ikmzrgfrtn qon 6 gryz qwk - ontario · gryz qwk auntyrie dy iswikaf mihkmy di afpxy bwcy num gixq...

7 = 2 + 5

7 = 2 + 5 quhfzy bwcy nfl gixq krnfikMzrgfrtn qoN 6 gryz qwk

mfipaF dI gfeIz

PUNJABI

7 = 2 + 5

quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk AuNtyrIE dy iswiKaf mihkmy dI afpxy bwcy nUM gixq krn ivwc mwdd krnf : mfipaF leI gfeIz df iewk suDiraf rUp hY. pyrYNt aYngyjmYNt dPqr (Parent Engagement Office) dI sFJIdfrI nfl iltrysI aqy inAUmrysI swkqryq (Literacy and

Numeracy Secretariat) vwloN iqafr kIqf igaf hY. ies aYzIsLn ivwc nvIaF cIjLF hn: TVOkids.com AuWqy KyzF aqy gqIivDIaF dy ilMk

smwgrI

quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz1

mfipaF leI not .....................................................................................................................2

mYN afpxy bwcy dI iswiKaf ivwc ikvyN mwdd kr skdf/skdI hF? ......................................2

sfzy bwicaF dy gixq iswKx dI Xogqf ivwc XkIn jrUrI ikAuN hY? ..................................3

islybl (curriculum)nfl kI sbMD hn? ..................................................................4

kuwJ idlpRcfvy vfly pirvfrk iswKx dy qjurb ........................................................................5

nMbr qF hr QF hn! ....................................................................................................5

ikMnf AuWcf? ikMnf nIvF? ikMnf? ikMnf Gwt? ................................................................ 15

quhfzf Aus AuWqy kI kox hY? ....................................................................................... 20

vfr vfr duhrfxf ! ................................................................................................... 24

cFs kI hn? ............................................................................................................. 29

afnlfeIn sRoq .................................................................................................................... 36

TVOkids.com aqy. gixq ................................................................................................ 37

ijMnf vDyry pirvfr afpxy bwicaF dI iswiKaf aqy ivwidak qrwkI ivwc mwdd krdy hn, sMBfvnf hY ik bwcy AuWnf hI vDyry cMgf skUl ivwc krngy aqy afpxI iswiKaf nUM jfrI rwKxgy.

Karen Mapp and Anne Henderson, 2002 A New Wave of Evidence:

The Impact of School, Family, and Community Connections on Student Achievement

mfipaF leI not

quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz2

mYN 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 socx aqy gwl krn bfry ruJfAux leI rsqy lwBdy ho, qusIN Ausdy BwivK dI sPlqf leI iewk mhwqvpUrx kuMjI pRdfn kr rhy ho. awj, aflocnfqmk soc, smwisaf hwl krnIaF, dlIl Xogqf aqy gixq dy qrIky nfl sMcfr krnf jrUrI hunr hn. ieh pRikirafvF AuNtyrIE skUlF ivwc gixq pVfAux dI buinafd hn. ieh Kyz df ihwsf bx jFdIaF hn jdoN qusIN ieh gfeIz ivwc suJfeIaF geIaF gqIivDIaF ivwc bwcy nUM ruJfAuNdy ho. iewkTy iswKx df afnMd mfxo!

• gixq bfry mjbUq, hF pwKI rveIey Ausfro: jdoN bwcy hF pwKI rUp ivwc ruwJy aqy sPl mihsUs krdy 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 KFdIaF hn: 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 mihsUs krdyho, AusnUM vrqo: quhfzf bwcf Aus BfsLf ivwc isDFqF nUM ibhqr smJygf ijs nUM vDIaf jfxdf hY.

mfipaF leI cotI dy nukqy

ikRpf krky not kro: Please note: ies gfeIz ivwc, mfpy sLbd mfipaF, srpRsqF, sMBfl krn vfilaF aqy pirvfr dy hor mYNbrF df hvflf dyNdf hY jo bwicaF nUM pVn aqy ilKx ivwc mwdd krdy hn.

mfipaF leI not

3

sfzy 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 drvfjLy Koldf 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 ieh gwl df ihsfb rwK skdy hF ik ikMnf jUs lwgdf hY qF jo asIN jfxIey ik hr hPqy ikMnf jUs KrIdxf hY)

• afpxy pYsy aqy smyN df pRbMD krnf (imsfl vjLoN, asIN igx skdy hF ik sfnUM kMm AuWqy jfx nUM ikMnf smF lwgdf hY, Kfxf bxfAux leI ikMnI smwgrI lwgdI hY aqy Kfxf KrIdx leI sfnUM ikMny pYsy dI loV hY)

• inwq idn dIaF pRsiQqIaF nUM sMBfl skIey ijhnF ivwc nMbrF dI sLmUlIaq huMdI hY (ijvyN ik pqf 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 ivsLvfsL krn dI loV hY. iewQy hI quhfzI sLmUlIaq sLurU huMdI hY. qusIN afpxy bwcy dy iswKx leI pihly rol mfzl ho skdy ho. jdoN qusIN afpxy bwcy nUM mwddgfr, sihj mfhOl ivwc ruJfAuNdy ho, quhfzf bwcf gixq nfl mOj msqI krdf hoieaf joKm lYx df afnMd mfxygf!

7 = 2 + 5

quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz

mfipaF leI not

4

islybs (curriculum)nfl kI sbMD hn?

ies gfeIz ivwc gqIivDIaF quhfzy bwcy nUM inwq idn dIaF gqIivDIaF ivwc gixq dyKx ivwc mwdd krn leI cuxIaF geIaF sn. ieh quhfzy bwcy dy KyzF pRqI ipafr nUM vI hwlfsLyrI dyNdIaF hn. aqy AuNtyrIE 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 idwqIaF sfrIaF gqIivDIaF nhIN krnIaF. Aqy BfvyN keI gqIivDIaF sLfml kIqIaF geIaF hn, Auh islybs df sfrf kuwJ sLfiml nhIN krdIaF. ieh gfeIz AuhnF gqIivDIaF df iewk nmUnf pysL krdI hY jo qusIN afpxy 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 (Thefivestrands) dy nfm pihcfx jfvogy.

pMj qwq (Thefivestrands)


nMbr df arQ (Number Sense)aqy aMk igxqI (Numeration)

nfp qol

jIEmYtrI aqy sQfn df arQ (Spatial Sense)

nmUnfbfjI aqy aljbrf

aMkVf pRbMD aqy sMBfvnf (Probability)

AuNtyrIE df ihsfb df islybs 7 pRikirafvF AuWqy jor dyNdf hY jo ihsfb iswKx leI jrUrI hn: hr gryz ivwc, iewk “mathematical process expectations” (ihsfbI pRikiraf dI qfk) df sYWt drsfAuNdf hY ik ikvyN bwcy srgrmI nfl iswKdy hn aqy ihsfbI smJ nUM apxfAuNdy hn.

