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13 April 2023 1
Calculation Techniques in Numbers
13 April 2023 2
7
MATHEMATICS
×+3 -
÷
5
8 =NUMBER AND
OPERATION
13 April 2023 3
13 April 2023 4
hy it ishy it is
WWimportantimportant?
13 April 2023 5
Analysis UPSR Mathematics Paper
Topic
Whole NumberOpr. + - × ÷Mixed OperationFractionsDecimalMoneyTimeLengthMassVolume of LiquidShape & SpaceAveragePercentageData HandlingTotal
The number of questions according to year.
2000
Paper
1 2 2 3 1 1 1 1 5 3 3 2 6 1 2 2 3 2 1 1 2 - 6 2 2 1 3 1 3 -40 20
2001
Paper
1 2 2 2 1 2 2 1 5 2 5 2 5 1 2 3 1 1 1 1 2 1 6 2 2 1 3 1 3 -40 20
2002
Paper
1 2 2 2 2 3 3 2 3 2 4 2 4 1 3 1 3 1 3 1 2 1 4 2 2 1 3 1 2 -40 20
2003
Paper
1 2 3 2 1 2 3 1 3 4 2 1 1 2 4 1 4 1 4 2 3 1 5 2 - 1 3 - 4 -40 20
2004
Paper
1 2 1 2 2 1 2 2 4 2 3 1 5 3 4 1 4 - 2 2 3 1 4 2 2 1 2 2 2 -40 20
2005
Paper
1 2 2 1 2 - 3 1 3 3 3 1 5 2 3 2 3 - 3 3 3 1 4 3 1 1 2 2 3 -40 20
2006
Paper
1 2 1 1 3 - 1 2 4 2 3 1 4 1 3 2 1 1 2 2 4 - 5 3 2 2 4 3 3 -40 20
13 April 2023 6
Example : 1 2 3 4 5 6 7
M T O
One million two hundred thirty-four thousand five hundred and sixty-seven.
1. Read numbers
Million Thousand Ordinary (1 digit) (3 Digits) (3 Digits)
NUMBER
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5 011 070Step 2 :
a) In words
Example : 3 2 0 9 6 4 0
M T O
Three million two hundrednine thousand six hundred
and forty.
2. Write numbers NUMBER
b) In numeral
Example : Five million eleven thousand
and seventy.
5 11 70M T O
Step 1 :
13 April 2023 8
a) Place value
3 2 0 9 6 4 0
MHTh
TThTh
OT
H
3. Value of Number NUMBER
b) Digit value
3 000 0000
90 000
4000
7
80050
3 0 9 4 8 5 7
13 April 2023 9
Partition the number
4. PARTITION
Example : 3 094 257
a) 3 000 000 + 90 000 + 4000 + 200 + 50 + 7
b) 7 + 50 + 200 + 4000 + 90 000 + 3 000 000
c) 4000 + 7 + 3 000 000 + 50 + 200 + 90 000
3 million + 9 ten thousand + 4 thousand
+ 2 hundred + 5 ten + 7 one
Write the number in extended notation
NUMBER
13 April 2023 10
5. Form the Number
94 5203
The biggest number
9 45 2 03 Write the biggest digit first.
The smallest number
4 52 0 93If there is the zero digit, put it after the first bigger numberthan Zero.
NUMBER
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6. Arrange the Number
Example : 4 567, 5 764, 7 546, 6 754
Ascending order
( 4 567, 5 764, 6 754 , 7 546 )
Descending order
( 7 546, 6 754, 5 764, 4 567 )
NUMBER
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7. Same Value
16 tens = 160 (ten has one zero)
Example :
121 hundreds = 12100 (hundred has two zeroes)
NUMBER
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8. Compare the Number
35 965 and 35 659Example :
35 965 > 35 659
More than
35 959 < 35 965
Less than
NUMBER
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Round off 23 654 to the nearest thousandsExample :
Step 1State the thousands place value 23 654
Step 323 654 is near to 24 000
24 000
NUMBER
Step 223 654 is near to 4000 or 3000 3 000
4 000
23 654
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Round off to the nearest hundreds
4 5 7 0 07 1
4 5 7 2 8 7 3 7 4 7 5 7 6 7 7 7 8 7 9
4 5 8 0 0
Near
NUMBER
Far
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Round off to the nearest ten thousands
1 3 5 0 0 0 05 1 5 2
5 3 5 4 5 5 5 6
1 3 5 7 4 9 25 8 5 9
1 3 6 0 0 0 0
Near
NUMBER
Far
13 April 2023 174×
+
9- ÷
27
=
Let’s have fun with the number!
