ປຶ້ມແບບຮຽນ ປ.5

[qf mu !) m;o7nog8adoyddkosko9eo;o4h;o

I. dyf9tde ’D *!( ' !$
pD $@!& ' *@#
!D 9q’j 0v[0Ao8q;8A’sko8+wxoUD
8q;1kj ’ G @!& ' !@
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dD !#& ' ) 0D @@* ' _ 7D $&@ ' !@
9D &@!# ' @# lD ($!@ ' &@ -D )@!& ' @!$

@D 9q’j 8nj,8k8t]k’8+wxD

8q;8A’sko 8q;sko dko0v[0Ao 9eo;o8q;g]d

*@$) $* $* V !WW < *@$) < $* V !WWW 0v’zqosko
@#* !$ #
!#&@ @&
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(!W& !@
!*#!$ )W$

II. .97;k,

grnvj 1kdsko9eo;o4h;o.sh9eo;o4h;o gIqk8hv’xt8y[af8k,0Ao8vofa’j oUG
!D -vdsk9eo;o8q;g]d0v’zqoskofh;pdko0v[0Ao8q;8A’sko fh;pmt;u76o

0v’8q;skoD
@D 8A’[A’g]dskogrnjv-vdskzqoskoD
#D d;f7nozqomjuwfhIa[D

8q;1jk’ G grnvj 1kdsko !W @*# ' ($ gIqk8hv’xt8y[af8k,0Ao8vofaj’oUG

48

dD oe.-hdko0v[0Ao9eo;o !W @*# fh;pmt;u76o0v’ ($D
($ V !WW < !W@*# < ($ V !WWW
zqosko16j]ts;kj ’ !WW c]t ! WWW c,jo9eo;omuj,u # 8q;g]d
0D 8A’[A’g]dsko _ !W@*# ($
($ gmnvj sq;Ihvp ($WW !#)
_ @)*# sq;|;j p
($ gmnjvsq;ly[ @@@W sq;ly[
W*$# sq;Ihvp
($ gmnjvsq;|;j p _ &_@
W&!
7D d;f7nozqomujwfhIa[
0PozqomjuwfhIa[G !W@*# = X($ V !#)? T &!
gIqklk,kfd;f7nowfhfaj’oUG !W@*# = !W@!@ T &! = !W@*#
.ooAo !W@!@ = ($WW T @@@W T &_@ ສະຫງສ.ວວນ.ລິສຂະສິດ

III. [qfg/ydsaf
!D 9q’j 0v[0Ao8q;8A’sko8+wxoUD
dD @$& ' ) S 0D $!@ ' !@ S 7D &&@ ' !* S ’D #*!( ' &$ S
9D &@!# ' @#& S lD ($!@ ' &!@ S -D )@*& ' @!$S pD @$*&) ' &@#D
@D 9q’j 8nj,8k8t]k’]5,j oUD

8q;8A’sko 8q;sko dko0v[0Ao 9eo;o8q;g]d0v’zqosko

@!) !$
$@# @&
#@&! $&
*W#@ *$
@$!W& #!@
$*@!) )W$

#D 9qj’skog]d8+wxoUD
dD *$) ' _ S 0D @)) ' !@ S 7D &&@ ' $* S ’D @)$& ' $W S
9D $@!# ' !&$ S lD *#!$ ' @#& S -D )$*@ ' $!@ S pD !*@*& ' @!$D

49

rkdmu & dkocdh39f[aosk

[qf mu !_ ;ymudkocdh39f[aosk

I. dyf9tde

!D 9qj’8n,j 9eo;o.lj[jvo9Ec,afD
dD !F $F (F !WF !#F D D D D D F D D D D D F @@F @&
0D !F @F $F )F !*F #@F *$F D D D D D F D D D D D
7D @WF !)F !*F !$F !@F D D D D D F D D D D D F D D D D D
’D !WWF _&F _WF )&F )WF D D D D D F D D D D D F D D D D D F *W

@D 9qj’-vds^addkoc]h;oe.-hs^addkofa’j djk;grnvj 8n,j 9eo;o.lj[jvo;kj ’.oI6[
lk,c9]5,j oUD

11 ສະຫງສ.ວວນ.ລິສຂະສິດ

47

13 42

#D 9t.-h\kddhP’9ad|;j p9bj’9t|adgmqkj da[\=h # |;j pL

50

$D 9qj’vu’.lj7ecotoe.odkogfuomk’8+wxoUc]h;[vdgInvomuj9tgfuomk’wx
g4y’D j j9kd95fg]uj,8Qowxmk’myfg|nvlk,8kdk3iF wxmyf8kg;aovvdsqd8k
dk3iF wxmk’myfg|nvluj8kdk3i c]t wxmk’myf8kg;ao8qdlv’8kdk3iD j j

myfg|nv

A myf8kg;ao8qd myf8kg;aovvd
C

B

myf.8h

95fg]uj,8Qo 8v[G gInvomujgfuomk’wxg4y’c,oj D D D D D D D D D D D D
ສະຫງສ.ວວນ.ລິສຂະສິດ
&D mhk; lq,lu -nhxB,0Po !@ sq;F ]k7kxB,0Posq;|bj’­­@ WWW ­du[D 4k,;jk
]k;9kj pg’yo-NxB,0Poma’\qf9addu[L
*D oE|ad0v’mhk; cl’ c]t ok’ 7e ];,daogmqkj da[ (_ kg, mhk; cl’
|add;jk ok’ 7e & kg. 4k,;kj ok’ 7e |adgmqkj .fdy3]dik,L
II. .97;k,

.odkocdh39f[aosk.f|’bj dvj ovonj \qf8hv’vkj o[qf39f[aosk.shg0Qk.9F -vd

I6h95fxtlq’0v’[qf39f Xly’j mu3j 9fdeoqf.shF ly’j muj39f8hv’dko1kdI6h? 9kdoAo

9b’j -vdsk;ymudkocdhD
III. [qfg/ydsaf

!D 9q’j 8n,j 9eo;o.lj[vj o9Eg,afD

dD @F (F !#F !)F @#F D D D D D F D D D D F #)F $#

0D !F &F _F !#F !(F @!F @&F D D D D F D D D D D D

7D #F *F !@F @$F $)F D D D D D F D D D D D D F D D D D D D D D

’D !WWF _*F _@F ))F )$F D D D D D F D D D D D D F D D D D D D F *)

51

@D 9t.-h\kddhP’9ad|;j p9b’j 9t|adgmqkj da[\kdvb # |j;pLrkdmu &

ສະຫງສ.ວວນ.ລິສຂະສິດ
#D 9q’j vu’.l7j ecotoe.odkogfu,mk’]5,j oUc]h;[vd gInvomu9j tgfuomk’wxg4y’D
j 9kd95fg]u,j 8Qowxmk’myf8kg;ao8qdlk,8kdk3iFwxmk’myfg|nvlu8j kdk3iF
wxmk’myf8kg;aovvdlv’8kdk3iF wxmk’myfg|nv|b’j 8kdk3i c]t wx
mk’myf8kg;ao8qdlk,8kdk3iD j j

myfg|nv

A myf8kg;aovvd

C myf8kg;ao8qd

B

D myf.8h

95fg]uj,8Qo
8v[G gInvomjugfuomk’wxg4y’c,jo D D D D D D D D D D D D

52

$D 9qj’-vds^addko c]h;oe.-hs^addko

faj’djk;grnvj 8nj,9eo;o.l[j vj o;jk’ 3456

.oI6[lk,c9D 96

12 8

13 4

&D 9qj’8n,j 9eo;o *F )F !W c]t !@ .lj .oI6[lk,c9
grnjv.sh9eo;o1j6c8]j t0hk’0v’ 2
I6[lk,c9,uzqo[;dgmqjkda[ !)D

ສະຫງສ.ວວນ.ລິສຂະສິດ
4

*D 9qj’-vdsklv’9eo;oF g,njvgvqklv’9eo;ooAo,k[;ddaogmqkj da[ !( c]t
g,njvgvqk,k76odaogmqjkda[ (@ L

(D ]5’mv’fu ]hP’gxaf !!$ 38 c]t ]hP’wdj @$& 38D 4k,;jk]5’mv’fu ,uwdj
s^kpd;kj gxaf9ad38L

)D ok’ cr’ -nhxB,c[[IPo7toyflkf c]t [yd ];,ma’\qfgxaog’yo (&WW
du[F Ih6;jk]k7kxB,c[[IPo7toyflkfgmqkj da[lv’gmnjv]k7k0v’[ydD
4k,;kj [yd,u]k7k9addu[L xN,c[[IPo7toyflkf,u]k7k9addu[L

_D vkp50v’ ok’f;’gfnvo c]t vkp50v’ohv’lk;];,daogmqjkda[ @W xuF
ok’f;’gfnvo ,uvkp5s^kpd;jkohv’lk; $ xuD 4k,;jkvkp5ohv’lk;0v’
]k;,u9adxuL vkp50v’ ok’f;’gfnvo ,u9adxuL

53

[qf mu @W dkocdh39f[aosk X8+?