• musLkl hwl krnI• dlIl aqy pRmfixq krnf• pRqIibMbk

hr gryz ivwc, ‘gixq pRikiraf dIaF afsF (mathematical process expectations) df iewk sYWt ibafn krdf hY ik bwcy iks qrF cusqI nfl gixq dI smJ iswKdy hn aqy lfgU krdy hn.

iewk gixqkfr vfgUM socxf aqy bolxf iswKxf

• sbMD joVnf• smwgrI cuxn aqy gixk

rxnIqIaF

• pysL krnf• sMcfr krnf

Ontario Mathematics curriculum: www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf

www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf

5

ikMzrg

ftn qoN gryz 3

nMbr hr QF AuWqy hn!

qusIN vyKogy ik sMqrI pMinaF AuWqy gqIivDIaF hn jo nMbrF dy arQ aqy aMk igxqI nUM mwdd dyNdIaF hn. ieh AuNtyrIE dy gixq dy islybs ivwc qwq (strand) hY jo nMbr ikvyN kMm krdy hn aqy ikvyN Auh iewk dUjy nfl myl KFdy hn, dI smJ bfry hY. ieh buinafdI ikRiafvF (basic operations) nUM vI kvr krdf hY: joV, GtfE, guxf aqy vMz. nMbr df arQ (Number Sense)aqy aMk igxqI (Numeration) ihsfbI soc leI afDfr pRdfn krdy hn.

lIjYNz (Legend)


ikMnf AuWcf?, ikMnf nIvF?, ikMnf? ikMnf QoVf?

quhfzf Aus AuWqy kI kox hY?

vfr vfr duhrfxf !

cFs kI hn?



ikMnIaF cIjLF hn igxn leI!

6

jdoN bwcy pihlI vfr igxnf sLurU krdy hn, Auh mhwqvpUrx gixqI iKafl iswKdy hn:

• iewk cIjL nfl iewk nUM imlfAuxf (iewk nMbr leI iewk vsqU)

• siQr qrqIb (asIN 1,2,3,4…igxdy hF nf ik 1,2,7,5,…)

• kfrzInYltI (Cardinality) (aKIrlf igixaf nMbr dwsdf hY ikMny hn)

lfB

nukqf!jdoN bwcy igxqI krnf iswKdy hn, Auh sprsL krnf psMd krdy hn, iesLfrf krky aqy vsqF nUM ihlf ky ijAuN Auh nMbrF nUM AuWcI boldy hn- so AuhnF nUM AuqsLfihq kro!

• afpxy bwcy nUM iKzOxy, rsoeI dy brqn, kwpVy dIaF afeItmF ijvyN Auh zrfier ivwcoN bfhr inkldIaF hn, sMgRih (ijvyN ik sitwkr, bwtn jF gIty) aqy koeI hor vsqU igxn idE jo quhfzy bwcy dI igxqI ivwc rucI dwsdI hY.

• iehnF nUM imlf idE! afpxy bwcy nUM vsqF dy iewk sYWt nUM igxn idE pRqUM sYWt ivwc vwKry QF qoN sLurU kro (imsfl vjLoN, sYWt dy sLurU dI bjfey awD ivwcoN igxnf sLurU kro. ieh ies iKafl nUM ivkisq krdf hY ik iewk sYWt ivwc vsqF dI igxqI iksy iewk vsqU nfl ikqy qoN vI sLurU ho skdI hY aqy iehnF df kwul qF vI AuhI rhygf.

• igxqI vfly gIq gfE aqy igxqI nUM koeI arQ BrpUr qrIky KyzF ivwc vrqo, ijvyN ik lukx mIcI, igxqI vflIaF KyzF, kivqfvF aqy gIq jo sfzy swiBafcfr ivwc mOjUd hn. keI igxqI vfly gIq aqy kivqfvF bwiciaF nUM iswDf aqy Aultf igxn ivwc mwdd krdy hn.

• vwzy grwupF dIaF vsqF jldI igxn leI afpxy bwcy nUM igxqI Cwzx idAu (do, pMjF jF dsF nfl igxqI krnf). blfk, pfsqf dy tuwkVy, twuQipwk (toothpicks) jF bwtnF nUM vrqo.


7

ikMzrg

ftn qoN gryz 3

nMbr hr QF AuWqy hn! nMbr df arQ (NUMBER SENSE)aqy aMk igxqI (NUMERATION)

ikMny?

ijAuN 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 |

lfB

• afpxy bwcy dI nMbrF nUM drsfAux leI vrqy gey pRqIkF dI jfgrqI iesnUM Kyz bxf ky ivkisq 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 AuWqy aqy tIm dy svYtrF AuWqy.

•ISpy (mYN jfsUs) df nMbr rUp (version) Kyzo. imsfl vjLoN, “ mYN Aus cIj dI jfsUsI krdf hF ijs 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 tybl dy 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.


8


inwq idn dIaF musLklF hwl kro


nukqf!afpxy bwcy gixq dI musLkl bfry gwl krn idE jF iesnUM ies qrIky ivKfE jo Aus leI arQ rwKdI hovy- imsfl vjLoN, quhfzf bwcf aYkitMg kr skdf hY, asl smwgrI nUM vrqo, iesnUM AusdIaF AuNglF AuWqy vfho!

afpxy bwcy nUM nMbrF nUM vrq ky musLklF hwl krn ivwc sLfml kro aqy hr rojL dy PYsly kro. qusIN hyT iliKaf puwC skdy ho:

• sfnUM rfq dy Kfxy vfsqy ctxI bxfAux vfsqy Cy tmftr cfhIdy hn, aqy sfzy kol isrP do hn. sfnUM hor ikMny KrIdx dI loV hY?

• quhfzy kol quhfzy kmry ivwc do isrhfxy hn aqy quhfzI BYx kol Ausdy kmry ivwc do srhfxy hn. quhfnUM ikMny isrhfixaF dy kvr Doxy pYxgy?

• “sfzy kol do mihmfn rfq df Kfxf Kfx af rhy hn. sfnUM ikMnIaF plytF dI loV hovygI? ikMny BFzy cfhIdy hoxgy?

vDyry cuxOqI BrIaF siQqIaF ivwc vwzy nMbrF df joV jF GtfE sLfml ho skdf hY jF Auh pRsiQqIaF ijwQy quhfzy bwcy nUM musLkl hwl krn leI iewk qoN vwD vfr joV jF GtfE krnf hY.

