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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:
v111 TeachingMathematicsatPrimaryLevel
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.
iv12 1TeachingMathematicsatPrimaryLevel
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.
v131 TeachingMathematicsatPrimaryLevel
• 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.
iv14 1TeachingMathematicsatPrimaryLevel
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
Suggested Time Frame12-14periods
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.
Resources:ActivityCards
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.
Resources:ActivityCards
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 =
Individual Activity (25 mins)
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
Suggested Time Frame12-14periods
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
Individual Activity (20 mins)
Learning Outcome:Solvereallifeproblemsinvolvingfractions.
Resources:Worksheet
Instructions:Preparetheworksheetasgivenbelow.
Basimbuysanewcolouringbox.Hehasapictureof10pencils.Hecoloursthepencilsasgivenbelow:
First,hecolours1/10ofthepencils.(Colourthemred).
Then,hecolours1/3oftheremainingpencils.(Colourthemblue).
Lastly,hecolourshalfoftheremainingpencils.(Colourthemgreen).
Howmanypencilsareleftwithoutcolour?Writeyouranswerasafractionalso.
Individual Activity (20 mins)
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
Individual Activity (20 mins)
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
Suggested Time Frame8-10periods
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
Individual Activity (20 mins)
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
Individual Activity (25 mins)
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
Lesson Plan Model Lesson Plan
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
Suggested Activities
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
Individual Activity (20 mins)
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.
Ticktock3minuteshavepassed.
Ticktock22minuteshavepassed.
Ticktock17minuteshavegoneby.
Ticktock21moreminuteshavepassed.
Howmuchtimedidshetaketoreachheraunt'shouse?
______________hours______________minutes.
Lesson Plan Model Lesson Plan
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
Suggested Time Frame
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
Suggested ActivitiesIndividual Activity (20 mins)
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
Lesson Plan Model Lesson Plan
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
Suggested Time Frame
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.
Suggested ActivitiesIndividual Activity (20 mins)
Learning Outcome:Identifydifferentkindsofangles,linesegments,parallelandnon-parallellines.
Resources:ActivitySheet
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.
Resources:ActivitySheet
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
Lesson Plan Model Lesson Plan
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
Suggested Time Frame
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.
Suggested Activities
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?
Lesson Plan Model Lesson Plan
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