keleri . pfafi
ISBN 978-9941-475-08-5
მოსწავლის რვეული
დაფინანსებულია „მოსწავლეების სახელმძღვანელოებით უზრუნველყოფის პროგრამის“ ფარგლებში
ელფის გამომცემლობა
.
karl-hainc keleri peter pfafi
მოსწავლის რვეული saredaqcio kolegia: germanuli mxare: vibke meieri, hendrik simoni, nina simoni (redaqtorebi); krista miuleri (fsiqologi), kornelia ziberi (konsultanti); Sps tif-eni, berlini / mario kuxinke-hoferi, miriam frici (ilustraciebi); Sps tif-eni, berlini /martin adami (fotoebi); Sps tif-eni, berlini (dizaini). helme haine (sagamomcemlo jgufi `belci~). qarTuli mxare: irma lazaria (mTavari redaqtori); leila kirTaZe (stilist-redaqtori), dali kereseliZe (mTargmneli), TinaTin didebuliZe (proeqtis xelmZRvaneli), naTia mzeqalaSvili (teqnikuri redaqtori), inga lazaria (redaqtori).
გრიფმინიჭებულია საქართველოს განათლებისა და მეცნიერების სამინისტროს მიერ 2018 წელს
yvela ufleba daculia germanuli saavtoro ufleba: © Mildenberger Verlag GmbH Offenburg/Germany, 2016 qarTuli saavtoro ufleba: © elfis gamomcemloba, 2016
ISBN 978-9941-475-08-5 gamocema: pirveli weli: 2018
www.mathematics.elf.ge misamarTi: kartozias q. 8 # Tbilisi 0177 telefoni: (032)2923570 elfosta: office@elf.ge
სახელი, გვარი:
სკოლა:
სასწავლო წელი:
cifrebis/ricxvebis aRmoCena
a b g d e 2
moswavlis wigni gv. 6
b 9
v
z
a
ricxvebis gaferadeba mocemul ferSi.
raodenobis gamosaxva xazebiT
moswavlis wigni gv. 7-9
1
2
1. suraTebis dakavSireba Sesabamisi raodenobis xazebTan.
3
marcxniv da marjvniv | zemoT da qvemoT
moswavlis wigni gv. 10,11
1
2
3
4
5
4
3-5. simbolos gadaadgileba miTiTebuli TanmimdevrobiT da Caxatva samizne ujraSi.
raodenobis gamosaxva xazebiT
1
1. raodenobebis dadgena, gamosaxva xazebiT da aTeulis velSi warmodgena.
moswavlis wigni gv. 13
2
5
ricxvebis warmodgena sxvadasxva modeliT 1
moswavlis wigni gv. 14
daakavSire. 2 0 1 5 4 6 3
2
Caxate da Cawere.
3
Caxate. 8 9
6
1. ricxvis dakavSireba saganTa Sesabamis raodenobasTan. 2,3. gamotovebuli raodenobis Caxatva.
raodenobebis dadgena
moswavlis wigni gv. 15, 16
1
0
1
2
3
3
4
5
6
7
8
9 10
6
7
8
9
3
4
5
6
2
1
2
3
4
6
7
8
9
2
3
4
5
3
4
5
6
7
8
9
10
5
6
7
8
3
4
5
2
3
4
5
6
7
8
9
10
4,5. ricxvis Sesabamisi raodenobis saganTa erTobliobis Caxatva da amis mixedviT davaleba 6-is Sevseba.
7
raodenobis dadgena aTeulis velSi 1
2
3
moswavlis wigni gv. 17
Caxate. 6
7
8
10
gadaxaze. 1
5
0
3
Caxate an gadaxaze. 1
0
10
2
4
9
4
8
1-3. ricxvis Sesabamisi raodenobis rgolebis Caxatva an zedmeti rgolebis gadaxazva.
xazebi da raodenobebi
moswavlis wigni gv. 18, 19
1
2
1
2
3
4
5
2
3
4
5
6
1
2
3
4
5
3
4
5
6
7
1
2
3
4
5
3
4
5
6
7
2
3
4
5
6
1
2
3
4
5
miuxate an gadaxaze.
1. saganTa raodenobis dadgena, Sesabamisi raodenobis ricxvis Semoxazva; mcdaris gadaxazva.