1 Red Apple1 Pillow

1 Plate


9

ikMzrg

ftn qoN gryz 3


joVnf aqy GtfAuxf mjLydfr bxfieaf

ieh KyzF Kyzx nfl, quhfzf bwcf iswKygf ik joVn aqy GtfAux df koeI shI qrIkf nhIN hY- ihsfbdfn keI iksm dIaF rxnIqIaF vrqdy hn.

lfB

nukqf!afpxy bwcy nUM Auh rxnIqI apnfAux leI AuqsLfihq kro jo Aus leI koeI mfanf rwKdI hY- imsfl vjLoN, “counting-on” rxnIqI quhfzy bwcy nUM gym ivwc 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 ivwc joV aqy GtfE sLfml huMdf hY. afpxy bwcy nUM nMbr kfrzF dy cfr jF vDyry sYWt bxfAux ivwc mwdd kro. hryk kfrz dy iewk sfeIz AuWqy iewk qoN 10 qwk iewk nMbr hovygf. iewQy kuwJ gymF krn vfsqy suJfeIaF geIaF hn:

• AuWcy nMbr. kfrzF nUM imlfE aqy Pyr AuhnF nUM iewk ZyrI bxf ky muwDy mUMh rwK idE. hr iKzfrI do kfrz lYNdf hY aqy AuhnF df joV krdf hY. ijs iKzfrI kol vwzf nMbr hY, Auh dUjy iKzfrI dy kfrz lYNdf hY. iKzfrI Kyzxf jfrI rwKdy hn aqy iewk vyly do kfrz joVdy hn jdoN qwk koeI vI kfrz nhIN bwcdf. vDyry kfrzF vflf iKzfrI jyqU hY. qusIN iesy Kyz nUM GtfAux nfl Kyz skdy ho, pRqUM iesnUM Gwt nMbr afiKaf jfvygf. Gwt Prk (jvfb) vflf iKzfrI afpxy kfrz dUjy iKzfrI nUM dyNdf hY. ijs ivakqI kol aMq ivwc swB qoN Gwt nMbr hn, Auh jyqU hY. qusIN iesy gym nUM guxf nfl Kyz skdy ho.

• nMbr ikAUb do vfrI (Number Cube Twice): hr iKzfrI do nMbr ikAUb roVdf hY aqy idwsdy nMbrF nUM joVdf hY. vwD nMbrF vflf ijwqdf hY. qusIN iesy gym nUM GtfE aqy guxf nfl Kyz skdy ho.


10


tuwty kYlkulytr dI Kyz

lfB ihsfbdfn jfxdy hn ik mfqrf nUM drsfAux dy vwKo vwKry qrIky huMdy hn- imsfl vjLoN, 18 nUM 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 ik Auh 8 dy bwtn qoN ibnf skrIn AuWqy 18 nUM ikvyN drsf skdf/skdI hY. (nmUny dy jvfb ivwc sLfml hY 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 kYlkulytr AuWqy ivKfAuxf cfhIdf hY ies kMm nUM hor sOKf jF vDyry cuxOqI vflf bxfE.


11

ikMzrg

ftn qoN gryz 3


iewk df awDf iewk dy awDy brfbr huMdf hY – jF kI ieh huMdf hY?

iewk Bfg (fraction) pUry aqy iewk ihwsy ivwc sbMD nUM drsfAuNdf hY. do BfgF nUM mukfblf krdy smyN, quhfzf bwcy iswKygf ik ieh “pUry’ df ikMnf sfeIjL hY.

lfB

bwcy ieh iswKdy hn ik iewk CotI cIjf df awD (ijvyN ik iewk CotI rwsI) iewk vwzI cIj (ijvyN ik iewk vwzI rwsI)L dy qIjy ihwsy qoN Cotf ho skdf hY. nukqf!

• afpxy bwcy nfl, iewko iksm dI bnfvt vflIaF vsqF iewkqr kro, ijvyN ik koeI qOlIaf, rwKx vflf 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 qoN ihwsy qoN vwzf huMdf hY? gwl alfihdf iksm dIaF siQqIaF vwl iljfx vfsqy hor smwgrI dI vrqoN kro, ijvyN ik vwKo vwKry iksm dIaF plytF dy ihwsy jF vwKry sfeIjL dy kmiraF dI QF.

= =



pYsy dIaF KyzF

12

lfB nMbrF nUM keI vwKry qrIikaF nfl drsfieaf jf skdf hY. ieh gixq df gur quhfzf bwcf pYsy dIaF KyzF Kyzx qoN iswKygf.

nukqf!bwcy iewk iksm dy iswikaF nUM joVnf sLurU kr skdy hn ikAuNik AuhnF nUM aijhf krnf 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 lwg skdf hY ik quhfzf bwcf iks nMbr nfl swikp kfAuNitMg (skip counting) krn ivwc sOK mihsUs krdf hY. keI iksm dy iswikaF nUM iewk ZyrI ivwc rwKo, aqy bwcy nUM hr iswky df joV lfAux leI afKo. 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 ik ikhVy iswky df joV pihlF lfAuxf hY. AusnUM suJfa idAu ik qusIN dovyN AuhnF iswikaF nUM joVn dI dOV lfE ijhnF nUM igxn ivwc quhfzf bwcf Gwt sOK mihsUs krdf hY. imsfl vjLoN, jykr quhfzy bwcy nUM inwkl (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 rol bdl 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 Gwt ikMny iswky hoxy cfhIdy hn.

3[ bYNk vflf: “myry bYNk ivwc 1 zflr 75 sYNt hn. myry kol ds iswky hn. ieh ikhVy iswky ho skdy 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 jF aOKf bxf skdy ho (imsfl vjLoN, isrP zfeIm (dimes) jF kuafrtr (quarters)


13

gryz 4 qoN g

ryz 6


myrf nMbr kI hY?

iewk nMbr dUjy nMbr nfl ikvyN qulnf ivwc hY jF sbMD bxfAuNdf hY, ies bfry socxf sfnUM nMbrF bfry ihsfbdfnF vfgUM socx ivwc mwdd krdf hY- Bfv lckIlpx nfl!

lfB

AuhnF rxnIqIaF nUM vyKo jo Kyzx vyly bwcf sMBfvnfvF NnUM Gwt krn leI vrqdf hY. myrf nMbr kI hY?nukqf!


• nMbr lfeIn (A number line) iewk njLr pYxf vflf Aupkrx hY jo nMbrF dI qulnf leI vriqaf jFdf hY. iewk nMbr lfeIn (A number line) dI imsfl hY:

• Qwly nUM jFdf ivKfeI dyNdf lfl qIr nMbr lfeIn (A number line) AuWqy zYsImfl (decimal) nMbr 3[2 drsfAuNdf hY.

• Kyz ivwc vrqx leI iksy zYsImfl (decimal) nUM soco. imsfl vjLoN, afpxy bwcy nUM afKo, “myrf zYsImfl (decimal) ies nMbr lfeIn AuWqy iksy QF AuWqy hY. ieh 1 qoN vwzf hY aqy 4 qoN Cotf hY.

• quhfzf bwcf suafl puwC ky nMbr df aMdfjLf lfAux dI koisLsL krdf hY ijs df jvfb qusIN hF jF koeI huMgfrf nf dy ky dyNdy ho. imsfl vjLoN, “kI nMbr 2 aqy 4 dy drimafn hY? kI nMbr 3[5 qoN vwzf hY?” Aus vyly qwk lwgy rho jdoN qwk quhfzf bwcf shI nMbr df bwuJ nhIN lYNdf aqy quhfzy nMbr nUM AuWQy nhIN ilK dyNdf ijwQy lfeIn AuWqy AusdI QF hY.

• afpxy rolF nUM bdl lvo aqy bwcy nUM iewk zYsIml nMbr aqy nMbr lfeIn cuxn idE aqy pRikiraf nUM duhrfE.

