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Infsnt Clcsses
Junior Infonts
/
Senior
0+1 :1
It
+1
onts
-
Number Focts
0+i:3
a+2*2
1+2-3
i2+2:4
-./)
2+1 -'3
3+1 ==4
tl+ 1 *J
5+1 :6
6+1 -7
1+3-4
2+3 -5
3+3-5
'3+2*5
4*2:6
$
7 +l :8
u+1 -9
9+1 ='10
4+3
{}::=J
-7
5+'3:B
16+2:8
6+3
"7
7
*?:9
-g
+3:1
0
E+2:1 0
* 4:4
0+5:5
0*'6=6
2+4-=6
n*5=6
2+5=7
I +-6 -7
2+6==g
3+-6--9
4+6==10
r0
1
*4:5
3+4:7
,4*{==g
5
+4:9
,6+4:10
0
I
+'/ -7
1*7:8
2*7:9
3+7:10
3*5=.8
e[*5==9
5+5==10
0+8==8'
1*8==9
2+8==
10
0+9-s
1+9:tr0
0+10:10
The
J.I.
& S.I. Teachers Will Use The Followino Mothemotical
Lanouoge Regording Addition
1. 2 and 3 moke 5
2. 2 and 3 is the some os 5
3. 2 ond 3 equols 5
4.2*3=5
5. 2 and 3 is how mony ?
6.2*V
7.
=$
f hoveZ.How mony more do I
need
to moke 5
?
l5uqggestil,on s1Fsr F,crrents
1.
JLu
IssirE,/Twins -- thlil idecl
thct
2+3 is the scrm€
Rsth*rr th,cln leqn'ning the tsbles
im
order -
rnlx tlhenr rgrouilrtC
31.
!4cq,u
fqst cun ! g,u qround ttre wheeel?
2
,05
3+!l
First CScss
I
IF
I
i
I
The First Closs Teochers Will Use the Following Mothernoticol
t""rr.t"
t" tr,"tt
Addition
i
i
i
t
1. Language"Counton"
J
I
I
I
z.
whot is
z
"Add"5+2
3. Moke o Toble Book
2+O=2
z+t=3
2+2=4
Add 5+Z
a
Tobles ore f o be learned the followin g way ond 0 ^. is colled Zero
_-_=_
t **'r=='o
etc.
Subtrcction
l.7take?is5
I
z. 7 minus Z
I
t
t
I
i
5ondzarel
morethon 5 ?
t_
I
5plus2=7
5ond2=7
I
i
S+2=7
Teochers will introduc e the
equals
a
sign
for subtroction.
D
3.7-2=5
4.
Teachers introduce the number line afterChristmos.
A- Use the number line to find whot is 2 less thanl
B. Stort ot 10 Count bock 3 7
=
c. rntroduce "count bock,, ond "tok e,, end,,subtroct,,
/
7-2=j
(countbock)
7 minus Z leaves 5
7 subtro ct Z = b
3
?
First
Closs
Put it into the bubble
13 unifs = Iten 3 units
Exomple
L
t"
->
*[l{l
*{mff000f
illllfl -.
ll
ffi000f[|f0000f0
1
"a
E.!.
6
,J
@
7
3
000
We use the following longuoge:
1.
2.
3.
4.
5.
NB. Alwoys count from the toP down'
6 units plus 7 units eguols 13 units
thon 9 units so we
Put the 13 units into the bubble becouse it is more
con chonge it to tens qnd units.
13 units equols l ten ond 3 units
ond bring the 1
Leovethe 3 units in the units section where it belongs
ten over to the tens.
from the top
6. Now odd up oll the tens qnd remember to stqrt
7. ! ten ond 1 ten eguols 2 tens.
8. Our qnsw er is ? tens ond 3 units = 23
4
J
!
I
!
I
I
t_
I
T
ii
i
i
i
I
I
I
t
I
I
1't.
