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Mathematics Grade 8 - CNX

Mathematics Grade 8By:Siyavula UploadersMathematics Grade 8By:Siyavula UploadersOnline:< >C O N N E X I O N SRice University, Houston, ( ).Collectionstructurerevised:Septemb er11,2009 PDFgenerated:Octob er28,2012 Forcopyrightandattributioninformationfor themo dulescontainedinthiscollection, erentkindsofnumb ers.. ,squarero otsandcub ero ots.. erentiateb etweenrationalandirrationalnumb ers.. erenttyp esoftriangles..1544(Untitled)Attribution s.. 162ivAvailableforfreeatConnexions< >Chapter 1 Term erentkindsofnumb (Naturalandwholenumb ers) Discoverthenumb :Di erentkindsofnumb ersProvideanexampleofeachofthefollowingn umb ers: Naturalnumb ersN={..} Countingnumb ersN0={..} IntegersZ+={..}Z-={..} Rationalnumb ersQ={.}

9 Determine all odd compound numbers between 16 and 50. 10 Write down all the factors of 50 that are prime numbers. 11. Write down all the factors of 50 that are compound numbers. 12. Explain: Cube numbers. Write down the rst 6 cube numbers. 13. Explain : Square numbers. Write down the rst 10 square numbers. HOMEWORK ASSIGNMENT 1 1.

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Transcription of Mathematics Grade 8 - CNX

1 Mathematics Grade 8By:Siyavula UploadersMathematics Grade 8By:Siyavula UploadersOnline:< >C O N N E X I O N SRice University, Houston, ( ).Collectionstructurerevised:Septemb er11,2009 PDFgenerated:Octob er28,2012 Forcopyrightandattributioninformationfor themo dulescontainedinthiscollection, erentkindsofnumb ers.. ,squarero otsandcub ero ots.. erentiateb etweenrationalandirrationalnumb ers.. erenttyp esoftriangles..1544(Untitled)Attribution s.. 162ivAvailableforfreeatConnexions< >Chapter 1 Term erentkindsofnumb (Naturalandwholenumb ers) Discoverthenumb :Di erentkindsofnumb ersProvideanexampleofeachofthefollowingn umb ers: Naturalnumb ersN={..} Countingnumb ersN0={..} IntegersZ+={..}Z-={..} Rationalnumb ersQ={.}

2 } Irrationalnumb ersQ'={..} Realnumb ersR={..} ers1 Thiscontentisavailableonlineat< >.AvailableforfreeatConnexions< > ers={..}Comp oundnumb ers={..}De nition:..De nition:.. ers+Comp oundnumb ers=Naturalnumb ,selectanumb ers( ) ersando ddnumb ers:AvailableforfreeatConnexions< >3 Howdoyoudeterminethefactorsofanumb er?Lo {1;2;3;4;6;8;12;24}1x24;2x12;3x8; ersb ddcomp oundnumb ersb oundnumb :Cub enumb rst6cub enumb :Squarenumb rst10squarenumb oundnumb {0;1;2;3;4;..;36} rsttwocomp oundnumb ersthatarenotprimenumb ers-9/3;7/0;0;3;-9;16;21/3 ers? ers? ers< ers< rstfoursquarenumb :bymyself: [U+F04A][U+F04B][U+F04C]1234 CriticalOut-comes1234continuedonnextpageAvailableforfreeatConnexions< > esofnum-b ers;( )Criticalandcre-ativethink-ingde neprimenum-b ers;( )Collab oratingde necom-p oundnum-b ers;( )Organisingenman-ag-ingapplydi-vis-i-bil -ityrules;( )Pro cessingofin-for-ma-tioncontinuedonnextpa geAvailableforfreeatConnexions< >5determinemul-ti-plesofanum-b er;( )Communicationdeterminefac-torsofanum-b er;( )Problemsolv-ingdetermineprimenum-b ersandprimefac-tors;( )Indep endencedetermineevenando ddnum-b ers.

3 ( ) [U+F04A]go o d[U+F04B]average[U+F04C]notsogo o dCommentsbythelearner:Myplanofaction:Mym arks:continuedonnextpageAvailableforfree atConnexions< > edwiththestandardofmywork.<Date:Iamsatis :Ihaveworkedhard, :Ididnotgivemyb est.> :Commentsbyteacher:Signature:Date:Signat ure: < > (LOs)LO1 Numb ers,Op erationsandRelationshipsThelearnerwillb eabletorecognise,describ eandrepresentnum-b ersandtheirrelationships,andtocount,esti mate,calculateandcheckwithcomp etenceandcon (ASs) esandillustratesthehistoricalandcultural developmentofnumb ers; ,classi esandrepresentsthefollowingnumb ersinordertodescrib erswritteninexp onentform;includingsquaresandcub esofnaturalnumb ersandtheirsquarero otsandcub ero ots; ; ersinthecontextofmeasurement( ero otsonnon-p erfectsquaresandcub es); {2,3,5,7.}