9
ricxvebis Sedgeniloba
moswavlis wigni gv. 22, 23
1
9 +
+
+
2
5
8 +
+
+
+
1+5
2+4
6+3
5+2
+
+
3
4
+
+
5
4+1+2 10
6+2+1 1,2,4. raodenobis gamosaxva ricxvebiT da Cawera SesakrebTa jamis saxiT.
ricxvi 5-isa da 6-is Sedgeniloba
5
1
moswavlis wigni gv. 24, 25
5
2
+
3 +
+
+ 0
+
4 +
+
+ 1
2 + 3
ganagrZe.
6
1
+ + +
6
4
+
+
+
+
+
+
+
+
+
+
+
+
+
6
5
+ 5 6
+
+ 4
+
+
+ 3
+
+
+
2 + 2 +
+ 2
5,6. ricxvis warmodgena SesakrebTa jamis saxiT.
+
11
geometriuli formebi 1
gaaferade
2
daiTvale.
,
,
moswavlis wigni gv. 27
,
4 12
2. erTnairi feris an formis figurebis daTvla da Cawera.
figurebis awyoba da daSla 1
aawyve da daiTvale.
2
daSale sxvadasxvagvarad da daiTvale. pirveli
moswavlis wigni gv. 28, 29
meore
1. figuris awyoba geometriuli formebiT (danarTi 2), raodenobebis Cawera.
13
ricxvi 7-is Sedgeniloba
moswavlis wigni gv. 30
7
1
+ +
2
+
7= 3 +
+
7=
+
7= 5 +
+
7=
+ 6
+ 3
7= 0 +
6
5
3
7
1+
3+
2+
3+
1+
4+
2+
2+
6+
2+ 2 +
4+ 1 +
5+ 1 +
4+ 1 +
2+ 2 +
3+ 2 +
4
14
7=
+
+ 2
7=
+
+ 4
7=
+
+ 3
7=
+
+ 2
7=
+
+ 1
2,3. Sedgenilobis Sevseba da aTeulis velSi warmodgena.
ricxvi 8-is Sedgeniloba
moswavlis wigni gv. 31
8
1
+ + 2
+
8= 4 +
+ +
8=
+ 1
+
8= 6 +
+
8=
+ 3
8= 4 +
3
5
6
7
8
4+
2+
4+
6+
2+
5+
1+
4+
5+
6+
2+
2+
1+ 3 +
1+ 2 +
5+ 1 +
2+ 3 +
1+ 2 +
5+ 1 +
2+ 3 +
4+ 2 +
4
4. aTeulis velis dakavASireba Sesabamis tolobasTan da Sevseba.
8=
+
+ 0
8=
+
+ 4
8=
+
+ 1
8=
+
+ 2
8=
+
+ 3 15
meti – naklebi – toli 1
moswavlis wigni gv. 32, 33
>, < Tu = ?
2
2
9
7
8
5
5
3
4
2 5
5
3
1
4
6
1
7
>, < Tu = ?
3
1
3
4
5
8
10
1
8
8
3
2
4
4
7
2
3
8
4
5
3
3
5
4
6
6
5
2
7
3
3
4
6
4
4
7
9
6
6
8
6
2<
8>
7<
>5
2<
8>
7=
=5
> 6
2<
8>
7>
<5
> 3
16
4 <
4. ricxvis gamosaxva wertilebiT da SedarebaE. 6. utolobis Sevseba.
saxaliso amocanebi Sekrebaze
moswavlis wigni gv. 36
1
3
+
=
+
=
+
=
2
3
4
5
+
=
6
+
=
6. saxaliso amocanis mofiqreba, daxatva, Sesabamisi magaliTis Sedgena da amoxsna.
+
= 17
Sekreba aTeulis velis gamoyenebiT
moswavlis wigni gv. 37, 38
1
2
+
=
+
=
+
=
+
=
Caxate da iangariSe. 4+5=
6+3=
7+1=
5+2=
3
+ 4
=
+
=
iangariSe.
1+5=
3+2=
2+2=
2+4=
4+2=
4+1=
1+3=
8+1=
3+5=
5+4=
5+2=
3+3=
6+1=
1+8=
4+3=
7+1=
5
ganagrZe.
