Smart PBD Mathematics Yr4_Anyflip

PENERBIT ILMU
BAKTI SDN. BHD.

Express Notes Unit Learning Area: Numbers and Operations QR Code on the first
page of each unit
Express Notes 1 Numbers and Operations contains digital files and
for quick Digital File e-RPH
revision Unit 1

Express Notes

1 The numbers 0, 1, 2, 3, 4, 5, … are 6 Even numbers are the numbers that
known as whole numbers. can be divided by 2, while the odd
numbers are the numbers that cannot
2 Whole numbers are read starting from be divided by 2.
the largest place value, that is, from
left to right. EXAMPLE
Even numbers: 2, 14, 16, 28, 30
EXAMPLE Odd numbers: 3, 15, 17, 39, 41
The number 36 452 can be read as
'thirty-six thousand four hundred and 7 Estimating a quantity of objects is
fifty-two. stating a reasonable quantity based
on a given reference quantity.
3 Each digit in a whole number has a
certain place value and digit value. EXAMPLE
BAKTI SDN. BHD.
EXAMPLE 50 ?
The table below shows the place value Given: Estimation:
of each digit in the number 83 475: 50 marbles 100 marbles

Ten Thousands Hundreds Tens Ones
thousands
8 A whole number can be rounded off
8 3 4 75 to a certain place value based on the
following steps:
The place value of digit 8 is ten (a) identify the digit of the place value
thousands and the digit value of 8 is to be rounded off,
80 000. (b) look at the digit on its right,
(c) if the digit is less than 5, maintain
4 A number can be partitioned according the digit to be rounded off,
to its place value and digit value. (d) if the digit is 5 or more than 5, add
1 to the digit to be rounded off,
EXAMPLE (e) replace all the digits on the right
Partition according to place value with 0.
83 475 = 8 ten thousands +
EXAMPLE
3 thousands + 4 hundreds Round off 72 631 to the nearest
+ 7 tens + 5 ones thousand.
Partition according to digit value
83 475 = 80 000 + 3 000 + 400 + 70 Thousands place
+5
72 631 73 000 Replace all
5 Whole numbers can be arranged in the digits
ascending order (starting from the +1 after 2 with
smallest number to the largest number) zeros
or in descending order (starting from The digit on the right is
the largest number to the smallest more than 5. So, add
number). 1 to the digit at the
'thousands' place

1

ILMU Date: Content Standard is tagged
DSKP Practice Name: Class: Textbook Pages: 1 – 3 based on the subtopic in the
textbook
DSKP Practices 1.1 Number Value
Read and circle the correct number. L.S 1.1.1 (i) PL1 50 250 50 205
Thumb Index to ease
searching of specific EXAMPLE
components in the
book Fifty thousand two hundred and five

1 Eighty-two thousand and seventy-nine 82 079 80 279
Name:
Class: Date: Textbook Pages
tagging as a
1.6 Basic70O0p0e2rations7w2i0th0i0n 100 000 Textbook Pages: 18 – 21 cross reference
Add. L.S 1.6.1 PL3 of the topic in the
2 Seventy thousand and two textbook

PENERBIT EXAMPLE 34 560 1 5 710 + 63 409 + 9 536 Example is
3 Thirty-four thousand five hundred and sixty 35 460 = 78 655 given as a guide
to answering
27 917 + 3 065 + 32 115 = 63 097 questions

11 91161 7158 11 1
61 158 63 409
4 Sixteen thousand one hundred and fifty-eight 27
5 710
32 115
+ 9 536
+ 3 065
Say and match the pairs of numbers correctNlya.mLe.:S 1.1.1 (ii) PL1 6 C3las0s:9 7 Date: 78 655

1.4 Round off Numbers Textbook Pages: 15 – 17

5 20 060Round off the following numbers toT:wLe.Snt1y.4.1thoPuLs3and and six 3 17 438 + 32 + 327 + 42 670
2 41 + 34 892 + 10 201 + 13 554

