calculation techniques in numbers
TRANSCRIPT
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13 April 2023 1
Calculation Techniques in Numbers
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7
MATHEMATICS
×+3 -
÷
5
8 =NUMBER AND
OPERATION
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hy it ishy it is
WWimportantimportant?
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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
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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 :
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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
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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
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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
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13 April 2023 174×
+
9- ÷
27
=
Let’s have fun with the number!
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6 + 7 =
6 + 4 + 3 = 13
1
6 + 6 + 1 = 13
2
BASIC FACT - ADDITION
Count on
3
ADDITION
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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
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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
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CUTTING SYSTEM
4379683765
+ 38
425321458
91457 + 700324
78563465938
1866399763
+ 103207
43
211 1
31331 2
ADDITION
033 183577 1811511
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GIMMICK NUMBERDo you want to know how to
SUBTRACT FASTER?
Let’s do it together…
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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
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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
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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
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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
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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
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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
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LATTICE MULTIPLICATION
4 6 ×
74
28
16
4
4
24
2
40
3
11
2D × 2D
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LATTICEMULTIPLICATION
3D × 2D
3 8 7 ×6
3
81
84 4
20
92
42
1
2
43 8 1
21
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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
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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
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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
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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
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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
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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
✕✓
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The value of tens digit is more than ones digit
Example:
=1 8++6 5 773 × 9 = +=9
✕✓
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Multiplication Finger for multiplication table 6, 7, 8, 9.
ASSUME THAT:
Little finger = 6
Ring finger = 7
Middle finger = 8
Pointer finger = 9
HOW ?
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ARITHMATICS WAY
1 5
+ 1 0
1 1 5
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ARITHMATICS WAY
4 9
3 5
4 2
+ 2 8
3 2 5 9 9
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ARITHMATICS WAY
3 6
1 6
2 7
+ 1 2
1 6 6 6
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ARITHMATICS WAY
3 6
4 8
1 8
0 6
0 8+ 0 3
6 1 7 6
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Can you remember ..?
Teachers
……. No problemPUPILS ?
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Can we find the product, if we only know timestable 2?
example: 8 x 7 @ 23 x 8 @ 19 x 23 @ 120 x 24
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RUSSIAN MULTIPLICATION
(÷2) (X2)39 57
19 114
9 228
4 456
2 912
1 1824
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DIVISION
Equal division
12 ÷ 3 =
Repeated subtraction
A B C
12- 3
9- 3
6- 3
3- 3
0
4
DIVISION
4
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2D ÷ 1D 3D ÷ 1D
111
7 21- 714
- 77
- 70
3 290
7 644-630
14-14
0
92
DIVISION
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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
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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
√
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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( )
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Question:
How to arrange the below symbols to form the correct mathematics sentence?
Answer
3 3 3 3 + - x = 103333 + _ x
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Fun & Easy
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FUN
CONVERT
Km
Kg
ℓ
m
g
mℓ
Question : Convert 8.03km to m / 8.03km = ________m
●
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FUN
CONVERT
Km
Kg
ℓ
m
g
mℓ
8 0 3
Question : Convert 8.03km to m / 8.03km = ________m
●
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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
●
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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
●
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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
●
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FUN
m
RM
cm
sen
4 7 5
Decimal point 1)475cm2)4m 75cm3)4.75m
1)RM4.752)475sen3)4.75m
●
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Any question?No
PPK KPM
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PPK KPM
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SEE YOU NEXT TIMESEE YOU NEXT TIME
Insyaallah ,
Thank YouTerima KasihSyukran