1 + 1 =
3 + 2 =
2 + 2 =
1 + 4 =
1 + 2 =
3 + 3 =
3 + 2 =
2 + 4 =
1 + 3 =
3 + 4 =
4 + 2 =
3 + 4 =
18
+
=
+
=
+
=
+
=
+
=
+
=
+
=
+
=
4. magaliTebis Sedgena aTeulis velis daxmarebiT. 5 kanonzomierebis amocnoba da Sevseba.
magaliTebi Sevsebaze 1
moswavlis wigni gv. 39
SevavsoT 8. 3+
=8
5+
=8
1+
=8
4+
=8
6+
=8
8+
=8
Caxate da Seavse. 2
3
2+
=7
4+
=7
2+
=5
4+
=5
2+
=6
4+
=6
2+
=4
4+
=9
1+
=8
3+
=4
4
5
6
7
5+
=8
3+
=7
+3=5
+3=7
4+
=6
6+
=8
+2=8
+6=7
1+
=7
2+
=4
+4=7
+5=8
3+
=5
6+
=6
+1=6
+2=5
1-3. aTeulis velSi magaliTis warmodgena da amoxsna. 4-7. magaliTebis amoxsna aTeulis velis gamoyenebiT.
19
rigobiTi ricxvebi 10-mde
moswavlis wigni gv. 40, 41
daakavSire.
1
mesame
meore
pirveli
meeqvse
meoTxe
meSvide
mexuTe
mecxre
meaTe
merve
3
2
pirveli
4
gaaferade.
meore
5
mesame
meeqvse
meore
meoTxe
pirveli
mexuTe
meSvide
daajgufe.
pirveli 20
2,3. Sesabamisi rigobiTi ricxvis dasaxeleba. 5. suraTebis Tanmimdevrobis amocnoba da Cawera.
ricxvi 9-is Sedgeniloba
moswavlis wigni gv. 42
1
9
9
+ +
2
+
9= 3 +
+
9=
+
9= 7 +
+
9=
+
+ 1
9= 6 +
+
3
+ 4
6
5
7
8
9
1+
2+
2+
6+
4+
4+
1+
6+
4+
8+
3+
5+
4+
2+
1+
3+ 1 +
4+ 1 +
2+ 4 +
2+ 3 +
7+ 1 +
5+ 0 +
3+ 2 +
7+ 0 +
4+ 1 +
3+ 4 +
4
9=
+
+ 7
9=
+
+ 4
9=
+
+ 6
9=
+
+ 5
9=
+
+ 2
1. ricxvis Sedgenilobis povna da Cawera. 4. aTeulis velis dakavSireba tolobasTan da Sevseba.
21
SesakrebTa gadanacvleba
moswavlis wigni gv. 44, 45
1
1+6=
4 + 3 =
6+1=
+
=
+
=
+
=
+
=
+
=
2
2 + 7 = +
3 + 6 = +
=
2 + 3 = +
=
1 + 8 = +
=
=
3
2+4=
+
=
+
=
4+2=
+
=
+
=
+
=
+
=
+
=
+
=
+
=
+
=
4
1 + 7 = +
5
4 + 5 = +
=
=
2 + 6 = +
=
iangariSe.
1+5=
8+1=
4+3=
2+5=
5+3=
1+6=
5+4=
3+6=
2+6=
2+4=
7+2=
7+1=
3+4=
3+5=
6+1=
1+4=
22
3,4. SesakrebTa gadanacvlebadobis Tvisebis angariSis xerxad gamoyeneba.
saangariSo samkuTxedi
moswavlis wigni gv. 46
1
2 1
3 3
4
3 4
1
6
4 3
3
2 7
2
3 5
2
6 2
2
3
5
3 1
5
4
2
5
6
6 2
1
5
3
3 5
4 2
7
9
3
8
1
9
1
3
2
2 2
1-3. saangariSo samkuTxedebis Sevseba.
3
1 2
23
saxaliso amocanebi gamoklebaze
moswavlis wigni gv. 50
1
8
−
=
−
=
−
=
2
3
4
5
− 24
=
6
−
=
−
=
1-6. saxaliso amocanebis Sedgena gamoklebaze. 6. naxatis daxatva da magaliTis Cawera.
gamokleba aTeulis velis gamoyenebiT
moswavlis wigni gv. 51,52
1
2
−
=
−
=
−
=
−
=
Caxate da iangariSe.
7−5=
8−4=
9−3=
6−2=
3
− 4
=
−
=
iangariSe.
6−5=
7−2=
9−7=
4−1=
3−1=
4−3=
6−2=
3−2=
8−4=
5−4=
8−6=
7−6=
9−6=
8−1=
5−2=
8−2=
5
daasrule.