14


anupfqk soc sfzy afly duafly hY

lfB qulnf krn dy kfPI qujrby qoN bfad, quhfzf bwcf afKr nUM anupfqk soc vwl qrwkI kr lvygf- 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 soc nUM 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 afpxI 25% 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. AusdI BYx afKdI hY ik Auh afpxy lfB df iewk cuQfeI ihwsf AusnUM dyvygI. kI gYbrIalf leI ieh cMgf sOdf hY? dwso ikAuN?

• ies vrnx df arQ ibafn kro. ies jfxkfrI nfl pirvfr kI PYsly kr skdf hY?

15

ikMzrg

ftn qoN gryz 3


qusIN vyKogy ik nfp df afDfr bxdIaF jo gqIivDIaF jfmnI rMg ivwc hn. ieh AuNtyrIE dy gixq dy islybs ivwc pMj qwq (Thefivestrands) hn jo quhfzy bwcy nUM jfxUM krvfAuNdy hn ik ihsfbdfn vsqF dI AucfeI, lMbfeI aqy cOVfeI ikvyN inrDfrq krdy hn. ieh vI ibafn krdy hn ik vsq jo Kyqr GyrdI hY, vsq jo mfqrf (smrwQf) lY skdI hY aqy sQfn (GxPl) jo vsq lYNdI hY, AuhnF nUM ikvyN inrDfrq krnf hY.

lIjYNz (Legend)




vfr vfr duhrfxf !

cFs kI hn?


16


Gr dy ierd igrd vsqF dI qulnf krnf

lfB mihjL Gr dy ierd igrd vsqF dI qulnf krn nfl, quhfzf bwcf nfp dy keI buinafdI isDFq smJxf 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 df Kfxf) df aMdfjLf krn leI afKo jo pirvfr nUM hPqy leI cfhIdIaF hn. AusnUM pwuCo,”qUM ikAuN socdf hYN ik ieh mfqrf cfhIdI hovygI?” hPqy dy aMq ivwc, bwcy nUM asl ivwc vrqIaF cIjLF dI igxqI krn idE.

• kwpborz ivwcoN kuwpIaF, zwby aqy pYk iewkTy kro. bwcy nUM iehnF nUM iksy qrqIb (imsfl vjLoN, lMby aqy Coty, ijafdf smfn smoNdy hn aqy Gwt smfn smoNdy hn, KflI aqy Bry hoey, Bfry aqy hlky) ivwc rwKx leI afKo.

• sfry afkfrF dy zwby iewkqr kro aqy iewk kOPI vflI kVCI, plfsitk df kwp jF lFzrI dI sfbx vflI kVCI. bwcy nUM ryq dy zwby ivwc ryq jF hOdI (sink) ivwc pfxI nfpx idE aqy keI zwibaF dI mfqrf dI qulnf krn idE. bwcy nUM nfp ky qulnf krn idE ik hr zwby nUM Brn leI ikMnIaF kVCIaF cfhIdIaF hn. puwCo, “ iks zwby ivwc ijafdf mfqrf afeI? iks zwby ivwc swB qoN Gwt mfqrf afeI?”


17

ikMzrg

ftn qoN gryz 3

nfp qol

ikMnI dyr lwgdI hY?

smyN dIaF mfnk XUintF () nUM vrqxf iswKx nUM aiBafs aqy qjurbf cfhIdf hY. jdoN quhfzf bwcf smyN dI bIqx nUM inwjI GtnfvF nfl joVn lwgdf hY, Auh smyN dI imafd dy nfp dIaF sLrqF (measurement terms) nUM smJxf sLurU kr dyvygf:

lfB

• lMbf aqy Cotf* •qyjL aqy hOlI* •pihlf aqy aKIrlf* •pihlF aqy bfad

• bwcy nUM smyN dy bIq jfx bfry jfnx leI sMkyqF dI vrqoN kro (imsfl vjLoN, “sfnUM qyry iKzOxy QF isr rwKx leI isrP do imMt lwgy”). bwcy nUM smF inwq jIvn dIaF gqIivDIaF dy pirpyK ivwc dwso (imsfl vjLoN, “hux qoN ds imMt qwk sLfm dy 7 vwj jfxgy aqy quhfzf nhfAux df smF hY”).

• afpxy bwc nfl, skUl jfx, Kfxf Kfx, sOx leI jF gym Kyzx nUM ikMnf smF lwgdf hY, jfnx leI iewk tfeIm pIs df iesqymfl kro.

• kYlMzr AuWqy inwjI aqy pirvfr dIaF GtnfvF nUM afXoijq krn leI bwcy nUM nfl sLfml rwKo. bwcy nUM AusdIaF mnpsMd “Gr qoN dUr krn vflIaF gqIivDIaF” ilKx idE (ijvyN ik Kyz Kyzxf, lfiebryrI jfxf jF iksy dosq kol jfxf) aqy gqIivDI ikMny vjLy hovygI (imsfl vjLoN, sOkr sLfmI 7 vjLy qoN 8 vjLy qwk)

mOsm aqy hor mOsm

• quhfzy aqy quhfzy bwcy dy vyKx leI iKVkI qoN bfhr rKx vflf iewk QrmfmItr rwKo. afpxy bwcy nfl hr rojL, hr hPqy jF kuwJ hPiqaF df qfpmfn nfpo. bwcy nUM AusdIaF irkfrizMgF lYx aqy ieh pqf krn ik ikhVf qfpmfn swB qoN grm aqy swB qoN vWD TMzf sI, leI afKo. bwcy nUM puwCo ik qfpmfn ny AusdIaF gqIivDIaF nUM ikvyN pRBfivq kIqf. bwcy nUM quhfzy bfhr rwKy QrmfmItr dy qfpmfn dI KbrF ivwc idwqy gey qfpmfn nfl qulnf krn idE. koeI Prk hovy aqy Ausdy sMBfivq kfrxF bfry crcf kro.


18


aMdfjLf : iewk mhwqvpUrx gixqI hunr

kdoN vDfAuxf hY aqy kdoN GtfAuxf hY, cwldy kwul df ihsfb ikvyN rwKxf hY-jld hI ieh rxnIqIaF quhfzy bwcy df dUsrf suBfa bx jfxgIaF!

lfB

nukqf!dosqfnf nMbr Auh huMdy hn ijhnF nfl idmfgI qOr AuWqy kMm krnf sOKf huMdf hY aqy 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 krky kuwl 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 afnlfeIn kYtflfg mwddgfr ho skdy hn). Dn rfsLI ilKy ibnf, bwcy nUM KrIdx vflIaF cIjLF cuxn idE. Auh bwjt dy ivwc rihx leI aMdfjLy lfvygf. Pyr, bwcy nUM asl Krc df joV krn idE. kI Auh bwjt dy ivwc irhf? iewk cuxOqI vjLoN, bwcy nUM koeI tYks df aMdfjLf lfAux idE.


