboutthepartsofacirclewiththewholeclass.• Distributetheactivitysheets.• Explainthetasktothem.

Activity Sheet

Lookthecircleandwritetheanswers.

1. Namethecentreofthecircle.

2. Howmanyradiiareshowninthegivencircle?

3. Namethediametersshowninthecircle. A

B

C

D E

F

v511 Geometry 7

Group Activity (20 mins)

Learning Outcome:Identificationofangles.


Instructions:

• Dividetheclassinto4groups.• Distributeactivitysheetstothestudentsandexplainthetask.• Takestudentstoschoolgroundandaskthemtospend15minutestherelooking

fordifferentkindsofanglesaroundthem.• Askthemtonotedowntheirfindingsintheactivitysheet.• Givethemexamplese.g.theymayspotatreebranchmakinganobtuseoracute

anglewiththetreetrunketc.• Tellthemtoidentifythekindofangleonlythattheobjectismakingandhence

theydonotneedtomeasureit.

Activity Sheet

Object Type of Angle

Individual Activity (15 mins)Learning Outcome:Drawingofparallelandperpendicularlines.

Resources:ActivitySheet.

Instructions:

• Haveashortdiscussionaboutparallelandperpendicularlineswiththestudents.• Drawfewlinesontheboardandaskthemtoidentify.• Givethemtheactivitysheetandexplainthetask.

Activity Sheet

Identifytheparallelandperpendicularlinesandwritetheirnamesinthespacegiven.

iv52 1Geometry7


Topic• Identificationofstraightline,linesegment,ray,andangle.• Constructionandmeasurementofangles.

Duration80minutes

Specific Learning ObjectivesBytheendofthelessonstudentsshouldbeableto:

• differentiatebetweenalinesegmentandaray.• constructanacuteangle.

Key Vocabularystraightline,linesegment,ray,angle,protractor

ResourcesBiggeometrybox,JapanesefanandA4sizesheet.

StrategyStarter:EngagementActivity(10mins)

DrawtwolinesABandCDofdifferentlengthontheboard.

Startyourlessonbygivingachallengetoyourstudents.Askthemiftheycantellwithoutmeasuringwhichlineislonger,ABorCD?

A B C D

Main Developmental Activity Theyalreadyknowwhatalineis.Nowintroducearayandlinesegment.Tellthemthespecificpointswhichdifferentiatebetweenalinesegmentandaray.Drawdifferentdiagramsontheboardshowingthemlinesegmentsandrays.

TakeaJapanesefantointroducethelessononangles.Turnonearmofthefansothatthegapbetweenthetwoarmsincreases.Tellthemangleisthespecialwordusedtodescribetheamountofturnbetweenthetwoarmsanditssymbolisº.Theunittomeasureanglesiscalleddegreeandiswrittenas°.

Nowwidenthegapsbetweenthetwoarmsofthefan,namingthedifferentangles:

1. Whenonearmishorizontallystraightandtheotherisverticallystraight,arightangleisformed.

2. Whentheangleissmallerthanarightangle,itiscalledanacuteangle.

v531 Geometry 7

3. Whenanangleisbiggerthanarightangle,butnotbigenoughtoformastraightline,itiscalledanobtuseangle.

4. Whentheanglegoesbeyondthestraightline,itiscalledareflexangle.

• Usewoodengeometryboxanddemonstrateontheboard,howtoconstructandmeasuretheangle.

• DistributewhiteA4sizepapertoindividualstudentsandaskthemtofollowyourdemonstration.

Inordertoconstructanangle,drawahorizontal,straightlineABfirst.PlacetheprotractorinsuchawaythatthemiddleofitsbottomlineisexactlyonA.Calloutanumber,say70.Putapoint,sayC,ontheboard,andseethenumber70ontheprotractorandthenjointhepointsAandCtomakethearmACoftheresultingangle.Themeasureofthisangleis70°andwewrite,∠CAB=70°.

70º

AB

C

Thereafter,theteacherdemonstratesthatwhenthefanmakesacompleteturn,acircleisconstructedandthecentralangleofacircleis360°.

Written Assignments (20 mins)Ex7bQ.11,12,13,14

Wrap up (10 mins)Endyourlessonbyaskingstudentsiftheclockshows3o'clock,whichangleisit?Andifitshowsquarterpast1,thenwhichangleisit?

1

iv54 1

8 InformationHandling


4-6periods

Learning CurveInClass3,childrenhaveworkedwithpictographs,theyknowhowtoreadandinterpretit.Here,theyreadandinterpretbarandlinegraphs.