9 − 1 =
9 − 8 =
5 − 4 =
8 − 2 =
9 − 2 =
8 − 7 =
6 − 3 =
8 − 3 =
9 − 3 =
7 − 6 =
7 − 2 =
8 − 4 =
−
=
−
=
−
=
−
=
−
=
−
=
−
=
−
=
5. kanonzomierebis principis amocnoba, aRwera da magaliTebis dasruleba.
25
ricxvi 10-^is Sedgeniloba | Sevseba 1
10
2
moswavlis wigni gv. 54, 55
10
3
10
+ 3
5 +
+ 1 + 2 + + 2 + 3 +
+ 1 +
+ 8
+ 3 + 4 +
+ 2 +
6 +
+ 4 + 5 +
+ 3 +
+ 9
+ 5 + 3 +
+ 4 +
0 +
+ 2 + 6 +
+ 5 +
+ 6
+ 1 + 3 +
+ 6 +
10 +
+ 4 + 2 +
+ 7 +
+ 7
+ 1 + 1 +
+ 8 +
9 +
+ 0 + 1 +
+ 9 +
+ 2
+ 10 +
0 +
4
3+
= 10
5+
= 10
6+
= 10
2+
= 10
8+
= 10
7+
= 10
5
6
1+
= 10
9+
= 10
+ 8 = 10
+ 2 = 10
4+
= 10
3+
= 10
+ 3 = 10
+ 6 = 10
8+
= 10
5+
= 10
+ 4 = 10
+ 5 = 10
7+
= 10
6+
= 10
+ 9 = 10
+ 7 = 10
26
5-6. SesakrebTa gadanacvlebadobis Tvisebis gamoyenebiT magaliTebis amoxsna.
moqmedebaTa urTierTSebrunebuloba
moswavlis wigni gv. 56, 57
1
9−
=
−
=
−
=
5+
=
+
=
+
=
2
6 − 3 = +
8 − 2 = +
=
7 − 7 = +
=
=
3
2 + 3 = −
7 + 2 = −
=
4 + 5 = −
=
4
=
5
9 − 3 =
4 + 3 =
+ 3 =
−
7 + 1 = −
+
=
6 − 2 = +
=
6
8 − 5 =
1 3
+
=
8 5 2
7 4 6
2
7
2 9
1
5 2
3
=
5 + 4 = −
=
=
5
8
4 7
−
=
6 − 1 =
5 6 0
4 + 2 =
5 10 0
3 4
7
4
2
2 1 5 8
9 3
3
4
3
6 0
8
4-7. magaliTebisa da maTi Sebrunebuli magaliTebis amoxsna. saangariSo borblebis Sevseba.
2 3
1 4
2 2
27
magaliTebis ojaxebi
moswavlis wigni gv. 59
1
4
2
2
6
+
=
+
=
−
=
−
=
2
7
2
9
3
8
3
+ = + = – = – = 5
6
4
6
10
8
10
+ = + = – = – =
ipove magaliTebis ojaxebi.
3
+ = + = – = – = 28
1
+ = + = – = – =
+ = + = – = – = 4
5
7
6
2
+ = + = – = – =
4
+ = + = – = – =
9
+ = + = – = – =
1-4. sami ricxvisgan yvela SesaZlo magaliTis Sedgena.
saangariSo kedeli
moswavlis wigni gv. 62,63
1
8 3
6
3
2
4
5
8
2
10
3
5
2
2
1
2
3
5
2
1
2
2
2
3
+2=
+3=
+4=
−4=
−6=
−5=
4
+
= 10
−
=6
+
=7 29
ricxvebi 20-mde | mezobeli ricxvebi 1
moswavlis wigni gv. 64, 65
Cawere gamotovebuli ricxvebi.
1
6
9
14
16 17
ipove wina da momdevno ricxvebi. gaaferade ujrebi ricxviTi mwkrivis Sesabamisad. 2
7
5
19
6
14
3 3
10
4
18
romeli ricxvebi aklia? Seavse. 3
5
12
20 5
4 13
4 16
daalage.
8
6
15
17
8 9 18 4
11
11 17
9
daakavSire wertilebi erTmaneTTan. 11
12 13 17
14
10 9
15
8
6
30
16 4
7
19
18
5
3
2
20 1
4. ricxviT Tokze ricxvebis zrdis mixedviT dalageba. 6. wertilebis SeerTeba zrdis mixedviT.
rigobiTi ricxvebi 20-mde
moswavlis wigni gv. 66
mesame meore pirveli
gamonabolqvi azianebs garemos!