19

gryz 4 qoN g

ryz 6

nfp qol

nfpqol mfany rwKdf hY

jdoN quhfzy bwcy nUM iewk vfr smJ af igaf ik mfqirk isstm (metric system) dI kMm krdf hY aqy iekfeIaF iewk dUjy nfl ikvyN sMbD bxfAuNdI hn, qbfdly krnf bhuq sOKf hovygf!

lfB

nukqf!

mfqirk isstm (metric system) ieMJ kMm krdf hY:

10 imlImItr= 1 sYNtImItr100 sYNtImItr= 1 mItr1000 mItr= 1 iklomItr

mfqirk isstm (metric system) bfry socx df dUjf qrIkf hY ik mItr lMbfeI dI buinafeI iekfeI hY:

iewk iklomItr ivwc 1000 mItr huMdy hniewk sYNtImItr 1/100 mItr brfbr huMdf hY1 imlImItr 1/1000 mItr brfbr huMdf hY

afpxy bwcy nfl AuhnF siQqIaF nUM vyKo ijwQy mfqirk isstm (metric system) vriqaf igaf hY, aqy AuhnF bfry ivcfr aqy qulnf kro:

• jdoN kuwJ pkf jF byk kr rhy ho, bwcy nUM ieh lwBx ivwc mwdd krn leI afKo ik grfmF ivwc idwqf igaf nfp iklogrfmF ivwc ikMnf hovygf (jF iesdf Aultf kro)

• jdoN kuwJ Ausfr rhy ho, qF bwcy nUM afKo ik pqf kry ik sYNtImItrF ivwc idwqf igaf nfp mItrF ivwc ikMnf hovygf.

• jdoN sPr krdy ho, bwcy nUM afKo ik pqf kry ik iklomItrF ivwc idwqf igaf nfp mItrF ivwc ikMnf hovygf.


20


qusIN pfEgy ik jIEmYtrI aqy akfsLI boD (Geometry and Spatial Sense) krvfAux ivwc mwddgfr gqIivDIaF lfl pMinaF AuWqy idwqIaF geIaF hn. ieh AuNtyrIE dy gixq dy islybs dy qwq (The strands) df ihwsf hY jo quhfzy bwcy dI ihsfb dI ies sLfKf aqy keI ikwiqaF, AusfrI aqy AudXoigk izjLfien qoN idRsLmfn klfvF (visual arts) qwk sPlqf df afDfr bxfAuNdf hY. jo bwcy afpxy mfhOl ivwc afkfrF aqy akfsLI sQfn dy sbMDF (spatial relationships) bfry jfxUM ho jFdy hn, Auh bfad dy gryzF ivwc jIEmYtrI dy isDFqF nUM smJx leI iqafr hoxgy.

lIjYNz (Legend)




vfr vfr duhrfxf !

cFs kI hn?


21

ikMzrg

ftn qoN gryz 3

jIEmYtrI aqy sQfn df arQ (SPATIAL SENSE)

sMkyqk Kyz

ieh Kyz bwcy dI jIEmYtrI dI soc (geometric thought) nfl jfx pihcfx krvfAuNdI hY, ik vsqF dy sQfn nUM ihsfb duafrf ibafn kIqf jf skdf hY.

lfB

• iewk vsq nUM AuTfE aqy afpxy bwcy nUM idsLfvF dI BfsLf ivwc AuhnF vsqF bfry aMdfjL lfAux idE: 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 myjL dy Qwly peI hY?

• bwcy nUM AuhnF vsqF bfry aMdfjLf idE jo dUjy kmry ivwc peIaF hn qF jo bwcy nMU vsq df ikafs 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 krky mYnUM afieqkfr mYt, kwpborz ivwcoN swB qoN vwzf bfks, cOrs afkfr df ibskut aqy gol plyt idE”.

• afpxy bwcy nUM Gr jF bfhr do afXfm dy afkfr ijvyN ik cwkr, cOrs, iqRkoxF aqy afieqkfr vyKx leI afKo. imsfl vjLoN, afpxy bwcy nUM keI iksm dy glIaF dy sfeIn lwBx leI afKo aqy jo 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 kro ik 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: mYN Aus vsq bfry I Spy Kyz irhf hF jo ik gol hY”. “mYN aijhI vsq bfry I Spy Kyz irhf hF jo islMzr dy afkfr vrgI hY”. ies Kyz nUM do afkfr dws ky Kyz nUM hor cuxOqI Biraf bxfE: mYN aijhIaF vsqF bfry “ I Spy Kyz irhf hF jo gol hY aqy Aus AuWqy vrgfkfr bixaf hoieaf hY”.


22


myry sMsfr dI nksLfvfhI krnf

ies gqIivDI ivwc, quhfzf bwcf nkisLaF dy kuwJ buinafdI isDFq iswKygf-swB qoN vDyry mhwqvpUrx ik nksLy AuWqy qsvIrF aqy pRqIk asl vsqUaF nUM drsfAuNdy hn.

lfB

iewk pwkf (iqMn afXfmI) nksLf bxfAuxf quhfzy bwcy nUM kfgjL AuWqy (do afXfmI) nkisLaF bfry DfrnfvF smJx ivwc mwdd dyNdf hY.

nukqf!


• 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 df nksLf (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 afpxy bwcy nfl gwlbfq kro. idsLfvF drsfAux vfly sLbd aqy iPkry vrqo, ijvyN ik nfl lwgdf aqy dy swjy pfsy . qusIN iml ky vwzIaF insLfnIaF (landmarks) aqy jfxy pihcfxy sQfnF dI insLfndyhI krky afpxy aFZ guaFZ df nksLf iml ky bxfE.

smfnqf (Symmetry) sfzy hr pfsy hY

• afpxy bwcy nfl sfry smfn vwzy (capital) awKrF dI pihcfx kro. afpxy bwcy nUM ies afDfr AuWqy vwzy (capital) awKr cuxn idE ik AuhnF ivwc iewk smfn ryKf hY jF do hn. imsfl vjLoN, C ivwc iewk lytvIN (horizontal) smfn ryKf hY; ivwc iewk iewk KVvIN (vertical) smfn ryKf aqy jdoN 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 ivwc lytvINaF (horizontal), KVvIaF (vertical) jF iqrCIaF smfn ryKfvF hn. vfl pyprF, PrsL dIaF tfeIlF, qsvIrF aqy pYikMgF dy zIjLfienF nUM vyKo.

Image 2PICTURES IN A STORYBOOK, PICTURES ON A SCREEN, PICTURES ON SIGNS

7 = 2 + 5

23

gryz 4 qoN g

ryz 6

jIEmYtrI aqy sQfn df arQ (SPATIAL SENSE)

ikhVy afkfr srMcnf (structure) nUM itkvF bxfAuNdy hn?

iehnF KyzF nUM Kyz ky, quhfzf bwcf smJ jfvygf ik kuwJ afkfr horF nfloN vDyry itkvyN huMdy hn.

lfB

AusfrI krn dIaF gqIivDIaF quhfzy bwcy nUM ieh smJx ivwc mwdd krdIaF hn ik ikvyN kuwJ afkfr cIjF nUM izwgx qoN bcfAuNdIaF hn.nukqf!


• afpxy bwcy nUM afpxy afp KVI ho swkx vflI srMcnf (structure) bxfAux leI 50 Cyd vflIaF pfeIpF (straws) jF Guwt ky rol kIqy aKbfr aqy QoVI typ vrqx idE. srMcnf (structure) PrsL jF iksy kMD jF iksy PrnIcr nfl bMnI nhIN hoxI cfhIdI.