Real-life ApplicationBardiagramsandlinegraphsareusefulwhileinterpretingrainfallrecords,peoplepreferences,costpriceanalysis,temperature,andcensus.

?OOPS

!

Frequently Made Mistakes

Studentsoftenmakemistakeswhiledrawingbargraphs,theyleavenospacebetweenthebarsandconfusebargraphswithhistogram.

Summary of Key Facts• Abargraphorbarchartisagraphicalpresentationofdatausingbarsof

differentheightsorlengths.• Bargraphscanbedrawnverticallyorhorizontally.• linegraphsareusefulwhenwewanttomeasuresomethingwhichisgradually

changing.


Pair Work ActivityLearning Outcome: Readandinterpretapicturegraph.

Resources: Worksheet

v551 InformationHandling 8

Instructions:Thisisapicturegraphof2Dand3Dlikedbythestudentsofclass4.

Usetheinformationfromthegraphtoanswerthequestionsgivenbelow:

2D

and

3D

shapes

Rectangle

Star

Cone

Cube

Circle

Triangle

1. Howmanystudentsliketriangles?

2. Howmanystudentslikerectangles?

3. Howmanystudentslikecircle?

4. Domorestudentslikecubesorcones?

5. Whichisthemostpopularshape?

6. Howmanystudentslikestars?

Individual WorkLearning Outcome: Readandinterpretalinegraph.

Resources: Worksheet.

Instructions:Ali’sfamilyhavekepttrackofhisheight,oppositeisthelinegraphshowinghowtallhehasgrownovertheyears.Usethegraphtoanswerthequestions.

iv56 1InformationHandling8

0

10

20

Birth 2 years

Ali's age

Hei

ght i

n in

ches

4 years 6 years 8 years 10 years

30

40

50

60

70

1) HowtallwasAliwhenhewas2yearsold?

2) HowmuchhasAligrownfromthetimehewasborntowhenhewas4yearsold?

3) HowoldwasAliwhenhewas50inchestall?

4) Howmanyinchesdidhisheightincreasefromwhenhewas8yearsoldtowhen

hebecame10yearsold?

5) Whenwashisgrowththefastest?


Topic Bargraphs

Duration80minutes

Specific Learning ObjectivesBytheendofthelessonstudentsshouldbeabletoreadandinterpretbargraphs.

Key Vocabularydata,information,andbargraphorbardiagrams

ResourcesChartpaperwithabargraphdrawnonit.

v571 InformationHandling 8

StrategyStarter: Engagement Activity (5 mins)Displayachartpapershowingthebargraphofstudentsandtheirfavouritesubjects.Askthestudentswhethertheyunderstandwhatinformationisgiveninthisbargraph?Cantheythinkofthemostfavouriteandleastfavouritesubjects?Helpthemoutifthereisanydifficultyorconfusion.

Main Developmental Activity (10 mins)Conductawholeclassdiscussionrecallingthepriorknowledgeofdatahandling.

Pair Work (10 mins)

Thesamechartpaperwillremainondisplay,askthefollowingquestionsandtrytoinvolveeachandeverystudentandmakethemclearoneachandeverypoint.

1. Whichsubjectisthemostpopularamongstudents?Whydoyouthinkso?

2. Whichsubjectisleastpopularamongstudents?Whydoyouthinkso?

3. Howmanystudentsarethereintotal?

4. HowmanystudentslikedthesubjectEnglish?

5. HowmanystudentslikedthesubjectUrdu?

Studentsofgrade4wereaskedaboutwhattheywanttobewhentheygrowup.Theirresponsesarerecordedinthegivenbargraph.Readthegraphcarefullyandanswerthequestionsgivenbelow:

9

8

7

6

5

4

3

2

1

0Doctor Engineer

Numberofstudents

Sportsman

Occupations

Teacher Scientist

Howmanystudentswanttobescientists?

Howmanystudentshavechosenengineeringastheirfuturecareer?

Howmanystudentsareinterestedinsports?

iv58 1InformationHandling8

Howmanystudentswanttotakeupthesamecareerastheirteachers?

Whichtwooccupationshavethesamenumberofvotes?

Howmanystudentswerepresentonthedayofthissurvey?

Written Assignments (30 mins)Ex8Q.1,2.

Wrap up (5 mins)Askstudentswheretheyapplybargraphsintheirdailylife?

v591

Notes

iv60 1

Notes

teaching guide - oup.com.pk

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