7 = 2 + 5 - EduGAINS

edugains.ca

7 = 2 + 5 - EduGAINS

smwgrImfipaF leI not......................................................................................................................2mYN afpxy bwcy dI iswiKaf ivwc ikvyN mwdd kr skdf/skdI hF?.......................................2sfzy bwicaF dy gixq iswKx dI Xogqf ivwc XkIn jrUrI ikAuN hY?...................................3islybl (curriculum)nfl kI sbMD hn?...................................................................4kuwJ idlpRcfvy vfly pirvfrk iswKx dy qjurb.........................................................................5nMbr qF hr QF hn!.....................................................................................................5ikMnf AuWcf? ikMnf nIvF? ikMnf? ikMnf Gwt?................................................................. 15quhfzf Aus AuWqy kI kox hY?........................................................................................ 20vfr vfr duhrfxf !.................................................................................................... 24cFs kI hn?.............................................................................................................. 29afnlfeIn sRoq..................................................................................................................... 36TVOkids.com aqy. gixq.................................................................................................... 37ijMnf vDyry pirvfr afpxy bwicaF dI iswiKaf aqy ivwidak qrwkI ivwcmwdd krdy hn, sMBfvnf hY ik bwcy AuWnf hI vDyry cMgf skUl ivwc krngyaqy afpxI iswiKaf nUM jfrI rwKxgy.Karen Mapp and Anne Henderson, 2002A New Wave of Evidence:The Impact of School, Family, and CommunityConnections on Student Achievementquhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz1


mfipaF leI notmYN afpxy bwcy dI isKlfeI ivwc ikvyN mwdd kr skdf hF?qusIN afpxy bwcy dI gixq dI pVfeI ivwc mhwqvpUrx ihwsydfr ho. jdoN qusIN bwcy nUM gixq bfry socxaqy gwl krn bfry ruJfAux leI rsqy lwBdy ho, qusIN Ausdy BwivK dI sPlqf leI iewk mhwqvpUrxkuMjI pRdfn kr rhy ho. awj, aflocnfqmk soc, smwisaf hwl krnIaF, dlIl Xogqf aqy gixq dyqrIky nfl sMcfr krnf jrUrI hunr hn. ieh pRikirafvF AuNtyrIE skUlF ivwc gixq pVfAuxdI buinafd hn. ieh Kyz df ihwsf bx jFdIaF hn jdoN qusIN ieh gfeIz ivwc suJfeIaF geIaFgqIivDIaF ivwc bwcy nUM ruJfAuNdy ho. iewkTy iswKx df afnMd mfxo!mfipaF leI cotI dy nukqy• gixq bfry mjbUq, hF pwKI rveIey Ausfro: jdoN bwcy hF pwKI rUp ivwc ruwJy aqy sPl mihsUskrdy hn, AuhnF dy hwl lwBx leI iksy gqIivDI jF musLkl dy nfl juty rihx dI vDyry sMBfvnf hY.• AuhnF gqIivDIaF nfl sLurU kro jo quhfzy bwcy dy gixq dI smJ dy pwDr nfl myl KFdIaFhn: musLklF hwl krn ivwc jld imlI sPlqf quhfzy bwcy dy svY-ivsLvfsL ivwc vfDf krygI.hOlI hOlI AuhnF gqIivDIaF vwl jfvo jo quhfzy bwcy nUM vDyry cuxOqI pysL krdIaF hn.• jykr qusIN aqy quhfzf bwcf aMgryjLI qoN ielfvf iksy hor BfsLf nUM vrqx ivwc sOK mihsUskrdyho, AusnUM vrqo: quhfzf bwcf Aus BfsLf ivwc isDFqF nUM ibhqr smJygf ijs nUM vDIaf jfxdf hY.ikRpf krky not kro:Please note: ies gfeIz ivwc, mfpy sLbd mfipaF, srpRsqF, sMBfl krnvfilaF aqy pirvfr dy hor mYNbrF df hvflf dyNdf hY jo bwicaF nUM pVn aqy ilKxivwc mwdd krdy hn.2quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


mfipaF leI notsfzy bwicaF dy gixq iswKx dI Xogqf ivwc XkIn jrUrI ikAuN hY?gixq nUM smJxf svY-ivsLvfsL ivwc vfDf krdf hY aqy keI nOkrIaF aqy kYrIarF dy drvfjLyKoldf hY. gixq dI smJ sfnUM kfbl bxfAuNdI hY:• musLklF hwl krn aqy vDIaf PYsly lYx dy• eh ivafiKaf krn dy ik asIN musLkl ikvyN hwl kIqI aqy asIN ieh Kfs PYslf ikAuN ilaf• musLklF hwl krn leI qknflojI (ijvyN ik kYlkulytr aqy kMipAUtr dy pRXog) vrqx dy• nmUny aqy ruJfn smJx dy qF jo asIN ikafs-arfeINaF kr skIey (imsfl vjLoN, asIN iehgwl df ihsfb rwK skdy hF ik ikMnf jUs lwgdf hY qF jo asIN jfxIey ik hr hPqy ikMnf jUsKrIdxf hY)• afpxy pYsy aqy smyN df pRbMD krnf (imsfl vjLoN, asIN igx skdy hF ik sfnUM kMm AuWqy jfx nUMikMnf smF lwgdf hY, Kfxf bxfAux leI ikMnI smwgrI lwgdI hY aqy Kfxf KrIdx leI sfnUM ikMnypYsy dI loV hY)• inwq idn dIaF pRsiQqIaF nUM sMBfl skIey ijhnF ivwc nMbrF dI sLmUlIaq huMdI hY (ijvyN ikpqf lfAuxf ik aglI bws ikMny vjLy afvygfI aqy iewk rsd nUM vMzxf)iesqoN pihlF ik quhfzf bwcf gixq isKy, AusnUM aijhf krn ivwc afpxI Xogqf ivwc ivsLvfsLkrn dI loV hY. iewQy hI quhfzI sLmUlIaq sLurU huMdI hY. qusIN afpxy bwcy dy iswKx leI pihly rolmfzl ho skdy ho. jdoN qusIN afpxy bwcy nUM mwddgfr, sihj mfhOl ivwc ruJfAuNdy ho, quhfzf bwcfgixq nfl mOj msqI krdf hoieaf joKm lYx df afnMd mfxygf!7 = 2 + 5quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz3


mfipaF leI notislybs (curriculum)nfl kI sbMD hn?ies gfeIz ivwc gqIivDIaF quhfzy bwcy nUM inwq idn dIaF gqIivDIaF ivwc gixq dyKx ivwc mwddkrn leI cuxIaF geIaF sn. ieh quhfzy bwcy dy KyzF pRqI ipafr nUM vI hwlfsLyrI dyNdIaF hn. aqyAuNtyrIE dy gixq dy islybs dIaF afsLfvF nUM iswKx ivwc vI mwdd krdIaF hn.cyqy rwKo ik quhfnUM afpxy bwcy dI gixq ivwc sPlqf nUM mwdd krn leI ies gfeIz ivwc idwqIaFsfrIaF gqIivDIaF nhIN krnIaF. Aqy BfvyN keI gqIivDIaF sLfml kIqIaF geIaF hn, Auh islybsdf sfrf kuwJ sLfiml nhIN krdIaF. ieh gfeIz AuhnF gqIivDIaF df iewk nmUnf pysL krdI hY jo qusINafpxy bwcy nUM gixq dy qrIky socx aqy gwl krn ivwc hwlfsLyrI dyx leI kr skdy ho!qusIN bwcy dI irport kfrz qoN AuNtyrIE gixq dy islybs dy pMj qwqF (The five strands) dy nfmpihcfx jfvogy.pMj qwq (The five strands)nMbr df arQ (Number Sense)aqyaMk igxqI (Numeration)nfp qolnmUnfbfjI aqy aljbrfaMkVf pRbMD aqy sMBfvnf (Probability)jIEmYtrI aqy sQfn df arQ(Spatial Sense)iewk gixqkfr vfgUM socxf aqy bolxf iswKxfAuNtyrIE df ihsfb df islybs 7 pRikirafvF AuWqy jor dyNdf hY jo ihsfb iswKx leI jrUrI hn: hrgryz ivwc, iewk “mathematical process expectations” (ihsfbI pRikiraf dI qfk) dfsYWt drsfAuNdf hY ik ikvyN bwcy srgrmI nfl iswKdy hn aqy ihsfbI smJ nUM apxfAuNdy hn.• musLkl hwl krnI• dlIl aqy pRmfixq krnf• pRqIibMbk• sbMD joVnf• smwgrI cuxn aqy gixkrxnIqIaF• pysL krnf• sMcfr krnfhr gryz ivwc, ‘gixq pRikiraf dIaF afsF (mathematical process expectations) df iewksYWt ibafn krdf hY ik bwcy iks qrF cusqI nfl gixq dI smJ iswKdy hn aqy lfgU krdy hn.Ontario Mathematics curriculum:www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf4quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