• afpxy bwcy nUM puwCo ik Ausdy iKafl ivwc ikhVy afkfr (vrgfkfr, iqRkox jF cwkr) srMcnf (structure) nUM siQr bxfAuxgy.

• afpxy bwcy nfl, srMcnf dy ZFicaF, ijvyN ik hfeIzroielYktirk tfvrF, rolr kostrF (roller coasters) aqy ltkvyN puwlF (suspension bridges) dIaF qsvIrF nUM vyKo. afpxy bwcy nUM puwCo ik afkfr dy ikhVy nksL AusnUM itkvF bxfAuNdy hn aqy AusnUM ivsQfr dyx idE ik ikAuN.

• afpxy bwcy nUM pwuCo ik kI zIjLfienF ivwc smfnqf (symmetry) dIaF imsflF hn. afpxy bwcy nUM ibafn krn idE ik AusnUM ikvyN jfxdf hY?

24

vfr vfr duhrfxf !

qusIN vyKogy ik nmUnfkfrI (Patterning) aqy aljbrf nUM mwdd krn vflIaF gqIivDIaF hry pMinaF AuWqy hn. ieh AuNtyrIE dy gixq dy islybs df qwq (strand) hY jo bwcy nUM vwzIaF klfsF ivwc jf ky nMbrF dI smJ, nfp, jIEmYtrI, aljbrf aqy aMkVf pRbMD leI iqafr hox ivwc mwdd krdf hY. nmUinaF (patterns) nUM smJx aqy pihcfnx dI Xogqf AuhnF dy inrIKx dy afDfr AuWqy anumfn lfAux ivwc mwdd krdI hY.

lIjYNz (Legend)




vfr vfr duhrfxf !

cFs kI hn?

7 = 2 + 5


25

ikMzrg

ftn qoN gryz 3

aMkVf pRbMD aqy sMBfvnf (PATTERNING AND ALGEBRA)

nmUinaF (Patterns) nUM suxnf

• afpxy hwQF nfl qfVI aqy iewk pYr nfl DrqI QpQpfAux nUM iewk qrqIb ivwc kro (ijvyN ik qfVI, qfVI, QpQfht, qfVI, qfVI, QpQfht, qfVI, qfVI, QpQfht). afpxy bwcy nUM iehI qrqIb 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 mOj msqI kro.

Gr jF aFZ guaFZ ivwc pYtrn

afpxy bwcy nUM ihsfbI sLbd , ijvyN ik duhrfAuxf, Pyr dubfrf, ieh qF AuhI hY aqy ieh bdldf hY, vrq ky pYtrnF nUM pihcfnx aqy ibafnx mwdd kro jo sfzy sfry pfsy mOjUd hn-

lfB

• quhfzf bwcf kwpiVaF, vflpyprF (wallpapers), tfeIlF ivwc, iKzOixaF AuWqy aqy ruwKF aqy PuwlF ivwc pYtrn pfvygf. pfey gey pYtrnF nUM ibafnx leI bwcy nUM AuqsLfihq kro. afpxy bwcy nUM 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 lwBx dI koisLsL kro.


26

vfr vfr duhrfxf !

pYtrnF nUM ibafnxf

pYtrnF nUM duhrfAux nfl, kyNdrI pYtrn Auh ihwsf hY jo vfr vfr duhrfieaf jFdf hY-imsfl vjLoN, ABB ABB ABB dy pYtrn ivwc, ABB kyNdrI pYtrn hY. afpxy bwcy nUM iehnF mOj msqI vfly aiBafsF ivwc duhrfey jfx vfly pYtrnF nUM pihcfnx ivwc mwdd kro!

lfB

cfrt, tybl aqy grfP pYtrnF nUM Aujfgr krn dy kuwJ qrIky hn. nukqf!


• nO cmicaF nUM iewk kqfr ivwc ieMJ rwKo ik hr iewk cmcy df hYNzl AuWqy jF Qwly vwl jFdf hY ijsdy pYtrn df kyNdr up, up, down (up, up, down; up, up, down; up, up, down) hY. . afpxy bwcy 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 leI afKo.

• 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?

27

gryz 4 qoN g

ryz 6

aMkVf pRbMD aqy sMBfvnf (PATTERNING AND ALGEBRA)

anumfn lfE ikMny

ieh gqIivDI quhfzy bwcy nUM socx ivwc mwdd krdI hY ik jo Auh vyKdf hY, pYtrn AusqoN awgy ikvyN jfrI rihMdy hn- ihsfbI BwivKbfxI df afDfr!

lfB

nukqf!


pYtrn dy duhrfey jfx vfly ihwsy Gwto Gwt 3 vfr ivKf ky bwcy nUM smJx ivwc 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 (jF sMugVn vflf) pYtrn bxfE. iewQy T awKr leI vwDx vfly pYtrn dI imsfl hY.

Size 1 Size 2 Size 3 Size 4 Size 5sfeIjL 1 sfeIjL 2 sfeIjL 3 sfeIjL 4 sfeIjL 5

• afpxy bwcy nUM pYtrn ivwc aglIaF iqMn tIaF (T’s) bxfAux leI afKo aqy puwCo ik pYtrn leI ikhVf nym vriqaf. drsfieaf igaf pYtrn iqMn blfkF nfl sLurU huMdf hY aqy hr vfr do blfk jmHF huMdy hn.

• afpxy bwcy nUM aMdfjLf lfAux leI afKo ik dy 15 T awKrF dy sfeIjL df pYtrn bxfAux leI AusnUM ikMny blfk cfhIdy hoxgy. ies qrF dy suafl bwcy nUM pYtrn dy nym bfry iewk afm Dfrnf bxfAux aqy hr vfr nvF pYtrn nf bxf ky vDyry guMJldfr pYtrnF dIaF musLklF hwl krn dyNdy 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.

28

vfr vfr duhrfxf !

myry nym nUM bwuJo!

• iewk sMiKafqmk pYtrn bxfE aqy bwcy nUM pYtrn dy aKIr ivwc iewk nMbr bwuJx leI afKo. imsfl vjLoN, bwcy nUM afKo ik 1, 4, 7, 10, ….vrgy pYtrn ivwc awTvyN sQfn AuWqy ikhVf nMbr afvygf.

Place

Number

1

1

2

4

3

7

4

10

5

• quhfzf bwcf iewk nMbr qoN dUjy qwk pYtrn nym vyKy aqy afKy, “mYN iewk nfl sLurU krdf hF aqy hr vfr 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 jmHF 7 vfr iqMn jF 1 + (3 × 7) = 1 + 21 = 22 .

guxF dy qwQF ivwc pYtrn vyKxy

jdoN bwicaF kol afpxI dlIl nUM ivkisq krn df avsr huMdf hY, Auh ihsfbI DfrnfvF dI vDyry smJ ivkisq krdy hn.nukqf!