13 April 2023 18
6 + 7 =
6 + 4 + 3 = 13
1
6 + 6 + 1 = 13
2
BASIC FACT - ADDITION
Count on
3
ADDITION
13 April 2023 19
56 + 79 =
3 56+ 79
15+ 12
135
ADDITION
2 120+ 15
135
50+ 70
6+ 9
120 +15135
56+ 79
11
83 64
+ 7916
226+ 21
129+ 683
10
812
12
+ 07
13 April 2023 20
4
4534 726
+ 838212
1364213
08
128+ 263
11
1069318
1234567890
12325+ 925647
03
391+
ADDITION
1512+
20170521
10+18
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1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11+ 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 210
Find the Pairs of Ten ADDITION
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2 356 709647 935768 171
1 452 355+ 84 953
3
2
2
2
1
3
0
3
1
3
3
2
5
ADDITIONFind the Pairs of Ten
13 April 2023 23
CUTTING SYSTEM
4379683765
+ 38
425321458
91457 + 700324
78563465938
1866399763
+ 103207
43
211 1
31331 2
ADDITION
033 183577 1811511
13 April 2023 24
GIMMICK NUMBERDo you want to know how to
SUBTRACT FASTER?
Let’s do it together…
13 April 2023 25
Cutting System
Ordinary way
3 4 - 1 8
2 6 3- 1 7 6
3 3 6 7 4 5 - 9 5 3 9 7
1 6
234
- 18
214
61 1
8 7
5
6
4 831
10
1010
2 3
101010
2 4
13 April 2023 26
Pairs of Ten
Ordinary way
34 - 18
1234- 786
12836 - 9628
1 00 2
234
- 18
214
SUBTRACTION
61
4
1
48
2
6
0823
13 April 2023 27
Less 1
Example : 1000 – 678 =
Ordinary way
1000- 678
322
10 - 1 = 9100 - 1 = 991000 - 1 = 999
1000 – 1 678 - 1
2
SUBTRACTION
999 - 677
23
13 April 2023 28
Ordinary way
27× 6
42 12
327× 4
2808
12
9374× 5
2035
15 45
2D × 1D 3D × 1D 4D × 1D
MULTIPLICATION27× 6162
+ 261 +
8 0 3 1 + 0 7 8 6 4
13 April 2023 29
9374× 5
12468× 4
123456× 7
4D × 1D 5D × 1D 6D × 1D
MULTIPLICATION
20 35
15 45 +
7 8 6 4
32 24
16 08
04
0 +
2 7 8 9 4
42 35 +
28 21
14 07
2 9 1 4 6 8
13 April 2023 30
2D × 2D
Ordinary way
68× 74 272
+ 476 5032
68× 74
Recreation
32
+
82× 88
7216
36× 34
1224
57× 53
3021
MULTIPLICATION
425624
2305
13 April 2023 31
LATTICE MULTIPLICATION
4 6 ×
74
28
16
4
4
24
2
40
3
11
2D × 2D
13 April 2023 32
LATTICEMULTIPLICATION
3D × 2D
3 8 7 ×6
3
81
84 4
20
92
42
1
2
43 8 1
21
13 April 2023 33
BASIC FACT – MULTIPLICATION ( 0 × 0 9 × 9)
Make the pupils understand that:1
Introduce that:2
a × b = b × a
Example : 2 × 3 = 3 × 24 × 5 = 5 × 4
? × 0 = 0? × 1 = the number itself
REY How To Teach Children Mathematics
MULTIPLICATION
13 April 2023 34
Train pupils to do ‘Skip Counting’3
Introduce the Repeated Addition4
2, 4, 6, 8, …………………….4, 8, 12, 16, ………………..7, 14, 21, 28, ………………
2 + 2 + 2 + 23 + 3 + 3 + 3 and etc.
Introduce the MultipurposeMultiplication Table*
MULTIPLICATION
13 April 2023 35
MMT (Multipurpose Multiplication Table)
1 2 3 4 5 6 7 8 9
2 4 6 8 10 12 14 16 18
3 6 9 12 15 18 21 24 27
4 8 12 16 20 24 28 32 36
5 10 15 20 25 30 35 40 45
6 12 18 24 30 36 42 48 54
7 14 21 28 35 42 49 56 63
8 16 24 32 40 48 56 64 72
9 18 27 36 45 54 63 72 81
MULTIPLICATION
13 April 2023 36
Train pupils with number patterns5
Times 6, 7, 8 DIFFICULT ?Use multiplication table that pupils know.
6
0, 4, 8, __, 16, __, ………………………24, 28, __, __, 40, 44, ………………..
Example : 8 × 7
( 8 × 5) + ( 8 × 2 )
MULTIPLICATION
40 + 16 = 56
13 April 2023 37
FINGER MULTIPLICATION – TIMES 9
Example: 4 x 9 = Bend the fourth finger on your left hand. So,
the three fingers on the left from the bent finger and the six fingers on the right give the answer, that is 36.
