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bjhl® k‰W« KGikahd kÂ¥ÕL 
ca®bjhl¡f ãiy – fz¡F 
(Kjš gUt«)
ifna£o‹ cŸns.... 
t. 
v© 
bghUsl¡f« 
1. tsu¿ kÂ¥ÕL (m), tsu¿ kÂ¥ÕL (M), bjhF¤j¿ kÂ¥ÕL 
2. tF¥giw¢ brašghLfŸ jå eg® ,ÁW FG, KG tF¥ò 
3. kÂ¥Õ£L¡ TWfŸ k‰W« Fiw Ô® f‰Ã¤jš 
4. fhy msÎ 
5. v®gh®¡f¥gL« f‰wš Ïy¡FfŸ 
6. ghlüèš Ïl« bg‰WŸs tsu¿¢ brašghLfŸ (6,7,8,tF¥ò) 
7. khÂç édh¤jhŸ (6,7,8,tF¥ò) 
8. K¡»a ghl¡fU¤J¡fŸ (6,7,8,tF¥ò) 
9. Áªjidia¤ ö©L« édh¡fŸ 
10. gçªJiu¡f¥gL« brašÂ£l§fŸ.
MÁça® ifna£oid¥ ga‹gL¤Jtj‰fhd têKiwfŸ 
jäHf murhš btëæl¥g£LŸs K¥gUt ghlüèš Kjš 
gUt¤Â‰Fça ca®bjhl¡f ãiy fâj brašghLfŸ 
Ï¡ifna£oš Ïl« bg‰WŸsJ. 
ifna£oš bfhL¡f¥g£LŸs brašfŸ mid¤J« têfh£lY¡F 
k£Lnk. 
bfhL¡f¥g£l brašghLfis¡ tF¥giwæ‹ ga‹gh£o‰nf 
‰g MÁça®fŸ m¥gona (mšyJ) kh‰¿aik¤J 
ga‹gL¤jyh«.
MÁça® ifna£oid¥ ga‹gL¤Jtj‰fhd têKiwfŸ 
tsu¿ kÂ¥Õ£oid, MÁça® kÂ¥ÕL brOEÍ« bghGJ 
khzt®fŸ Rikahf ãid¡fhjthW nk‰bfhŸs Áw¥ò¡ ftd« 
vL¤J¡bfhŸSjš nt©L«. 
f‰wš f‰Ã¤jèš MÁça®, khzt®fë‹ ãiyæid cz®tj 
‰F«, f‰wiy nk«gL¤Jtj‰F« Ï¡ifnaL cjΫ.
tsu¿ kÂ¥ÕL (m) 
ghl¤ÂYŸs xU fU¤ij¡ f‰Ã¡F« nghJ fU¤J 
cUthtj‰F« f‰wiy tY¥gL¤Jtj‰F« brašghLfë‹ 
mo¥gilæš ãfH¡ ToajhF«. 
ÏJ f‰wš eilbgW«bghGJ brOEÍ« kÂ¥ÕlhF«.
tsu¿ kÂ¥ÕL (m) é‹ Áw¥g«r§fŸ 
 j‹id¤ jhnd nrh¤J m¿a khzt®fS¡fhd xU msÎ nfhš. 
 Fiwa¿ k‰W« Fiwfis¥ ngh¡f elto¡if vL¡f Mrça®fS¡fhd 
têfh£o. 
 FG¢brašgh£o‹ _y« thoeéaš Âw‹fshd KobtL¤jš, Ãu 
¢ridfis¡ fisjš, e£òwit nk«gL¤Jjš, T® Áªjid k‰W« rçahd 
jftš bjhl®ò ngh‹wt‰iw nk«gL¤j cjÎtJ. 
 khzt®fë‹ f‰wš ntf¤Â‰nf‰g brašghLfŸ mik¡f¥gl nt©L«.
tsu¿ kÂ¥ÕL (m) - gÂÎ brOEjš 
 tF¥Ãš cŸs x›bthU khztU« Fiwªjg£r« 4 brašghLfis 
x›bthU gUt¤ÂY« nk‰bfh©L mt‰¿š Áwªj 2 
brašghLfis MÁça® kÂ¥Õ£o‰F vL¤J¡ bfhŸs 
nt©L«. 
 (2 brašghLfŸ x 10 kÂ¥bg©fŸ = 20 kÂ¥bg©fŸ)
tsu¿ kÂ¥ÕL (m) [FA (a)] é‰fhd Áy brašghLfŸ) 
t. 
v© brašghL t. 
v© brašghL 
1 braš £l« (Project) 9 brOEJ f‰wš (Learning by doing) 
2 Ãu¢rid Ô®¤jš 
(Problem Solving) 
10 x¥gil¥òfŸ (Assignments ) 
3 étu§fis¢ nrfç¤jš 
(Data Collection) 
11 éisah£LfŸ (Games) 
4 fU¤J tiugl« 
(Concept mapping) 
12 fh£Á¥ gL¤Jjš 
(Visualisation) 
5 bghUŸ és¡f« jUjš (Interpretation) 13 kÂ¥ÃLjš k‰W« njhuha« fhzš 
(Estimation and Approximation) 
6 ò® (Puzzle) 14 ca® Áªjidia¤ ö©L« édh¡fŸ 
(Higher order thinking Questions) 
7 c‰W neh¡Fjš (Observation) 15 
khzt®fis¡ fâj bkhê gçkh‰w¤Â‰F 
tênfhYjš 
( Mathematical Communication) 
8 f©lhuhOEjš (Investigation)
tsu¿ kÂ¥ÕL (M) 
 ghl¤ÂYŸs xU fU¤ij¡ f‰Ã¤j Ëò f‰wiy kÂ¥ÕL 
brOEtjhF«. 
 x›bthU khztU¡F« FW»a fhy mséš el¤j¥gL« xU 
ÁW vG¤J nj®thF«.
tsu¿ kÂ¥ÕL (M) - Áw¥g«r§fŸ 
 jå¢ brašgh£o‹ _y« x›bthU khztUila f‰wš milit cW 
brOEa¥gL»wJ. 
 khzt®fŸ j§fŸ f‰wš milit¤ j‹id¤jhnd nrh¤J m¿a cjΫ 
msÎnfhyhF«. 
 Fiwa¿ k‰W« FiwÔ® elto¡iffis vL¡f MÁça®fS¡F xU tê 
fh£oahf mik»wJ.
tsu¿ kÂ¥ÕL (M) – gÂÎ brOEjš 
 tF¥Ãš cŸs x›bthU khztU« Fiwªjg£r« 4 brašghLfis 
x›bthU gUt¤ÂY« nk‰bfh©L mt‰¿š Áwªj 2 
brašghLfis MÁça® kÂ¥Õ£o‰F vL¤J¡bfhŸs 
nt©L«. 
 (2 brašghLfŸ X 10 kÂ¥bg©fŸ = 20 kÂ¥bg©fŸ)
tsu¿ kÂ¥ÕL (M) [FA (b)] é‰fhd Áy édh¡fŸ 
t. 
v© édh¡fŸ t. 
v© édh¡fŸ 
1. gyΟ bjçÎ 
(Multiple Choice) 
6 tçir¥gL¤Jjš (Sequencing) 
2. nfho£l Ïl§fis ãu¥òjš 
(Fill in the blanks) 7 ca® Áªjidia¤ ö©L« édh¡fŸ (Higher 
order Thinking question) 
3. bghU¤Jjš (Matching) 8 ÁW édh¡fŸ (Short Answer 
Question) 
4. édho édh (Quiz) 9 FW édh¡fŸ 
(Very short Answer Question) 
5. 
fâj fU¤Jfis ãidÎ TWjš 
(Recalling Mathematical 
Concepts) 
10 tiufiy mik¥òfŸ 
(Graphic Organisers)
bjhF¤j¿ kÂ¥ÕL 
x›bthU gUt¤Â‹ ÏWÂæš 60 kÂ¥bg©fS¡F eilbgW« 
vG¤J nj®thF«. 