I. dyf9tde

!D 9q’j 8n,j 9eo;o !F @F #F $ c]t & .lj.oI6[9t85]af]5,j oUgrnjv.shzqo[;d8k,4ao
c]t c4;gmqjkda[ !WD

@D 4hk3,’]5,j oUltcf’g;]kxt95[ao.odkogfuomk’D ]qfde]a’9tgfuo

mk’wxg,nv’.fL g;]k]qfvvd g,nv’muj]qfwx

11: 20 g,nv’ A

12:01 g,nv’ B
ສະຫງສ.ວວນ.ລິສຂະສິດ
12:10 g,nv’ C

12:55 g,nv’ D

8v[G ]qfde]a’9tgfuomk’wxg,nv’ D D D D D D D D D D D

#D 9q’j xP[mP[gonhvmju0v’I6[]5j,oU c]h;0Po-nIj 6[8k,fe]a[goNvmujc8j|hvpsk

s^kp.lj[vj o9Eg,afD I6[lujc90hk’

0t|ko

I6[7k’\6

I6[9t85]af I6[lk,c9

...................<......................<....................<.................

54

ສະຫງສ.ວວນ.ລິສຂະສິດII. .97;k,

grnvj cdh39f[aosk gIqk[+rP’c8j-vdI6h0=h,6omuj9egxaogmqkj oAoF c8j8hv’-vdI6h
8n,j vud;kj 0=h,6o.f[+maorP’r= 9t-vdwfh1j6.l c]t fh;p;ymudkoc[[.fL

III. [qfg/ydsaf

!D 9qj’0uf # mvj o-nj.lIj 6[sqdc9ltg\u]5j,oUgrnvj .shwfhI6[lk,c9gmqjkdaoD

@D @* 9qj’8nj,9eo;o @WF @!F @@F c]t @(
.lj .oI6[lk,c9F grnjv.sh9eo;o16j

@) c8]j t0hk’0v’I6[lk,c9,uzqo[;dgmqjkda[ (&D
#D oUc,joxt8ymyole]a[gfnvomao;kD

gfnvo mao;k

myf 9ao 7ko r5f rtsaf l5d glqk
! @ #$

& * ( ) _ !W !!
!@ !# !$ !& !* !( !)
!_ @W @! @@ @# @$ @&
@* @( @) @_ #W #!

;aolt4kxkok lxx]k; c,jo;aomulv’gfnvomao;k s^a’9kd;aolt4kxkok
lxx]k; c]h; ly[gvaf;ao8+,kc,oj ;aogduf0v’mkj o wdlvo rq,;yskoD
4k,;jk;aomu.f c,jo;aogduf0v’mkj o wdlvo rq,;yskoL

$D zh6veo;pdko3I’IPoxt4q,csj’|bj’8hv’dko.shoadIPo xD& 9eo;o &#
7qo oa’j IPo38t]t # 7qoD 4k,;kj gryoj 8hv’dko38tma’\qf9ad-5fL

55

rkdmu * 9eo;omqfltoypq, c]t g]dlj;o

[qf mu @! zqoskogxao9eo;omqfltoypq,

I. dyf9tde

!D 9q’j la’gdf8q;1jk’c]h;7yfw]j 0=h8+wxD $@ ' &* = DDDDDDDDDDDDDDDL
@@ ' $ = DDDDDDDDDDDDDDDL

@@ $ $@FW &*
@W &F& @)W WF(&
W WW

9b’j wfh @@' $ = &F& 9b’j wfh $@ ' &* = WF(&
’D $ ' & =..............
dD !W ' $ =.............. 9D @$ ' #@ =..............
0D !@ ' & =.............. lD * ' $) =..............
7D !! ' @ =.............. ສະຫງສ.ວວນ.ລິສຂະສິດ

@D g-nvdglAo|bj’pk; @# m gryjo8hv’dko8afgxao $ glAogmqkj daoD 4k,;kj c8]j t

glAo9tpk;9adc,af L
II. .97;k,
.odkosko9eo;o4h;o.sh9eo;o4h;oG
{ .od=]tou8q;8A’skos^kpd;kj 8q;sko 4hk8q;glf8kj ’l6o gIqk8hv’\kp95f.lj
zqosko c]t 76o8q;glfda[ !W c]h;sko8+wxgrnvj rtpkpk,.sh8q;glf
gmqjkl6oD 8q;1kj ’G !$@ ' $ !$@ $
@@ #&F&
@W
W
#& c,oj 7jkr=xt,ko0v’zqosko !$@ .sh $D
!$@ = X#& V $? T @

56

{ .od=]tou8q;8A’sko|hvpd;jk8q;sko8hv’0Pol6o.lzj qoskoc]h;\kp95f
c]t 76o8q;8A’skoda[ !W 9kdoAosko8+wxD

8q;1jk’!G @( ' #W = DDDDDDDDDDDDDDD 8q;1kj ’ @G $& ' !@& = DDDDDDDDDDDDDDD
@(W #W
WW WF_ $&W !@&
(W&WW WF#*
9b’j wfh @( ' #W = WF_ 9b’j wfh $& ' !@& = WF#*

III. [qfg/ydsaf

!D 9q’j skog]d8+wxoU9qod;jk8q;glf9tgmqjkl6oc]h;0PozqowfhIa[.lj[jvo9Ec,afD
&) ' $ = . . . . #* ' (@ = . . . .
@#$ ' @$ = . . . . !@* ' !$W = . . . .

#*@ ' !* = . . . . !#& ' @&W = . . . .
ສະຫງສ.ວວນ.ລິສຂະສິດ
@D 9q’j skog]d8+wxoUG

@& $ !@# ) ) #@ @) #&

#D l;o0v’ ]5’cdh; gxaoI6[lucj 9lkd,ugoNvmugj mqjkda[ $(& m@ c]t ];’pk;
gmqjkda[ @& m. 9qj’7yfw]j];’d;hk’0v’l;oD

$D I6[9t85]afI6[|bj’,u];’Iv[gmqkj da[ !#W mm. 9qj’7yfw]]j ;’pk;0v’0hk’
0v’I6[9t85]affa’j djk;D

&D gryoj gvqkoEfbj,[=]yl5f9eo;o !& ]yf ,kc[j’.lj0;fgmqjkdaowfh #W 0;f r=fuD
4k,;kj c8]j t0;f[ao95oE9ad]yfL

57

[qf mu @@ zqoskogxao9eo;omqfltoypq, X8+?

I. dyf9tde

!D 9q’j skog]d8+wxoUG

@& $ #) _ #*@! !( _@ #

@D 7qozh6|bj’pjk’ @@& dhk; ]k;wxwfh !#& gg,afD 4k,;kj ]k;pjk’dhk;|b’j wx

wfh9adgg,afL

#D fyo8vo|b’j gxaoI6[lk,c9 ,ugoNvmuj @#* m2 c]t ];’l6’ @$ m. 9q’j -vd

sk];’pk;0v’0hk’rNo0v’fyo8vooAoD

II. .97;k,

.odkoskog]dgIqkvkfrq[r=hlv’d=]toufa’j oUG ສະຫງສ.ວວນ.ລິສຂະສິດ

!D dkoskolYol5fc,oj zqoskogxao9eo;o4h;o sn^ 9eo;omqfltoypq, c]t

,u8q;glfgmqjkl6oD

8q;1jk’ G

dD zqoskogxao9eo;o4h;o 0D zqoskogxao9eo;omqfltoypq,

$&W * $&W ' * = (& #) ) #) ' ) = $F(&

#W (& $&W = (& V * *W $F(& #)= $F(& V )

W $WW #)= X$ V )?T*

@D dkosko[+lYol5fc,jozqoskogxao7jkr=xt,koF ,u8q;glf8jk’l6oD

8q;1kj ’ G !!) **
&@W !F()(D D
&)W

&@W
&)

58

!F( c,oj zqoskor=xt,ko-afg9oIvf WF! X,u8q;g]ds^a’95f|bj’8q;?D
!F() c,oj zqoskor=xt,ko-afg9oIvf WFW! X,u8q;g]ds^a’95flv’8q;?D

!F()( c,jozqoskor=xt,ko-afg9oIvf WFWW! X,u8q;g]ds^a’95flk,8q;?D

III. [qfg/ydsaf ’D _ ' &W = . . . . .
9D @# ' $& = . . . . .
!D 9qj’skog]d8+wxoUG lD $& ' *W = . . . . .
dD #&$ ' # = . . . . .
0D _#& ' ) = . . . . .
7D &#&) ' !& = . . . . .

@D 9qj’skog]d8+wxoUG
dD #) ' ( = . . . . . Xzqoskor=xt,ko-afg9oIvf WFW!?
0D @#* ' !$ = . . . . . Xzqoskor=xt,ko-afg9oIvf WFWW!?
ສະຫງສ.ວວນ.ລິສຂະສິດ
#D 8bds^a’|b’j ,u &@ -Ao c]t ,u];’l6’ @@! m. 4k,;jk3fpltg]jpc]h; c8]j t
-Aol6’9adc,afL

$D l;o8vo|b’j gxaoI6[9t85]af ,u];’Iv[gmqjkda[ *_@ m. 4k,;kj 0hk’0v’
l;o8vooAopk;9adc,afL

&D fk;goa[86o XNeptune? 1j6skj ’9kd8kg;ao #W gmnjv0v’w]ptsjk’c8j|j;p
3]dsk8kg;aoD 4k,;kj w]ptsjk’c8j|;j p3]dg4y’8kg;ao,ugmqkj .fL Ih6;kj w]
ptskj ’c8fj k;goa[86osk8kg;aoc,oj $ &WW WWW WWW km.