0* 1:
1
1*1: 2
2+ 1- 3
3+1- 4
4*7: 5
5+1: 6
6+ 1- 1
7*1:
8*1: I
9+ 1:
10+ 1:1i
11+-7:12
12+ 1 : 13
B
1C)
0*4:
1*4:
2+ 4:
3-r44* 4:
5*4:
6+ 4 =
4
5
6
- 6th. Addition Focts
0*2: 2
7*2: 3
2+2- 4
3+2- 5
4+2* 6
5+2* 7
6+2- g
7 +2- 9
I 2: l0
9 + ?:11
J-
10 +
2>
12
l1+ 2:73
12+Z:t4
0+5:
1t-5:
?+{:
5
6
a
t-)t
8
3+54J'5: I
9
10
5 + 5 = 10
6 -f'5:11
1
g
7+4:11
8 +,+ :72
9+4:13
7+5:12
8+5:13
9+5:14
14
10 +' 5 15
11 +'5:16
72 +'
17
10r 4:
11+
4:15
12+4:16
:
5:
0*3:
1+3:
2+33+3:
4+35+36t-3:
7
3
4
5
6
7
B
9
+3:10
8+3:X.1
9+3:12
3:
13
0*6:
1*6:
2*6=
6
7
10 +
11 + 3
:"14
1,2+3 = 15
g
3-F6: 9
4+6:10
5+6=i1
6+6:12
7+
C;: 1.3
8+6:14
+ 6: 15
i0 + 6:76
11+ 6:17
72+ 6:18
9
0+'7: 7
\*J:
B
2+'7: 9
3+7: l0
2+
E
4-ll:11
6+7:13
6+E--14
7
+'7:14
B+7:.15
16
-:1.7
11+ 7:I8
9+7
10 + 7
12+7:79
0+10-10
1+
10:1L
2+tA:t2
3+10:13
4+10:14
+ t0: 15
+ ,1.0: 16
7 + L0:17
8 + ll0 = 1B
5
6
9+trO=19
10+ X0=20
11 l- l[0 : 21
12 + \0 :22
"2+9 -
- 10
3+E-11
4+E:12
5+E-13
5+'7:1?
0+9- 9
1 + 9: 10
0*E: I
1*E- 9
1n
3+9:tz
4+9:13
5+9:tzl
6+9-15
I + 9: 16
7+E:15
8+E:16
g+E-17
8+9:1'l
9+9-18
10+ 9:19
11+ 9:20
10+E:18
:19
11 +- E
12 + E :20
1.2
+ 9 :21
0+11:11 -l 0+17:12
t*t2=1,3
1+t!:IZ
I
7+\1 :13
I z*12':71
:*12:\'3+11.:!4
I
;-;i:rq
I ++12:16
+-1-lil-rJ
5+[i:16
I 5+12':17
6+ll I=17
I 0*12:1!
7+\1:18 I z*12':19
I
B+11:19 i s*12':20
9+l[ l:20
i I{-'g*12=?,\
r r'1' - LL
I
10 + t:21
tr
+ I!:22
11+11:"/'2
11
tz
t
-t1
--
?3
rr + 12:23
|Irr-rr'z;-
--*-Lgt tz:lt-
Suggestionrs for Farents
i. ;;in Snr. Inf. Mix tabl'Bs wheur examiming
orlvn number wtrreel
2. Encourage chilrdttlo wrilfrp his
6
Seeond Ctoss
Second Closs
The Second Closs Teachers Will Use the Following Mothemoticat
Languoqe in Their Teochino of Addition subtroction ond
Problem-solving
A.
Languooe ond oddition
.
.
Look
- more thon
Add
And
- sum of
- totol
Plus
all together mokes
counf on
for doubles, near doubles, numbers thot moke 10
fn 3 digit oddition olwoys do whqt's
in
the brocket first
B. Lanouoqe - subtroction
-
toke oway
minus
subtroct
less
f ind fhe diff erence
- f ewer
- count bock
- from
- less thon
- left
.
Diffe?ence / decomposif ion 16 ----------> 99
The ' diff erence' betweenT ond 2 is 5
3 minus 2equalsl
Tobles 3-2= i
C, Problem Solving
Strotegy
. R.U.D.E
o R. - Reod the Problem
r U. - Underline impo,rtant words - Longuoge f or oddition
r
o
ond subtraction.
[. - Drow o picture / write o sum to help solve
f. - Estimote the answer , using rounding slrategies
Subtroction Focts
1-1:0
2-l:
3-1: 2
4-1- 3
5-1: 4
6-l: 5
V-l: 6
8-1: 7
9-1:8
10-1:9
1
2-2:
4-2:
5 -2:
6-2:
7 -2:
8-2:
9 -2:
10 -2:
17 -2:
Znd.
- 6rh.