édh totik¥Ã‹ mo¥gilæš édh¤jhŸ jahç¡f¥gL«. 
 f‰wš neh¡f§fshd m¿jš, òçjš, ga‹gL¤Jjš k‰W« 
Âw‹ bgwš v‹w mo¥gilæš mik¡f¥g£LŸsJ. 
 mªj¥ gUt¤Âš bfhL¡f¥g£l ghl¤Â£l¤ij cŸsl¡»ajhf 
ÏU¡F«.
jå eg® brašghL 
KGikahd k‰W« bjhl® kÂ¥Õ£oš x›bthU khztiuÍ« f 
‰wèš cWÂ brOEa jå eg® brašghL mtÁakh»wJ. 
tF¥giwæš khzt®fë‹ v©â¡if Fiwthf ÏU¡F« nghJ Ï 
¢brašghL V‰òilajhf mikÍ«. 
 Ï¢brašgh£il mik¡F« nghJ MÁça® x›bthU 
khztçl¤ÂY« ftd« brY¤Â, f‰wš 
bjhOEé‹¿ eilbgW»‹wjh? v‹gij cWÂ brOEa nt©L«. 
 jå eg® brašgh£o‹ _y« eilbgW« f‰wyhdJ, Ú©l 
eh£fS¡F ãiy¤J ã‰F«. nkY«, f‰wš bghUSilajhf 
ÏU¡F«.
ÁW FG brašghL 
tF¥giwæš khzt®fë‹ v©â¡if mÂfkhf ÏU¡F« nghJ 
MÁça® khzt®fis 5mšyJ mj‰F nk‰g£l ÁW 
FG¡fshf¥ Ãç¤J f‰wš brašgh£il mik¡f nt©L«. 
 ÁW FG¡fshf¥ Ãç¡f¥gLtjhš x›bthU FGédU¡F« f 
‰wš f‰Ã¤jš Jiz¡fUéfŸ brašfis mik¥gj‰F K‹d® 
tH§Ftij cWÂ brOEjš nt©L«. 
 Ï¢brašgh£o‹ nghJ tF¥giw xG§F e‹Kiwæš mika 
MÁça® f©fhâ¡f nt©L«. 
 x›bthU khztUila g§fë¥ò« Ïl« bgWkhW MÁça® 
cWÂ brOEa nt©L«.
KG tF¥ò brašghL 
MÁça® ghl¤Â£l¤Âš cŸs Áy Âw‹fis¤ jåeg® 
brašghL, Ïiz brašghL kwW« FG¢ brašghL 
_ykhfnth el¤j Ïayhj bghGJ tF¥Ãš cŸs mid¤J 
khzt®fisÍ« xnu FGthf¡ mik¤J brOEJ fh£lš, c 
‰Wneh¡fš (m) bghUŸ és¡f« jUjš _y« ghl¥bghUis 
khzt®fS¡F f‰Ã¤jš nt©L«. 
cjhuzkhf brOEKiw toéaèš cŸs t£l eh‰fu« tiujš 
v‹w ghl¥bghUis¢ brOEJfh£lš _y« f‰Ã¤jš.
tsu¿ kÂ¥ÕL (m) - és¡f¡ F¿¥òfŸ 
j‹dh®t« (Initiative) 
<LghL (Involvement) 
g§nf‰wš (Participation) 
élhKa‰Á (Perseverence) 
Óuhf¢ brOEjš (Perfection) 
khztå‹ brašghLfis kÂ¥ÃL«bghGJ milΤÂw‹ k£Lä‹¿, 
nk‰F¿¥Ã£l bghJthd IªJ és¡f¡ F¿¥òfis kd¤Â 
‰bfh©L kÂ¥ÕL brOEjš nt©L«.
kÂ¥Õ£L¡ TWfŸ- tsu¿ kÂ¥ÕL (m) 
kÂ¥bg© 
fŸ 
ju« kÂ¥Õ£L fhuâfŸ 
10 äf e‹W *** 
· brašgh£oid KGikahfΫ bjëthfΫ, xG§FlD« Ko¤jš 
· brašgh£oid cçaKiwæš brOEjš k‰W« gil¥gh‰wš 
Âw‹ btë¥gL« tifæš Ko¤jš. 
· brašgh£oid m¿th®ªjKiwæš Ko¤jš 
8-9 e‹W** 
· brašgh£oid KGikahf, xG§fhf, ca®ªj Kiwæš k‰W« 
ftdkhfΫ brOEJ Ko¤jš 
6-7 ÂU¥Âfu«* · brašgh£oid KG <Lgh£Ll‹ Ko¤jš 
5 Ka‰Á njit  
· brašgh£oid ãiwÎbrOEa nt©oæUªjhnyh, <LghL 
njit¥g£lhnyh Ï¡F¿p£oid ÏLjš nt©L«
FiwÔ® f‰Ã¤jš 
 tsu¿ kÂ¥ÕL ( m ) k‰W« tsu¿ kÂ¥ÕL ( M) Ïš KGikahf¢ 
brašglhj, Ka‰Á njit¥gL« khzt®fS¡F Û©L« f‰wèš KGikaila 
MÁça® cjéÍl‹ mnj brašgh£ilnah mšyJ khzt® vL¤J¡bfh©l 
brašgh£o‰F Ïizahd, vëikahd kh‰W brašgh£ilnah më¡f 
nt©L«. 
 FiwÔ® f‰Ã¤jiy khzt®fŸ KGikahd f‰wš milÎ bgW« tiu 
bjhl®ªJ brOEJ mij kÂ¥ÕL brOEJ cça ju« tH§»lnt©L«.
fhy msÎ-Mwh« tF¥ò 
t. v©. ghl myF 
f‰Ã¡f 
njit¥gL« 
ÃçntisfŸ 
tsu¿ brašgh£ 
o‰F 
njit¥gL« 
ÃçntisfŸ 
bkh¤j 
ÃçntisfŸ 
1. v©âaš 40 4 44 
2. msitfŸ 10 2 12 
3. toéaš 6 2 8 
4. brOEKiw toéaš 4 2 6 
bkh¤j« 60 10 70
fhy msÎ-VHh« tF¥ò 
t. v©. ghl myF 
f‰Ã¡f 
njit¥gL« 
ÃçntisfŸ 
tsu¿ brašgh£ 
o‰F 
njit¥gL« 
ÃçntisfŸ 
bkh¤j 
ÃçntisfŸ 
1. v©âaš 31 4 35 
2. Ïa‰fâj« 23 2 25 
3. toéaš 18 2 20 
4. brOEKiw toéaš 9 1 10 
5 étu§fis ifahSjš 12 1 13 
bkh¤j« 93 10 103
fhy msÎ-v£lh« tF¥ò 
t. v©. ghl myF 
f‰Ã¡f 
njit¥gL« 
ÃçntisfŸ 
tsu¿ brašgh£ 
o‰F 
njit¥gL« 
ÃçntisfŸ 
bkh¤j 
ÃçntisfŸ 
1. v©âaš 36 4 40 
2. msitfŸ 20 3 23 
3. toéaš 11 2 13 
4. brOEKiw toéaš 13 1 14 
bkh¤j« 80 10 90
Mwh« tF¥Ã‰fhd brašghLfŸ 
tsu¿ kÂ¥ÕL (m) [FA (a)] 
 jiy¥ò : v©âaš 
 ghl¥bghUŸ : fhuâfŸ 
 f‰wš neh¡f« : fhuâfis f©l¿jš 
 Ïy¡F : FG¢brašghL
Mwh« tF¥Ã‰fhd brašghLfŸ 
tsu¿ kÂ¥ÕL (m) [FA (a)] 
1 Kjš 100 tiu v©fŸ vGj¥g£l m£ilfis (v© m£ilfis 
khzt®fë‹ v©â¡if¡nf‰g) MÁça® khzt®fS¡F tH§f 
nt©L«. 