nMbr hr QF AuWqy hn!qusIN vyKogy ik sMqrI pMinaF AuWqy gqIivDIaF hn jo nMbrF dy arQ aqy aMk igxqI nUM mwdddyNdIaF hn. ieh AuNtyrIE dy gixq dy islybs ivwc qwq (strand) hY jo nMbr ikvyN kMm krdyhn aqy ikvyN Auh iewk dUjy nfl myl KFdy hn, dI smJ bfry hY. ieh buinafdI ikRiafvF (basicoperations) nUM vI kvr krdf hY: joV, GtfE, guxf aqy vMz. nMbr df arQ (NumberSense)aqy aMk igxqI (Numeration) ihsfbI soc leI afDfr pRdfn krdy hn.ikMzrgftn qoN gryz 3lIjYNz (Legend)nMbr hr QF AuWqy hn!ikMnf AuWcf?, ikMnf nIvF?, ikMnf? ikMnf QoVf?quhfzf Aus AuWqy kI kox hY?vfr vfr duhrfxf !cFs kI hn?quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz5


nMbr hr QF AuWqy hn! nMbr df arQ (Number Sense)aqy aMkigxqI (Numeration)ikMny?ikMzrgftn qoN gryz 3lfBijAuN bwcy igxqI krdy hn, Auh sMiKafvF nUM (ijvyN ik pMj bwtn) nMbrF dy nfm nfl(ijvyN ik sLbd pMj)aqy icMnH(ijMvyN 5) joVnf iswKdy hn |• afpxy bwcy dI nMbrF nUM drsfAux leI vrqy gey pRqIkF dI jfgrqI iesnUM Kyz bxf kyivkisq kro. afpxy Gr aqy guaFZ ivwc nMbrF dy pRqIkF leI vyKo: tYlIvIjLn dy irmot AuWqy,mfeIkrovyv AuWqy, tYlIPUn dy kI-pYz (keypad) AuWqy, PlfierF aqy mIzIaf ivwc, sfeInF AuWqyaqy tIm dy svYtrF AuWqy.• I Spy (mYN jfsUs) df nMbr rUp (version) Kyzo. imsfl vjLoN, “ mYN Aus cIj dI jfsUsI krdf hFijs AuWqy nMbr pMj hY,” jF “mYN Aus cIjL dI jfsUsI krdf hF ijsdy ies kmry ivwc iqMn hn”.• afpxy bwcy nUM Gr ivwc cIjLF igxn ivwc mwdd dyx leI afKo. “mYN socdf hF ik sfzy kol tybldy duafly ikMnIaF kursIaF hn? ies kmry ivwc? mkfn ivwc?” iKVkIaF, lfeItF dIaF sivwcF,lYNp jF bYWz igxo. qusIN nMbrF aqy qsvIrF df sumyl vrq ky ‘ikMnIaF’ df irkfrz rwK skdy ho.quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz7


nMbr hr QF AuWqy hn! nMbr df arQ (Number Sense)aqy aMkigxqI (Numeration)joVnf aqy GtfAuxf mjLydfr bxfieafikMzrgftn qoN gryz 3lfBieh KyzF Kyzx nfl, quhfzf bwcf iswKygf ik joVn aqy GtfAux df koeI shI qrIkf nhINhY- ihsfbdfn keI iksm dIaF rxnIqIaF vrqdy hn.nukqf!afpxy bwcy nUM Auh rxnIqI apnfAux leI AuqsLfihq kro jo Aus leI koeImfanf rwKdI hY- imsfl vjLoN, “counting-on” rxnIqI quhfzy bwcy nUM gymivwc skor df trYk rwKx ivwc mwddgfr ho skdI hY, vwzy nMbr qoN sLurU krky(ijvyN ik 12) aqy Pyr bfkI dI igxqI krnI (ijvyN ik 13,14, 15…)qusIN nMbr ikAUbF (number cubes) aqy nMbr kfrzF nUM vrq ky gymF bxf skdy ho ijhnF ivwcjoV aqy GtfE sLfml huMdf hY. afpxy bwcy nUM nMbr kfrzF dy cfr jF vDyry sYWt bxfAux ivwc mwddkro. hryk kfrz dy iewk sfeIz AuWqy iewk qoN 10 qwk iewk nMbr hovygf. iewQy kuwJ gymF krn vfsqysuJfeIaF geIaF hn:• AuWcy nMbr. kfrzF nUM imlfE aqy Pyr AuhnF nUM iewk ZyrI bxf ky muwDy mUMh rwK idE. hr iKzfrIdo kfrz lYNdf hY aqy AuhnF df joV krdf hY. ijs iKzfrI kol vwzf nMbr hY, Auh dUjy iKzfrI dykfrz lYNdf hY. iKzfrI Kyzxf jfrI rwKdy hn aqy iewk vyly do kfrz joVdy hn jdoN qwk koeI vIkfrz nhIN bwcdf. vDyry kfrzF vflf iKzfrI jyqU hY. qusIN iesy Kyz nUM GtfAux nfl Kyz skdyho, pRqUM iesnUM Gwt nMbr afiKaf jfvygf. Gwt Prk (jvfb) vflf iKzfrI afpxy kfrz dUjyiKzfrI nUM dyNdf hY. ijs ivakqI kol aMq ivwc swB qoN Gwt nMbr hn, Auh jyqU hY. qusIN iesygym nUM guxf nfl Kyz skdy ho.• nMbr ikAUb do vfrI (Number Cube Twice): hr iKzfrI do nMbr ikAUb roVdf hY aqyidwsdy nMbrF nUM joVdf hY. vwD nMbrF vflf ijwqdf hY. qusIN iesy gym nUM GtfE aqy guxf nfl Kyzskdy ho.quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz9


nMbr hr QF AuWqy hn!tuwty kYlkulytr dI KyzlfBihsfbdfn jfxdy hn ik mfqrf nUM drsfAux dy vwKo vwKry qrIky huMdy hn- imsfl vjLoN, 18nUM 20-2 aqy 15+3 vjLoN drsfieaf jf skdf hY.• afpxy bwcy nUM afKo ik Auh ieh bhfnf kry ik kYlkulytr df 8 bwtn tuwitaf hoieaf hY. AusnUM puwCo ikAuh 8 dy bwtn qoN ibnf skrIn AuWqy 18 nUM ikvyN drsf skdf/skdI hY. (nmUny dy jvfb ivwc sLfmlhY 20-2 aqy 15+3).• hor tuwty hoey bwtn vrq ky AusnUM iesy iksm dy hor suafl puwCo. Aus nMbr nUM bdl ky jo bwcy nUM kYlkulytrAuWqy ivKfAuxf cfhIdf hY ies kMm nUM hor sOKf jF vDyry cuxOqI vflf bxfE.10quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