4
3-3:
4-3:
5-3:
6-3:
J -3:
4
5
6-J:
5
0
3 -2,=
-
1
2
3
0
1
2
3
9-3: 6
10 - 3 : 7
11-3: 8
l2-3: 9
6
7
8
9
11- 1:10
12-2,- l0
13
13 - 1 :
13
i4-3:11
12-1:11
4-4:
5-4:
6 - 4:
F1
A-
t-+-
12
0
I
2
a
J
8-4: 4
9 - 4: 5
10-4: 6
11-4: 7
L2-4:
13-4: 9
14 - 4: 10
B
15-4:11
16-4:12
-2:11
14-2:12
15 - 3
5-5: 0
6-5:
7 -5: 2
8-5: 3
9-5: 4
10-5: 5
11-5: 6
l2-5: V
13-5: 8
14-5: 9
:72
6- 6:
7 - 68- 6:
9- 6:
1
10- 611- 6:
12- 6:'
13- 6:
0
I
2
3
4,
5
6,
7'
t4- 5- I
6:
16 - 6: i0,
15-
15-5:10
L6-5:1i
17
-3:10
9,
17-5:11
18- 6:12
-5=12
I
r
ti
I
-',|:
8-7:
9-7:
I0-7:
It ^7 =
12-7:
7
F
r
!
Ir
!
tT
r
r
r
I
t
t
I
I
73
=',J:
I4-J:
15-7:
8-8: 0
9-8:
10-8: 2
11 - 8: 3
12-8: 4
0
1
1
2
3
4
13-8= 5
5
14-8: 6
15-8: 7
16'8: 8
17-8: 9
6
7
8
16-'7: 9
17 - 7: 10
18-8:10
19-8:11
20-8:12
18-7:11
19-7:L2
9
11- i1: 0
12- 11: 1
13- 11: 2
14- 11: 3
15- 11: 4
16- 11: 5
17- 11= 6
18- 11: 7
19- 11: I
20- 11: 9
0
2L
n0:
11- n0:
t2- 1fJ :
2
x.0:
J
10 -
13 -
1415 -
i61718 -
t920-
2rrra
LL-
0
1
1rJ :
10:
10:
10:
10:
10:
10:
L0:
10:
4
5
6
7
8
1
1 1
1
2
- 11:10
22- 11:11
23
- 7l:72
9- 0
10- 9,1
11- 9- 2
L2- 9: 3
13- 9-- 4
t4- 9- 5
15 - 9- 6
L6- 9: 7
t7- 9:
18- 9- I
9-
B
20-
9: 10
9: LL
12-
12:
19-
2I- 9:12
13-
72=
0
1
12: 2
tJ- 12: 3
16- 12: 4
17- 12: 5
t8 - 12: 6
19- 12: 7
20- 12: 8
2L- 12: 9
1,4
-
22- 12: I0
23- 12: 11
24- t2: 72
2 Bii,sit /tdditilom : rftea*lhina
TIU
12
T
IU
A>
,7
A
l- 6'
I
.d
/b\
r.)
t{Ed
,9
/W
R:emernber the l"ollowing Poirnts:
1. Use dividirag line brltwee,n tens and ranits"
21."
Pupil to say "stsrll witftlr unailts, s€art
(Freparriation for tallne away).
ona
top"'
7+5=='LA
3.
Priif 12 in thLc bubbl,rs for rlistribution"
Discuss an<X rreclisfi ilbute,,
e.jg. 2 units and L tr;:rru at the niglht hand slde
6 (subsr;rliPt).
t[. A;gain, hegrirn at top, line o.g. 2a-6+!=9
10
of
the
$ar&;1tqaELiog
E{effiff$utriisng
L' Always h*gfire
rnt
}il.assg
2
top line. A.lways begim 'rs'ith
narnits:
See exanffiple:
TU.
34 1L
-L 7
24
ll. Use T' araqf U
sy'nnholsi,
3" F,amlgaeag{i:" Us# tlake, aEso iieatnoduce
siubtra,et"
efl,.
rnairuaas ansd
Need for goodl usaderutaaadirng of plaae
flnequnrexatRy msimlg
v;BXele,
revise
eorrcrnrte martenials wtrlene pcrssilble.
tn$t En$ie ttf,rfi'xffit' as this arls&lteaets we
ilr*gixa at tBae foo{llq}m Eira'{,r assd Oauses eoaafuseoru"
*'
@ggfu1zu
EFo
(l}{reecil
for
eoaasirsteurcy}"
1T
Sulllirtractions
{Jse ?reras anrd Ultrilts
{Jse taFre or rmirnels (or sunbtna*t)
,X:
IilxanaBrle:
U,
{1
=Jl
ll. Gme take
seyem X tcsffitiilot do'
!1, So I[ regnruup flhre feuagt
i"e,
!1"
,4
I unai'f :
teras,
Noqy tr halire tlsrere
3 tflems, ltr umits.
amd ,eRevem umits,
tesa$l
TU
wnirfifeas a$r:
u4
1tr
a4t
-l.