18, 21, 30, 42, 60 ngh‹w v©fis MÁça® jiuæš 
vGÂ t£lälš nt©L«. 
MÁça® 18 v‹wÎl‹ mj‹ fhuâfis 3, 6, 2 , 9 v‹w 
nrhofëš khzt®fis t£l¤Â‹ ÛJ ã‰f¢ brOEayh«. 
khzt®fŸ rçahd v© t£l¤Â‹ ÛJ cŸsduh v‹gij MÁça® 
kÂ¥ÕL brOEa nt©L«.
Mwh« tF¥Ã‰fhd brašghLfŸ 
tsu¿ kÂ¥ÕL (m) [FA (a)] 
 jiy¥ò : toéaš 
 ghl¥bghUŸ : Ïiz nfhLfŸ, 
br§F¤J¡nfhLfŸ 
f‰wš neh¡f« : 
M§»y vG¤J¡fëš ÏiznfhLfŸ br§F¤J¡nfhLfŸ m¿ªJ 
bfhŸsš, 
khzt®fS¡F Ïiz¡nfhLfŸ,br§F¤J¡nfhLfŸ g‰ 
¿ bjëthdÁªjid V‰gL¤Jjš
Mwh« tF¥Ã‰fhd brašghLfŸ 
tsu¿ kÂ¥ÕL (m) [FA (a)] 
MÁça® M§»y vG¤J¡fëš ÏiznfhLfŸ 
br§F¤J¡nfhLfis f©l¿ªJ v.fh x‹iw¡ T¿ ÏJ 
ÏiznfhLfsh mšyJ br§F¤J¡nfhLfsh vd édh 
vG¥Ã khzt®fël« éil fh©f. 
X›bthU khzt®fël« br§F¤J¡nfhLfŸ, 
ÏiznfhLfŸ cŸs vG¤J¡fis f©l¿a¢ brOEf. 
nkY« br§F¤J k‰W« ÏiznfhLfŸ ÏizªJ tU« 
vG¤J¡fisÍ« g£oaèLf.
VHh« tF¥Ã‰fhd brašghLfŸ 
tsu¿ kÂ¥ÕL (m) [FA (a)] 
jiy¥ò : bkOEba©fë‹ bjhF¥ò 
ghl¥bghUŸ : KG¡fë‹ bgU¡fš 
f‰wš neh¡f« : xU Fiw KGit k‰bwhU Fiw 
KGthš bgU¡Fjiy v© 
mik¥ò Ó® _y« òçªJ bfhŸSjš. 
Ïy¡F : FG¢brašghL - 
c‰Wneh¡Fjš Kiw
VHh« tF¥Ã‰fhd brašghLfŸ 
tsu¿ kÂ¥ÕL (m) [FA (a)] 
 xU Fiw KGit k‰bwhU FiwKGthš bgU¡Ftj‰F 
K‹ MÁça® Fiw KG x äif KG = FiwKG v‹w 
éÂia v© mik¥ò Ó® Kiwæš Ñoe¡f©lthW 
ã%áf nt©L«. 
 (+2 ) x (+10) = (+20 ) 
 (+1 ) x (+10) = (+10 ) 
 0 x (+10) = 0 
 (-1 ) x (+10) = 
 (-2 ) x (+10) =
VHh« tF¥Ã‰fhd brašghLfŸ 
tsu¿ kÂ¥ÕL (m) [FA (a)] 
Ï›thnw Ñoe¡f©l m£ltizia ó®¤Â brOEJ 
 FiwKG x Fiw KG = äifKG v‹w éÂia¥ bgWf 
 (-2 ) x 3 = 
 (-2 ) x 2 = 
 (-2 ) x 0 = 
 (-2 ) x (-1 ) = 
 (-2 ) x (-2 ) = 
 khzt, khzéfis v©â¡if¡nf‰g FG¡fshf¥ 
Ãç¤J, x›bthU FGé‰F« mt®fns nk‰f©lthW 
v©fis nj®ªbjL¤J MÁça® brOEjJ nghš v© 
mik¥ò Ó®Kiwæš f©LÃo¤J m¿a¢ brOEf.
VHh« tF¥Ã‰fhd brašghLfŸ 
tsu¿ kÂ¥ÕL (m) [FA (a)] 
jiy¥ò : Ïa‰fâj« 
ghl¥bghUŸ : x¤j cW¥òfS« 
khWg£l cW¥òfS« 
f‰wš neh¡f« : x¤j cW¥ò¡fisÍ« 
khWg£l cW¥òfisÍ« m¿ªJ bfhŸSjš. 
Ïy¡F : FG¢brašghL - 
tif¥gL¤Jjš
VHh« tF¥Ã‰fhd brašghLfŸ 
tsu¿ kÂ¥ÕL (m) [FA (a)] 
 xU m£il¥ bg£oæš a, b, c, . . . . z tiu vGj¥g£l 3 
br£ m£ilfŸ, 0 Kjš 9 tiu vGj¥g£l 3 br£ m£ilfŸ k 
‰W« +, -, ´, ¸ F¿pLfŸ vGÂa 3 br£ m£ilfis 
tiugl jhëš vGÂ¥ nghl nt©L«. Ëò x›bthU 
khzt®fisÍ« jå¤jåahf miH¤J ËtU« brašghLfis 
bfhL¡fyh«. 
 kh¿ia vL¡f¢ brOEjš. 
 kh¿èia vL¡f¢ brOEjš. 
 F¿pLfis¡ bfh©L x¤j cW¥òfis vL¡f¢ brOEjš. 
 F¿pLfis¡ bfh©L nt‰¿d cW¥òfis vL¡f¢ brOEjš.
v£lh« tF¥Ã‰fhd brašghLfŸ 
tsu¿ kÂ¥ÕL (m) [FA (a)] 
jiy¥ò : toéaš 
ghl¥bghUŸ : K¡nfhz¤Â‹ 
rkå‹ik¥g©ò 
f‰wš neh¡f« : xU K¡nfhz¤Â‹ 
VnjD« ÏUg¡f msÎfë‹ TLjš _‹whtJ g¡f msitél mÂf« vd 
m¿jš. 
Ïy¡F : jå¢brašghL – 
brOEJ f‰wš Kiw
v£lh« tF¥Ã‰fhd brašghLfŸ 
tsu¿ kÂ¥ÕL (m) [FA (a)] 
braš : 
khzt®fis btŸis¤jhëš neh£L¥ò¤jf¤Âš g¡f§fë‹ k‰W« 
nfhz§fë‹ mo¥gilæY« 6 tifahd K¡nfhz§fis tiua¢ brOEf. 
tiuªj K¡nfhz¤Â‹ Ús§fis msªJ vGj¢ brOEf. 
g¡f« 88š cŸs m£ltizia tiuªj K¡nfhz¤Â‹ g¡f 
msÎfis¡ bfh©L ó®¤Â brOEa brOEf. 
m£ltizæèUªJ K¡nfhz¤Â‹ rkå‹ik¥ g©ig khzt®fë‹ _y« 
bgWf.
v£lh« tF¥Ã‰fhd brašghLfŸ 
tsu¿ kÂ¥ÕL (m) [FA (a)] 
 jiy¥ò : toéaš 
 neh¡f« : tot§fŸ k‰W« g©òfis 
milahs§fhz¢ brOEjš 
 fhy msÎ : 1 ghlntis 
 f‰wš Ïy¡F : FG¢ brašghL
v£lh« tF¥Ã‰fhd brašghLfŸtsu¿ kÂ¥ÕL 
(m) [FA (a)] 
 MÁça® fh»j¤Âš f¤jç¡f¥g£l tot§fis¤ jah® brOEJ bfhŸsΫ. 