1
pirveli
2
gaaferade pirveli davalebis manqanebi miTiTebul ferebSi. meore, merve, meTormete, meCvidmete
meoTxe meTerTmete, meToTxmete, meoce. 3
mesame, meSvide, meTxuTmete, meTeqvsmete
pirveli, meeqvse, meaTe, mecxramete.
mexuTe, mecxre, mecamete, meTvramete
gadaxti ricxvebis mwkrivSi da ganagrZe.
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
ganagrZe. gamoiyene ricxviTi mwkrivi. 2, 4, 6, 4
20, 17, 14, 1, 6, 21, 18, 15, 1. manqanebis dajgufeba rigobiT ricxvebTan da Cawera.
31
aTeuli da erTeuli
moswavlis wigni gv. 68
1
10
+ 4 aT.
10
+
erT.
+ 2 aT.
+
10
= =
+
aT.
10
= erT.
+ 7
=
= erT.
+ 6 aT.
+
=
= erT.
=
2
+ aT.
+
= erT.
+ aT.
+
= 15
aT.
erT.
+ 3 aT.
10
+
= 18
aT.
+ 6 aT.
10
+
+
+
1
aT.
= erT.
+ 7 aT.
=
=
=
+ 6
= erT.
+
1
aT.
= erT.
= 19
+ 5 +
1
=
+
erT.
= 20
5
= erT.
erT.
+
4
10
=
+
=
3
32
+
aT.
= =
erT.
20 aT.
20
= =
+ 7 erT. =
+ 1 +
= erT.
+ 3 aT.
20
+
= erT.
+ 4 aT.
+
=
= =
erT.
=
3-5. ricxvebis aTeulisa da erTeulis saxiT warmodgena.
ricxvebis Sedareba | angariSi 20-mde
moswavlis wigni gv. 69
1
10 +10 10 + 9
20
19
>, < Tu =? 13 > 12
18
2
3
15
15
10 + 5
12
17
10 + 6
15
19
6
16
10 + 8
17
10
10 + 9
11
20
14
4
10 + 2
12
18
10 + 7
4
5
10 + 8 =
6 + 10 =
4+
= 14
10 +
= 20
10 + 2 =
3 + 10 =
7+
= 17
10 +
= 12
10 + 5 =
9 + 10 =
1+
= 11
10 +
= 16
6
7
13 −
= 10
12 −
= 10
− 2 = 10
− 8 = 10
19 −
= 10
18 −
= 10
− 5 = 10
− 3 = 10
20 −
= 10
17 −
= 10
− 7 = 10
− 9 = 10
8
10 + 1 =
19 − 9 =
10 +
= 17
− 1 = 10
10 + 2 =
18 − 8 =
10 +
= 16
− 2 = 10
10 +
=
17 −
=
10 +
= 15
− 3 = 10
+
=
−
=
+
=
−
= 10
+
=
−
=
+
=
−
= 10
2-7. angariSi SesaZlebelia svetebis an kubikebis daxmarebiTac. 8. kanonzomierebis amocnoba da Sevseba.
33
aTeuli da erTeuli _ grovebi
moswavlis wigni gv. 70, 71
+
=
+
=
eE rTeuli
aTeuli
=
eE rTeuli
=
eE rTeuli
aTeuli
eE rTeuli
+
+
aTeuli
=
=
eE rTeuli
+
+
aTeuli
=
aTeuli
+
eE rTeuli
aTeuli
1
+6=
aTeuli
eE rTeuli eE rTeuli
eE rTeuli
10 + 9 =
aTeuli
+
=
eE rTeuli
5
eE rTeuli
4
aTeuli
3
aTeuli
= 17
+
34
aTeuli
eE rTeuli
aTeuli
2
+
=
1,3,4. grovebis aTeulebad Semoxazva, Sedegebis Setana Tanrigebis cxrilSi, magaliTebis Cawera.
fuli 1
moswavlis wigni gv. 76-79
ramdeni TeTria?
TeTri 2
TeTri
lari
lari
ramdeni laria?
lari 3
TeTri
daalage da Caxate.
16 lari
lari 11 lari
lari
7 lari 5 lari
9 lari
lari
1,2. fulis raodenobis amocnoba. 3. calkeuli nivTebisTvis saWiro monetebisa da banknotebis Caxatva.
35
analogiuri magaliTebi Sekreba-gamoklebaze 1
jer aTeulSi iangariSe.