4, F im,aliy
tr
setbrtriarct
tr uasits tmke 7
3 terns talqle X fem
/r
U
&'l
-17
,,2
4
*$B.eqffierlraben,i
Elo sqof ug*l t'fnor{ett as tleis asstnrmes
we helgisl srtt tlae hottonin lirne
caiut
sl
aued
es com llu sio rn. (I{eerrE co n'asiistrem cy).
L2
Third Closs
I
I
I
I
I
I
I
l
Subtroction Rong 3
The oim is to continue the progress mode in subtrqction into third class in
renoming for subtraction sums qnd then to continue with this method with them
up to Rong 6. Hence by the ?:OtB -?OI9 school yeor oll closses in the school will
be using this opprooch to subtroction sums.
Example
T U
nE ,2
1
I
_?
8
2
4
T
I
I
H
Exomple 2
1
r
I
I
I
t
I
H
Exomple 3
n
E
TU
34' '5
B
7
5
8
T
U
q'\g
7
5
4
5
I
T
13
b
'O
For the Exomple 3 sum the longuogewe cqn use is:
1. Zero units toke five units cannot do so renome the hundreds ond tens in
f
the toP line.
2. 5o I regroup the 500 qs 4 hundreds, ten tens qnd zaro units
3. Agoinzero units toke five units f connot do so renome the tens ond units
to nine tens ond ten units.
4. Now the top line of 500 is regrouped osr
4 hundreds, nine tens ond 10 units.
5. We are now oble to complete the sum:
Ten units toke five units leoves five units.
Nine tens take seven tens leaves two tens.
Four hundreds take zero hundredsleaves four hundreds'
Remember
t.
Alwoys begin ot the top line. Alwoys begin with units.
Z.
Languaget
lJsethe words toke ond olso the words minus ond subtroct.
3. you needo good understonding of
ploce volue and revise
it f requently using
concr et e moteriqls wher e poss ible'
4.
Do not use "from" os
couse confusion
this
qssumes we begin
L4
of the bottom line ond may
I
Multiplication Focts Rcng 3
I
- Rong 6
I
I
2xQ-0
2x1=2
2x2:=l
2x3=g
2x4=B
1x0-:'C)
1xl=1
1 rr 2 =
1rc3-3
1x4=4
1 x 5 =r5
1x6=6
1x7-7'
1xg=E
1xg=9
2l
I
I
I
2 x 5 ='10
2 x 6'=12
2x7:*'[4
2 x 8='16
?x9='18
1 N 10 = 10
2x10 = 20
I
I
4x
[=
5 x 4 =20
5 x 5 =25
5 x 6=30
5 x 7 = 35
5 x 8=40
5 x 9=45
4"x10,=40
6 x 5=30
6 x 6=3€i
6 x 7=42.
6 >r 8=48
6 x 9=54
6x 10=60
5:r 10 = 50
x 0 =0
V x 1 =7
7
*
0
5
5x2=10
5 x 3=15
x 4 '* 16
4.x 5==20
4 x 6;2r1
4 x 7*ZB
4'x B=32
4'x 9c36
6Ii J=6
6 x. 2= 12
6 x 3=1E
6 x 4=24
0=
5x1-
4.
0
3 x 10 = i30
5x
0
4.x 'l '= 4
4 x 2- I
4 x 3.=1?-
6r:
3 x Q= 0
3xf=3
3 x 2= 6
3 x l= g
3 x 4=12
3 x 5.= 15
3 x 6=18
3 x 7=21
3 x 8=24
3 x g=27
x 2=14
7x
'7 3=2'l
x 4=28
7 x 5=35
7 x 6=4i2
V
7 x 7,=t!g
7 x 8=56
7 x 9=6i3
7 >r 10 =7r0
15
8x0=0
8x1=8
8x2=16
Ex
Ex
Ex
Ex
3
=24
4 = 32
5=,40
6=,48
Ex7=56
E x 8=64
8 x 9 ='72
Bx10=E0
9x$=C)
10x
10x
10x
10x
10x
10x
10x
10x
9:x'l '=9
9x
2 -='lB
3==27
9;x
9 x 4-i]6
I x 5=45
I x 6=tll
9 x 7=S3
I x B=72
I x 9=B'l
0=
I = 1Cl
Ci
2=ZCl
3=30
4=44
5=50
6=60
'/=74
8=80
10x $=90
10 x
9x10={)0
10x 10 = 100
The Rang 3 Teachers Will Use The Following Mothemctical
Languoge Regording MultiPlicotion
l.