nMbr hr QF AuWqy hn! nMbr df arQ (Number Sense)aqy aMkigxqI (Numeration)iewk df awDf iewk dy awDy brfbr huMdf hY – jF kI ieh huMdf hY?ikMzrgftn qoN gryz 3lfBiewk Bfg (fraction) pUry aqy iewk ihwsy ivwc sbMD nUM drsfAuNdf hY. do BfgF nUM mukfblfkrdy smyN, quhfzf bwcy iswKygf ik ieh “pUry’ df ikMnf sfeIjL hY.nukqf!bwcy ieh iswKdy hn ik iewk CotI cIjf df awD (ijvyN ik iewk CotI rwsI) iewkvwzI cIj (ijvyN ik iewk vwzI rwsI)L dy qIjy ihwsy qoN Cotf ho skdf hY.• afpxy bwcy nfl, iewko iksm dI bnfvt vflIaF vsqF iewkqr kro, ijvyN ik koeI qOlIaf, rwKxvflf mYt, Poto df Prym, sLIsLf, irsflf aqy ikqfb.• bwcy nUM hr vsq df awD ivKfAux leI afKo, sLfied iksy Dfgy nUM awD nfpx leI vrq ky.quhfzy bwcy leI ieh vyKx df vI avsr hY ik BfgF dy twukVy brfbr sfeIjL dy hoxy cfhIdy hn.• iewk qOlIey dy awD dIM iewk kMbl dy cOQy ihwsy nfl qulnf kro. puwCo, “kI awDf sdf hI cOQy qoNihwsy qoN vwzf huMdf hY? gwl alfihdf iksm dIaF siQqIaF vwl iljfx vfsqy hor smwgrI dIvrqoN kro, ijvyN ik vwKo vwKry iksm dIaF plytF dy ihwsy jF vwKry sfeIjL dy kmiraF dI QF.= =quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz11


nMbr hr QF AuWqy hn!pYsy dIaF KyzFlfBnMbrF nUM keI vwKry qrIikaF nfl drsfieaf jf skdf hY. ieh gixq df gur quhfzf bwcfpYsy dIaF KyzF Kyzx qoN iswKygf.nukqf!bwcy iewk iksm dy iswikaF nUM joVnf sLurU kr skdy hn ikAuNik AuhnF nUM aijhfkrnf sOKF jfpdf hY. quhfzf bwcf ikhVy iswky df joV pihlF lfAuNdf hY: zfeIm(dimes) jF kuafrtr (quarters)• pqf lfE ik quhfzf bwcf iks iswky df joV pihlF lfAux nUM pihl dyNdf hY. iesqoN quhfnUM pqf lwgskdf hY ik quhfzf bwcf iks nMbr nfl swikp kfAuNitMg (skip counting) krn ivwc sOK mihsUskrdf hY. keI iksm dy iswikaF nUM iewk ZyrI ivwc rwKo, aqy bwcy nUM hr iswky df joV lfAux leIafKo. imsfl vjLoN, inwklF (nickels) ivwc 85 sYNt ho skdy hn aqy 50 sYNt zfeImF (dimes) ivwc.afpxy bwcy nUM iswky alihdf krdy aqy joVdy hoey vyKo. afpxy bwcy nUM puwCo ik Ausny ikvyN cuixaf ikikhVy iswky df joV pihlF lfAuxf hY. AusnUM suJfa idAu ik qusIN dovyN AuhnF iswikaF nUM joVn dI dOVlfE ijhnF nUM igxn ivwc quhfzf bwcf Gwt sOK mihsUs krdf hY. imsfl vjLoN, jykr quhfzy bwcy nUMinwkl (nickels) igxn ivwc sOK mihsUs krdf hY , qF kuafrtr (quarters) igxn dI dOV lfE.AuhnF iswikaF df joV pihlF lfAux vflf ivakqI ijwqdf hY.• pYsy dI Kyz. iewk ivakqI bYNk vflf hY aqy dUjf akfAuNtYNt. qusIN Kyz ivwc afpxy bwcy nfl rolbdl skdy ho. Auh pYsy vrqo ijhnF nUM isrP iswikaF rfhIN hI ivKfieaf jf skdf hY- imsfl vjLoN,1 zflr 75 sYNt.1[.bYNk vflf: myry bYNk ivwc 1 zflr 75 sYNt hn. myry kol ikhVy iswikaF dy juwt(combination) ho skdy hn? akfAuNtYNt iewk jF vwD sMBfivq juwt ivKfAuNdf hY.2[.bYNk vflf: myry bYNk ivwc 1 zflr 75 sYNt hn. ieh rfsLI bxfAux leI myry kol Gwt qoM GwtikMny iswky hoxy cfhIdy hn.3[.bYNk vflf: “myry bYNk ivwc 1 zflr 75 sYNt hn. myry kol ds iswky hn. ieh ikhVy iswky hoskdy hn? akfAuNtYNt rfsLI dwsx leI ds iswky vrqdf hY.• qusIN iswikaF dy nMbrF dI igxqI bdl ky jF iswikaF dI iksm nUM Gwt krky pYsy dI Kyz nUM sOKf jFaOKf bxf skdy ho (imsfl vjLoN, isrP zfeIm (dimes) jF kuafrtr (quarters)12quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


nMbr hr QF AuWqy hn!anupfqk soc sfzy afly duafly hYlfBqulnf krn dy kfPI qujrby qoN bfad, quhfzf bwcf afKr nUM anupfqk soc vwl qrwkI krlvygf- iesdf Bfv hY, guxf krky qulnf krn dy kfbl hoxf.nukqf!guxfqmk qulnf: “bflg bwcy nfloN lMbf hY”.Xogfqmk qulnf: “bflg bwcy nfloN 100 sYNtImItr lMbf hY”.gixqk qulnf: “bflg bwcy nfloN do guxf lMbf hY”.asl jIvn ivwc anupfqk soc dI sLmUlIaq vflIaF siQqIaF nUM vyKdy rho. afpxy bwcy nUM AusdI socnUM ibafnx idE. kuwJ imsflF iewQy idwqIaF geIaF hn:• sRI sI dI kfr dIaF lfeItF pUrI qrF kMm nhIN kr rhIaF. Auh mwDm pY rhIaF hn aqy afpxI25% cmk guaf rhIaF hn. kI AusnUM rfq nUM kfr clfAuxI cfhIdI hY? ikAuN aqy ikAuN nhIN?• gYbrIalf afpxI BYx nfl Ausdf kfgjLI rUt bxfAux ivwc mwdd krn df vfadf krdI hY. AusdIBYx afKdI hY ik Auh afpxy lfB df iewk cuQfeI ihwsf AusnUM dyvygI. kI gYbrIalf leI ieh cMgfsOdf hY? dwso ikAuN?• ies vrnx df arQ ibafn kro. ies jfxkfrI nfl pirvfr kI PYsly kr skdf hY?14quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