*D 9vd.sp|j j;p|bj’[ao95oEwfh @& -a’8u]yf 4hkgryoj gvqkoE.o9vd.spjwx4vd
.lj9vdohvpwfh9eo;o !W |;j pD 4k,;kj 9vdohvpc8j]t|;j p9t[ao95oEwfh

gmqkj .fL X9vdohvpc8j]t|j;p[ao95oEwfhgmqkj dao?

59

[qf mu @# g]dl;j o{dkoc[j’lj;o

I. dyf9tde

!D 9qj’la’gdfdkoc[j’c4[g9hpgxaol;j ogmqjkMdaoc]h;0Po.lj[jvo9Eg,afD

dD c[’j c4[g9hpgxaoly[lj;ogmqjkMdaoD

!!W !!W !!W !!W !!W !!W !!W !!W !!W !!W

c8j]tlj;ogmqjkda[ D D D D D D D D D
0D c[’j c4[g9hpgxaolk,lj;ogmqjkdaoD

!# DDDDDDDDDDDDDDDDDDDDDDDDDD DDDDDDDDDDDDDDDDDDDDDDDDDD

c8j]tlj;ogmqkj da[ D D D D D D D D D D .sa4nd8hv’D ສະຫງສ.ວວນ.ລິສຂະສິດ
@D 9q’j la’gdf8q;1kj ’c]h;0Po8nj,.lj c[j’gxao ) lj;ogmqjkMdao

8q;1kj ’G g]dlj;omu,j u7kj gmqkj dao
c[’j gxaolulj ;j ogmqjkMdao

lj;o0uf]kpltcf’ ! l;j o0uf]kpltcf’ @
$ )
! @
fa’j oAo $ = )

dD 0D

@ = * # = )
# $

60

7D CD

! = ) @ = !W
@ &

9D lD

@ = !@ $ = @!
* (

#D 9q’j la’gdf8q;1kj ’c]h;0Po8n,j .lj .sh4nd8hv’D

8q;1kj ’ 0 1

0 1 2 3 4
4 4 4 4 4
0 1

0 1 2 3 4 5 6 7 8ສະຫງສ.ວວນ.ລິສຂະສິດ
8 8 8 8 8 8 8 8 8

0 = 0 1 = 2 2 = 4 3 = 6 4 = 8
4 8 4 8 4 8 4 8 4 8

!D 0 1
0 1 2 3

3 3 3 3

0 1

0 1 2 3 4 5 6

6 6 6 6 6 6 6
1
= 2 = 3 =
dD 0D 7D3 3 3
@D 0 1

0 1 2 3 4 5 6
6 6 6 6 6 6 6
0 1

0 1 2 3 4 5 6 7 8 9 10 11 12

12 12 12 12 12 12 12 12 12 12 12 12 12
dD 1 5
6 = = 3 =
0D 7D6 6
CD 2
6 = = 4 =
6 9D lD6 6

61

$D 9q’j 8n,j 8q;g]d]q’.o .sh4nd8hv’D

dD 1 = 1 VV = 3 0D 2 = 2 VV = 4
3 9 5 5 10
3

7D 3 = 3 VV = 12 CD 5 = 5 VV = 15
4 4 16 9 9 27

&D 9qj’la’gdfI6[c]h;0Po8n,j .l[j vj o9Eg,af.sh4nd8hv’D

11 1 + 18 = 2 = .......
88 8 8

1 1 + 14 = ....... = .......
14 4
2
1 + 12 = ....... = .......
II. .97;k, 2

{ 4hkc[’j c4[g9hpmu,j u];’pk;|b’j sq;|;j p.shgxao & l;j ogmqkj daol;j o0uf]kp

gryoj 0Po 1 D ສະຫງສ.ວວນ.ລິສຂະສິດ

5

{ c[’j c4[g9hpmu,j u];’pk;|bj’sq;|j;p.shgxao ) l;j ogmqkj dao lj;o0uf]kp

gryjo0Po 1 D

8

{ c[’j c4[g9hp.shgxao # lj;ogmqkj daoD { c[j’c4[g9hp.shgxao !* l;j ogmqkj daoD

1 + 1 + 1 = 1 8 + 5 + 3 = 16 = 1
3 3 3 16 16 16 16

{ g]dlj;ogmqjkdaoD

III. [qfg/ydsaf 1 = 2
3 6

!D 9qj’0Pog]dlj;ocmol;j omjugxao]kpD
...... ......
dD ...... 0D ...... 7D ......
......

62

CD ...... 9D ...... -D ......
...... ...... ......

@D 9q’j la’gdf8q;1jk’c]h;8nj,8q;g]d.lj .sa4nd8hv’D

8q;1jk’G 6 = 6 ' 3 = 2
9 9 ' 3 3
dD 0D
4 = 4 ' = 2 12 = 12 ' = 4
6 6 ' 3 15 15 ' 5

7D 8 = 8 ' = 2 CD 16 = 16 ' = 4
12 12 ' 3 20 20 ' 5

#D 9qj’8nj,8q;g]d.lj .sh4nd8hv’D

dD 6 = 6 0D 14 = 3 7D 6 = 4
12 21 8

CD 12 = 3 9D 6 = 15 ສະຫງສ.ວວນ.ລິສຂະສິດlD14=8
18 30 16

-D 80 = 30 = 6 pD 24 = 27 = 9
120 54

$D 9qj’0Po8n,j .lj[jvo9Eg,af.og]dlj;o]5,j oU.sh4nd8hv’D

dD 12 = : 0D 1 = : 7D 3 = :
12 5 15 4 20

CD 2 = : 9D 1 40 = : lD 6 = :
3 18 30 9 18

-D 15 = : pD 2 = : = :
20 5 15 40

fD 42 = 8 = : 8D 49 = 2:7 = 4:5
: 20

63

[qf mu @$ dko[;d c]t dko]q[g]dl;j o

I. dyf9tde ’D

!D 9qj’la’gdf8q;1kj ’.o0=h d c]h;7yfw]j0=h8+wxD

dD 0D 7D

3 + 5 = 8 2 + 4 = ........ 2 + 5 = ........ 3 + 5 = ........
10 10 10 9 9 8 8 12 12

@D 9qj’la’gdf8q;1jk’.o0=h d c]h;7yfw]0j =h8+wxD

dD 1 + 2 = 1 + 2 = 3 0D 7 + 2 = ..........
5 5 5 5 10 10

7D 3 + 3 = .......... CD 8 + 5 = ..........
6 6 20 20
ສະຫງສ.ວວນ.ລິສຂະສິດ
#D 9q’j la’gdf8q;1kj ’.o0=h d c]h;7yfw]j0=h8+wxD

dD

3 _ 1 = 2
4 4 4
0D

2 _ 1 =
4 4

$D 9qj’la’gdf8q;1jk’.o0=h d c]h;7yfw]j0=h8+wxD

dD 5 - 3 = 5 - 3 = 2 0D 8 - 5 = ...........
8 8 8 8 9 9

7D 12 - 7 = .......... CD 6 - 1 = ..........
15 15 16 16

64

II. .97;k,

!D dko[;dg]dl;j omuj,ur6f7ndaoF gIqk[;d9eo;or6fda[9eo;or6f l;j or6fIad

lkw;h7ngdqjkD 8q;1jk’ G 1 + 2 = 1 + 2 = 3
8 8 8 8

@D dko]q[g]dlj;omu,j ur6f7ndaoF gIqk]q[9eo;or6fda[9eo;or6f lj;or6fIadlk

w;h7ngdqjkD 8q;1kj ’ G 5 - 3 = 5 - 3 = 2
7 7 7 7

III. [qfg/ydsaf

!D 9q’j 7yfw]cj ]h;8nj,.l[j voj 9Eg,afD

3 + 4 = ....... 1 + 5 = ....... 12 + 2 = ....... 9 + 12 = .......
8 8 9 9 16 16 25 25
ສະຫງສ.ວວນ.ລິສຂະສິດ

7 - 2 = ....... 14 - 8 = ....... 12 - 8 = ....... 15 - 9 = .......
10 10 16 16 20 20 25 25

@D 9qj’[;d c]t ]q[g]dl;j o]5,j oUG

0dDD 1 5122 ++5115=2 .......... lD 65 - 1 = ..........
= .......... 6

-D 4 - 2 = ..........
9 9

C7DD 1 27704 ++ 1 = .......... pD 13 - 7 = ..........
10 = .......... 24 24

4 fD 7 - 3 = ..........
24 16 16

9D 1 121 + 1 = .......... 8D 10 - 5 = ..........
12 5 5

65

[qf mu @& dko[;d c]t dko]q[g]dlj;o X8+?

I. dyf9tde 7D

!D 9q’j la’gdf0=h d c]h;7yfw]0j =hwxD

dD 0D

1 + 1 = 3 1 + 1 = ..... 1 + 1 = ........
2 4 4 3 2 6 2 5 ........