a.
groups of 2/3
et c .
f-count in
[rcount in
Groups of 2 and 3
(Children re ad from 1eft
2l
I
eLc.
3;J
--' right) (2 3s) is the same as (3 2s)
lntroduce sign for multiplication
-
2x3
2
groups
2 trmes
of
3
3
*
children learn to spell these words
2 multiply by 3
4'.]
:LJS
_
\\
Introduce the product of
Introduce commutative
tl
.
"
.: x
law
e3, l"x 3
t6
_ 3 x J.
Efie;m{;!qlxe }B
Ib€eeE€ii
.A Siut
He
ffii
t FtaNse 3
hlot;a whsre rilre "oi,ilrrying" tatrles plaee.
a-,
HxamPte
l:
Examphe 2:
17t
Division Focts Rang 3
I,
I
1!=
2
1
1!+ 1J+ 1oT' iJ+
a
U'
)+
+-
10
1:
I
3
4
4
12+3=
5
7A+2=
5
7
9
10
1:li
72+ l: 12
1l
1l r
4+,4:
8+4:
12+ 4:
16+ 4:
2A+4:
1
6+2:
E+2:
6
i-
.,
aJTJ_
1
6+3:
9+3:
3
t-
2+2:
- Rang 6
1
2
.tl
:1
:
')
2:
Itl,+)=
75+2:
18+2:
l',2
6
X8+3=
6
7
t\1
zi.
8
9
la
5+5:
1() +5=
15 + 5:
20+5:
25+5:
30+5:
3lj +5:
40+5:
45+5:
4
5
2A+2:70
2)+2=11
, a
3
tr5+3:
+
^,{
ztl=,/.-LL
-
2
1
2
,
I=J-
a
Fl
_
I
24+3:
itJ+j:
8
9
!I0+3:10
33 + 3:71
36+3:12
6+6:
1
, /
4
14
L
TL?O_ -
9
i8+6: 3
24+6: 4
30+6: 5
36+ 6: 6
42+ 6:.7
48+ 6: 8
54+ 6: 9
48+4:12
50+5-10
)3+):.!,I
6tCt +5:li2
60+ 6=10
66= 6=11
72+ 6:12
+7:1
8+8:1
3
4
5
24+4--
5
7
28+4:
32+ 4= I
36+4: I
40-4:10
44: ,1: 11
'/
14+7:2
+7 =
28:'J =
21
35-7:
42+7:
t[) +'J:
56:7 :
()3+7==
3
4
5
6
7
8
9
16+&=
4
5
6
7
8
2
24+8:3
32+8:4
40+8:5
48: 8: 6
56+E:7
64=8:8
72+8:9
80+8=i0
+ 7 ==70
'77 + 7 :LI
88:8:1i
84=7:I2
96 =
'30
3
8:72
18
9+9:
18+9:
27+9:
36+9:
t
?
3
tl
45+9='5
54+9: 6
63+9- 1
72+9:
81 +9: 9
B
90+9:1{l
99 + 9:11
108 + 9:Lil'
I
I
I
I
I
I
I
I
t
t
I
10+10:1
20+70- 2
33+11=3
4
44+
1I:
4
5i3
5
55+11:5
6
66+11=
6
+ i0:
6t0 + 10:
7,a ' 7o: 7
8t0+ 10: 8
90+10:9
100 + 10:10
110 + 10:11
120 + 70:12
1.I: i
BE+ 11: 8
99+ 11: 9
7'7
+
110+ li:10
721 + 1i :11
132 + Itr :12
We say:
1. Two divided by two is one
Four divided by two is two
Six divided by two is three
A lso
2. Two into two is one
I
I
A
I
2
3
Two into four is two
Two into six is lhree
I
22+ 1L:
1
+ 10:
4.0 + 10:
313
I
I
11+ 11=
lso
3. How rnany twos in two?
How many twos in four?
How many twos in six?