ikMnf AuWcf?, ikMnf nIvF?, ikMnf? ikMnf QoVf?qusIN vyKogy ik nfp df afDfr bxdIaF jo gqIivDIaF jfmnI rMg ivwc hn. ieh AuNtyrIE dy gixqdy islybs ivwc pMj qwq (The five strands) hn jo quhfzy bwcy nUM jfxUM krvfAuNdy hn ikihsfbdfn vsqF dI AucfeI, lMbfeI aqy cOVfeI ikvyN inrDfrq krdy hn. ieh vI ibafn krdyhn ik vsq jo Kyqr GyrdI hY, vsq jo mfqrf (smrwQf) lY skdI hY aqy sQfn (GxPl) jo vsqlYNdI hY, AuhnF nUM ikvyN inrDfrq krnf hY.ikMzrgftn qoN gryz 3lIjYNz (Legend)nMbr hr QF AuWqy hn!ikMnf AuWcf?, ikMnf nIvF?, ikMnf? ikMnf QoVf?quhfzf Aus AuWqy kI kox hY?vfr vfr duhrfxf !cFs kI hn?quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz15


ikMnf AuWcf?, ikMnf nIvF?, ikMnf? ikMnf QoVf?Gr dy ierd igrd vsqF dI qulnf krnflfBmihjL Gr dy ierd igrd vsqF dI qulnf krn nfl, quhfzf bwcf nfp dy keI buinafdI isDFqsmJxf sLurU kr skdf hY.• keI vfr, asIN mfqrf df aMdfjLf lf skdy hF. sfnUM hmysLf hI pUrf nfp nhIN cfhIdf huMdf.• iewko vsq nUM keI qrIikaF nfl nfipaf jf skdf hY.• nfpx vfly XMqr nUM hmysLf iewk qrIky hI vrqxf huMdf hY.• afpxy bwcy nUM grOsrI dIaF cIjLF ( imsfl vjLoN, Pl jF sbjLI dI iksm, brYWz jF pflqU jfnvr dfKfxf) df aMdfjLf krn leI afKo jo pirvfr nUM hPqy leI cfhIdIaF hn. AusnUM pwuCo,”qUM ikAuN socdfhYN ik ieh mfqrf cfhIdI hovygI?” hPqy dy aMq ivwc, bwcy nUM asl ivwc vrqIaF cIjLF dI igxqIkrn idE.• kwpborz ivwcoN kuwpIaF, zwby aqy pYk iewkTy kro. bwcy nUM iehnF nUM iksy qrqIb (imsfl vjLoN, lMby aqyCoty, ijafdf smfn smoNdy hn aqy Gwt smfn smoNdy hn, KflI aqy Bry hoey, Bfry aqy hlky) ivwcrwKx leI afKo.• sfry afkfrF dy zwby iewkqr kro aqy iewk kOPI vflI kVCI, plfsitk df kwp jF lFzrI dI sfbxvflI kVCI. bwcy nUM ryq dy zwby ivwc ryq jF hOdI (sink) ivwc pfxI nfpx idE aqy keI zwibaFdI mfqrf dI qulnf krn idE. bwcy nUM nfp ky qulnf krn idE ik hr zwby nUM Brn leI ikMnIaFkVCIaF cfhIdIaF hn. puwCo, “ iks zwby ivwc ijafdf mfqrf afeI? iks zwby ivwc swB qoN Gwt mfqrfafeI?”16quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


ikMnf AuWcf?, ikMnf nIvF?, ikMnf? ikMnf QoVf?aMdfjLf : iewk mhwqvpUrx gixqI hunrlfBkdoN vDfAuxf hY aqy kdoN GtfAuxf hY, cwldy kwul df ihsfb ikvyN rwKxf hY-jld hIieh rxnIqIaF quhfzy bwcy df dUsrf suBfa bx jfxgIaF!nukqf!dosqfnf nMbr Auh huMdy hn ijhnF nfl idmfgI qOr AuWqy kMm krnf sOKf huMdf hYaqy bwcy AuhnF nUM iksy cIjL df aMdfjLf lf ky jvfb dyx leI vrq skdy hn.quhfzf bwcf kuwl aMk pUry krn leI ikhVy dosqfnf nMbr vrqdf hY? kuafrtr?jF zflr?• jdoN qusIN sLfipMg krdy ho, jo cIjLF qusIN KrIddy ho, bwcy nUM vsqF dIaF kImqF nUM AuWqy jF Qwly krkykuwl kImq imlfAux idE. iewk cuxOqI vjLoN, qusIN ikMny pYsy Krc krogy, AusdI iewk hwd inXq kro.• bwcy nUM iewk kflpink Dn rfsLI Ausdy mncfhy stor AuWqy Krcx leI idE (Plfier jF afnlfeInkYtflfg mwddgfr ho skdy hn). Dn rfsLI ilKy ibnf, bwcy nUM KrIdx vflIaF cIjLF cuxn idE. Auhbwjt dy ivwc rihx leI aMdfjLy lfvygf. Pyr, bwcy nUM asl Krc df joV krn idE. kI Auh bwjt dyivwc irhf? iewk cuxOqI vjLoN, bwcy nUM koeI tYks df aMdfjLf lfAux idE.18quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


quhfzf Aus AuWqy kI kox hY?qusIN pfEgy ik jIEmYtrI aqy akfsLI boD (Geometry and Spatial Sense) krvfAuxivwc mwddgfr gqIivDIaF lfl pMinaF AuWqy idwqIaF geIaF hn. ieh AuNtyrIE dy gixq dy islybsdy qwq (The strands) df ihwsf hY jo quhfzy bwcy dI ihsfb dI ies sLfKf aqy keI ikwiqaF, AusfrIaqy AudXoigk izjLfien qoN idRsLmfn klfvF (visual arts) qwk sPlqf df afDfr bxfAuNdf hY. jobwcy afpxy mfhOl ivwc afkfrF aqy akfsLI sQfn dy sbMDF (spatial relationships) bfry jfxUM hojFdy hn, Auh bfad dy gryzF ivwc jIEmYtrI dy isDFqF nUM smJx leI iqafr hoxgy.lIjYNz (Legend)nMbr hr QF AuWqy hn!ikMnf AuWcf?, ikMnf nIvF?, ikMnf? ikMnf QoVf?quhfzf Aus AuWqy kI kox hY?vfr vfr duhrfxf !cFs kI hn?20quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


jIEmYtrI aqy sQfn df arQ (Spatial Sense)sMkyqk KyzikMzrgftn qoN gryz 3lfBieh Kyz bwcy dI jIEmYtrI dI soc (geometric thought) nfl jfx pihcfx krvfAuNdIhY, ik vsqF dy sQfn nUM ihsfb duafrf ibafn kIqf jf skdf hY.• iewk vsq nUM AuTfE aqy afpxy bwcy nUM idsLfvF dI BfsLf ivwc AuhnF vsqF bfry aMdfjL lfAuxidE: AuWqy, Qwly, AuWpr, qoN Gwt, ivckfr, afrpfr, lfgy, ipwCy, sfhmxy aqy swB qoN AuWqy.• qusIN Kyz nUM hor cuxOqI BrI bxf skdy ho.• do ihwisaf ivwc inrdysL idE- imsfl vjLoN, “ieh myjL dy AuWqy aqy notbuwk dy swjy pfsy peI hY.• afpxy bwcy nUM suafl krn idE ijvyN ik “kI iesdI isKrlI Cwq pwDrI hY?” “kI ieh myjLdy Qwly peI hY?• bwcy nUM AuhnF vsqF bfry aMdfjLf idE jo dUjy kmry ivwc peIaF hn qF jo bwcy nMU vsq dfikafs krnf pvy.sfzy sMsfr ivwc jfxy pihcfxy afkfr• afpxy bwcy nfl gwl krdy hoey, cIjLF nUM AuhnF dy afkfr aqy sfeIjL qoN pihcfx kro: ikRpf krkymYnUM afieqkfr mYt, kwpborz ivwcoN swB qoN vwzf bfks, cOrs afkfr df ibskut aqy gol plytidE”.• afpxy bwcy nUM Gr jF bfhr do afXfm dy afkfr ijvyN ik cwkr, cOrs, iqRkoxF aqy afieqkfrvyKx leI afKo. imsfl vjLoN, afpxy bwcy nUM keI iksm dy glIaF dy sfeIn lwBx leI afKo aqyjo AuhnF AuWqy afkfr bxy hn, AuhnF df nfm rwKo.• 3 zI dI Bfl (3-D Hunt) afpxy bwcy nUM iqMnF afXfmI vsqF lwBx ivwc mwdd kro: ikAUb, konF,Gyzy (ijvyN ik gyNd), ipRjLm (prisms) (ijvyN ik iewk bfks), iprfimz aqy islMzr. crcf kroik ikvyN iewk pOp (pop) df zwbf aqy pypr tfvl rol (paper towel roll) islMzr vFg hn.• afpxy bwcy quhfzy vwloN sLnfKq kIqI geI vsq dy afkfr qoN vsq lwBx dI I Spy Kyz Kyzo: mYNAus vsq bfry I Spy Kyz irhf hF jo ik gol hY”. “mYN aijhI vsq bfry I Spy Kyz irhf hF joislMzr dy afkfr vrgI hY”. ies Kyz nUM do afkfr dws ky Kyz nUM hor cuxOqI Biraf bxfE: mYNaijhIaF vsqF bfry “ I Spy Kyz irhf hF jo gol hY aqy Aus AuWqy vrgfkfr bixaf hoieaf hY”.quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz21