12 + 4 =
16 + 3 =
+
=
2+4=
6+3=
+
=
15 + 3 =
11 + 6 =
+ 2
+
=
=
+
=
16 − 3 =
19 − 4 =
−
=
6−3=
9−4=
−
=
19 − 8 =
18 − 3 =
13 + 5 = +
−
=
3
jer aTeulSi vangariSob.
+
16 − 4 = −
=
17 − 6 =
=
−
15 + 4 =
=
19 − 7 =
=
−
=
=
14 + 3 = +
=
13 + 2 = +
=
+
=
ipove msgavsi magaliTi. +
=
3 + 4 = +
=
5 + 3 = 36
17 + 2 =
jer aTeulSi iangariSe.
−
4
moswavlis wigni gv. 82, 83
−
=
8 − 4 = −
=
6 − 2 =
5 + 1 = +
=
4 + 4 =
4. yoveli magaliTisTvis analogiuri magaliTis povna da orives amoxsna.
mezobeli magaliTebi 1
3
moswavlis wigni gv. 84, 85 2
5+3=
9−5=
5+4=
8−5=
8−2=
6+2=
8−3=
7+2=
3+4=
6−3=
3+3=
7−3=
7−2=
4+5=
7−1=
3+5=
iangariSe aTeulis velis daxmarebiT.
8−2=
4+6=
8−4=
3+5=
8−3=
4+5=
7−4=
4+5=
4
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
5+2=
15 + 4 =
5+3=
16 + 4 =
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
5
8−3=
17 − 4 =
9−3=
17 − 5 =
iangariSe ricxviTi sxivis daxmarebiT.
12 + 5 =
9−6=
6+3=
17 − 4 =
12 + 6 =
8−6=
6+2=
18 − 4 =
4+2=
19 − 3 =
13 + 3 =
8−5=
4+3=
19 − 2 =
12 + 3 =
9−5=
6
1-5. magaliTebis amoxsna aTeulis velisa da ricxviTi sxivis daxmarebiT.
37
mdebareoba | saangariSo cxrilebi
moswavlis wigni gv. 86, 87
1
2
+
4
5
6
+
2 12
4
5
6
+
3 2
3
4
5
4
5
6
5 15
3
−
5
6
7
−
8 18
6
7
8
−
8 9
5 15
4
2
+
4
3
−
4 7
6 38
17 10
3 13
5 13 13
6
+
12 13
2
3
4 15 17 18
1. obieqtis mdebareobis gansazRvra da cxrilSi `~-iT aRniSvna. 2-4. saangariSo cxrilebis Sevseba.
gaormageba | ganaxevreba
moswavlis wigni gv. 90-91
1
3+3=
7+
2
=
3
+
â&#x20AC;&#x2030;
+
=
â&#x20AC;&#x2030;
+
=
4
= 10
= 18
+
5
6=3+
10 =
6
7
= 9
14 =
+
+
8
+
+
=
=
+
Seavse cxrili.
velosipedebi borblebi
1 2
3
8
6 8
10
2 14
9
20
1-4. gaormagebis Sevseba, magaliTebis Cawera. 5-7. magaliTebis mixedviT Sua gamyofi xazis gavleba.
39
luwi da kenti ricxvebi
moswavlis wigni gv. 92
daalage ricxvebi.
1
11
6
2
17
14
16
12
8
10
3
20
7
1
19 15
luwi ricxvebi
2, kenti ricxvebi 2
kentia Tu luwi?
6
3
TanmimdevrobiT daakavSire jer luwi, Semdeg ki kenti ricxvebi. 20
18 16
1 3
14 6 12
10 8 2
11
4
5
15
5 7
9 11
3
15 13
40
17
1
14
8
7
19 17
10
13
9
6 2 19
4
12
16
18 20
2. luwi raodenobis ujrebis gaferadeba mwvaned, kenti raodenobis â&#x20AC;&#x201C; wiTlad.
mimateba 20-is farglebSi 1
iangariSe gigis msgavsad.
9+
2
moswavlis wigni gv. 93-96
7
=
4+
8
=
8+
6
=
9+ 1 + 6 =
4+
+
=
8+
+
=
7+
5
=
6+
7
=
5+
9
=
7+
+
=
6+
+
=
5+
+
=
iangariSe gigis msgavsad.