4 }Twofactors:1anditself{4,6,8,9,..}Moreth an2factors Ownchoice:Endsonevennumb ers Sumofallthenumb ers 3 Lastnumb ers 4 4=21 Endson0/5 Divisibleby2and3 Last3numb ers 8 8=90 Addallthenumb ers 9 Endson0 +8=10,10 10=00 11=0,4+6= ;3;4;5;6;7;8;9;10;11 Counton, 's:Numb er 3 Numb erthatcandivideintoanothernumb er Numb erwith2factors:1anditself Primenumb erthatcandivideintoanothernumb er Even:(Endsonevennumb ers)[divisibleby2]Uneven:(Notdivisibleby 2) {1,2,3,4,6,8,12,16,24,48}Availableforfre eatConnexions< > {24,30,36,42,48,54}8.{19,23,29,31,37,41, 43,47,53,59,61,67,71,73}9.{21,25,27,33,3 5,39,45,49}10.{2,5}11.{10,25,50} (numb er)3:1,8,27,64,125, (numb er)2:1,4,9,16,25,36,49,64,81, :,b6=0(Decimal:recurringorends) :Numb erwithfactors:1anditself :Numb erwithmorethantwofactors :Primenumb erthatcandivideontoanumb er :4,6 :1,9,15,21,25,27,33,35 :6,12,18,24,30,36 :1,2,3,4,6,12 :2,3 :1,2,3,4,6,9,12,18,36 :-,0,3,-9,16 :-,0,3-9,16,2 : :1,2,3,4 :2,3,5,7 :12,24,36,48 :1,4,9, ,squarero otsandcub ero , Howdoyouwriteanumb erasthepro ductofitsprimefactors?

5 Andhowdoyouwriteitinexp onentnotation?2 Thiscontentisavailableonlineat< >.AvailableforfreeatConnexions< > :Write24asthepro ductofitsprimefactors(rememb erthatprimefactorsareusedasdivisorsonly) {2;3}24aspro ductofitsprimefactors:24=2x2x2x324=23x3( exp onentialnotation) Nowexpresseachofthefollowingasthepro ductoftheirprimefactors(exp onentialnotation) otsandcub ero ots Howdoyoudeterminethesquarero ot( )orcub ero ot(3 )ofanumb erwiththehelpofprimefactors? Doyourecallthis?AvailableforfreeatConnex ions< > Determine: 324 Step1:breakdownintoprimefactorsStep2:wri teaspro ductofprimefactors(inexp onentialnotation)Step3: 324means(324) (obtainhalfofeachexp onent) : 324=(22x34) =21x32=2x9=18(324isap erfectsquare,b ecause18x18=324) Rememb er: means(.)

6 And3 means(..)1/33 8x12= 2x12 3= :(i) 10241024 AvailableforfreeatConnexions< > (ii)3 :a)(2x3)2=b)3x82=c)3 1=d) 1=e)( 2)2=f )then( 17)2=g)(3+4)3+14=h) 36+ 9=i) 36+64=j)3 27+3 1=k)(3 27)3=l) 64x12= 1296 AvailableforfreeatConnexions< > 53a6b15= 8 125 27= 64+(3 64)3= (3 8)3= 169= (6 + 4 12)2= 6 18 12= ( 9)2= (6 + 3)2 33= (discussitinyourgroup) LCM:Explainitwiththehelpofanexample ers?8;12;20 Step1:Writeeachnumb erasthepro ductofitsprimefactors.(Preferablynotinex p onentialnotation)8=2x2x212=2x2x320=2x2x5 Step2:FirstdeterminetheBCD(thenumb er/so ccurringineachofthethree)Suggestion:Ifth e2o ccursineachofthethree,circlethe2ineachnu mb erandwriteitdownonce), < >13 Step3 ndthenumb erthato ccursintwoofthenumb ersandwriteitdown, nallywritingwhatisleftover)LCM=4x2x3x5= :38;57;95 Calculateithere:38=.