@D 9q’j la’gdf 8q;1kj ’ c]h;7yfw]0j =h8+wxD

8q;1kj ’ G • 1 + 5 = 1 # 2 + 5 = 2 + 5 = 2 + 5 = 7
3 6 3 # 2 6 6 6 6 6

• 2 + 3 = 2 # 4 + 3 # 3 = 8 + 9 = 8+9 = 17
3 4 3 # 4 4 # 3 12 12 12 12

dD 1 + 1 = ...... 0D 1 + 4 = ...... ສະຫງສ.ວວນ.ລິສຂະສິດ
2 6 2 7

7D 2 + 1 = ...... CD 3 + 3 = ......
3 5 10 4

#D 9qj’la’gdf0=h d c]h;7yfw]0j =h8+wxD 7D
dD 0D

1 - 1 = 1 1 - 1 = ........ 1 - ......... = ........
2 4 4 2 3 6 2 5 10

$D 9qj’la’gdf8q;1jk’ c]h;7yfw]j0+wxD

8q;1jk’ G 3 - 1 = 3 # 3 - 1 # 5 = 9 - 5 = 9- 5 = 4
dD 5 3 5 # 3 3 # 5 15 15 15 15
7D
5 - 1 = ...... 0D 3 - 1 = ......
8 4 5 2

2 - 1 = ...... CD 2 - 1 = ......
5 4 3 5

66

II. .97;k,

dko[;d sn^ ]q[g]dlj;omuj,ur6f8kj ’dao dvj ovnjogIqk8hv’gIaf.shr6f7ndao3fp

gvqk9eo;ofP;dao,k76oda[9eo;or6f c]t r6fD 9kdoAo 9bj’xt8y[af7ndaoda[

dko[;d s^n ]q[g]dlj;omuj,ur6f7ndaoD

8q;1jk’ G dD 1 + 1 = 1 + 1 # 2 = 1 + 2 = 1 + 2 = 3
4 2 4 2 # 2 4 4 4 4

Xgvqk @ 76oda[9eo;or6f c]t r6f0v’g]dlj;o 1 ?
2

0D 4 - 2 = 4 # 5 - 2 # 3 = 20 - 6 = 20 - 6 = 14
3 5 3 # 5 5 # 3 15 15 15 15

Xgvqk & 76oda[9eo;or6f c]t r6f0v’g]dlj;o $# S gvqk #
76oda[9eo;or6f c]t r6f0v’g]dl;j o 2 ?
5

III. [qfg/ydsaf ສະຫງສ.ວວນ.ລິສຂະສິດ

!D 9qj’7yfw]gj ]dl;j o]5j,oU

dD 1 53 - 2 = ........... lD 15 + 29 = ............
3 16 32
0D 46 - -D
5 = ........... 7 + 2 = ............
12 9 18

7D 23 - 1 = ........... pD 35 + 17 = ............
4 3 4

CD 56 - 1 = ........... fD 9 + 5 = ............
2 7 2

9D 11 31 - 14 = ........... 8D 42 + 21 = ............
26 5 4

@D 9q’j 8n,j 9eo;omuj4nd8hv’.lj[vj o9Eg,af]5j,oUD

dD 6 + 9 = ....... + 9 = ....... 7D 17 - 7 = 17 - ........ = .......
26 ....... 26 ....... 30 15 30 ....... .......
13

0D 4957 + 36 = ....... + 36 = ....... CD 7 - 5 = ....... - 5 = .......
190 190 190 ....... 14 28 28 28 .......

67

[qf mu @* I6[c[[dko0Pog]dlj;o c]t mqfltoypq,

I. dyf9tde

!D 9q’j 0Po9eo;o8+wxoU.ljglAo9eo;oD
9 S 3 S 4 S 0,7 S 0,1 S 0,6 D
10 10 10

0 0,2 0,4 0,5 0,8 0,9 1

11 13 4
10 5 25 5

@D 9q’j 0Po9eo;omugj mqkj dao.o9eo;o]5j,oU.lj[jvo9Eg,afD

dD 2, 5 ; 5 ; 34 ; 250 ; 10 ; 35 ; 3 - 0, 5 ; 15 .
2 4 100 4 10 6

............ = ............ = ............ = ............ = ............ = ............

0D 8 ; 2 + 2 ; 2, 6 ; 40 ; 80 ; 16 ; 36 ; 25
3 3 15 30 6 10 9
ສະຫງສ.ວວນ.ລິສຂະສິດ
............ = ............ = ............ = ............ = ............

#D 9qj’la’gdf8q;1jk’c]h;7yfw]j0=h8+wxD

8q;1kj ’G 12, 2 = 122 ; 5 = 25 = 2, 5.
10 2 10

dD 13, 4 = .......... CD 14 = .......... = ..........
5

0D 80, 6 = .......... 9D 18 = .......... = ..........
4

7D 19, 7 = .......... lD 51 = .......... = ..........
2

II. .97;k,

9eo;o|b’j lk,kf0Powfhs^kp;ymu c]t rkp.8hs^kpI6[c[[c8d8kj ’dao

g-ajoG rkp.8hI6[c[[mqfltoypq, s^n I6[c[[g]dlj;oD

68

8q;1kj ’G dD 12, 5 = 125 = 25
10 2

0D 3, 125 = 3125 = 25
1000 8

F g]dl;j olk,kf0Porkp.8hI6[c[[mqfltoypq,wfhF 4hk;jkdkoskooAo

gxaodkoskolYol5fD

8q;1kj ’ G 25 = 12, 5
2
F g]dlj;o[+lk,kf0Porkp.8hI6[c[[mqfltoypq,wfhF 4hk;kj dkoskooAo

gxaodkosko[+lYol5fD

8q;1jk’ G 1 = 0, 3333...
3

III. [qfg/ydsaf

!D 9qj’\kp9eo;o]5,j oU.lgj lAo9eo;oD ສະຫງສ.ວວນ.ລິສຂະສິດ

14 ; 8 ; 75 ; 7 ; 2 + 1 ; 5 ; 30
7 2 20 2 4 2 10

2 3 4

@D 9qj’0Po9eo;omqfltoypq,8+wxoUrkp.8hI6[c[[g]dlj;oD
$F!@)S WF(#@S #F&S $F)S !(F(&S WF!@&S WF&D

#D 9qj’0Polj;o8+wxoUrkp.8hI6[c[[9eo;omqfltoypq,D

1750 ; 14 ; 625 ; 35 ; 25 ; 18 ; 25 ; 3264
1000 10 100 10 8 4 100 100

$D 9qj’la’gdfg[yj’8q;1jk’c]h;0Po9eo;omugj \ktlq,.lj[jvo9Eg,afD

8q;1jk’ G 10 = 9 + 1 = 3 + 1
3 3 3 3

dD 16 = .......... + .......... = .......... + ...........
5
0D
13 = .......... + .......... = .......... + ...........
2

69

[qf mu @( ]efa[9eo;omqfltoypq, c]t g]dlj;o

I. dyf9tde

!D 9qj’la’gdfI6[]5,j ouhc]h;0Pog]dlj;o s^n 9eo;omqfltoypq,.l.j o D

dD 0D

111 1 14 5
10 2 4 1 44 4

0,1 0,2 0,3 0,5 0,75 1,25

@D 9qj’9af]Po9eo;omqfltoypq,.o0h= ! 8k,]efa[c8j|hvpsks^kp.l8j k8t]k’ສະຫງສ.ວວນ.ລິສຂະສິດ

]5,j oUD

dD WF! 0D WF@&

11
10 4

#D 9q’j 0Pog]dl;j o s^n 9eo;omqfltoypq,.l.j o .sh4nd8hv’D

0 3 6
10 10 10

0,1 0,4 0,8

11 15 20
10 10 10

1,3 1,7

70

II. .97;k,

grnvj 1kd9af]Polv’9eo;omqfltoypq,muj,ulj;o4h;ovaofP;dao 8hv’xt8y[af
fa’j ohuG
d=]toumu!G 8hv’la’gdfg[y’j 8q;g]dmu|bj’s^a’9kd95f0v’lv’9eo;o 4hk8q;
g]d.fs^kpd;kj d=c,jo9eo;ooAos^kpd;kj D
8q;1kj ’G 6,8 > 6,1 grkt;kj 8 > 1
6,8 > 6,4 grkt;kj 8 > 4
d=]toumu@G 4hk8q;g]dmu|b’j s^a’9kd95f0v’lv’9eo;ogmqjkdao gIqkxP[mP[
8q;g]dmu @F mu # c]t 8+Mwxfaj’d=]toumu !D
8q;1jk’G 6,104 > 6,1029 grkt;jk 4 > 2

III. [qfg/ydsaf

!D 9q’j 0Pog]dlj;o s^n 9eo;omqfltoypq,.l.j o .sh4nd8hv’D

2 5 8 10 13

10 10 10 10 10
ສະຫງສ.ວວນ.ລິສຂະສິດ
0,3 0,6 1 1,2

16 20 21 25
10 10 10 10

1,7 2 2,3 2,7

@D 9q’j xP[mP[9eo;omqfltoypq,8+wxoU3fp8n,j g7njv’\kp < c]t > .l[j vj o9Eg,afD

1,25...............1,28 3,18.................3,14 5,42.................5,47

7,209.............7,203 1,415...............1,418 13,14...............13,12

25,102...........25,107 17,264.............17,269 45,148.............45,109

#D 9qj’9af]Po9eo;o8+wxoUc8|j hvpsks^kpD @F& !F_
dD !F( @F! @F( *F@_ $F*)
0D !F& WF!* (F@$ !*F@! !*F @W&
7D !*F!W_ !*F@W( !*F!W#

71

[qf mu @) ]efa[9eo;omqfltoypq, c]t g]dl;j o X8+?