6 20 006 Number Nearest ten Sixty thhN=oueunasdra5ree8nsddt68th8ree hutnhNdoeruaesrdaensatdnd Ntehaoruessatntden= 60 467
twenty-six 40 000
1 44 789 11 11 1 1
7 63 326
44 790 44 800 34 42850901200 17 438
10 42 670

Twenty thousand and 1si3xty5 5 4 327
+ 7040100
2 70 468 70 470 70 500 58 688 70 000 + 32
8 60 326 3 29 107 29 110 30 000 60 467
Sixty-three thousand three hundred

and twe2n9ty1-0s0ix 29 000

Write the following4 num5b6er0s0i5n numerals5o6r 0w1o0rds. L.S 1.1.1 5(ii6i) 0P0L01 56 000 60 000

Solve. L.S 1.6.1 PL3 40 000

9 12 908 5 35 6T7w0elve thousa3n5d6n7i0ne hund4red 3a5nd70e0ight 36 000 5 11 1 1 6
+
1 11 71 142 11 1
60 10000 1 2 7 15 612
PdPc 6 60 365 50 899 + 8 859
Tutorial 60 370 60 +400 3 5 2 1 60 000 80 09000 1 2 8 56 009
Video
10 43 110 Forty-three thousand one hundred and5te4n 4 2 0 7 508

7 83 486 83 490 83 500 83 000 79 129

11 66 748 Sixty-six thousand seven hundred and forty-eight
Write five numbers which become 90 000 when rounded off to the nearest ten thousand.

L.S 1.4.1 PL3

8 3 (a)7 8 i -THINK 9
+
85 500 1 12 2B51ubbl7e2 M72ap8 11 1 2
41 302
66 087 34 608
14 577 735

(e) + (b1)9 469 11 329
80 683 + 87 4 163

94 000 86 100 67 636 50 835

(d) (c) 12
92 400 90 000
Any number from 85 000 to
94 999 is a correct answer.

PdPc Tutorial Video Learning Standard (LS) dan
Scan the QR code or visit https://youtu.be/OjFC0AaBLdM to watch a tutorial Performance Level (PL) are
video on rounding numbers to the nearest thousand and ten thousand. tagged for related practices

For educational purpose only

10

P1

Day: Day: DaDtae:te:

PdPc Pembelajaran
Abad ke-21 Activities

Activity 1 Puzzle it Out

Unit 1 Numbers and Operations
Materials: Number cards, pencils and papers.
Steps:

1 Pupils are divided into groups of four.
2 Each group is given five different one-digit number cards and a piece of paper.

EXAMPLE

58013
PENERBIT ILMU
BAKTI SDN. BHD.
3 Each group is required to construct as many five-digit numbers as possible and write those
numbers on paper.

EXAMPLE

(a) 50 813
(b) 51 803
(c) 53 801
(d) 58 013
4 Each group presents the numbers in front of the teacher and other group members.

Activity 2 Gallery Walk

Unit 1 Numbers and Operations
Materials: Binary codes, pencils and papers.
Steps:

1 Pupils are divided into groups of four.
2 Teacher gives a binary code representing the digits 0 to 9 to each group.

EXAMPLE

05

16
27
38
49

P6

Mathematics Year 4 KSSR Class:

Pupil's Name:
Teacher's Name:

Content Standard Learning Standard Page Performance Performance
LEARNING AREA: NUMBERS AND OPERATIONS Level ( ) Achieved
Unit 1 Numbers and Operations ( ) Not Achieved
1.1 Number Value PENERBIT ILMU
BAKTI SDN. BHD.1.1.1 (i), (ii), (iii) 3 1
1.2 Odd Numbers and Even Numbers 1.1.2 (i) 4 2
1.3 Estimate 1.1.2 (ii) 5 2
1.4 Round off Numbers 1.1.2 (iii) 6 2
1.5 Number Patterns 1.1.2 (iv) 7 2
1.6 Basic Operations within 100 000 1.1.2 (v) 7 2
1.2.1 8 2
1.7 Mixed Operations 1.2.2 8 2
1.8 Usage of Unknown 1.3.1 9 3
1.9 Problem Solving 1.4.1 10 3
Unit 2 Fractions, Decimals and Percentages 1.5.1 11 2
2.1 Fractions 1.5.2 11 2
1.6.1 12 – 13 3
1.6.2 14 3
1.6.3 15 3
1.6.4 16 – 18 3
1.6.5 19 – 21 3
1.7.1 22 3
1.7.2 23 3
1.8.1 24 3
1.8.2 24 3
1.9.1 25 – 29 4
1.9.2 30 4

2.1.1 37 2
2.1.2 38 3

P13

Contents

Unit Numbers and Operations Tutorial Quiz Extra
Video Practice
1
Express Notes 1
DSKP Practice 3
Summative Practice 1 31

Unit Fractions, Decimals and Percentages Tutorial Quiz Extra 35
Video Practice 37
2 Express Notes 49
PENERBIT ILMUDSKP Practice
BAKTI SDN. BHD.Summative Practice 2 52
53
Unit Money Quiz Extra 64
Practice
3 67
Express Notes 68
DSKP Practice 76
Summative Practice 3
79
Unit Time Tutorial Website Quiz Extra 80
Video Practice 89
4
Express Notes 92
DSKP Practice 93
Summative Practice 4 99

Unit Length, Mass and Volume of Liquid Quiz Extra 101
Practice 102
5 109
Express Notes
DSKP Practice 112
Summative Practice 5 113
118
Unit Space Tutorial Quiz Extra 121
Video Practice
6 Scan the
Express Notes QR code to
DSKP Practice download the
Summative Practice 6
Teacher’s
Unit Coordinates, Ratio and Proportion Tutorial Quiz Extra Resource
Video Practice
7 P1
Express Notes P6
DSKP Practice P13
Summative Practice 7 P16

Unit Data Handling Tutorial PIB PAK-21 Extra
Video Activity Practice
8
Express Notes
DSKP Practice
Summative Practice 8

Ujian Akhir Sesi Akademik

e-Questions

Scan the QR code to download

• Pupil's Performance Record
• Answers

User Guide
Pembelajaran Abad ke-21 Activities
Pupil's Performance Record
Instrumen Penjaminan Kualiti (Pemantauan)

Unit Learning Area: Numbers and Operations

1 Numbers and Operations
Digital File
Unit 1

Express Notes

1 The numbers 0, 1, 2, 3, 4, 5, … are 6 Even numbers are the numbers that
known as whole numbers. can be divided by 2, while the odd
numbers are the numbers that cannot
2 Whole numbers are read starting from be divided by 2.
the largest place value, that is, from
left to right. EXAMPLE
Even numbers: 2, 14, 16, 28, 30
EXAMPLE Odd numbers: 3, 15, 17, 39, 41
The number 36 452 can be read as
'thirty-six thousand four hundred and 7 Estimating a quantity of objects is
fifty-two. stating a reasonable quantity based
on a given reference quantity.
3 Each digit in a whole number has a
certain place value and digit value. EXAMPLE

EXAMPLE
The table below shows the place value
of each digit in the number 83 475:
PENERBIT ILMU 50 ?
Ten BAKTI SDN. BHD.Thousands HundredsTensOnesGiven: Estimation:
thousands 50 marbles 100 marbles

8 3 4 75 8 A whole number can be rounded off
to a certain place value based on the
The place value of digit 8 is ten following steps:
thousands and the digit value of 8 is (a) identify the digit of the place value
80 000. to be rounded off,
(b) look at the digit on its right,
4 A number can be partitioned according (c) if the digit is less than 5, maintain
to its place value and digit value. the digit to be rounded off,
(d) if the digit is 5 or more than 5, add
EXAMPLE 1 to the digit to be rounded off,
Partition according to place value (e) replace all the digits on the right
83 475 = 8 ten thousands + with 0.