quhfzf Aus AuWqy kI kox hY?myry sMsfr dI nksLfvfhI krnflfBies gqIivDI ivwc, quhfzf bwcf nkisLaF dy kuwJ buinafdI isDFq iswKygf-swB qoN vDyrymhwqvpUrx ik nksLy AuWqy qsvIrF aqy pRqIk asl vsqUaF nUM drsfAuNdy hn.nukqf!iewk pwkf (iqMn afXfmI) nksLf bxfAuxf quhfzy bwcy nUM kfgjL AuWqy (do afXfmI)nkisLaF bfry DfrnfvF smJx ivwc mwdd dyNdf hY.• afpxy bwcy nUM CotIaF cIjLF nUM vwzIaF cIjLF drsfAux leI vrq ky (ijvyN ik iewk pypr kilwp(paperclip) iewk bYWz jf iewk blfk iewk ruwK nUM drsf skdf hY) iksy jfxI pihcfxI prsiQqI dfnksLf (ijvyN ik Ausdf sOx df kmrf jF pfrk) bxfAux ivwc mwdd kro.• quhfzy Gr quhfzy bwcy dy dosq Gr jF nwukr df stor dy mukfbly ivwc ikwQy siQq hY, ies bfry afpxybwcy nfl gwlbfq kro. idsLfvF drsfAux vfly sLbd aqy iPkry vrqo, ijvyN ik nfl lwgdf aqy dy swjypfsy . qusIN iml ky vwzIaF insLfnIaF (landmarks) aqy jfxy pihcfxy sQfnF dI insLfndyhI krkyafpxy aFZ guaFZ df nksLf iml ky bxfE.smfnqf (Symmetry) sfzy hr pfsy hY• afpxy bwcy nfl sfry smfn vwzy (capital) awKrF dIpihcfx kro. afpxy bwcy nUM ies afDfr AuWqy vwzy (capital)awKr cuxn idE ik AuhnF ivwc iewk smfn ryKf hY jF dohn. imsfl vjLoN, C ivwc iewk lytvIN (horizontal) smfnryKf hY; ivwc iewk iewk KVvIN (vertical) smfn ryKf aqyjdoN ik dUjI lytvIN (horizontal) hY.• smfnqf dI Koj ivwc jfE. afpxy bwcy nfl afpxy Gr dy afly duafly AuhnF afkfrF, cIjLF,nmUinaF aqy zIjLfienF nUM lwBo ijhnF ivwc smfn ryKfvF hn. crcf kro ik kI AuhnF ivwclytvINaF (horizontal), KVvIaF (vertical) jF iqrCIaF smfn ryKfvF hn. vfl pyprF,PrsL dIaF tfeIlF, qsvIrF aqy pYikMgF dy zIjLfienF nUM vyKo.22quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


jIEmYtrI aqy sQfn df arQ (Spatial Sense)ikhVy afkfr srMcnf (structure) nUM itkvF bxfAuNdy hn?gryz 4 qoN gryz 6lfBiehnF KyzF nUM Kyz ky, quhfzf bwcf smJ jfvygf ik kuwJ afkfr horF nfloN vDyry itkvyNhuMdy hn.nukqf!AusfrI krn dIaF gqIivDIaF quhfzy bwcy nUM ieh smJx ivwc mwdd krdIaFhn ik ikvyN kuwJ afkfr cIjF nUM izwgx qoN bcfAuNdIaF hn.• afpxy bwcy nUM afpxy afp KVI ho swkx vflIsrMcnf (structure) bxfAux leI 50 CydvflIaF pfeIpF (straws) jF Guwt ky rol kIqyaKbfr aqy QoVI typ vrqx idE. srMcnf(structure) PrsL jF iksy kMD jF iksyPrnIcr nfl bMnI nhIN hoxI cfhIdI.• afpxy bwcy nUM puwCo ik Ausdy iKafl ivwc ikhVyafkfr (vrgfkfr, iqRkox jF cwkr) srMcnf(structure) nUM siQr bxfAuxgy.• afpxy bwcy nfl, srMcnf dy ZFicaF, ijvyN ikhfeIzroielYktirk tfvrF, rolr kostrF(roller coasters) aqy ltkvyN puwlF(suspension bridges) dIaF qsvIrF nUM vyKo.afpxy bwcy nUM puwCo ik afkfr dy ikhVy nksLAusnUM itkvF bxfAuNdy hn aqy AusnUM ivsQfrdyx idE ik ikAuN.• afpxy bwcy nUM pwuCo ik kI zIjLfienF ivwc smfnqf(symmetry) dIaF imsflF hn. afpxy bwcy nUMibafn krn idE ik AusnUM ikvyN jfxdf hY?quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz23


vfr vfr duhrfxf !qusIN vyKogy ik nmUnfkfrI (Patterning) aqy aljbrf nUM mwdd krn vflIaF gqIivDIaF hrypMinaF AuWqy hn. ieh AuNtyrIE dy gixq dy islybs df qwq (strand) hY jo bwcy nUM vwzIaF klfsFivwc jf ky nMbrF dI smJ, nfp, jIEmYtrI, aljbrf aqy aMkVf pRbMD leI iqafr hox ivwc mwddkrdf hY. nmUinaF (patterns) nUM smJx aqy pihcfnx dI Xogqf AuhnF dy inrIKx dy afDfr AuWqyanumfn lfAux ivwc mwdd krdI hY.lIjYNz (Legend)nMbr hr QF AuWqy hn!ikMnf AuWcf?, ikMnf nIvF?, ikMnf? ikMnf QoVf?quhfzf Aus AuWqy kI kox hY?vfr vfr duhrfxf !cFs kI hn?7 = 2 + 524quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