I. dyf9tde

!D 9q’j xP[mP[g]dlj;o3fpoe.-hg7njv’\kp = , < c]t > .
8q;1kj ’ G

1 = 2 1 < 2
3 6 3 3

3 .......................... 2 2 .......................... 4
4 4 4 8

4 .......................... 10 6 ..........................ສະຫງສ.ວວນ.ລິສຂະສິດ8
8 16 16 16

@D 9q’j la’gdf8q;1kj ’ c]h;0Po9eo;o8nj,.l.j o .sh4nd8hv’D

8q;1jk’ G 1 = 2
5 10

1 = 1 # 2 = 2
5 5 # 2 10

Xgvqk @ 76oda[r6f c]t 9eo;or6f0v’g]dlj;o 1 ?
5

1 = 8 ; 1 = 6 ; 1 = 21 ;
4 ; 3 7

2 = 6 3 = 15
3 5

72

#D 9qj’0Pog]dl;j o8+wxoU.lgj lAo9eo;oD

dD 2 ; 5 ; 7 ; 10 ; 13 ; 17 ; 23 .
4 4 4 4 4 4 4

0 1 2 3 4 5 6
16 24
0 4 8 12 4 20 4
4
4 4 4 2 3

0D 8 ; 4 ; 10 ; 13 ; 17 ; 25 .
10 10 10 10 10 10

0 1

II. .97;k,

dD dkoxP[mP[g]dl;j o

!D 4hkr6fgmqjkdaoF g]dlj;omu,j u9eo;or6fs^kpd;jk 9t,u7jks^kpd;kj D
ສະຫງສ.ວວນ.ລິສຂະສິດ
8q;1jk’ G 1 < 2 ; 2 < 4 ; 2 < 3 .
3 3 7 7 5 5

@D 4hkr6f[+gmqkj daoF gIqkgIaf.shg]dl;j ogs^qkj oAo.sh,ur6fgmqjkdaodvj oc]h;

9bj’gvqk,kxP[mP[daoD

8q;1jk’ G 4hk8hv’dkoxP[mP[ 3 da[ 17
5 25

- gIaf.shg]dlj;o,ur6f7ndaoG gvqk & 76oda[r6f c]t 9eo;or6f0v’

g]dlj;o 3 D
5

3 = 3 # 5 = 15
5 5 # 5 25

- xP[mP[9eo;or6f9twfh G 15 < 17
25 25

fa’j oAo 3 < 17
5 25

73

0D dko\kpg]dlj;o.lgj lAo9eo;o,us^kp;ymuD

8q;1kj ’G !g$rn.jvs1h k#dc\]ktp-g]vddlsj;kozqo13s4k.olmgj ujl4hnado9ce]ot;o7kj g.Idqkh7xPt’8Dy[9afkfdaj’ooAoU 9bj’
!D sko

\kpzqosko.ljglAo9eo;oF .od=]touoUzqoskoc,jo $F***DDDD

0 1 2 3 4 5

4,666

@D sko !$ .sh #F -vdskzqoskogxao9eo;o4h;o c]t 0Po8q;glf.oI6[

c[[0v’g]dl;j oD

!$ sko.sh # zqoskogmqjk $S 8q;glfc,oj @ gIqk9b’j wfhG 14 = 4 + 2
3 3

0 1 2 3 4 5

14 ສະຫງສ.ວວນ.ລິສຂະສິດ

3

#D 0v[0Ao !$ fh;pmt;u76o0v’ # g-y’j c,oj lv’9eo;omuj16j.dh7P’7n !@ c]t

!& gIqkwfhG 12 < 14 < 15 c]t 4 < 14 < 5
3 3 3 3

14 = 12 + 2 = 4 + 2
3 3 3 3

0 1 2 3 4 5

0 3 6 9 12 14 15
3 3 3 3 3 3

III. [qfg/ydsaf

!D 9q’j xP[mP[g]dl;j o8+wxoU3fpoe.-hg7nvj ’\kp < c]t > .

1 ........... 2 ; 4 ........... 3 ; 4 ........... 1 ; 6 ........... 8 ;
5 5 5 5 7 7 14 14

3 ........... 7 ; 6 ........... 4 ; 12 ........... 14 ; 13 ........... 18 .
25 25 10 10 19 19 32 32

74

@D 9qj’xP[mP[g]dlj;o8+wxoU3fpoe.-hg7nvj ’\kp = ; < c]t >

3 ........... 2 ; 2 ........... 4 ; 4 ........... 10 ; 2 ........... 6 ;
5 5 5 10 7 14 3 9

1 ........... 2 ; 1 ........... 3 ; 5 ........... 1 ; 2 ........... 8 .
15 5 8 16 20 4 7 14

#D 9q’j 0Po9eo;o8n,j .l[j vj o9Eg,af.sh4nd8hv’D

1 = ........ ; 1 = ........ ; 2 = ........ ; 2 = ........ ; 3 = ........ .
6 12 8 16 7 21 9 18 4 20

$D 9qj’0Pog]dlj;o8+wxoU.lgj lAo9eo;oD

dD 1 ; 6 ; 9 ; 10 ; 14 ; 18 ; 22
4 4 4 4 4 4 4

0 1 2 3 4 5 6 ສະຫງສ.ວວນ.ລິສຂະສິດ

0 4 8 12 16 20 24
4 4 4 4 4 4

0D 3 ; 9 ; 10 ; 15 ; 17 ; 20 ; 25
10 10 10 10 10 10 10

0 1 2 3

&D 9qj’9af]Po9eo;o8+wxoU8k,]efa[c8j|hvpsks^kpD

dD 1 ; 1 ; 1 ; 3 ; 10 ; 12 .
2 4 16 4 4 10

0D 4 ; 4, 1 ; 4, 11 ; 4, 01 ; 4, 21 ; 4, 121 .

75

rkdmu ( g]0k7toyf c]t dko;afcmd

[qf mu @_ dko;afcmd];’pk;

I. dyf9tde

!D c8[j 6Iko,kxt-k-qo]k;g7up.-h 7n[F lvdF c0o c]t ;k grnjvcmd];’pk;D

oadIPo9q’j .-h7n[0v’8qogv’ c]t [aomafgrnvj cmdlvdF c0oF ;k c]t

];’l6’0v’8qogv’ c]h;0Po8n,j .l8j k8t]k’]5j,oUG

ly’j mucj md lvd c0o ;k ];’l6’ Iv[cv;
sq;|;j p;afcmd
7n[
-a’8uc,af (cm)
ສະຫງສ.ວວນ.ລິສຂະສິດ
@D 9kdmkj gfnjvsk;P’9ao,uw]ptmk’ @! km, 9kd;P’9aowxskxkd-ao ,uw]pt
mk’ !&@ km. 4k,;jkw]ptmk’9kdmkj gfnvj wxskxkd-ao ,uw]ptmk’gmqkj
.fL

 xkd-ao

mkj gfnvj 21 km ;P’9ao 125 km

II. .97;k,

{ sq;|;j p;afcmd];’pk;mujoypq,.-hles^a[;afcmd];’pk;F ];’d;hk’F ];’

l6’F w]ptskj ’F ];’Iv[F ]tfa[l6’F ]t]a[g]yd c]t 7;k,|kc,joc,af

Xm?D ovd9kdoAo gryjopa’oe.-hdy3]c,af X1km = 1 000 m?S -a’8yc,af X1m

= 100 cm? c]t ,yo]uc,af X1m = 1 000 mm?

76

8k8t]k’dkorq;rao]ts;kj ’sq;|j;p;afcmd
V 1000 V 1000

km hm dam m dm cm mm

403 = 4m 3cm

6 0 4 = 6dm 4mm

1 3 0 0 = 1km 300m

III. [qfg/ydsaf

!D 9q’j gvqk9eo;o]5,j oU0Po.l8j k8t]k’D

dD 60,54 m km hm dam m dm cm mm
0D 60 54
7D 7 km 5hm 9 dam
CD 750 m
9D 846 dm
lD
32,07 dam
0,3 mm

@D 9q’j xjPo9eo;o8+wxoUgxaosq;|;j pmujwfhdeoqfw;hD ສະຫງສ.ວວນ.ລິສຂະສິດ

3km 6hm 2m = ....................m 0,72 dm = ................cm

36 720m =.....................km 2 m =..................cm
3hm 6dam =.....................m 10 =..................mm
35,72hm =.....................km
6 m
1 000
#D 9qj’7eo;og]d]5,j oUG

3m 15cm + 4m 75cm + 1m 60cm = ........................
20m 10cm _ 10m 5cm = .....................

9m 212mm + 235m + 1m 1cm = .......................

30m 15cm ' 5m 3mm = .....................

