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={.}

2 } Countingnumb ersN0={..} IntegersZ+={..}Z-={..} Rationalnumb ersQ={..} 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.

3 ;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.

4 ( )Indep endencedetermineevenando ddnum-b ers.( ) [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).

5 {2,3,5,7,..}Twofactors:1anditself{4,6,8, 9,..}Morethan2factors 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.

6 {21,25,27,33,35,39,45,49}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? 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?

7 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(..) 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 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=..57=..95=..BCD=..and LCM=..AssessmentAvailableforfreeatConnex ions< > :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.

9 ( )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.<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?

10 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.[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.