calculation techniques in numbers

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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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+

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