I
19
12+ 12: 1
24+ 12: 2
36+ 72: 3
48+12:4
60: 12: 5
72 +
84 +
7'2:
12:
96+ 12:
108 + 12=
6
il
8
Q
120 + 72 =70
132 + 12:11
744 + 12:12
Division Sums Rang 3
4
Exomple
+r-
1
2
[8-
Two into eight goes four times.
Exonple
2
2
l-g-
Eight divided by two is four
4
Example3
-.---.------.-T---
Exomple
--F-
4
B=2=4
8 -A
I
3,
4l g
Four into nine goes two times
remoind
Erqrnjlej 49
2
r 1'
er
one.
Nine divided by four is two
with o remcinder of one-
20
Fsurth Clcss
Leng Muliplicstion Rang 4 (2 digits x Z- digits)
1'- Leave a f ree row of boxes between the top ond bottom
num bers.
2. Emphosis on multiplicqfion x 10 by adding a zero ot the end of
line 2.
3. Agoin note where the "corrying', takes ploce.
4. Revision of ploce
volue.
Carrying for tens
3- 9
s-/
X 6u
4
+
5 5
2
g
qJ
7.''
I 3
(x7)
g
1
51
Exomple 4
Exomple 5
Z3S divided by 5 is 47
047 ->
7
235
zero in red
4 (3 digits + 1 dioit\
2'3'5
Example 2
Exomple 3
=-+ Pencil
4
(x6o)
->Put
-3 3
Division Rsng
Example
Carrying for units
5 into 235 is 47
=47
235=5=47
-+
uT - z5T divided by 7 is 36
0 3 6r5 withcremcinder of 5
| 2'5
w
O36r
5
->7
21
into
257 is 36 remaind
er 5
Fifth / Sixth Closses
J
I
I
I
I
I
|
I
|
Long Muttiplication Rong
1
5 (3 digits x 2 digits)
. Leavea
free row of boxes between the top
und bottom numbers.
2. Emphasis on multiplication x 10 by adding a zero,
,. Again note where "carryrng"
takes place.
4. Revision of place value.
Carrying for tBns
F'
5
X
4
,,
+
)
-
6u
Carrying for units
f.''
3
q
2 3 1
(x7) ---D Fencil
,
5 4
(x6o) ----+Put zero in red
4 0 5- 3
I'
22
Long Division Rong 5
/
Rong 6
Note thot we introduce the conc ept of long division vio exomple 1
below bef ore the pupils ore introducedto long division sums proper in
exomple 2. This qlso helps with their obility to estimate onswers
which will moke them o lot more proficient and occurote at long
division
Also note fhat sums with divisors from t - t2 ore short division sums
ond sums with divisors from 13 * ore long division sums.
Exomple: 744 = 72 = 12|. 144
-
012
Exomple 1 - Using Multiples of RePested Subtroction
i
l
520+23=?
I
I
(i .on
(c)
to.
I
Could I subtroct [orger groups of twentg-three-eoch time?
Wou[d mu[tiples of 10 groups of 23 be o better wcg?
How mong such groups could I subtroct?
Coul.d I then subtrcrct three groups of 23?
520
-2]9
- 230
<- (23 x 10)
60
-46
Another wcg to crsk
this question is
<- (23 x 10)
2q0
I
I subtracted 23 from 520
twentg-two times cnd
the remoincler is '14.
520+23=22R14
Check bg multiplging
+- (23 x 2)
22x23)+14=52A
14
I
.., I
C-
\)
Exomple 2
-
Long division Sum (3 digits = 2 digits)
7332 + 31
Moking on Estimste f irst
of the overoll onswer
is o good ideo.
1. Round both numbers off to thenearesf ten- fherefore:
7332
30
31
2. So our estimote
3Q
is:
borh by
1o
733 --L'?'t
. A^
T
3. R,emamber to proctice estimoting guickly or else it will be of
little
use.
0236
31)7332
_621
113 l___
-93+
I
Z r0r[__+
- L1 8r5
r- 16
Ans.
Rounding off to the nearest ten 110+ 3o:
1
113- 110- 11-a
x 3:93 (correct
3
Rounding off to the nearest ten 200-i
200
202
_
3i
30:6.
20
2
J
31 x 6:186 (con'ect)
-L
-u
:236 r. 1.6 (our estimate of 244 was accurate)
* Remember: 1. Pmt the zero in red.
2. Bring down th'e "3" in red (This avoids
confusion).