ÃwF khzt®fisFGthf¥ Ãç¡fΫ. 
 f¤jç¡f¥g£l mid¤J tot§fisÍ« MÁça® xU FGél« më¡f nt©L«. 
MÁça® g©òfis¡ Tw m¡FG g©Ã‰F cfªj tot§fis milahs§f©L 
Ãç¡f nt©L«. mL¤j FGéd® m¡FGé‹ brašgh£il c‰Wneh¡f 
nt©L«. 
 MÁça® T¿a g©òfS¡F V‰wthW m¡FG ÏWÂahf milahs§f©l 
tot« rçahdjh, Ïšiyah v‹gij k‰w FGédUl‹ éth¡fyh«. 
 tot§fS¡F cfªj g©ig milah§fh©gnjhL k£Lä‹¿, k‰w g©nghL 
khzt®fŸ x¥ÃL»wh®fsh v‹gij MÁça® c‰Wneh¡f¥gl nt©L«.
tsu¿ kÂ¥ÕL (M) [FA (b)] édh tif 
 édhé‹ tif : édho édh 
xU t£l¤Âš cŸs fhš t£l§fë‹ v©â¡if v‹d? 
 édhé‹ tif: fâj¡ fU¤J¡fis ãidé‰F 
bfh©L tUjš. 
xU rkg¡f K¡nfhz gu¥Ã‹ N¤Âu« ahJ?
tsu¿ kÂ¥ÕL (M) [FA (b)] édh tif 
édhé‹ tif: tçir¥gL¤Â vGJjš 
AC = 7 brÛ msΟs nfh£L¤J©o‰F ika¡F¤J¡nfhL 
tiua nt©oa goãiyfis tçir¥gL¤Jf. 
m) C I ikakhf¡ bfh©L tiua¥gL« mnj MuKŸs t£lé‰fŸ Kªija 
é‰fis X k‰W« Y òŸëfis bt£LkhW tiuf 
M) AC =7 brÛ msΟs nfh£L¤J©L tiuf. 
Ï) XY I nr®¡f. nfh£L¤J©L AC I Oéš bt£L»wJ 
<) Aia ikakhf¡ bfh©L AC Ús¤ij gh¡F nkš MuKŸs t£lé 
‰fŸ, AC nfh£L¤J©o‰F nkY« ÑG« mikÍkhW tiuf 
c) XY MdJ AC æ‹ ika¡F¤J¡nfhL MF«
kd¡ fz¡FfŸ 
xU br›tf¤ij v¤jid têfëš ghÂah¡fyh«? 
86 ‹ ghÂia él¥ bgça 5‹ kl§F ahJ? 
ò®fŸ 
eh‹ X® M¿y¡f v©iz ãid¡»nw‹. mj‹ Ïy¡f§fë‹ TLjš 43 
våš 
ËtU« T‰Wfëš Ïu©L k£Lnk bkOE 
m) mJ xU t®¡f v© 
M) mJ xU fd v© 
Ï) m›bt© 500000I él¢ Á¿aJ 
mªj v© ahJ?
Áªjidia¤ ö©L« édh¡fŸ 
1) x‹W éilahf tUkhW 10 édh¡fis / T‰Wfis jah® brOEf. 
2) ó{ía« éilahf tUkhW 10 édh¡fis / T‰W¡fis cUth¡Ff. 
3) – 2 éiltUkhW 10 édh¡fis / T‰W¡fis cUth¡Ff. 
4) 
. . . . . . . . . . . 
. . . . . . . . . . . 
. . . . . . . . . . . 
. . . . . . . . . . . 
. . . . . . . . . . . 
M»a òŸëfis¡ bfh©L gšntW cUt§fis cUth¡Ff.
Âwªjãiy¡ nfŸéfŸ 
(Open ended questions) 
 xU khzt‹ xU fz¡»‹ éil 3 v‹W T¿dhš m¤Ô®Î fhz fz¡»id mik¡f. 
F¿¥ò : v©z‰w édh¡fŸ mik¡fyh«. mš T£lš, fê¤jš, 
bgU¡fš, tF¤jš, Û.Á.k, Û.bg.t, Ëd§fŸ, gu¥gsÎ, é»j« ngh‹w 
ghl¡fU¤J¡fis¥ ga‹gL¤jyh«.
Áªjidia¤ Jh©L« édh¡fŸ 
1. Ïu©L Ëd§fis¡ T£odhš éil 3/8 Ït‰¿š x›bth‹¿‹ gFÂÍ« 8 
Mf ÏUªÂU¡f nt©L« v‹gJ rçah? Ïšiybaåš vL¤J¡fh£L x‹iw¤ 
jUf. 
2. 120 nfhèfis xUt® 4 bg£ofëš Ã‹tUkhW g§»£lh®. 
Kjš bg£oæ‹ v©â¡if, Ïu©lh« bg£oæ‹ v©â¡if M»a é»j« 
MdJ _‹wh«, eh‹fh« bg£oæ‹ v©â¡iffS¡»ilna Md é»j¤Jl‹ 
é»j rk¤Âš cŸsJ v‹whš mt® nfhèfis v›thW g§»£lh®. 
3. bgU¡fš gyid él mÂfkhd T£L¤ bjhif cŸs 3 KG¡fbs©fŸ fhz 
mnrh¡ Kaš»wh®. Ú§fŸ cjt ÏaYkh? 
4. Ïu©L KG v©fë‹ bgU¡f‰gy‹ 96, mt‰¿‹ TLjš 30 él FiwÎ 
våš Ïay¡Toa ÏU v©fis¡ TWf?
MOEÎãiy¡ fz¡FfŸ 
 ghjhs¢ rh¡filæ‹ Mëw§F FêfŸ V‹ rJukhf ÏU¥gšiy? 
e«ik R‰¿ÍŸs bghUŸfŸ, fUéfŸ Ït‰¿‹ totik¥òfŸ, 
mt‰¿‹ ga‹gh£Ll‹ bjhl®òŸsik¡F vL¤J¡fh£LfŸ jUf. 
 xU jhëš Ïu©L bt›ntW jå¤jå rJu§fŸ cŸsd. mit 
Ïu©L« Ïizªjhš xU òÂa rJu« »il¡Fkh?
Ïu©lh« gUt¤Â‰fhd gçªJiu¡f¥gL«brašÂ£l§fŸ 
khzt®fis 0 Kjš 9 tiuæyhd ä‹m£ilfis jahç¡f¢ brhšè mÂèUªJ 
VnjD« 5 v© m£ilfis bfh©L 
(m) 5 Ïy¡f v©fis cUth¡f¢ brOEjš. 
(M) mªj 5 Ïy¡f v©fë‹ VWtçir k‰W« Ïw§Ftçiræš mik¡f. 
(Ï) mš, äf¥bgça 5 Ïy¡f v© mik¤jš. 
(<)mš, äf¢ Á¿a 5 Ïy¡f v© mik¤jš. 
(c) Ïu©o‰F« cŸs ntWgh£il m¿jš 
(C) ä‹m£ilia¡ bfh©L Ëd§fis cUth¡f¢ brhšè, Ë m¥Ã‹d§fë‹ 
T£lš, fê¤jš, bgU¡fš, tF¤jš brašghLfis brOEa¢ brOEjš.
nfhz§fŸ cUthF« Ïl§fŸ 
m‹hwhl thoeéš Ú§fŸ fhQ« nfhz§fŸ cUthF« Ïl§fŸ 
10 –id g£oaèl¢ brOEf. 
mitfŸ v›tif nfhz§fŸ v‹gij TWf. 