aMkVf pRbMD aqy sMBfvnf (Patterning and Algebra)nmUinaF (Patterns) nUM suxnfikMzrgftn qoN gryz 3• afpxy hwQF nfl qfVI aqy iewk pYr nfl DrqI QpQpfAux nUM iewk qrqIb ivwc kro (ijvyNik qfVI, qfVI, QpQfht, qfVI, qfVI, QpQfht, qfVI, qfVI, QpQfht). afpxy bwcy nUM iehIqrqIb duhrfAux idE. iesqoN bfad imlky ies pYtrn ivwc qbdIlaF pYdf kro.• afpxy bwcy nUM Auh nfc ijs ivwc kdmF aqy hrkqF dI qrqIb sLfml huMdI hY, isKf ky mOjmsqI kro.Gr jF aFZ guaFZ ivwc pYtrnlfBafpxy bwcy nUM ihsfbI sLbd , ijvyN ik duhrfAuxf, Pyr dubfrf, ieh qF AuhI hY aqy iehbdldf hY, vrq ky pYtrnF nUM pihcfnx aqy ibafnx mwdd kro jo sfzy sfry pfsy mOjUdhn-• quhfzf bwcf kwpiVaF, vflpyprF (wallpapers), tfeIlF ivwc, iKzOixaF AuWqy aqy ruwKF aqyPuwlF ivwc pYtrn pfvygf. pfey gey pYtrnF nUM ibafnx leI bwcy nUM AuqsLfihq kro. afpxy bwcynUM pYtrn dy Auh ivsLysL gux pihcfnx dI koisLsL krn idE jo duhrfAuNdy hn.• afpxy bwcy nfl ieMtrnYWt AuWqy “patterns around us” vrgy sLbd vrq ky qsvIrF lwBxdI koisLsL kro.quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz25


vfr vfr duhrfxf !pYtrnF nUM ibafnxflfBpYtrnF nUM duhrfAux nfl, kyNdrI pYtrn Auh ihwsf hY jo vfr vfr duhrfieaf jFdf hY-imsflvjLoN, ABB ABB ABB dy pYtrn ivwc, ABB kyNdrI pYtrn hY. afpxy bwcy nUM iehnF mOjmsqI vfly aiBafsF ivwc duhrfey jfx vfly pYtrnF nUM pihcfnx ivwc mwdd kro!nukqf!cfrt, tybl aqy grfP pYtrnF nUM Aujfgr krn dy kuwJ qrIky hn.• nO cmicaF nUM iewk kqfr ivwc ieMJ rwKo ik hr iewk cmcy df hYNzl AuWqy jF Qwly vwl jFdf hY ijsdypYtrn df kyNdr up, up, down (up, up, down; up, up, down; up, up, down) hY. . afpxybwcy nUM ies pYtrn nUM awgy vDfx leI afKo.• ies kfrj nUM hor cuxOqI Biraf bxfE aqy afpxy bwcy nUM pYtrn ibafn krn aqy AuWcI bolx leIafKo.• pYtrn dyN kyNdr nUM lMbf bxfE- imsfl vjLoN, up, up, down, up; up, up, down, up; up,up, down, up.• c qwqF ivwcoN iewk nUM bdl idE- imsfl vjLoN, up, up, down, sideways; up, up, down,sideways; up, up, down, sideways.• afpxy bwcy nfl tUQipwk jF strfa (toothpick or straw) vrq ky pYtrn vDfAux dy qrIky Kojo.afpxy bwcy nUM afKo ik pYtrn vDfANdf jfvy. puwCo ik iesqoN bfad kI?26quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


aMkVf pRbMD aqy sMBfvnf (Patterning and Algebra)anumfn lfE ikMnygryz 4 qoN gryz 6lfBieh gqIivDI quhfzy bwcy nUM socx ivwc mwdd krdI hY ik jo Auh vyKdf hY, pYtrn AusqoNawgy ikvyN jfrI rihMdy hn- ihsfbI BwivKbfxI df afDfr!nukqf!pYtrn dy duhrfey jfx vfly ihwsy Gwto Gwt 3 vfr ivKf ky bwcy nUM smJxivwc mwdd kro. 3, 6, 5, 10, 9, 18, 17, imsfl vjLoN, dy pYtrn ivwc,pYtrn nUM afiKaf jf skdf hY ik nMbr nUM duwgxf kro aqy iewk GtfE,nMbr nUM duwgxf kro aqy iewk GtfE, nMbr nUM dwugxf kro aqy iewk GtfE.• afpxy nfm df pihlf aKwr vrqdy hoey brYWz dy tYg jF blfkF nfl iewk vwDx vflf (jFsMugVn vflf) pYtrn bxfE. iewQy T awKr leI vwDx vfly pYtrn dI imsfl hY.sfeIjL Size 1 1 sfeIjL Size 2 2 sfeIjL Size 3 3 Size sfeIjL 4 4 Size sfeIjL 5 5• afpxy bwcy nUM pYtrn ivwc aglIaF iqMn tIaF (T’s) bxfAux leI afKo aqy puwCo ik pYtrnleI ikhVf nym vriqaf. drsfieaf igaf pYtrn iqMn blfkF nfl sLurU huMdf hY aqy hr vfr doblfk jmHF huMdy hn.• afpxy bwcy nUM aMdfjLf lfAux leI afKo ik dy 15 T awKrF dy sfeIjL df pYtrn bxfAux leIAusnUM ikMny blfk cfhIdy hoxgy. ies qrF dy suafl bwcy nUM pYtrn dy nym bfry iewk afm DfrnfbxfAux aqy hr vfr nvF pYtrn nf bxf ky vDyry guMJldfr pYtrnF dIaF musLklF hwl krndyNdy hn. (15 T awKrF dy sfeIjL df pYtrn bxfAux leI 31 blfk lwgxgy.• rol bdlo aqy bwcy nUM quhfzy leI awKrF df iewk pYtrn bxfAux leI afKo.quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz27


vfr vfr duhrfxf !myry nym nUM bwuJo!• iewk sMiKafqmk pYtrn bxfE aqy bwcy nUM pYtrn dy aKIr ivwc iewk nMbr bwuJx leI afKo. imsflvjLoN, bwcy nUM afKo ik 1, 4, 7, 10, ….vrgy pYtrn ivwc awTvyN sQfn AuWqy ikhVf nMbr afvygf.Place12345Number14710• quhfzf bwcf iewk nMbr qoN dUjy qwk pYtrn nym vyKy aqy afKy, “mYN iewk nfl sLurU krdf hF aqy hrvfr iqMn jmHF krdf hF.” pYtrn nUM vDf ky, Auh awTvyN sQfn df muwl kwZ lvygf (1, 4, 7, 10, 13,16, 19, 22) jF quhfzf bwcf sQfn aqy nMbr ivwc sbMD vyK skdf hY, ijvyN ik awTvF sQfn 1 jmHF7 vfr iqMn jF 1 + (3 × 7) = 1 + 21 = 22 .guxF dy qwQF ivwc pYtrn vyKxynukqf!jdoN bwicaF kol afpxI dlIl nUM ivkisq krn df avsr huMdf hY, AuhihsfbI DfrnfvF dI vDyry smJ ivkisq krdy hn.• bwcy nUM ieh keI pwKF qoN GoKx ivwc mwdd kro ik pYtrn AusnUM guxF dy qwqF nUM cyqy rwKx ivwc mwddkr skdy hn. imsfl vjLoN, jykr quhfzf bwcf 6 × 4 df guxfPl (jvfb) nhIN dws skdf aYpr6 × 2 df pqf hY, Auh do guxf dy phfVy dy igafn nUM duwgxf krn dI qrkIb vrq ky hwl kr skdfhY. jdoN 6 × 2 dy guxPl (jvfb) nUM duwgxf kIqf jFdf hY qF ieh AuWnF hI hY ijMnf 6X4 df guxfPl(jvfb)• jykr quhfzy bwcy nUM 3 × 7 df guxfPl nhIN pqf pr Auh jfxdf hY ik 2 × 7 = 14 hUMdf hY, iewkIbxfAux leI Auh 7 df iewk hor grupw jmHF kr skdf hY. ieh qrkIb Cy dy phfVy ivwc vI kMmafAuNdI hY. bwcy sOKy nMbr 5 dy phfVy ivwc afpxI sOK vrq ky 6 dy phfVy nUM hwl krn leI vrqskdy hn- imsfl vjLoN, 4 × 6 df jvfb AuWnf hI hY ijMnf ik 24 bxfAux leI 4 × 5 df guxfPl(jvfb) + 4 df iewk hor grwup.28quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