$D ,nhmevyf ok’ l5,k]u 8ej czjocrwfh !& m $W cm, ,nhmulv’8ej wfh !@ m )Wcm
c]t ,nhmulk,8+kwfh @ gmnvj 0v’,nhmulv’D 4k,;jk rkp.olk,,nh]k;8+kczjo
crwfh9adc,afL
& ]qf7ao|b’j c]oj wxwfh ]qf317ao0ovAo’cw]]pjotwxmwkf’hcm]a’h;\9adqfdF Iy3]6h;cjk,w]afpLtmk’ma’\qfgmqkj
!@W km. 4k,;kj

77

[qf mu #W dkooe.-h9eo;omqfltoypq, c]t g]dl;j o

g0Qk.odko;afcmd];’pk;

I. dyf9tde

.oI6[c8h,oad;y9yf8tde g]3vok gfu c;’-u wfhdeoqfvaf8klj;o0v’7qoz6h|b’j

fa’j oUG sq;gmqkj da[ 1 0v’];’l6’F |hkgmqkj da[ 1 0v’];’l6’ c]t
8 10
8uogmqjkda[ 1 0v’];’l6’D ,ngmqjkda[|hk c]t lvd|b’j gmqjkda[ @ sq; 7n
6
gmqkj da[ 1 0v’];’l6’D
4
{ 9qj’-vdsk0t|kf0v’c8jrkdl;j o

0v’7qozh6|bj’8k,dko7yfw]j0hk’gmy’D

4hk;kj 7qozh6oAol6’ !F)WmD

{ 9q’j vtmy[kp;kj gxaospa’ j jlvd|bj’9bj’gmqkj

@ @ sq; sn^ gmqkj da[ 1 0v’];’l6’D
4 ສະຫງສ.ວວນ.ລິສຂະສິດ

II. .97;k,

dko;afcmd];’pk;0v’;af45.f|bj’ 8hv’;afcmd.sh-afg9og-ajoG dko;af

cmd];’pk;0v’l=fe Xfa’j I6[]5j,oU?D

];’pk;0v’l=fegmqjk !@ cm * mm s^n !@ cm 6 s^n !@F* cm D c]t
10

dko;afcmdl=fegxao cm ,u G 12 6 s^n 12, 6
10

78

III. [qfg/ydsaf 62548 m = .........km
2458 m = .........km
!D 9q’j 8n,j 9eo;o.l[j vj o9Eg,af]5j,oUG 3,25 m = .........cm
843 mm = ..............cm

4,6 m = ..............cm

6,41 dm = ..............cm

4 km = ..............m 1 m = .........cm
5 4

3 km = ..............m 2 m = .........mm

4 5

@D lt]vpoE|;j p|bj’pk; @& m. 4hkoad]vpoE8hv’dko]vp.sh.fh !WW m ສະຫງສ.ວວນ.ລິສຂະສິດ
9t]vpwx c]t da[9adgmnvj L

#D 3I’IPos^a’|bj’8A’1j6wd9kd8ts^kf $F* km c]t 8ts^kf1j6wd9kd3I’\=
@F# kmD 4k,;jk3I’IPosa^’oAo1j6wd9kd3I’\=gmqkj .fL XIh6;kj 8ts^kf1j6]t

s;kj ’3IPIPo c]t 3IP\=?D
$D czjocr8vo|bj’pk; &F# m gvqkwx8afglnhv !F(& m c]t 8afgIaf-q[\vo

@F&& m. 4k,;kj cr8vooAopa’gsn^vgmqjk.fL
&D oadIPozh6|bj’gg]jovvdde]a’dkpgxaoxqddt8y;ao]t #F& km. 4k,;jk.o #W
;ao oadIPozh6oAo9tc]oj vvdde]a’dkpwfhma’\qf9addy3]c,afL

*D g-nvdglAo|b’j pk; &@ m gryjo8afgvqkwxgIafg-nvd,af’q; 1 0v’g-nvd c]t
4

8afwxgIafzPd8kdg7njv’ 1 0v’g-nvdD 4k,;kj g-nvdglAooAopa’gs^nvgmqjk
2

.f m L

(D w,h $ mjvo ,u];’pk;faj’oUG mjvomu|bj’pk; #F& c,afF mjvomulv’gmqjk @ gmnjv

0v’mvj omu|b’j Fmjvomulk,pk;gmqkj g7y’j |b’j 0v’mjvomu|bj’c]tmjvomulujpk;

gmqkj lv’gmnv0v’mvj omulk,D 4hkgryjogvqkw,h $ mvj o,k8+.ljdao9t,u];’pk;

ma’\qfgmqjk.fL

79

[qf mu #! dko-aj’,;olko

I. dyf9tde

!D 9q’j la’gdf c]t 0Po8nj,.lj8k8t]k’.sh4nd8hv’D

ly’j 0v’ oE|ad zyffPj ’
\kd,j;’ ! 4q’ 7kf7tgo -aj’8q;9y’
\kddhP’ ! 4q’ 0,5 kg
\kdlufk.spj ! |j;p 1,5 kg 2 kg
\kds5j’ ! |j;p
\kddtmao ! 4q’ 2000 g 1800 g

5 0uf 8 0uf
7 0uf 10 0uf

1,65 kg 1500 g

@D 7qo]k;gIqk[vdoE|ad0v’7egxao[kfF ltsb^’ c]t s5oF oE|ad7e ! [kf ສະຫງສ.ວວນ.ລິສຂະສິດ
gmqjkda[ $ ltsb^’ s^n !& g, 7e|b’j lts^b’|ad !W s5oD
7e & [kf|adgmqkj da[ D D D ltsb^’ s^n gmqjkda[ D D D s5o s^n gmqjkda[ D D D g

#D dtiafgxaosq;|;j pmu.j -h[vdoE|adgrafF rvp D D D D
graf ! dtiaf Xcarat? gmqjkda[ @WW mg, cs;ograf;q’|bj’|ad & dtiafF
9t|ad9ad g L 4hkcs;ograf|ad @ g 9t,u9addtiafL

II. .97;k,

!D sq;|j;pdko-a’j ,;olkomuoj ypq,.-hc,jo dik,Xg?F ovd9kdoUgryjopa’oe.-h
• dy3]dik, Xkg? grnvj -aj’,;olkomq;j wxg-aoj G \kdw,hF zadF -Uo D D D D
• 38o Xt? c,oj sq;|;j pmu-aj’,;olkomu|j ads^kpg-ajoG g0QkF oE,ao D D D
• ,yo]udik,X mg ? c,josq;|j;pgrnjv.-h-a’j ,;olko0v’;af45g[qkg-aoj G
1kF 7eF g’yoD D D D

@D .odko-a’j ,;olko0v’;af45.f|bj’gryoj .-h-y’lv’zk’ s^n -y’zk’fP;D
V8k180t00]k’dkorq;rao0Vv’10s0q;0|j;p,;olkoV 1000

tq kg hg dag g dg cg mg

1000
1000
1000

80

oE|ad0v’7e oE|ad0v’graf
! [kf = $ lts^b’ = !& g & dtiaf (Carat) = 1g
! lts^b’ = !W s5o

\kpgsfG 3fpmqj;wxc]h;gryjo.-h7e;jk j j oE|ad j j cmo7e;jk j j,;olko j j

III. [qfg/ydsaf
!D 9qj’g]nvdsq;|;j pdko-aj’,;olko0v’;af45]5,j oUG
{ ,;olko0v’lkp7=7e ! glAoD { ,;olko0v’graf16j.osq;cs;oD
{ ,;olko0v’\kdvb ! |j;pD { ,;olko0v’wdj ! 38D
{ ,;olko0v’7qoz6h|b’j D { ,;olko0v’]qf[aom5d7ao|bj’D

@D 9qj’xjPosq;|;j p;afcmd]5j,oUG 2,5 g = …................... mg ສະຫງສ.ວວນ.ລິສຂະສິດ
2 kg 5 hg 3 g =…..... g 6 dg = ….....................mg
6 kg = ........................ hg
32 cg =….................. g 2,5 t = ..................….g
2725 g = ................... kg 6458 kg = …................t
2,5 t = …................... kg
232524 kg =…...….... t

#D 9qj’8v[7e4k,8+wxoUG
{ oE\ad @ dy3]dik, ) 0uf gxao9ad0ufL XI6h;jk 1 0uf = 100g)
{ oE\ad # dy3]dik, #WW dik, gxao9addik,L
{ oE|ad & t gxao9addy3]dik,L

$D gfnvoc]h;oU ok’,k]u |ad #) kg )WW g gfnvooU|ad #_ kg $WW gD 4hk
ok’ ,k]u 1kd,uoE|ad $W kg .ogfnvo|hk,k]u8hv’gru,j oE|advudgmqjk.fL

&D g0Qklko|bj’gxqJk|ad _) kg. 4hk-nhg0Qklko !@(& gxJqk 9t|adgmqjk.fL
{ 4hk.-h]qf7ao|bj’0qog0Qk,klqj’mugj Invo 9t0qowfh9ad4hP;9bj’9t\qfL

Ih6;kj 4hP;|b’j 0qo.fh !& gxqJkD

81

[qf mu #@ dkooe.-h9eo;omqfltoypq, c]t g]dl;j o

g0Qk.odko-a’j ,;olko

I. dyf9tde

!D 9q’j 9af]efa[0v’graf16j.o8k8t]k’8k,,;olkoc8|j hvpsks^kp Ih6;jkgraf

! dtiafgmqkj da[ @WW mg s^n 1 g.
5
Xdtiaf c,oj sq;|j;p;afcmd3]stxtglufg-aoj G grafF rvpDDDDDDD?