5 +
7
5 + 5 + 2 = 6 +
9
=
+
+
=
10
=
+
=
3 + +
7
=
5
+
8 +
4
=
4
+
+
=
+
9 +
5
=
+
+
=
7 +
6
=
+
+
=
2
+
+
+
+
iangariSe sesilis msgavsad. 3
4
5+5=
7 + 7 =
10 + 6 =
5+6=
+ 7 =
+ 6 =
5+7=
9 + 7 =
8 + 6 =
5
5 + 10 = 5 +
=
5 + 8 =
Sen rogor angariSob?
8+7=
4+9=
5+6=
9+9=
4+8=
5+8=
7+7=
9+8=
9+3=
6+7=
9+4=
6+5=
6+6=
9+5=
8+3=
7+4=
1-5. angariSis sxvadasxva xerxis gamoyeneba.
41
gamokleba 20-is farglebSi 1
iangariSe maris msgavsad.
12 −
2
7
=
13 −
8
=
15 −
9
=
12 − 2 − 5 =
13 −
−
=
15 −
−
=
14 −
6
=
11 −
5
=
17 −
9
=
14 −
−
=
11 −
−
=
17 −
−
=
iangariSe maris msgavsad.
13 −
7
7
=
13 − 3 − 4 = 14 −
5
=
−
−
=
3
3
+
15 −
8
=
−
−
=
12 −
6
=
−
−
=
4
+
+
+
iangariSe anas msgavsad.
12 − 7 = 7+
14 − 6 =
= 12
6+
15 − 6 = + 4
moswavlis wigni gv. 97-99
17 − 9 =
= 14
+
13 − 8 = +
=
=
12 − 5 = +
=
=
Sen rogor angariSob?
13 − 6 =
15 − 7 =
11 − 9 =
16 − 9 =
14 − 8 =
17 − 9 =
16 − 7 =
13 − 8 =
11 − 4 =
12 − 6 =
13 − 4 =
12 − 3 =
42
1-4. angariSis sxvadasxva xerxis gamoyeneba.
magaliTebi Sekrebasa da gamoklebaze
moswavlis wigni gv. 100
amoxseni magaliTebi da gamoicani winadadeba.
1
1 2 c l
3 s
4 m
5 q
6 n
7 u
8 e
9 a
10 11 12 13 14 15 o v b x i d
15 − 6 =
15 − 8 =
15 − 14 =
12 − 7 =
10 + 5 =
15 − 2 =
11 − 9 =
13 − 4 =
18 − 8 =
4 + 4=
8 + 4=
6+ 5=
15 − 11 =
20 − 14 =
16 − 8 =
7 + 7=
5 + 5=
10 − 8 =
13 − 10 =
9+ 5= 18 − 9 =
. 2
3 12
8
17 8
9
7
12
6
7 13
3
4
+
3 4 5
6
7
8
9
15
5
−
7 12 16
8
7
6
5
+
7 8
1-3,5. saangariSo samkuTxedebisa da cxrilebis Sevseba. 4. Sevseba da Secdomis povna.
6 12
8
9
15 43
gamoyenebiTi angariSi
moswavlis wigni gv. 101
yovelTvis 12 TeTri.
1
9 T. +
T. = 12 T
18 T. −
T. = 12 T
3 T. +
T. = 12 T.
yovelTvis 8 TeTri.
2
T. −
T. = 8 T
T. +
T. = 8 T.
T. −
T. = 8 T
+
= 14
yovelTvis 19
3
+
= 14
20
−
= 14
4 3
4
2
1
44
1,2. monetebis Sesabamisad damateba (Caxatva) an mokleba (gadaxazva) da magaliTebis Cawera.
gamoyenebiTi angariSi
5
3
1
moswavlis wigni gv. 102, 103
4
2
6
12
7
ra Rirs?
2
Rirs 2
Rirs
lari.
Rirs
lari.
risi yidva SegiZlia? Caxate.
Rirs 3
lari.
lari.
Rirs 10 lari.
Rirs 20 lari.
ramdenis yidva SegiZlia?
3
5
saTlelis.
saRebavebis yuTis.
1. fulis raodenobebis Caxatva, Sekreba da jamis Cawera. 2. Sesabamisi sagnebis Caxatva, jamis Cawera.
45
Sekrebis cxrili | mezobeli magaliTebi 0
+
1
2
3
4
5
6
mosw. wigni gv. 108, 109
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 sad weria magaliTebi? gaaferade Sesabamisi ujrebi, iangariSe da Sedegebi Cawere cxrilSi. 1
2+5=
4+3=
8+7=
6+1=
8+3=
10 + 5 =
6+9=
4+7=
ipove mezobeli magaliTebi, iangariSe da Sedegebi Cawere.