étu§fis¡ ifahSjš 
VnjD« xU brOE¤jhëš cŸs xU g¤Âia 
vL¤J¡bfh©L mÂYŸs 2 vG¤J¡fŸ, 3 vG¤J¡fŸ k 
‰W« 4 vG¤J¡fis¤ bjç΢ brOEJ, mjid¡ bfh©L 
ãfoebt© g£oaiy jah® brOEf.
e‹¿

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Cce upper primary maths new

  • 1. bjhl® k‰W« KGikahd kÂ¥ÕL ca®bjhl¡f ãiy – fz¡F (Kjš gUt«)
  • 2. ifna£o‹ cŸns.... t. v© bghUsl¡f« 1. tsu¿ kÂ¥ÕL (m), tsu¿ kÂ¥ÕL (M), bjhF¤j¿ kÂ¥ÕL 2. tF¥giw¢ brašghLfŸ jå eg® ,ÁW FG, KG tF¥ò 3. kÂ¥Õ£L¡ TWfŸ k‰W« Fiw Ô® f‰Ã¤jš 4. fhy msÎ 5. v®gh®¡f¥gL« f‰wš Ïy¡FfŸ 6. ghlüèš Ïl« bg‰WŸs tsu¿¢ brašghLfŸ (6,7,8,tF¥ò) 7. khÂç édh¤jhŸ (6,7,8,tF¥ò) 8. K¡»a ghl¡fU¤J¡fŸ (6,7,8,tF¥ò) 9. Áªjidia¤ ö©L« édh¡fŸ 10. gçªJiu¡f¥gL« brašÂ£l§fŸ.
  • 3. MÁça® ifna£oid¥ ga‹gL¤Jtj‰fhd têKiwfŸ jäHf murhš btëæl¥g£LŸs K¥gUt ghlüèš Kjš gUt¤Â‰Fça ca®bjhl¡f ãiy fâj brašghLfŸ Ï¡ifna£oš Ïl« bg‰WŸsJ. ifna£oš bfhL¡f¥g£LŸs brašfŸ mid¤J« têfh£lY¡F k£Lnk. bfhL¡f¥g£l brašghLfis¡ tF¥giwæ‹ ga‹gh£o‰nf ‰g MÁça®fŸ m¥gona (mšyJ) kh‰¿aik¤J ga‹gL¤jyh«.
  • 4. MÁça® ifna£oid¥ ga‹gL¤Jtj‰fhd têKiwfŸ tsu¿ kÂ¥Õ£oid, MÁça® kÂ¥ÕL brOEÍ« bghGJ khzt®fŸ Rikahf ãid¡fhjthW nk‰bfhŸs Áw¥ò¡ ftd« vL¤J¡bfhŸSjš nt©L«. f‰wš f‰Ã¤jèš MÁça®, khzt®fë‹ ãiyæid cz®tj ‰F«, f‰wiy nk«gL¤Jtj‰F« Ï¡ifnaL cjΫ.
  • 5. tsu¿ kÂ¥ÕL (m) ghl¤ÂYŸs xU fU¤ij¡ f‰Ã¡F« nghJ fU¤J cUthtj‰F« f‰wiy tY¥gL¤Jtj‰F« brašghLfë‹ mo¥gilæš ãfH¡ ToajhF«. ÏJ f‰wš eilbgW«bghGJ brOEÍ« kÂ¥ÕlhF«.
  • 6. tsu¿ kÂ¥ÕL (m) é‹ Áw¥g«r§fŸ  j‹id¤ jhnd nrh¤J m¿a khzt®fS¡fhd xU msÎ nfhš.  Fiwa¿ k‰W« Fiwfis¥ ngh¡f elto¡if vL¡f Mrça®fS¡fhd têfh£o.  FG¢brašgh£o‹ _y« thoeéaš Âw‹fshd KobtL¤jš, Ãu ¢ridfis¡ fisjš, e£òwit nk«gL¤Jjš, T® Áªjid k‰W« rçahd jftš bjhl®ò ngh‹wt‰iw nk«gL¤j cjÎtJ.  khzt®fë‹ f‰wš ntf¤Â‰nf‰g brašghLfŸ mik¡f¥gl nt©L«.
  • 7. tsu¿ kÂ¥ÕL (m) - gÂÎ brOEjš  tF¥Ãš cŸs x›bthU khztU« Fiwªjg£r« 4 brašghLfis x›bthU gUt¤ÂY« nk‰bfh©L mt‰¿š Áwªj 2 brašghLfis MÁça® kÂ¥Õ£o‰F vL¤J¡ bfhŸs nt©L«.  (2 brašghLfŸ x 10 kÂ¥bg©fŸ = 20 kÂ¥bg©fŸ)
  • 8. tsu¿ kÂ¥ÕL (m) [FA (a)] é‰fhd Áy brašghLfŸ) t. v© brašghL t. v© brašghL 1 braš £l« (Project) 9 brOEJ f‰wš (Learning by doing) 2 Ãu¢rid Ô®¤jš (Problem Solving) 10 x¥gil¥òfŸ (Assignments ) 3 étu§fis¢ nrfç¤jš (Data Collection) 11 éisah£LfŸ (Games) 4 fU¤J tiugl« (Concept mapping) 12 fh£Á¥ gL¤Jjš (Visualisation) 5 bghUŸ és¡f« jUjš (Interpretation) 13 kÂ¥ÃLjš k‰W« njhuha« fhzš (Estimation and Approximation) 6 ò® (Puzzle) 14 ca® Áªjidia¤ ö©L« édh¡fŸ (Higher order thinking Questions) 7 c‰W neh¡Fjš (Observation) 15 khzt®fis¡ fâj bkhê gçkh‰w¤Â‰F tênfhYjš ( Mathematical Communication) 8 f©lhuhOEjš (Investigation)
  • 9. tsu¿ kÂ¥ÕL (M)  ghl¤ÂYŸs xU fU¤ij¡ f‰Ã¤j Ëò f‰wiy kÂ¥ÕL brOEtjhF«.  x›bthU khztU¡F« FW»a fhy mséš el¤j¥gL« xU ÁW vG¤J nj®thF«.
  • 10. tsu¿ kÂ¥ÕL (M) - Áw¥g«r§fŸ  jå¢ brašgh£o‹ _y« x›bthU khztUila f‰wš milit cW brOEa¥gL»wJ.  khzt®fŸ j§fŸ f‰wš milit¤ j‹id¤jhnd nrh¤J m¿a cjΫ msÎnfhyhF«.  Fiwa¿ k‰W« FiwÔ® elto¡iffis vL¡f MÁça®fS¡F xU tê fh£oahf mik»wJ.