8k8t]k’oE|ad0v’graf

-njgraf oE|adgxaodik, s^n dtiaf
graflu2hk $$F& dtiaf
grafxk-k $W dtiaf
graf,q’3do !&(F& dik,
graffk;.8h
grafvvd]q[ @*!F)) dtiaf
#_F_@ dik,
ສະຫງສ.ວວນ.ລິສຂະສິດ
@D ]\5’qf7ce],tug0cQk[l’j k.osmhxa’hk\cdqfh;*W31kg0v]’kg;0wQkflhck[o’j m.sa’h]\5’afgDr4afk,41;kj 0Gv’g0Qklkoma’
{ ]5’grafwfhg0Qklko9addy3]dik,L
{ xhkcdh;wfhg0Qklko9addy3]dik,L

#D 9q’j xPj og]dl;j oxtlq,]5j,oU gxao9eo;omqfltoypq,D

8q;1jk’ G 2 1 =2+ 1 = 2 # 2 + 1 = 5 = 2, 5
2 2 2 2

dD 2 1 = ........... CD 15 1 = ...........
4 2

0D 3 2 = ........... 9D 21 3 = ...........
3 4
7D lD
4 1 = ........... 45 1 = ...........
3 5

II. .97;k,
.odkocdh39f[aosk.f|b’j 4hksq;|;j p;afcmd,;olkoskd8jk’daogIqk
8hv’xPj osq;|j;p;afcmdoAo.sh7ndaolkdvj o c]h;9bj’fegouodkocdh8+wxD

82

8q;1jk’G 4hkgIqk9tdeoqfgvqksq;|j;p;afcmdgxaodik,gIqk8hv’xPj osq;
|;j pdtiaf,kgxaodik, s^n 4hkdeoqfgvqk|;j p;afcmdgxaodtiaf
8hv’xPj osq;|;j pdik,,kgxaodtiafD

III. [qfg/ydsaf

!D grvjn gIfa 0v’s;koles[^a & 7oq doy grojy 8vh ’dkol;j oxtl,q .odkox’5 c8’j f’ja ],j5 oGU

{ g0Qklk76 1 dy3]dik, Xkg?D { 4qj;gsn^v’ 1 dy3]dik,D
2 4
{ ,aogznvd ! dy3]dik,D { oE8ko !F& dy3]dik,D
{ oEdtmy\kdrhk; @F& dy3]dik,D
9q’j -vdsk,;olko0v’c8]j tl;j oxtlq,gxaodik,D
@D 9qj’7yfw]jc]h;0Po7e8v[.lj[jvo9Eg,afD
dD 350 g = …......... kg ;
2,6 g =…......…mg ;

0,05 kg =….........g ; 25 g =…........…hg ;

0D 625 g =…............kg ; 5g V 1000 =….......kg ;
18 mg V 1000 =…..g ;
2,348 kg =….......g ;
650 g _ ……g = 1hg ;
7D 950 g + .......... g = 1kg ; 1kg _ ….. g = 850 g .
ສະຫງສ.ວວນ.ລິສຂະສິດ
3 dg +…..dg = 1g ;

#D 9qj’xPj o9eo;omqfltoypq,gxaog]dl;j ofkpD

dD WF(& S 0D $F@& S 7D !F& D

\kpgsfG g]dlj;ofkpc,oj g]dlj;omu[j +lk,kf7af9hvowfhD

$D 9q’j xjPog]dl;j oxtlq,gxaog]dlj;ofkp c]h;xjPogxao9eo;omqfltoypq,D

dD 5 2 ; 0D 13 1 ; 7D 75 3 .
5 2 5

&D gryjo.shoE|adltg]pj 0v’xvfF sq;.9 c]t lt\v’0v’7qozh6|bj’oa[c8,j Ngduf
9qog4y’vkp5 @W xu faj’8k8t]k’]5j,oUD 9qj’[vd;kj vtw;pt;t.fgruj,0Bos^kp
d;kj \6j c]t vtw;pt;t.fgru,j 0Bo|hvpd;jk\6Lj

vtw;pt;t g]u,j gduf @W xu
xltv\f v ’
sq;.9 40 g 1 000 g
320 g 1 300 g
15 g
280 g

83

[qf mu ## dko;afcmd[=]y,kf[ao95

I. dyf9tde

!D 9q’j 9af]Pork-tot]5,j oU 8k,[=]y,kf[ao95c8j|hvpsks^kpD

@D 9qj’8nj,8k8t]k’]5j,oU.shleg]af ສະຫງສ.ວວນ.ລິສຂະສິດ
gryjogvqkoE &!@ 9vd ,kzv’.lrj k-totc8]j t-toyf 3fpvu’.lsj q;|j;pdko
zv’]5j,oUG
$ 9vdgmqjkda[ ! 34
$ 34gmqjkda[ ! dt85d
$ dt85gmqjkda[ ! 75
$ 75 gmqjkda[ ! dt4a’

9vd 34 dt85d 75 dt4a’
75 dt4a’
rk-tot 34 dt85d
oE &!@ 9vd

84

II. .97;k,

dkozv’lk,kfxP[mP[wfhfaj’oUG

!D zv’9kdrk-tot|bj’wx.lj @D g]nvdgvqkrk-tot|b’j gxaosq;|;j p
vudrk-tot|bj’D mujlk,kfltcf’7kj ;afcmdgxao

(a ) mt;u76o c]t v5xt76o0v’dkozv’

(b)

(b) (c) (a) (b) (c)

a > b > c a = 2b ; b = 2c

III. [qfg/ydsaf ສະຫງສ.ວວນ.ລິສຂະສິດ

!D 8k8t]k’oUltcf’zqowfhIa[dkozv’ 3fp.-hsq;|;j pfa’j ]5j,oUG

D ! 9vdohvpD

D ! 9vddk’,u[=]y,kf[ao95gmqjkda[ # 9vdohvpD

D ! 9vd.spj,u[=]y,kf[ao95gmqkj da[ # 9vddk’D

rk-tot 9vd.spj 9vddk’ 9vdohvp

a 2 18 12
b 2 9 21
c 2 15 18
d 3 2 6
e 3 0 9

dD 9qj’-vdsk[=]y,kf[ao950v’rk-totc8]j tvao 3fpgvqk9vdohvpgxaosq;
|;j p;afcmdD
0D xt8y[af.omeov’fP;daoda[ 0=h d c8gj vqk9vddk’gxaosq;|j;p;afcmdD
7D 9q’j 9af]Po]efa[rk-totc8j]tvao8k,[=]y,kf[ao95c8j|hvpsks^kpD

85

[qf mu #$ sq;|j;p;afcmd[=]y,kf[ao95

I. dyf9tde

!D mhk; dycdh; gvqk34muj[ao95oE ! ,kgm.ljda[fa’j I6[]5j,oUD 4k,;jk,uoEgmqjk
.f dm3.

1dm3 1

oE 1 = . . . . . dm3
ສະຫງສ.ວວນ.ລິສຂະສິດ
1dm

1dm

1dm

@D 9qj’la’gdf8q;1kj ’c]h;0Po9eo;o]5,j oU .l8j k8t]k’.sh4nd8hv’D

8q;1jk’ G V 10 V 10 V 10 V 10 V 10 V 10

1000 h da d cm

! 1
1000
1000 m 256
2 56c

0,567 ; 8d 5 c ; 0,001 ; 56,78 h ;
73 d ; 2 3d ; 1m ; 25 ;
365 h ; 32458 d ; 780 da ; 325 m ;

86

II. .97;k,
!D sq;|j;p0v’dkozv’muoj ypq,.-hc,oj ]yf X ? ovdoAopa’,ad.-h,yo]u]yf Xm ?
grnjvzv’;af45mu,j uxt]y,ko|hvpD
sq;|;j p0v’dkozv’oUpa’mP[gmkqj da[sq;|;j p0v’dko;afcmd[=]y,kf7nG
oEltvkf 1 = 1 dm3
1000 = 1 m3

@D 8k8t]k’rq;raodao0v’sq;|j;pdkozv’D

V 10 V 10 V 10 V 10 V 10 V 10

1000 h da d cm

V 1000 V 1000

1 = 1000 m ; 1h = 100 ; 1m = 0,001 .

III. [qfg/ydsaf ສະຫງສ.ວວນ.ລິສຂະສິດ

!D 9qj’xPj osq;|;j p;afcmd]5j,oUD

7 8 c = ........................... ; 2576 c = ............................ ;

3 8 d = .........................d ; 1258 c = ..........................d ;

4 d 6 c = ......................m ; 236 c = ..........................m ;

2 56 c = ......................c ; 3252 m = .........................c ;

658 c = ..........................h ; 45656 d = .........................h ;

@D 9qj’xjPog]dlj;o]5j,oUgxao9eo;omqfltoypq,D

1 ; 3 1 ; 1 ; 2 1 ; 6 3 ;
2 2 4 4 4

3 ; 6 ; 75 ; 100 ; 125 .
4 10 100 4 5

#D oExkws|b’j [ao95 !& gryjo0kpwxc]h; ) &Wc D 4k,;kj oExk9tpa’gs^nv
16jgmqkj .fL

$D oE,aog7nvj ’ ! ]k7k @& WWW du[F 4hk-nh & 9t9kj pg’yogmqkj .fL

87

[qf mu #& dkooe.-h9eo;omqfltoypq, c]t g]dl;j o

g0Qk.odko;afcmd[=]y,kf[ao95

I. dyf9tde

!D .o,N|bj’7qoz6h|bj’7;ofnj,oE.shwfh @ cc]8t.j op8a’qv;9udy’90adhv9pvfdnj,9wb’j f9hrtPwf’h8ck8,j 1de21oqfLD
4k,;jk,N|bj’0hvpfnj,oEwfh9ad9vdL