2
1 + 9 =
2
3
+
9
=
46
=
+
=
+
=
3 + 8 =
+
=
+
=
+
=
+
=
+
=
+
=
+
=
6 + 4 =
7 + 6 =
+
=
ipove mezobeli magaliTebi, iangariSe da Sedegebi Cawere. 3 + 3 =
4
+
3
+
4
=
+
=
+
=
+
=
+
=
+
=
+
=
7 + 2 =
+
=
+
=
Seitane gamotovebuli Sedegebi cxrilSi.
9 + 8 =
mezobeli magaliTebi gamoklebis cxrilSi 0
−
1
2
3
4
5
6
moswavlis wigni gv. 110
7
8
9
10
20 19 18 17 16 15 14 13 12 11 10 sad weria magaliTebi? gaaferade Sesabamisi ujrebi, iangariSe da Sedegebi Cawere cxrilSi. 1
2
15 − 7 =
12 − 8 =
19 − 3 =
14 − 6 =
18 − 7 =
17 − 2 =
16 − 4 =
13 − 9 =
ipove mezobeli magaliTebi, iangariSe da Sedegebi Cawere.
15 − 4 =
14
3
−
4
=
=
−
=
−
=
18 − 6 =
−
=
−
=
17 − 9 =
−
=
−
=
−
=
−
=
−
=
−
=
13 − 5 =
ipove mezobeli magaliTebi, iangariSe da Sedegebi Cawere. 11 − 3 =
4
−
−
=
−
=
11
− −
4
= =
18 − 3 =
−
=
−
=
20 − 8 =
−
=
−
=
−
=
Seitane gamotovebuli Sedegebi cxrilSi. 47
gamoyenebiTi angariSi
moswavlis wigni gv. 112
1
kote yidulobs
7
lari
darCa
lari.
darCa
lari.
darCa
lari.
darCa
lari.
2
nana yidulobs
8
5
lari 3
vaso yidulobs
12
3
lari 4
ana yidulobs
3 8
lari 48
1
1-4. situaciebis gaTamaSeba saTamaSo fuliT; darCenili Tanxis daxatva; raodenobebis Cawera.
gamoyenebiTi angariSi 1
moswavlis wigni gv. 113 2
9
16
2 0 2 mekuTvnis
lari.
3
mekuTvnis
lari.
4
14
mekuTvnis
6
lari.
5
mekuTvnis
lari.
6
11
mekuTvnis
13
lari.
7
mekuTvnis
lari.
8
12
mekuTvnis 3 lari.
6
mekuTvnis 14 lari.
1-6. situaciebis gaTamaSeba saTamaSo fuliT, angariSis Cawera. 7,8. banknotebis Caxatva, angariSis Cawera.
49
erTi dRe saaTTan erTad 1
2
50
moswavlis wigni gv. 114, 115
romeli saaTia suraTebze?
9 saaTia.
saaTia.
saaTia.
saaTia.
saaTia.
saaTia.
daxate Sesabamisi drois maCvenebeli isari.
Tavsatexebi
ras niSnavs ? = 10 = 5 = 1 ese igi 10 + 5 + 1 + 1+ 1 = 18 = G
1
2
ra weria wignze? gamoicani. miniSneba: 18 = s gaSifre saidumlo Setyobineba.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
a b g d e v z T i k l m n o p J r s t u f q R y S C c Z w W x j h 51
cifri 1 1
erTi
2
52
cifri 2 1
ori
2
53
cifri 3 1
sami
2
54
cifri 4 1
1
2
2
oTxi
44
44 44 44 44 4 4 4 4 4 4 4 4
55
cifri 5 1
1 2
xuTi
2
56
cifri 6 1
eqvsi
2
57
cifri 7 1
1
Svidi 2
2
58
cifri 8 1
rva
1 2
2
59
cifri 9 1
cxra
2
60
cifri 0 1
nuli
2
00
00 00 00 00 0 0 0 0 0 0 0 0
61
laris simbolo 3
4
2
1
lari
62
1
1
1
1
0
0
0
0
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
7
7
7
7
8
8
8
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22
9 10 11 12 13 14 15 16 17 18 19 20 21 22
9 10 11 12 13 14 15 16 17 18 19 20 21 22
9 10 11 12 13 14 15 16 17 18 19 20 21 22
danarTi 1: ricxviTi sxivi
63
danarTi 2: geometriuli dafa
danarTi 3: fuli