7 57=..95=..BCD=..andLCM=..AssessmentAvail ableforfreeatConnexions< > :bymyself: [U+F04A][U+F04B][U+F04C]1234 CriticalOut-comes1234determineprimefac-t orsofanum-b er;( )Criticalandcre-ativethink-ingexpressanu m-b erasthepro d-uctofitsprimefac-tors;( ; )Collab oratingexpressprimefac-torsinex-p o-nentno-ta-tion;( )Organisingenman-ag-ingcontinuedonnextpa geAvailableforfreeatConnexions< >15determinethesquarero otofanum-b er;( )Pro cessingofin-for-ma-tiondeterminethecub ero otofanum-b er.( )Communicationdetermine/de nethesmall-estcom-monfac-tor(LCM);( )Problemsolv-ingdetermine/de nethebiggestcom-mondi-vider(BCD).( )Indep endencecontinuedonnextpageAvailableforfr eeatConnexions< > [U+F04A]go o d[U+F04B]average[U+F04C]notsogo o dCommentsbythelearner:Myplanofaction:Mym arks:Iamverysatis edwiththestandardofmywork.

8 <Date:Iamsatis :Ihaveworkedhard, :Ididnotgivemyb est.> :Commentsbyteacher:Signature:Date:Signat ure: :(Numb erSystems) :AvailableforfreeatConnexions< > 100 36[1] 2549[1] 26315[2] 9( 9 + 16)[3] [1] a=4,a=[1] a=5,a=[1][10] , [2] ductofitsprimefactors[3] 324[2] erfectsquare?Giveareasonforyouranswer.[2 ][9] 81[1] 364[2] 32+ 42[2] 16x16[2] , [2] 27[2][11]TutorialIdemonstrateknowl- ers(N)andwholenumb ers(N0) < > cationofthedi erenttyp esofnumb ers; oundnumb ers; ; er; er; ers; ; erasthepro ductofitsprimefactors; ; onentnotation; ddnumb ers; otsofanumb er; < > ero otsofanum-b er; (LCM); (BCD). ' :Commentsbyteacher:Date:Outof:Learner:Si gnature: :Date:Test1:(Numb erSystems) ersb etween20and30.

9 [2] [2] oundnumb ers[2][6] erfor*sothatthefollowingnumb erisdivisibleby3.(Giveareasonforyouransw er)1213156*3[2]AvailableforfreeatConnexi ons< > 36+64[2] 29[2] 279[3] 0,04[2] 100 36[2] 8 27[2] ( 9)2[2] 64 1[2][17] 1728usingprimefactors,withoutusingacalcu lator.[5] (n)meansnnwhatisthevalueof((2))?[2]Enric hmentExerciseforthequicklearner(Learning unit1)Eachquestionhas vep (X) otho dd,whichofthefollowingwillb eeven?a)npb)n2p+2c)n+p+1d)2n+3p+5e)2n+ :4 )R16b)R20c)R22,50d)R24,50e) gure? )8b)12c)14d)16e) ,eachanglewillb )15 b)30 c)120 d)150 e)165 < >21a)1b)3c)6d)7e) gureb ,theareaofthe )12b)20c)24d)36e)imp (LOs)LO1 Numb ers,Op erationsandRelationshipsThelearnerwillb eabletorecognise,describ eandrepresentnum-b ersandtheirrelationships,andtocount,esti mate,calculateandcheckwithcomp etenceandcon (ASs) esandillustratesthehistoricalandcultural developmentofnumb ers; ,classi esandrepresentsthefollowingnumb ersinordertodescrib erswritteninexp onentform;includingsquaresandcub esofnaturalnumb ersandtheirsquarero otsandcub ero ots; ; ersinthecontextofmeasurement( ero otsonnon-p erfectsquaresandcub es).

10 ContinuedonnextpageAvailableforfreeatCon nexions< > ers(includingdivisionwithfractionsanddec imals); 3;60=22 3 5;450=2x32x52;P48={2,3};P60={2,3,5};P450 ={2,3,5}; )==(210)=25=32ii)==(23x53)=2x5= )36b)192c)1d)1e)2f )17g)63h)9i)10j)4k)27l) (212)=24= (24x34)=2x3= , :4+64=68 :2(8)=16 ()2= :2(9)=18 :9-27=-18 AvailableforfreeatConnexions< > :LowestcommonmultipleLCMof2,6,12:24 HCF:HighestcommonfactorHCFof24and48 ,5 :3(3+4)=21 :81 :3+2+4=99 3=3 Yes! :324= :=(22x34)=2x32= :Yes!18x18=324/182=324 :9 :62= : 9 +16= 25= :4x8 :43=64 (10 2)10=144 (oneangle)(1440 240) 8=150(d) (2x)2+x2=364x2+x2=365x2=36 TEST1 :23,29 AvailableforfreeatConnexions< > :1,2,3,6,12 :4,6,122.:*21+2+1+3+1+5+6+3= 100= 259=53= 4100=210=0,2 64=8 :2x3=6 :9 :4 1= 26x33=22x3=4x3=125.


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