Ih6;jkG

{ 1 [j;’dkg2[ao95wfh WF& c D

{ 1 [;j ’8ad0v’s;ko[ao95wfh @ gmqjk

[j;’dkg2D

{ 1 [j;’8adcd’[ao95wfh 1 [j;’dkg2

c]t ! [;j ’8ad0v’s;koD
ສະຫງສ.ວວນ.ລິສຂະສິດ
{ 1 9vd[ao95wfh 11 [;j ’8adcd’

( [j;’8ad0v’s;ko c]t #

[j;’dkg2D

@D 9qj’0Po9eo;omqfltoypq,]j5,oU rkp.8hI6[c[[g]dlj;oD
WF@ S 1F@& S @F#&$ S @(F & S #*F1&*( S (F#* D

#D oEcdh;|b’j [ao95wfh 1(& c F 4hk,u ) cdh;9t,uoE9ad L s^n 9ad dm3D

II. .97;k,

.odkocdh39f[aoskdPj ;da[[=]y,kf[ao95.f|b’j F 4hksq;|;j p;afcmd[=]y,kf

[ao95skd8kj ’daogIqk8hv’xPj osq;|;j p;afcmdoAo .sh7ndaodjvo 9b’j fegouo

dkocdhD

88

III. [qfg/ydsaf

!D 9q’j 8nj,9eo;omu4j nd8hv’.l[j vj o9Eg,af]5j,oUG

2 = ….. c 20 c +…… = 1

235 c = ….. 7 d +…….. = 1
4 = ….. d 4 _…….... = 3,6

3,6 d = ….. c 6,4 +…… = 10
45 = ….. d 10 c _……..= 3,5c
0,5 d = ….. c
3 d = ….. c 2,5 V……....= 4
0,5 d V…… = 15c

0,2 = ….. m 4,6 ' ……..= 2,3

@D 9q’j 0Pog]dlj;o]5,j oU rkp.8hI6[c[[9eo;omqfltoypq,D ສະຫງສ.ວວນ.ລິສຂະສິດ

1 ; 3 1 ; 2 1 ; 6 1 ; 3 .
2 2 4 4 4

#D 0hvp4vdoE.l3j 4gxqjk|;j p|b’j !& gmnvj M]t 1 D 4k,;jk34|;j poAo[ao95oE
3

gmqkj .fL

$D oEfn,j [=]yl5f0;kf|b’j [ao95oEwfh WF& F 4hk-nh @W 0;kf9twfhoEfb,j 9ad L

&D dt4a’|j;p|bj’lk,kf[ao95oEg8a, )W F 4hk.odt4a’|j;poAo,uoE16jc]h;

#&F*) . 4k,;jk9tgvqkoE8n,j .lvj ud9ad 9bj’9tg8a,4a’L

*D xhkf;’ ,uoEgzY’ #F& ]k;gvqk,k.ljdt85d @ |j;pF |j;pmu|j b’j [ao95]njo

|j;pmujlv’ WF#* . 4k,;jkdt85dc8j]t|;j p[ao95oEgzY’9ad L

89

rkdmu ) ];’Iv[ c]t goNvmuj

[qf mu #* sq;|;j p;afcmdgoNvmuj

I. dyf9tde

!D 9q’j la’gdf8q;1kj ’c]h;8nj,.l[j jvo9Eg,afD
8q;1kj ’G !W@ = !W V !W = !WW !W&=...V...V...V...V... = ...
!W# = !W V D D D VD D D = D D D !W*=...V...V...V...V...V... =...
!W$ = D D DV D D D V D D D V D D D = D D D

@D g9hpczjo|bj’gxaoI6[lucj 9lkd ];’d;hk’cmdwfh )$W mm ];’pk;cmdwfh
!!))mm ,ugonvj mjuxt,ko ! m2D gryjoc[’j g9hpczoj oAovvdgxaoshkl;j o8kj ’
dao7nG
,u];’d;hk’ &_$ mm c]t ];’pk;gmqkj )$W mmD
A! !?D ,u];’d;hk’ $@W mm c]t ];’pk;gmqkj &_$ mm. ສະຫງສ.ວວນ.ລິສຂະສິດ
A@ ,u];’d;hk’ @_( mm c]t ];’pk;gmqjk $@W mm.
A# ,u];’d;hk’ @!W mm c]t ];’pk;gmqjk @_( mm.
A$ 9qj’7yfw]gj oNvmu8j q;9y’0v’g9hpczjooAoD

@?D 99qqj’’j 7oyef.w-]hzjgoqoNv0mvuj0’vd’klo;j 7oyfwA]!j0,hk’Ag@m,y’gAr#njvc1]A’t1noA;kj$G
#?D

A = 2A! 594 mm 420 mm 420 mm 594 mm

A! = 2A@ 840 mm A! A@ 1444442444443
A@ = 2A# A# 297Am$ m
210 mm

A# = 2A$ A A$

II. .97;k, 1188 mm

sq;|;j p;afcmdgoNvmju muoj ypq,oe.-hdaoc,oj G 8k]k’-a’8yc,af Xcm2? 8k]k’
c,af Xm2? c]t 8k]k’dy3]c,af Xkm@?D ovdoAo.odko;afcmdgoNvmu0j v’

fyogryoj pa’.-hsq;|j;p;afcmdgxao gIad8kXha? vkXa? c]t -a’9k Xca?D

90

8k8t]k’dkorq;rao0v’sq;|j;p;afcmdgoNvmuj
km2 hm2 dam2 m2 dm2 cm2 mm2

140000
200
150000

ha a ca

!$ m2 = !$W WWW cm2
@ hm2 = @ ha = @WW a = 200 dam2


!& hm2 = !& ha = ! &WW a = !&W WWW ca = !&W WWW m2
III. [qfg/ydsaf
!D 9qj’8n,j 9eo;o.lj[vj o9Eg,af.o8k8t]k’]5,j oUD

gxao Xm2? gxao Xdm2? gxao Xm2? gxao Xcm2?

#$FF@) DD DD DD DD DD $@ DDDDD
DD DD DD DD DD _$#&$)W #F)& DDDDD
WF@_ D D D D D * DDDDD
D D D D D @$)$
D D D D D $)*@W
ສະຫງສ.ວວນ.ລິສຂະສິດ
@D 9qj’xPj osq;|;j pdko;afcmd]5j,oUgxaosq;|;j p;afcmdmudj eoqfw;hD
dD $gx#ao@&mc@m@ S @$ dam@ S
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. . . =
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$ cm@ + ) mm@ + @ dm@ = . . . . . . . . . . . . . . . . . mm@
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(@ $#) mm@ _&F& cm@ = . . . . . . . . . . . . . . . . . cm@
$D 9qj’[vdsq;|j;pmujg\ktlq,grnvj ;afcmdgoNvmuj]5j,oUG
{ goNvmu0j v’xtgmf { goNvmu0j v’shv’IPo
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dD 0D 7D

7cm 5 cm 10 cm
5 cm 6 cm 6 cm
5 cm 8 cm 8 cm

7 cm 5 cm 10 cm

];’Iv[ DDDDDDDDDDDD cm ];’Iv[ DDDDDDDDDDD cm ];’Iv[ DDDDDDDDDDDDD cm

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dD goNvmujDDDDDDDDDDDDDDDDDDDDDDDcm2 0D
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8 cm

7D 3 cm 5 cm

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];’Iv[ = ];’pk; T ];’d;hk’ T ];’pk; T ];’d;hk’
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goNvmuj= ];’pk; V ];’d;hk’D 8q;1kj ’G I6[lujc9lkdmuj,u];’pk;
A= L V gmqjk * cm c]t ];’d;hk’gmqkj $ cm.
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P ];’Iv[ T goNvmu0j v’I6[lujc9lkdc,jo
A goNvmuj
4c m A = 6 cm V 4 cm = 24 cm2
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III. [qfg/ydsaf
!D 9q’j -vdsk];’Iv[ c]t goNvmuj0v’I6[]5j,oUD 7D $ 8k
dD 0D * 8k $ 8k
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#&W m gryjowfhgIafmk’vhv,.sh,u )$W m
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A goNvmuj

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ສະຫງສ.ວວນ.ລິສຂະສິດ
goNvmuj = . . . 8kdk3i; goNvmuj = . . . 8kdk3i; goNvmuj = . . . 8kdk3i; goNvmuj = . . . 8kdk3i;

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4k,;kj c8]j t8vo,ugoNvmugj mqjk.fL

36 m

II. .97;k, 79 m

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8q;1kj ’G ];’Iv[0v’I6[lk,c9 ABC = AB + BC +AC

A P = 4 cm + 8 cm + 6 cm = 18 cm

4 cm 6 cm

C

B 8 cm

96

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!D 9q’j -vdsk];’Iv[0v’I6[lk,c9]j5,oUD
A AA

24 cm 52 cm
18 cm 22 cm 22 cm 20 cm

ສະຫງສ.ວວນ.ລິສຂະສິດB 33 cmB 42 cm
C B 22 cm C C

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A

12 cm 24 cm

B 39 cm C BC D
45 cm

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$F ]5’lk]u ,ul;o8vo|bj’gxaoI6[lk,c9g-y’j c8]j t0hk’cmdwfhfa’j oUD
A
AB = 28 m ; BC = 42 m ; AC = 50 m
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4k,;kj ]k;9t.-h|k,\kd9a[pk;9adc,afL B 42m C

97