LET’S TRY: 7x9 6x9 3x9
2x9 8x9 5x9
13 April 2023 38
2D X 9Multiplication of two digits number
to number 9 can be done with fingers, BUT the value of tens digit
must less than ones digit.
HOW ?
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The value of tens digit must be less than ones digit
Example:
36 × 9 = =9++ ✓3 2 4
✕
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The value of tens digit equals to ones digit
Example:
=1 8++6 9 377 × 9 = +=9
✕✓
13 April 2023 41
The value of tens digit is more than ones digit
Example:
=1 8++6 5 773 × 9 = +=9
✕✓
13 April 2023 42
Multiplication Finger for multiplication table 6, 7, 8, 9.
ASSUME THAT:
Little finger = 6
Ring finger = 7
Middle finger = 8
Pointer finger = 9
HOW ?
13 April 2023 43
ARITHMATICS WAY
1 5
+ 1 0
1 1 5
13 April 2023 44
ARITHMATICS WAY
4 9
3 5
4 2
+ 2 8
3 2 5 9 9
13 April 2023 45
ARITHMATICS WAY
3 6
1 6
2 7
+ 1 2
1 6 6 6
13 April 2023 46
ARITHMATICS WAY
3 6
4 8
1 8
0 6
0 8+ 0 3
6 1 7 6
13 April 2023 47
Can you remember ..?
Teachers
……. No problemPUPILS ?
13 April 2023 48
Can we find the product, if we only know timestable 2?
example: 8 x 7 @ 23 x 8 @ 19 x 23 @ 120 x 24
13 April 2023 49
RUSSIAN MULTIPLICATION
(÷2) (X2)39 57
19 114
9 228
4 456
2 912
1 1824
13 April 2023 50
DIVISION
Equal division
12 ÷ 3 =
Repeated subtraction
A B C
12- 3
9- 3
6- 3
3- 3
0
4
DIVISION
4
13 April 2023 51
2D ÷ 1D 3D ÷ 1D
111
7 21- 714
- 77
- 70
3 290
7 644-630
14-14
0
92
DIVISION
13 April 2023 52
Division of 2D
Example: 4397 ÷ 24 =
24 4397 - 24
199 - 192
77- 72
5
÷ 24
DIVISION
224681012141618
448
12162024283236
2424487296
120144168192216
123456789
1 8 3
13 April 2023 53
OBJECTIVE QUESTION
24
8 × 3
12 × 2
4 × 6
Example : 502 584 ÷ 24 = A 2941B 20941C 20940D 29410
Answer without remainder
DIVISION
1256464 502584
-4 10 - 8
22 -20
25 -24
18 -16
24-24
0
209416 125646
-12 56
-54 24
-24 6
-60
√
13 April 2023 54
S A M D O B
REMEMBER!
BASIC RULES
The solution must follow the basic counting/sequence.
of×
Divide÷
Muptiply×
Add+
Subtract-
1 2 3 4
COUNTING
3
4
Is a family
Is another family
Solution: Must follow the rules.
MIXED OPERATION
Bracket( )
13 April 2023 55
Question:
How to arrange the below symbols to form the correct mathematics sentence?
Answer
3 3 3 3 + - x = 103333 + _ x
13 April 2023 56
Fun & Easy
13 April 2023 57
FUN
CONVERT
Km
Kg
ℓ
m
g
mℓ
Question : Convert 8.03km to m / 8.03km = ________m
●
13 April 2023 58
FUN
CONVERT
Km
Kg
ℓ
m
g
mℓ
8 0 3
Question : Convert 8.03km to m / 8.03km = ________m
●
13 April 2023 59
FUN
CONVERT
Km
Kg
ℓ
m
g
mℓ
8 0 3
1)8030m2)8.030km3)8km 030m
Question : Convert 8.03km to m / 8.03km = ________m
0
●
13 April 2023 60
Km
Kg
ℓ
m
g
mℓ
2 4 2 5
4 6 3 1
7 0 5 6
ADDITION
1
+
FUN
1)7056g2)7.056kg3)7kg 56g
●
13 April 2023 61
Km
Kg
ℓ
m
g
mℓ
7 2 1 9
5 1 3 6
2 0 8 3
101
-
SUBTRACTIONFUN
1)2083m2)2.083km3)2km 83m
●
13 April 2023 62
FUN
m
RM
cm
sen
4 7 5
Decimal point 1)475cm2)4m 75cm3)4.75m
1)RM4.752)475sen3)4.75m
●
13 April 2023 63
13 April 2023 64
Any question?No
PPK KPM
13 April 2023 65
PPK KPM
13 April 2023 66
SEE YOU NEXT TIMESEE YOU NEXT TIME
Insyaallah ,
Thank YouTerima KasihSyukran