  • 11. tsu¿ kÂ¥ÕL (M) – gÂÎ brOEjš  tF¥Ãš cŸs x›bthU khztU« Fiwªjg£r« 4 brašghLfis x›bthU gUt¤ÂY« nk‰bfh©L mt‰¿š Áwªj 2 brašghLfis MÁça® kÂ¥Õ£o‰F vL¤J¡bfhŸs nt©L«.  (2 brašghLfŸ X 10 kÂ¥bg©fŸ = 20 kÂ¥bg©fŸ)
  • 12. tsu¿ kÂ¥ÕL (M) [FA (b)] é‰fhd Áy édh¡fŸ t. v© édh¡fŸ t. v© édh¡fŸ 1. gyΟ bjçÎ (Multiple Choice) 6 tçir¥gL¤Jjš (Sequencing) 2. nfho£l Ïl§fis ãu¥òjš (Fill in the blanks) 7 ca® Áªjidia¤ ö©L« édh¡fŸ (Higher order Thinking question) 3. bghU¤Jjš (Matching) 8 ÁW édh¡fŸ (Short Answer Question) 4. édho édh (Quiz) 9 FW édh¡fŸ (Very short Answer Question) 5. fâj fU¤Jfis ãidÎ TWjš (Recalling Mathematical Concepts) 10 tiufiy mik¥òfŸ (Graphic Organisers)
  • 13. bjhF¤j¿ kÂ¥ÕL x›bthU gUt¤Â‹ ÏWÂæš 60 kÂ¥bg©fS¡F eilbgW« vG¤J nj®thF«. édh totik¥Ã‹ mo¥gilæš édh¤jhŸ jahç¡f¥gL«.  f‰wš neh¡f§fshd m¿jš, òçjš, ga‹gL¤Jjš k‰W« Âw‹ bgwš v‹w mo¥gilæš mik¡f¥g£LŸsJ.  mªj¥ gUt¤Âš bfhL¡f¥g£l ghl¤Â£l¤ij cŸsl¡»ajhf ÏU¡F«.
  • 14. jå eg® brašghL KGikahd k‰W« bjhl® kÂ¥Õ£oš x›bthU khztiuÍ« f ‰wèš cW brOEa jå eg® brašghL mtÁakh»wJ. tF¥giwæš khzt®fë‹ v©â¡if Fiwthf ÏU¡F« nghJ Ï ¢brašghL V‰òilajhf mikÍ«.  Ï¢brašgh£il mik¡F« nghJ MÁça® x›bthU khztçl¤ÂY« ftd« brY¤Â, f‰wš bjhOEé‹¿ eilbgW»‹wjh? v‹gij cW brOEa nt©L«.  jå eg® brašgh£o‹ _y« eilbgW« f‰wyhdJ, Ú©l eh£fS¡F ãiy¤J ã‰F«. nkY«, f‰wš bghUSilajhf ÏU¡F«.
  • 15. ÁW FG brašghL tF¥giwæš khzt®fë‹ v©â¡if mÂfkhf ÏU¡F« nghJ MÁça® khzt®fis 5mšyJ mj‰F nk‰g£l ÁW FG¡fshf¥ Ãç¤J f‰wš brašgh£il mik¡f nt©L«.  ÁW FG¡fshf¥ Ãç¡f¥gLtjhš x›bthU FGédU¡F« f ‰wš f‰Ã¤jš Jiz¡fUéfŸ brašfis mik¥gj‰F K‹d® tH§Ftij cW brOEjš nt©L«.  Ï¢brašgh£o‹ nghJ tF¥giw xG§F e‹Kiwæš mika MÁça® f©fhâ¡f nt©L«.  x›bthU khztUila g§fë¥ò« Ïl« bgWkhW MÁça® cW brOEa nt©L«.
  • 16. KG tF¥ò brašghL MÁça® ghl¤Â£l¤Âš cŸs Áy Âw‹fis¤ jåeg® brašghL, Ïiz brašghL kwW« FG¢ brašghL _ykhfnth el¤j Ïayhj bghGJ tF¥Ãš cŸs mid¤J khzt®fisÍ« xnu FGthf¡ mik¤J brOEJ fh£lš, c ‰Wneh¡fš (m) bghUŸ és¡f« jUjš _y« ghl¥bghUis khzt®fS¡F f‰Ã¤jš nt©L«. cjhuzkhf brOEKiw toéaèš cŸs t£l eh‰fu« tiujš v‹w ghl¥bghUis¢ brOEJfh£lš _y« f‰Ã¤jš.
  • 17. tsu¿ kÂ¥ÕL (m) - és¡f¡ F¿¥òfŸ j‹dh®t« (Initiative) <LghL (Involvement) g§nf‰wš (Participation) élhKa‰Á (Perseverence) Óuhf¢ brOEjš (Perfection) khztå‹ brašghLfis kÂ¥ÃL«bghGJ milΤÂw‹ k£Lä‹¿, nk‰F¿¥Ã£l bghJthd IªJ és¡f¡ F¿¥òfis kd¤Â ‰bfh©L kÂ¥ÕL brOEjš nt©L«.
  • 18. kÂ¥Õ£L¡ TWfŸ- tsu¿ kÂ¥ÕL (m) kÂ¥bg© fŸ ju« kÂ¥Õ£L fhuâfŸ 10 äf e‹W *** · brašgh£oid KGikahfΫ bjëthfΫ, xG§FlD« Ko¤jš · brašgh£oid cçaKiwæš brOEjš k‰W« gil¥gh‰wš Âw‹ btë¥gL« tifæš Ko¤jš. · brašgh£oid m¿th®ªjKiwæš Ko¤jš 8-9 e‹W** · brašgh£oid KGikahf, xG§fhf, ca®ªj Kiwæš k‰W« ftdkhfΫ brOEJ Ko¤jš 6-7 ÂU¥Âfu«* · brašgh£oid KG <Lgh£Ll‹ Ko¤jš 5 Ka‰Á njit  · brašgh£oid ãiwÎbrOEa nt©oæUªjhnyh, <LghL njit¥g£lhnyh Ï¡F¿p£oid ÏLjš nt©L«
  • 19. FiwÔ® f‰Ã¤jš  tsu¿ kÂ¥ÕL ( m ) k‰W« tsu¿ kÂ¥ÕL ( M) Ïš KGikahf¢ brašglhj, Ka‰Á njit¥gL« khzt®fS¡F Û©L« f‰wèš KGikaila MÁça® cjéÍl‹ mnj brašgh£ilnah mšyJ khzt® vL¤J¡bfh©l brašgh£o‰F Ïizahd, vëikahd kh‰W brašgh£ilnah më¡f nt©L«.  FiwÔ® f‰Ã¤jiy khzt®fŸ KGikahd f‰wš milÎ bgW« tiu bjhl®ªJ brOEJ mij kÂ¥ÕL brOEJ cça ju« tH§»lnt©L«.
  • 20. fhy msÎ-Mwh« tF¥ò t. v©. ghl myF f‰Ã¡f njit¥gL« ÃçntisfŸ tsu¿ brašgh£ o‰F njit¥gL« ÃçntisfŸ bkh¤j ÃçntisfŸ 1. v©âaš 40 4 44 2. msitfŸ 10 2 12 3. toéaš 6 2 8 4. brOEKiw toéaš 4 2 6 bkh¤j« 60 10 70
  • 21. fhy msÎ-VHh« tF¥ò t. v©. ghl myF f‰Ã¡f njit¥gL« ÃçntisfŸ tsu¿ brašgh£ o‰F njit¥gL« ÃçntisfŸ bkh¤j ÃçntisfŸ 1. v©âaš 31 4 35 2. Ïa‰fâj« 23 2 25 3. toéaš 18 2 20 4. brOEKiw toéaš 9 1 10 5 étu§fis ifahSjš 12 1 13 bkh¤j« 93 10 103
  • 22. fhy msÎ-v£lh« tF¥ò t. v©. ghl myF f‰Ã¡f njit¥gL« ÃçntisfŸ tsu¿ brašgh£ o‰F njit¥gL« ÃçntisfŸ bkh¤j ÃçntisfŸ 1. v©âaš 36 4 40 2. msitfŸ 20 3 23 3. toéaš 11 2 13 4. brOEKiw toéaš 13 1 14 bkh¤j« 80 10 90
  • 23. Mwh« tF¥Ã‰fhd brašghLfŸ tsu¿ kÂ¥ÕL (m) [FA (a)]  jiy¥ò : v©âaš  ghl¥bghUŸ : fhuâfŸ  f‰wš neh¡f« : fhuâfis f©l¿jš  Ïy¡F : FG¢brašghL
  • 24. Mwh« tF¥Ã‰fhd brašghLfŸ tsu¿ kÂ¥ÕL (m) [FA (a)] 1 Kjš 100 tiu v©fŸ vGj¥g£l m£ilfis (v© m£ilfis khzt®fë‹ v©â¡if¡nf‰g) MÁça® khzt®fS¡F tH§f nt©L«. 18, 21, 30, 42, 60 ngh‹w v©fis MÁça® jiuæš vG t£lälš nt©L«. MÁça® 18 v‹wÎl‹ mj‹ fhuâfis 3, 6, 2 , 9 v‹w nrhofëš khzt®fis t£l¤Â‹ ÛJ ã‰f¢ brOEayh«. khzt®fŸ rçahd v© t£l¤Â‹ ÛJ cŸsduh v‹gij MÁça® kÂ¥ÕL brOEa nt©L«.