• bwcy nUM ieh keI pwKF qoN GoKx ivwc mwdd kro ik pYtrn AusnUM guxF dy qwqF nUM cyqy rwKx ivwc mwdd kr skdy hn. imsfl vjLoN, jykr quhfzf bwcf 6 × 4 df guxfPl (jvfb) nhIN dws skdf aYpr 6 × 2 df pqf hY, Auh do guxf dy phfVy dy igafn nUM duwgxf krn dI qrkIb vrq ky hwl kr skdf hY. 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, iewkI bxfAux leI Auh 7 df iewk hor grupw jmHF kr skdf hY. ieh qrkIb Cy dy phfVy ivwc vI kMm afAuNdI hY. bwcy sOKy nMbr 5 dy phfVy ivwc afpxI sOK vrq ky 6 dy phfVy nUM hwl krn leI vrq skdy 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.

29

ikMzrg

ftn qoN gryz 3

cFs kI hn?

qusIN vyKogy ik gulfbI pMinaF AuWqy aMkVf pRbMD aqy aMdfjLy ivwc mwdd krn vflIaF gqIivDIaF hn. ieh AuNtyrIE dy gixq islybs df qwq (strand) hY jo bwcy dI jfx pihcfx krvfAuNdf hY ik jfxkfrI nUM iewkqr, anuvfd aqy sMgiTq ikvyN krnf hY. hr rojL bwicaF nUM vwzI mfqrf ivwc jfxkfrI idwqI jFdI hY, aqy ies ivwc kfPI ijafdf ivwc nMbr sLfml huMdy hn.

lIjYNz (Legend)




vfr vfr duhrfxf !

cFs kI hn?

7 = 2 + 57 = 2 + 5


cFs kI hn?

jIvn leI CFt krnI

30

bwcy dy CotI Aumry Gr dy afly duafly dIaF cIjLF nUM CFtx aqy vrgIkrx krn dy anuBv aMkVf iqafr krn aqy arQ BrpUr vrg bxfAux leI iqafr krn ivwc shfeI huMdy hn.

lfB

bwcy amUmn dws skdy hn ik AuhnF ny cIjLF dI CFtI ikvyN kIqI pRqUM ieh smJx ivwc musLkl af skdI hY ik dUijaF ny cIjLF dI CFtI ikvyN kIqI.

nukqf!

• sfDfrx CFtI dy nymF nUM socdy hoey sLurUafq kro (ijvyN ik “gruwp ivwc hr cIjL nIlI hY”), aqy kuwJ cIjLF 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 kwpborz ivwc 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 soc bfry 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?”


31

ikMzrg

ftn qoN gryz 3

aMkVf pRbMD aqy sMBfvnf (PROBABILITY)

vDyry Duwp vfly idn jF mINh vfly idn?

aMkVy df arQ bxfAux ivwc mwdd krn leI Coty bwcy vI sfDfrx grfP, phfVy, cfrt aqy hor qsvIr vfly sMgTkF nUM vrq skdy hn.

lfB

iewk ipktogrfP (pictograph) Auh huMdf hY jo iewk sMiKafqmk aMkVy nUM drsfAux leIqsvIrF dI vrqoN krdf hY.

nukqf!

• hr idn dy mOsm rwKx df irkfrz krn leI afpxy bwcy nUM kYlMzr AuWqy qsvIrF vfhux idE. hPqy jF mhIny dy aKIr ivwc, Aus mhIny ivwc ikMny Duwp vfly, bwdlvfeI vfly aqy mINh vfly idn sn, drsfAuNdf hoieaf iewk ipktogrfP (pictograph) bxfE.


32

cFs kI hn?

iewk pirvfrk smfgm dI Xojnf leI aMkVy nUM vrqxf

ieh gqIivDI bwcy nUM jfxkfr bxfeygI ik asIN pihly sQfn AuWqy aMkVy iewkqr aqy sMgiTq ikAuN krdy hF- Kfskrky, suaflF dy jvfb dyx leI aqy BwivK leI XojnfvF bxfAux leI!

lfB

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 ) duafrf

jF sMkyqF nUM vfh ky.

• quhfzf bwcf af rhy pirvfrk smfgm leI iewk srvy krnf cfh skdf hY- imsfl vjLoN, “ pirvfr dy mYNbr iks iksm dI gqIivDI ijafdf krnI psMd krngy?” “iks iksm df Kfxf aqy pya pdfrQ 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 pdfrQ psMd krogy?

• afpxy bwcy nUM cuxn idE ik iksnUM srvy krnf hY (isrP nyVy dy pirvfrk mYNbr?, ivsqirq pirvfr 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 ikvyN pRBfivq kIqf


33

ikMzrg

ftn qoN gryz 3

aMkVf pRbMD aqy sMBfvnf (PROBABILITY)aMkVf pRbMD aqy sMBfvnf (PROBABILITY)

aksr, kdy kdfeIN jF kdy nhIN Kyz

lfBKyzF duafrf, qusIN afpxy bwcy nUM Aus BfsLf df prIcY krvf skdy ho jo ihsfbdfn iksy Gtnf 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 pirvfr hmysLf, aksr aqy kdy kdfeIN krdf hY aqy kuwJ cIjLF quhfzf pirvfr kdy nhIN krdf. afpxy bwcy nUM puwCo ik inwq idn dIaF hor ikhVIaF GtnfvF hn ijhnF bfry Auh ies qrF dI BfsLf vrq ky gwl kr skdf hY.

• ieh Kyz kfr clfAux vyly Kyzx dI koisLsL kro. GtnfvF dy nfm lvo aqy afpxy bwcy nUM PYslf krn idE ik iehnF df hoxf mumikn jF gYr mumikn jF kdy nhIN hoxgIaF. qusIN isrP afpxI 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.

ZOO


cFs kI hn?

asIN vIkaYNz AuWqy afpxf smF iks qrF ibqfAuNdy hF?

ieh pirvfrk srvy quhfzy bwcy nUM buinafdI aMkVf iewkqr krn ivwc anuBv dyNdf hY- srvyKxF, ivcfrF aqy qjuribaF rfhIN iswDy iewkqr kIqy jfxkfrI dy tukVy.

lfB

34

nukqf!


bwcy nUM aMkVy bfry socx leI sLurU kr vfsqy AuqsLfihq kro: • Auh kuwJ ikhVy qrIky hn ijhnF rfhIN qusIN aMkVy nUM iewkqr aqy

irkfrz kr skdy ho? • jykr vIkaYNz sLfml kIqy jfx qF aMkVf ikvyN idwsygf? • quhfzIaF lwBqF quhfzy pirvfr dy vIkaYNz AuWqy KflI smyN dI vrqoN nUM ikvyN pRBfivq krngIaF?

• lokI KflI smyN dI ishqmMd vrqoN bfry bihs krdy hn. vwKo vwKry lokF dy vwKry ivcfr hn. afpxy bwcy nfl ies ivsLy bfry iKafl lYx leI gwlbfq kro.

• afpxy bwcy nUM quhfzy pirvfr dy KflI smyN bfry aMkVf iewkTf krn idE-imsfl vjLoN, aMdrUnI bnfm bfhr dIaF gqIivDIaF, KyzF, imlx jfx aqy sYr AuWqy ibqfieaf smF aqy prdy dy sfhmxy ibqfieaf smF (ijvyN ik tYlIvIjLn, kMipAUtr, vIzIE gym jF hwQ ivwc PV ky clfAux vflf XMqr).