3. A-lso, bring th,e "2" down in red.
24
Addition ond Subtroction of Fractions Rang 5
/
6
1. 1,6-7
,
888
2. 7 2999
Remember
5
that you connot odd or subtrocf froctions
ore in the some denominotor.
2 i
3. --r-
3
35
10,9
15t- 15
4. 1_1
25
15
!_?_
3
10
10
10
5
t9
'.4
t;
s: +3*
6
+i- J2
=J(t-:)= Jt
7
6i. +';
Q+(i3. fr)
8.
rI
-2
5;_JE
115
<
.-
J lzo
8\
zol
'\(* -,il -):,
25
unless they
Time
Addition, Toke Awo)r Multiplicotion and Division Sums
f
Uoing the work in
the bubbles helps to ovoid "clutter" in the surns.
1. Add:
hrs. mins.
Jtz,4-32
- 39
7 - tt
2. Take Away:
3. Multiply:
h.s. mins.
7 - 0tt
3r --45
3-26
hrs.
4
+32
71 mins.
-
t hr,
11 mins.
50 + 11=71 mins.
6Yi
mins.
-35
Xr
3
13-45
4. Divide:
l@
Ve'
hrs. mins.
il+ -Azt I stai
1-27
26
]
l
Glossory
-e
Any number which is to be added;
A number is divisible by another
Fn
''b -/ - ) = /
(2 and 5 are the addends).
number if the second number is
factor of the first;
e.g. 6 is di'rrstble
!,,^,. ui
I
^i u.
addilio/'r
2.
combining; e-g.3
+
4
to largest
)ltLtt
co1+7=7+3ond4:<6=6x4
-b'-
I
U)
-^^
t] tu:c.
e.g.
J
=L)
sone result
to smallest.
dlfferel'ace
By how much a number is bigger or
smaller than another.
I
symbols 0
to
To multiply a sum bY a number is the
same as multiplying each addend by the
number and then adding the products;
,
11,
The result when two or more numbers
are multiplied;
e.g. t!1? pradtta af 2, -7 an,1 + is 24,
x l0
I
at"
'
3 x (4 + 2) = (3'x 4) +
3 x 6 = 12 + 6
18 =
Px
2)
28 s,eriale
i-
i
A number which
2. Difference (finding a difference)
3. Complementary addition (finding a
complement).
to be divided
sull
mulliplicallon
The result when two or more numbers
A mathematical operation;
,--7,,1-t)
v,K.
/ ,\ 4
ti
are added.
^''4
is
used in
three types of situations:
l. Take awaY
30,
l:
) L
-
t L
') L\ : ) Lt ! ) L| L] --
by
are added.
lA
ta
31,
19, nunrb'er
An indication of quantiry.
27
tOial
The result when cwo or more numbers
achieve the same result;
another number;
a/r
.-4-o ) I + ? l;5; linir^r'=ltll>Lt)
rn order.
A mathematical oPeration
-
dlvidend
lo'put
' suh1rac{i'on
ariihil']etia
Repeated addition can also be used to
18
arranged
in some order.
a9.
18,
se'qileilce
A set of numbers or obiects
Blocks used to give a concrete
representation of numbers, showing
the aspect of place value in base ten.
rc qig$-Puilve.JalY
a/'lir/7:.r\
- l+tJ a itJJ T \/ - -)
16 product
blocks)
Any one of the ten
(inclusive) used to write numbers.
9
in
=9A+il=\al
bflocfl<s (Ease Ten
dig'r
eg
e.3. +./ -:+
!nverse op,erati'on
t? m il.:ltibase
secono. third.
A method of simplifying a problem
order to calculate the solution;
Opposite operations; addition and
subtraction are inverse operations;
multiplication and division are inverse
operations; halving and doubling are
also inverse operations.
The arrangement of numbers from
fr:i
i5' paititiOning
I 0A0 00r)
= l0x l0x l0x l0x l0x lC
= 106 where 6 is the inCe:< or
= 6.) x lA x l0
= 6.2 x !03
t6,
desceardin€i ord'er
,
e,g.
e.g. 6200
Consecutive numbers follow in order
without interruption; e.g, I l, 12, 13.
largest
an ordered sequence;
exponeni ond IA is t'he bose.
T
nunrber
A number which indicates position in
numbers as products of repeated
factors;
the way change is Paid ofler o
I4-
to be divided into
A shortened way of writing large
consecutive
.e
addition, subtraction, multiplication and
division.
notation
15 in{dex
a set.