  • 25. Mwh« tF¥Ã‰fhd brašghLfŸ tsu¿ kÂ¥ÕL (m) [FA (a)]  jiy¥ò : toéaš  ghl¥bghUŸ : Ïiz nfhLfŸ, br§F¤J¡nfhLfŸ f‰wš neh¡f« : M§»y vG¤J¡fëš ÏiznfhLfŸ br§F¤J¡nfhLfŸ m¿ªJ bfhŸsš, khzt®fS¡F Ïiz¡nfhLfŸ,br§F¤J¡nfhLfŸ g‰ ¿ bjëthdÁªjid V‰gL¤Jjš
  • 26. Mwh« tF¥Ã‰fhd brašghLfŸ tsu¿ kÂ¥ÕL (m) [FA (a)] MÁça® M§»y vG¤J¡fëš ÏiznfhLfŸ br§F¤J¡nfhLfis f©l¿ªJ v.fh x‹iw¡ T¿ ÏJ ÏiznfhLfsh mšyJ br§F¤J¡nfhLfsh vd édh vG¥Ã khzt®fël« éil fh©f. X›bthU khzt®fël« br§F¤J¡nfhLfŸ, ÏiznfhLfŸ cŸs vG¤J¡fis f©l¿a¢ brOEf. nkY« br§F¤J k‰W« ÏiznfhLfŸ ÏizªJ tU« vG¤J¡fisÍ« g£oaèLf.
  • 27. VHh« tF¥Ã‰fhd brašghLfŸ tsu¿ kÂ¥ÕL (m) [FA (a)] jiy¥ò : bkOEba©fë‹ bjhF¥ò ghl¥bghUŸ : KG¡fë‹ bgU¡fš f‰wš neh¡f« : xU Fiw KGit k‰bwhU Fiw KGthš bgU¡Fjiy v© mik¥ò Ó® _y« òçªJ bfhŸSjš. Ïy¡F : FG¢brašghL - c‰Wneh¡Fjš Kiw
  • 28. VHh« tF¥Ã‰fhd brašghLfŸ tsu¿ kÂ¥ÕL (m) [FA (a)]  xU Fiw KGit k‰bwhU FiwKGthš bgU¡Ftj‰F K‹ MÁça® Fiw KG x äif KG = FiwKG v‹w éÂia v© mik¥ò Ó® Kiwæš Ñoe¡f©lthW ã%áf nt©L«.  (+2 ) x (+10) = (+20 )  (+1 ) x (+10) = (+10 )  0 x (+10) = 0  (-1 ) x (+10) =  (-2 ) x (+10) =
  • 29. VHh« tF¥Ã‰fhd brašghLfŸ tsu¿ kÂ¥ÕL (m) [FA (a)] Ï›thnw Ñoe¡f©l m£ltizia ó®¤Â brOEJ  FiwKG x Fiw KG = äifKG v‹w éÂia¥ bgWf  (-2 ) x 3 =  (-2 ) x 2 =  (-2 ) x 0 =  (-2 ) x (-1 ) =  (-2 ) x (-2 ) =  khzt, khzéfis v©â¡if¡nf‰g FG¡fshf¥ Ãç¤J, x›bthU FGé‰F« mt®fns nk‰f©lthW v©fis nj®ªbjL¤J MÁça® brOEjJ nghš v© mik¥ò Ó®Kiwæš f©LÃo¤J m¿a¢ brOEf.
  • 30. VHh« tF¥Ã‰fhd brašghLfŸ tsu¿ kÂ¥ÕL (m) [FA (a)] jiy¥ò : Ïa‰fâj« ghl¥bghUŸ : x¤j cW¥òfS« khWg£l cW¥òfS« f‰wš neh¡f« : x¤j cW¥ò¡fisÍ« khWg£l cW¥òfisÍ« m¿ªJ bfhŸSjš. Ïy¡F : FG¢brašghL - tif¥gL¤Jjš
  • 31. VHh« tF¥Ã‰fhd brašghLfŸ tsu¿ kÂ¥ÕL (m) [FA (a)]  xU m£il¥ bg£oæš a, b, c, . . . . z tiu vGj¥g£l 3 br£ m£ilfŸ, 0 Kjš 9 tiu vGj¥g£l 3 br£ m£ilfŸ k ‰W« +, -, ´, ¸ F¿pLfŸ vGÂa 3 br£ m£ilfis tiugl jhëš vGÂ¥ nghl nt©L«. Ëò x›bthU khzt®fisÍ« jå¤jåahf miH¤J ËtU« brašghLfis bfhL¡fyh«.  kh¿ia vL¡f¢ brOEjš.  kh¿èia vL¡f¢ brOEjš.  F¿pLfis¡ bfh©L x¤j cW¥òfis vL¡f¢ brOEjš.  F¿pLfis¡ bfh©L nt‰¿d cW¥òfis vL¡f¢ brOEjš.
  • 32. v£lh« tF¥Ã‰fhd brašghLfŸ tsu¿ kÂ¥ÕL (m) [FA (a)] jiy¥ò : toéaš ghl¥bghUŸ : K¡nfhz¤Â‹ rkå‹ik¥g©ò f‰wš neh¡f« : xU K¡nfhz¤Â‹ VnjD« ÏUg¡f msÎfë‹ TLjš _‹whtJ g¡f msitél mÂf« vd m¿jš. Ïy¡F : jå¢brašghL – brOEJ f‰wš Kiw
  • 33. v£lh« tF¥Ã‰fhd brašghLfŸ tsu¿ kÂ¥ÕL (m) [FA (a)] braš : khzt®fis btŸis¤jhëš neh£L¥ò¤jf¤Âš g¡f§fë‹ k‰W« nfhz§fë‹ mo¥gilæY« 6 tifahd K¡nfhz§fis tiua¢ brOEf. tiuªj K¡nfhz¤Â‹ Ús§fis msªJ vGj¢ brOEf. g¡f« 88š cŸs m£ltizia tiuªj K¡nfhz¤Â‹ g¡f msÎfis¡ bfh©L ó®¤Â brOEa brOEf. m£ltizæèUªJ K¡nfhz¤Â‹ rkå‹ik¥ g©ig khzt®fë‹ _y« bgWf.