cFs kI hn?qusIN vyKogy ik gulfbI pMinaF AuWqy aMkVf pRbMD aqy aMdfjLy ivwc mwdd krn vflIaF gqIivDIaFhn. ieh AuNtyrIE dy gixq islybs df qwq (strand) hY jo bwcy dI jfx pihcfx krvfAuNdf hYik jfxkfrI nUM iewkqr, anuvfd aqy sMgiTq ikvyN krnf hY. hr rojL bwicaF nUM vwzI mfqrf ivwcjfxkfrI idwqI jFdI hY, aqy ies ivwc kfPI ijafdf ivwc nMbr sLfml huMdy hn.ikMzrgftn qoN gryz 3lIjYNz (Legend)nMbr hr QF AuWqy hn!ikMnf AuWcf?, ikMnf nIvF?, ikMnf? ikMnf QoVf?quhfzf Aus AuWqy kI kox hY?vfr vfr duhrfxf !cFs kI hn?7 = 2 + 57 = 2 + 5quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz29


cFs kI hn?jIvn leI CFt krnIlfBbwcy dy CotI Aumry Gr dy afly duafly dIaF cIjLF nUM CFtx aqy vrgIkrx krn dy anuBvaMkVf iqafr krn aqy arQ BrpUr vrg bxfAux leI iqafr krn ivwc shfeI huMdy hn.nukqf!bwcy amUmn dws skdy hn ik AuhnF ny cIjLF dI CFtI ikvyN kIqI pRqUM ieh smJxivwc musLkl af skdI hY ik dUijaF ny cIjLF dI CFtI ikvyN kIqI.• sfDfrx CFtI dy nymF nUM socdy hoey sLurUafq kro (ijvyN ik “gruwp ivwc hr cIjL nIlI hY”), aqy kuwJcIjLF nUM nym muqfbk CFtI kro. afpxy bwcy nUM nym buwJx idE. afpxy rol bdlo.• quhfzy bwcy nUM GrylU vsqF dI CFtI krn idE- kryanF (crayons) nUM rMg muqfbk, ktlrI (cutlery)nUM AusdI iksm jF afkfr muqfbk, rfsfeIkilMg bfks leI smwgrI jF rYPrIjIrytr aqy kwpborzivwc afeItmF nUM.• afpxy bwcy nUM cIjF do gruwpF ivwc CFtI krn idE: AuhnF ijhnF dy Kfs lwCx hn aqy ijhnF dy nhIN(imsfl vjLoN, kwpiVaf df iewk juwt jo hYNgrF AuWqy jFdf hY aqy iewk juwt jo nhIN jFdf) bwcy dI socbfry ieh puwC ky gwl kro, “ qusIN iehnF dI CFtIN ikvyN kIqI?” “cIjLF iks qrIky ieko ijhIaF hn?vwKrIaF ikvyN? “kI qusIN iehnF nUM iksy hor qrIky CFtI kr skdy ho?”30quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


cFs kI hn?iewk pirvfrk smfgm dI Xojnf leI aMkVy nUM vrqxflfBieh gqIivDI bwcy nUM jfxkfr bxfeygI ik asIN pihly sQfn AuWqy aMkVy iewkqr aqysMgiTq ikAuN krdy hF- Kfskrky, suaflF dy jvfb dyx leI aqy BwivK leI XojnfvFbxfAux leI!nukqf!bwcy nUM iehnF bfry PYsly lYx idE:• srvy ivwc ikhVy suafl puwCxy hn• aMkVf ikvyN iewkqr krnf hY (ijvyN ik srvy dy suaflF df jvfb kOx dyvygf)• aMkVy nUM sMgiTq ikvyN krnf hY (ijvyN ik nfvF qoN ibnf tYlI (tally ) duafrfjF sMkyqF nUM vfh ky.• quhfzf bwcf af rhy pirvfrk smfgm leI iewk srvy krnf cfh skdf hY- imsfl vjLoN, “ pirvfrdy mYNbr iks iksm dI gqIivDI ijafdf krnI psMd krngy?” “iks iksm df Kfxf aqy pyapdfrQ lokI psMd krngy?• bwcy nUM Auh srvy suafl iqafr krn leI AuqsLfihq kro ijhnF df hF jF nf qoN vwD jvfb hovy .(imsfl vjLoN, ieh pwuCx dI QF ik “kI qusIN jUs psMd krogy?” “qusIN iks iksm df pya pdfrQpsMd krogy?• afpxy bwcy nUM cuxn idE ik iksnUM srvy krnf hY (isrP nyVy dy pirvfrk mYNbr?, ivsqirqpirvfr dy mYNbr? sfry bwcy? bwcy aqy bflg?)• puwCo ik quhfzf bwcf srvy jfxkfrI df ikvyN iDafn rwKygf aqy sFJI krygf.• srvy qoN bfad, afpxy bwcy nUM puwCo ik ijhnF df srvy(nmUnf) kIqf igaf, AuhnF nqIijaF nUM ikvyNpRBfivq kIqf32quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


aMkVf pRbMD aqy sMBfvnf (Probability)aksr, kdy kdfeIN jF kdy nhIN KyzikMzrgftn qoN gryz 3lfBKyzF duafrf, qusIN afpxy bwcy nUM Aus BfsLf df prIcY krvf skdy ho jo ihsfbdfn iksyGtnf dy hox dI sMBfvnf nUM drsfAux leI vrqdy hnL: insicq, mumikn, gYr-mumikn,asMBv aqy brfbr dI sMBfvnf• afpxy bwcy nUM AuhnF cIjLF dIaF qsvIrF bxfAux jF Aus bfry gwlF krn idE jo quhfzf pirvfrhmysLf, aksr aqy kdy kdfeIN krdf hY aqy kuwJ cIjLF quhfzf pirvfr kdy nhIN krdf. afpxybwcy nUM puwCo ik inwq idn dIaF hor ikhVIaF GtnfvF hn ijhnF bfry Auh ies qrF dI BfsLfvrq ky gwl kr skdf hY.• ieh Kyz kfr clfAux vyly Kyzx dI koisLsL kro. GtnfvF dy nfm lvo aqy afpxy bwcy nUM PYslfkrn idE ik iehnF df hoxf mumikn jF gYr mumikn jF kdy nhIN hoxgIaF. qusIN isrPafpxI klpnf ijMnf hI bMny hoey ho! imsfl vjLoN:• asIN jnvrI ivwc qYrFgy.• asIN jnvrI ivwc bfhr qYrFgy.• sfzI rsoeI dI iKVkI ivwcoN iewk GoVf AuWz ky afvygf.• pqJwV ivwc pwqy rMg bdlxgy.• sQfnk icVIafGr ivwc iewk zfienfsor af irhf hY.ZOOquhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz33