The method of 'subtracting'which
changes the subtraction to an addition;
,]
,1
I
another number;
e.g.2l + 3 (the divisor is 3),
r..--L
I
The four operations of arithmetic:
and division.
e.g. 7 - 3
operali0n
z3
r+. gldlnalis
lC
A symbol used to represent a number.
t[ divls,or
'Counting on' to a higher total;
I
'
= l?: 4 + 7 >
nilrnerai
ea
/t
A number which
The complement is the amount needed
7.
t/-
This is not the same for subtraction
gfues the
a
-uo ,i
- +7
5
com pilem,entrary ad'd ltio n
,l
r/-
Fq
uses
numbers and operation sYmbols;
Repeated subtraction can also be used
achieve the same result.
result;
PU t
jr.@
A mathematical sentence that
to
The order in which two numbers are
added or multiplied does not affect the
e.g.
o
2l + 7 = 3 is ihe inverse of
'
7 x 3 = 2l
e.g
coilnt?rLltatrive lalv
6.
2 becouse 2 is
The inverse operation of multiplication;
The arrangement of numbers from
to complete
a
l3 djvls:on-
ascendin'E order
smallest
b,v
' A line on which equally spaced points
i are marked. Points corresPond, in
order, to the integers.
JULLUT
A mathematical operation that involves
t.
ao,lnumber iine
la, dlvisible
add end
,-.__-.
,vhole nilrnber
The numbers 0,1,2,3,4,.. are called
whole numbers'
B.l"
This is a rule for performing
oPerations in" expressions
which have more than
one oPeration, to ensure
calculations are handled in
Bra.ckets (
lndex notatlon
IMu]Tlpllaation
the same way.
Division
rAd dition
I
Some calculators use an
'algebraic operating system'
(AOS).This is used to follow
the Rule of Order.
L
su btracti
o
)
23
x
+
+
A statement of
n
.
Note:
between two
e.g.3x
Multiplication and division are equally powerful oPerations,
completed left to right in order as they appear, as are
addition and subtraction.
equality
expressions;
symbols or pictures over
and over.
4= 6+ 6
e.g.3,4,3,4,3.'.
fradion is a number that describes part of a
group.
.,, numerator
A
,a"
4-{
-:-r4 <-
vinculum
.+__._
lI
denominaior
has a ...
denonnilnaior
is the number below the line, indicating how many
equal parts the whole number is divided into; and a ...
which
nurmerator
which is the number above the line, indicating how many of
l,i ptime nu4!el9
A prime number is a
number that can be divided
these parts are in consideration.
evenly by only
e.g. 2, 3,
o
, T'h'ere Are different trie,es
:-
...
l. proper ftactrons 3. mlxed nuHerals
A mixed nurneral .is both
A proper fraction
is a fraction where
a whole number and a
the value ofthe
numerator is
smaller" than the
proper fraction;
denom!nator;
I
e.g. 2
irnFr:oFer fractlonS
An improper fraclion
is a fl'action where
the numerator is
larger than the
factor.
?,
factorisalion
To represent a counting
number as the Product
of counting numbersl
24=4x5;8x3; l2x2;
24xl
To show 24 as a Product
A number that
of its prime factors, it
would look like this:
leaves
a remainder of I when
divided by 2.
5
=2x2x2x3
R
Y. multioles
i
24
ccmDosite numbers
are all equal to each
4
other. They are
by more than itself and
l;
equirralent fractio ns.
a
3
e.g"4,6,8,9,12 (i.e. not
.
I
e.g.
A composite number is a
number that can be divided
denominatorl .
AII numbers excePt
have more than one
12.
divisible by two.
value e.ren though the.
numerals are dlfierent;
8
of l2 are 1,7,3,4,5 and
nrime factors
Whole number exactly
Fract!ons that narne
the same numerical
t234
Ad 2 4 5
'
A prime factor is a Prime
number that will divide
evenly into a given number;
even numb,er
z
A factor of a number
is a number that will
divide evenlY into that
number; e.g. the factors.
5,7, I l, I 3 and I 7.
e.g.2,3 and 5 are prime
factors of 3 0.
f. equivalent fractions
I
oo
I
".g.
I and itself;
6 l3ctois
prime number).
A multiple of a
number is that number
multiplied bY other
whole numbers; e.g. the
multiples of 5 are 5, 10,
I 5,20,25 and so on.