  • 34. v£lh« tF¥Ã‰fhd brašghLfŸ tsu¿ kÂ¥ÕL (m) [FA (a)]  jiy¥ò : toéaš  neh¡f« : tot§fŸ k‰W« g©òfis milahs§fhz¢ brOEjš  fhy msÎ : 1 ghlntis  f‰wš Ïy¡F : FG¢ brašghL
  • 35. v£lh« tF¥Ã‰fhd brašghLfŸtsu¿ kÂ¥ÕL (m) [FA (a)]  MÁça® fh»j¤Âš f¤jç¡f¥g£l tot§fis¤ jah® brOEJ bfhŸsΫ. ÃwF khzt®fisFGthf¥ Ãç¡fΫ.  f¤jç¡f¥g£l mid¤J tot§fisÍ« MÁça® xU FGél« më¡f nt©L«. MÁça® g©òfis¡ Tw m¡FG g©Ã‰F cfªj tot§fis milahs§f©L Ãç¡f nt©L«. mL¤j FGéd® m¡FGé‹ brašgh£il c‰Wneh¡f nt©L«.  MÁça® T¿a g©òfS¡F V‰wthW m¡FG ÏWÂahf milahs§f©l tot« rçahdjh, Ïšiyah v‹gij k‰w FGédUl‹ éth¡fyh«.  tot§fS¡F cfªj g©ig milah§fh©gnjhL k£Lä‹¿, k‰w g©nghL khzt®fŸ x¥ÃL»wh®fsh v‹gij MÁça® c‰Wneh¡f¥gl nt©L«.
  • 36. tsu¿ kÂ¥ÕL (M) [FA (b)] édh tif  édhé‹ tif : édho édh xU t£l¤Âš cŸs fhš t£l§fë‹ v©â¡if v‹d?  édhé‹ tif: fâj¡ fU¤J¡fis ãidé‰F bfh©L tUjš. xU rkg¡f K¡nfhz gu¥Ã‹ N¤Âu« ahJ?
  • 37. tsu¿ kÂ¥ÕL (M) [FA (b)] édh tif édhé‹ tif: tçir¥gL¤Â vGJjš AC = 7 brÛ msΟs nfh£L¤J©o‰F ika¡F¤J¡nfhL tiua nt©oa goãiyfis tçir¥gL¤Jf. m) C I ikakhf¡ bfh©L tiua¥gL« mnj MuKŸs t£lé‰fŸ Kªija é‰fis X k‰W« Y òŸëfis bt£LkhW tiuf M) AC =7 brÛ msΟs nfh£L¤J©L tiuf. Ï) XY I nr®¡f. nfh£L¤J©L AC I Oéš bt£L»wJ <) Aia ikakhf¡ bfh©L AC Ús¤ij gh¡F nkš MuKŸs t£lé ‰fŸ, AC nfh£L¤J©o‰F nkY« ÑG« mikÍkhW tiuf c) XY MdJ AC æ‹ ika¡F¤J¡nfhL MF«
  • 38. kd¡ fz¡FfŸ xU br›tf¤ij v¤jid têfëš ghÂah¡fyh«? 86 ‹ ghÂia él¥ bgça 5‹ kl§F ahJ? ò®fŸ eh‹ X® M¿y¡f v©iz ãid¡»nw‹. mj‹ Ïy¡f§fë‹ TLjš 43 våš Ã‹tU« T‰Wfëš Ïu©L k£Lnk bkOE m) mJ xU t®¡f v© M) mJ xU fd v© Ï) m›bt© 500000I él¢ Á¿aJ mªj v© ahJ?
  • 39. Áªjidia¤ ö©L« édh¡fŸ 1) x‹W éilahf tUkhW 10 édh¡fis / T‰Wfis jah® brOEf. 2) ó{ía« éilahf tUkhW 10 édh¡fis / T‰W¡fis cUth¡Ff. 3) – 2 éiltUkhW 10 édh¡fis / T‰W¡fis cUth¡Ff. 4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M»a òŸëfis¡ bfh©L gšntW cUt§fis cUth¡Ff.
  • 40. Âwªjãiy¡ nfŸéfŸ (Open ended questions)  xU khzt‹ xU fz¡»‹ éil 3 v‹W T¿dhš m¤Ô®Î fhz fz¡»id mik¡f. F¿¥ò : v©z‰w édh¡fŸ mik¡fyh«. mš T£lš, fê¤jš, bgU¡fš, tF¤jš, Û.Á.k, Û.bg.t, Ëd§fŸ, gu¥gsÎ, é»j« ngh‹w ghl¡fU¤J¡fis¥ ga‹gL¤jyh«.
  • 41. Áªjidia¤ Jh©L« édh¡fŸ 1. Ïu©L Ëd§fis¡ T£odhš éil 3/8 Ït‰¿š x›bth‹¿‹ gFÂÍ« 8 Mf ÏUªÂU¡f nt©L« v‹gJ rçah? Ïšiybaåš vL¤J¡fh£L x‹iw¤ jUf. 2. 120 nfhèfis xUt® 4 bg£ofëš Ã‹tUkhW g§»£lh®. Kjš bg£oæ‹ v©â¡if, Ïu©lh« bg£oæ‹ v©â¡if M»a é»j« MdJ _‹wh«, eh‹fh« bg£oæ‹ v©â¡iffS¡»ilna Md é»j¤Jl‹ é»j rk¤Âš cŸsJ v‹whš mt® nfhèfis v›thW g§»£lh®. 3. bgU¡fš gyid él mÂfkhd T£L¤ bjhif cŸs 3 KG¡fbs©fŸ fhz mnrh¡ Kaš»wh®. Ú§fŸ cjt ÏaYkh? 4. Ïu©L KG v©fë‹ bgU¡f‰gy‹ 96, mt‰¿‹ TLjš 30 él FiwÎ våš Ïay¡Toa ÏU v©fis¡ TWf?
  • 42. MOEÎãiy¡ fz¡FfŸ  ghjhs¢ rh¡filæ‹ Mëw§F FêfŸ V‹ rJukhf ÏU¥gšiy? e«ik R‰¿ÍŸs bghUŸfŸ, fUéfŸ Ït‰¿‹ totik¥òfŸ, mt‰¿‹ ga‹gh£Ll‹ bjhl®òŸsik¡F vL¤J¡fh£LfŸ jUf.  xU jhëš Ïu©L bt›ntW jå¤jå rJu§fŸ cŸsd. mit Ïu©L« Ïizªjhš xU òÂa rJu« »il¡Fkh?
  • 43. Ïu©lh« gUt¤Â‰fhd gçªJiu¡f¥gL«brašÂ£l§fŸ khzt®fis 0 Kjš 9 tiuæyhd ä‹m£ilfis jahç¡f¢ brhšè mÂèUªJ VnjD« 5 v© m£ilfis bfh©L (m) 5 Ïy¡f v©fis cUth¡f¢ brOEjš. (M) mªj 5 Ïy¡f v©fë‹ VWtçir k‰W« Ïw§Ftçiræš mik¡f. (Ï) mš, äf¥bgça 5 Ïy¡f v© mik¤jš. (<)mš, äf¢ Á¿a 5 Ïy¡f v© mik¤jš. (c) Ïu©o‰F« cŸs ntWgh£il m¿jš (C) ä‹m£ilia¡ bfh©L Ëd§fis cUth¡f¢ brhšè, Ë m¥Ã‹d§fë‹ T£lš, fê¤jš, bgU¡fš, tF¤jš brašghLfis brOEa¢ brOEjš.
  • 44. nfhz§fŸ cUthF« Ïl§fŸ m‹hwhl thoeéš Ú§fŸ fhQ« nfhz§fŸ cUthF« Ïl§fŸ 10 –id g£oaèl¢ brOEf. mitfŸ v›tif nfhz§fŸ v‹gij TWf. étu§fis¡ ifahSjš VnjD« xU brOE¤jhëš cŸs xU g¤Âia vL¤J¡bfh©L mÂYŸs 2 vG¤J¡fŸ, 3 vG¤J¡fŸ k ‰W« 4 vG¤J¡fis¤ bjç΢ brOEJ, mjid¡ bfh©L ãfoebt© g£oaiy jah® brOEf.