cFs kI hn?asIN vIkaYNz AuWqy afpxf smF iks qrF ibqfAuNdy hF?lfBieh pirvfrk srvy quhfzy bwcy nUM buinafdI aMkVf iewkqr krn ivwc anuBv dyNdf hYsrvyKxF,ivcfrF aqy qjuribaF rfhIN iswDy iewkqr kIqy jfxkfrI dy tukVy.nukqf!bwcy nUM aMkVy bfry socx leI sLurU kr vfsqy AuqsLfihq kro:• Auh kuwJ ikhVy qrIky hn ijhnF rfhIN qusIN aMkVy nUM iewkqr aqyirkfrz kr skdy ho?• jykr vIkaYNz sLfml kIqy jfx qF aMkVf ikvyN idwsygf?• quhfzIaF lwBqF quhfzy pirvfr dy vIkaYNz AuWqy KflI smyN dI vrqoN nUMikvyN pRBfivq krngIaF?• lokI KflI smyN dI ishqmMd vrqoN bfry bihs krdy hn. vwKo vwKry lokF dy vwKry ivcfr hn. afpxybwcy nfl ies ivsLy bfry iKafl lYx leI gwlbfq kro.• afpxy bwcy nUM quhfzy pirvfr dy KflI smyN bfry aMkVf iewkTf krn idE-imsfl vjLoN, aMdrUnIbnfm bfhr dIaF gqIivDIaF, KyzF, imlx jfx aqy sYr AuWqy ibqfieaf smF aqy prdy dy sfhmxyibqfieaf smF (ijvyN ik tYlIvIjLn, kMipAUtr, vIzIE gym jF hwQ ivwc PV ky clfAux vflf XMqr).34quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


aMkVf pRbMD aqy sMBfvnf (Probability)aMkVy dI Bflgryz 4 qoN gryz 6lfBafpxy bwcy df dUjy krm dy aMkVy (secondary data) dy iKafl nfl prIcY krvfE –iewk irsfly, aKbfr, srkfrI dsqfvyjL jF zYtfbys ivwcoN aMkVf- ies mnorMjk gqIivDIduafrf.• afpxy bwcy nfl aKbfrF ivwc afey iksy hflIaf muwdy bfry gwl kro ijs ivwc AusdI idlcspIhY. quhfzy bwcy dy ivcfr, socxI aqy suafl kI hn? quhfzf bwcf ies bfry hor kI jfnxf psMdkr skdf hY?• afpxy bwcy nfl, dUjy krm dy aMkVy (secondary data) bfry ieh pRsLn ivcfro:• aMkVy dy sRoq kI hn? qusIN kI socdy ho ik aMkVf ikMnf ku BrosyXog hY? quhfzy kI pRsLnho skdy hn?• ikhVf nukqf njLr awgy ilaFdf igaf hY? ies aMkVy dIaF kI sImfvF hn? kI kuwJgfieb hY?• jo qusIN lwBx dI koisLsL kr rhy ho, Aus dy sMdrB ivwc aMkVf ikMnf ku lfhyvMd hY? kIkoeI aMcBy jF rucI dIaF vsqF hn jo qusIN not kIqIaF?• kI aMkVf quhfzy leI koeI nvyN suafl KVy krdf hY?quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz35


afnlfeIn sRoqEsso Family Mathies sfeIt Auwqy gqIivDIaF, Koj aqy jfxkfrImfipaF aqy bwicaF nUM surwiKaq aqy afrfm BrymfhOl ivwc AuhnF dI soc aqy smJ sFJf krn ivwcmwdd krdI hY. AuhnF dI soc sLFJI krnaqy ihsfb dI iewkwww.edu.uwo.ca/essofamilymathMath FrogiewQy quhfnUM gryz 4, 5 aqy 6 dy leIsRoq aqy afnlfeIn KyzF imlxgIaF.http://cemc2.math.uwaterloo.ca/mathfrog/main.shtmlABC Life Literacyieh sRoq bwicaF nUM ivwqI sfKrqf nfl jfxkfrkrvfAuNdf hY aqy isKfAuNdf hY.http://abclifeliteracy.ca/financial-literacy-tips-andresourcesFigure Thisies sfeIt AuWqy bwicaF duafrf mfipaF nfl krnvflIaF gixq dIaF KyzF aqy cuxOqIaF hn.www.figurethis.orgMath Wireies sfeIt AuWqy keI iksm dy ihsfbI sRoq, tYst aqyKyzF mOjUd hn.http://mathwire.comPedagoNetiewQy quhfnUM ihsfb dy ilMk aqy KyzF imlxgIaFwww.pedagonet.comMath Dictionary for Kidsieh afnlfeIn sfDn bwicaF nUM ihsfb dI sLbdfvlIdIaF pRIBfsLfvF iswKx ivwc mwdd krdf hY.www.amathsdictionaryforkids.comMath Forumies sfeIt AuWqy Kfskrky aYlImYNtrI ivwidafrQIaF leInukqy, cflF aqy ihsfb dIaF smwisafvF pfeIaF geIaFhn.www.mathforum.org/students/elem/probs.htmlNational Library of VirtualManipulativesies afnlfeIn sfDn AuWqy Aumr dy ihsfb AUtfh stytXUnIvristI (Utah State University) qoN vfsqivkkOsLlqf vfly suafl pfey gey hn.http://nlvm.usu.edu/en/nav/vlibrary.htmlKid SitesiewQy qusIN bwicaF leI ihsfb dIaF sfeItF iewk ilstpfEgy.www.kidsites.com/sites-edu/math.htmMath Playgroundies sfeIt AuWqy ihsfb dI pVfeI leI Aumr aqygryz leI AupXukq KyzF aqy vrksLItF hn.www.mathplayground.com36quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz


TVOkids.com aqy gixqnMbr df arQ (Number Sense) aqy aMk igxqI (Numeration)ikMzrgfrtn qoN gryz 3Caterpillar Countwww.tvokids.com/games/caterpillarcountConnect the Dots with Arttwww.tvokids.com/games/connectdotsarttCount with Arttwww.tvokids.com/games/countarttnfp qolikMzrgfrtn qoN gryz 3Clock Talkwww.tvokids.com/games/clocktalkgryz 4 qoN gryz 6Tumbleweed’s MathMaze(sLurUafqI aqy drimafnf pwDr)www.tvokids.com/games/tumbleweedsmathmazeBruce McBruce Doodle Dotswww.tvokids.com/framesets/play.html%3Fgame%3D51Tumbletown Mathleticswww.tvokids.com/games/tumbletownmathleticsBig Wig Sub Shopwww.tvokids.com/games/bigwigsubshopgryz 4 qoN gryz 6Beat the Clockwww.tvokids.com/games/beatclockTumbletown Mathleticswww.tvokids.com/games/tumbletownmathleticsjIEmYtrI aqy sQfn df arQ (Spatial Sense)ikMzrgfrtn qoN gryz 3Shapevillewww.tvokids.com/games/shapevillegryz 4 qoN gryz 6Triangle Alleywww.tvokids.com/games/trianglealleyBuild Math Citywww.tvokids.com/activities/buildmathcityPirates Maps and Trapswww.tvokids.com/games/piratesmapsandtrapsaMkVf pRbMD aqy sMBfvnf (Patterning and Algebra)ikMzrgfrtn qoN gryz 3gryz 4 qoN gryz 6A Lotta Dessertwww.tvokids.com/games/lottadessertaMkVf pRbMD aqy sMBfvnf (Probability)Flower Frenzywww.tvokids.com/games/flowerfrenzyikMzrgfrtn qoN gryz 3Sort Itwww.tvokids.com/games/sortitgryz 4 qoN gryz 6Space Trek Galaxywww.tvokids.com/games/spacetrekgalaxyafpxy bwcy dy sfKqrf ivkfs, ihsfb aqy sfieMs ivkfs leI PrI vIzIE, gymF aqy gqIivDIaFleI www.tvokids.com AuWqy jfE. afpxy bwcy dy iswKx dy sPr ivwc mwdd dyx leI AuNtyrIEAuWqy kyNdirq sRoqF leI www.tvoparents.com AuWqy vI jfE.quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz37


7 = 2 + 5Ontario Ministry of EducationCette publication est disponible en français.ISBN 978-1-4435-9373-1 (Print) ISBN 978-1-4435-9374-8 (PDF)ISBN 978-1-4435-9375-5 (TXT) © Queen’s Printer for Ontario, 2012

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