35

gryz 4 qoN g

ryz 6

aMkVf pRbMD aqy sMBfvnf (PROBABILITY)aMkVf pRbMD aqy sMBfvnf (PROBABILITY)

aMkVy dI Bfl

afpxy bwcy df dUjy krm dy aMkVy (secondary data) dy iKafl nfl prIcY krvfE – iewk irsfly, aKbfr, srkfrI dsqfvyjL jF zYtfbys ivwcoN aMkVf- ies mnorMjk gqIivDI duafrf.

lfB

• afpxy bwcy nfl aKbfrF ivwc afey iksy hflIaf muwdy bfry gwl kro ijs ivwc AusdI idlcspI hY. quhfzy bwcy dy ivcfr, socxI aqy suafl kI hn? quhfzf bwcf ies bfry hor kI jfnxf psMd kr 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 pRsLn ho skdy hn?

• ikhVf nukqf njLr awgy ilaFdf igaf hY? ies aMkVy dIaF kI sImfvF hn? kI kuwJ gfieb hY?

• jo qusIN lwBx dI koisLsL kr rhy ho, Aus dy sMdrB ivwc aMkVf ikMnf ku lfhyvMd hY? kI koeI aMcBy jF rucI dIaF vsqF hn jo qusIN not kIqIaF?

• kI aMkVf quhfzy leI koeI nvyN suafl KVy krdf hY?


afnlfeIn sRoq

Esso Family Mathies sfeIt Auwqy gqIivDIaF, Koj aqy jfxkfrI mfipaF aqy bwicaF nUM surwiKaq aqy afrfm Bry mfhOl ivwc AuhnF dI soc aqy smJ sFJf krn ivwc mwdd krdI hY. AuhnF dI soc sLFJI krn aqy ihsfb dI iewkwww.edu.uwo.ca/essofamilymath

Math FrogiewQy quhfnUM gryz 4, 5 aqy 6 dy leIsRoq aqy afnlfeIn KyzF imlxgIaF. http://cemc2.math.uwaterloo.ca/mathfrog/

main.shtml

ABC Life Literacyieh sRoq bwicaF nUM ivwqI sfKrqf nfl jfxkfr krvfAuNdf hY aqy isKfAuNdf hY.http://abclifeliteracy.ca/financial-literacy-tips-and-

resources

Figure Thisies sfeIt AuWqy bwicaF duafrf mfipaF nfl krn vflIaF gixq dIaF KyzF aqy cuxOqIaF hn. www.figurethis.org

Math Wireies sfeIt AuWqy keI iksm dy ihsfbI sRoq, tYst aqy KyzF mOjUd hn.http://mathwire.com

PedagoNetiewQy quhfnUM ihsfb dy ilMk aqy KyzF imlxgIaFwww.pedagonet.com

Math Dictionary for Kidsieh afnlfeIn sfDn bwicaF nUM ihsfb dI sLbdfvlI dIaF pRIBfsLfvF iswKx ivwc mwdd krdf hY.www.amathsdictionaryforkids.com

Math Forumies sfeIt AuWqy Kfskrky aYlImYNtrI ivwidafrQIaF leI nukqy, cflF aqy ihsfb dIaF smwisafvF pfeIaF geIaF hn.

www.mathforum.org/students/elem/probs.html

National Library of Virtual Manipulativesies afnlfeIn sfDn AuWqy Aumr dy ihsfb AUtfh styt XUnIvristI (Utah State University) qoN vfsqivk kOsLlqf vfly suafl pfey gey hn.http://nlvm.usu.edu/en/nav/vlibrary.html

Kid SitesiewQy qusIN bwicaF leI ihsfb dIaF sfeItF iewk ilst pfEgy.www.kidsites.com/sites-edu/math.htm

Math Playgroundies sfeIt AuWqy ihsfb dI pVfeI leI Aumr aqy gryz leI AupXukq KyzF aqy vrksLItF hn.www.mathplayground.com

36quhfzy bwcy nfl gixq krnf, ikMzrgfrtn qoN 6 gryz qwk: mfipaF leI gfeIz

37

TVOKIDS.COM aqy gixq

nMbr df arQ (Number Sense) aqy aMk igxqI (Numeration)

ikMzrgfrtn qoN gryz 3Caterpillar Countwww.tvokids.com/games/caterpillarcount Connect the Dots with Arttwww.tvokids.com/games/connectdotsartt Count with Arttwww.tvokids.com/games/countartt

gryz 4 qoN gryz 6Tumbleweed’s MathMaze

(sLurUafqI aqy drimafnf pwDr)www.tvokids.com/games/tumbleweedsmathmaze Bruce McBruce Doodle Dotswww.tvokids.com/framesets/play.html%3Fgame%3D51 Tumbletown Mathleticswww.tvokids.com/games/tumbletownmathletics Big Wig Sub Shopwww.tvokids.com/games/bigwigsubshop

nfp qolikMzrgfrtn qoN gryz 3Clock Talkwww.tvokids.com/games/clocktalk

gryz 4 qoN gryz 6Beat the Clockwww.tvokids.com/games/beatclock Tumbletown Mathleticswww.tvokids.com/games/tumbletownmathletics

jIEmYtrI aqy sQfn df arQ (Spatial Sense)

ikMzrgfrtn qoN gryz Shapevillewww.tvokids.com/games/shapeville

3 gryz 4 qoN gryz 6Triangle Alleywww.tvokids.com/games/trianglealley Build Math Citywww.tvokids.com/activities/buildmathcity Pirates Maps and Trapswww.tvokids.com/games/piratesmapsandtraps

aMkVf pRbMD aqy sMBfvnf (Patterning and Algebra)

ikMzrgfrtn qoN gryz 3A Lotta Dessertwww.tvokids.com/games/lottadessert

gryz 4 qoN gryz 6Flower Frenzywww.tvokids.com/games/flowerfrenzy

aMkVf pRbMD aqy sMBfvnf (Probability)

ikMzrgfrtn qoN gryz 3Sort Itwww.tvokids.com/games/sortit

gryz 4 qoN gryz 6Space Trek Galaxywww.tvokids.com/games/spacetrekgalaxy

afpxy bwcy dy sfKqrf ivkfs, ihsfb aqy sfieMs ivkfs leI PrI vIzIE, gymF aqy gqIivDIaF leI www.tvokids.com AuWqy jfE. afpxy bwcy dy iswKx dy sPr ivwc mwdd dyx leI AuNtyrIE AuWqy kyNdirq sRoqF leI www.tvoparents.com AuWqy vI jfE.


www.tvokids.com/games/catipillarcount

www.tvokids.com/games/connectditsartt

www.tvokids.com/games/countartt

www.tvokids.com/games/shapeville

www.tvokids.com/games/lottadessert

www.tvokids.com/games/sortit

www.tvokids.com/games/spacetrekgalaxy

www.tvokids.com/games/flowerfrenzy

www.tvokids.com/games/piratesmapsandtraps

www.tvokids.com/activities/buildmathcity

www.tvokids.com/games/trianglealley

www.tvokids.com/games/tumbletownmathletics

www.tvokids.com/games/beatclock

7 = 2 + 5

7 = 2 + 5

Ontario 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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