3 thousands + 4 hundreds EXAMPLE
+ 7 tens + 5 ones Round off 72 631 to the nearest
Partition according to digit value thousand.
83 475 = 80 000 + 3 000 + 400 + 70
+5 Thousands place

5 Whole numbers can be arranged in 72 631 73 000 Replace all
ascending order (starting from the the digits
smallest number to the largest number) +1 after 2 with
or in descending order (starting from zeros
the largest number to the smallest The digit on the right is
number). more than 5. So, add
1 to the digit at the
'thousands' place

1

Name: Class: Date:

1.1 Number Value Textbook Pages: 6 – 8
Arrange the numbers in ascending order. L.S 1.1.2 (iv) PL2
15 750
1 15 350, 15 630, 15 230, 15 520, 15 750
72 585
15 230 15 350 15 520 15 630

2 72 585, 72 535, 72 515, 72 545, 72 565

72 515 72 535 72 545 72 565
PENERBIT ILMU
BAKTI SDN. BHD.3 35 564, 42 473, 33 382, 41 210, 37 456

33 382 35 564 37 456 41 210 42 473

Arrange the numbers in descending order. L.S 1.1.2 (iv) PL2 PdPc
4 21 320, 21 032, 21 023, 21 230, 21 302

21 320 21 302 21 230 21 032 21 023 Tutorial

Video

5 53 240, 53 452, 53 144, 53 640, 53 762

53 762 53 640 53 452 53 240 53 144

6 80 120, 70 450, 70 504, 80 210, 80 450

80 450 80 210 80 120 70 504 70 450

Complete the following number sequences. L.S 1.1.2 (v) PL2

7 18 125 19 400 20 543 21 621 22 156

8 32 681 32 870 36 347 36 748 37 657

9 52 416 52 345 52 246 52 107 52 049

10 99 874 98 745 98 245 97 321 97 210

(Accept any reasonable answers.)

PdPc Tutorial Video

Scan the QR code or visit shorturl.at/dgnuQ to watch a tutorial
video on arranging numbers in ascending and descending order.

For educational purpose only

7

Name: Class: Date:

1.4 Round off Numbers Textbook Pages: 15 – 17
Round off the following numbers to: L.S 1.4.1 PL3

Number Nearest ten Nearest Nearest Nearest ten
hundred thousand thousand
40 000
1 44 789 44 790 44 800 45 000 70 000
70 000 30 000
2 70 468 70 470 70 500 29 000 60 000
56 000 40 000
3 29 107Tutorial 29 110 29 100 36 000 60 000
60 000 80 000
4 56 005Video 56 010 56 000 83 000

5PENERBIT ILMU35 67035 670 35 700
PdPc 6 BAKTI SDN. BHD.60 36560 37060 400

7 83 486 83 490 83 500

Write five numbers which become 90 000 when rounded off to the nearest ten thousand.

L.S 1.4.1 PL3

8 (a) i -THINK

Bubble Map

85 500

(e) (b)

94 000 86 100

(d) (c) Any number from 85 000 to
92 400 90 000 94 999 is a correct answer.

PdPc Tutorial Video

Scan the QR code or visit https://youtu.be/OjFC0AaBLdM to watch a tutorial
video on rounding numbers to the nearest thousand and ten thousand.

For educational purpose only

10

Name: Class: Date:

1.6 Basic Operations within 100 000 Textbook Pages: 30 – 36
Complete the following cross-number puzzle. L.S 1.6.4 PL3

11 2
34600 4

51

2
6 88000
PENERBIT ILMU
BAKTI SDN. BHD.8 0 7
1
35 4
4030 100

73 1 6

66
0 1 2 46620

5 3
19145

3 6 8

7
1836

Across Down
1 6 568 × 10 =
1 346 × 100 = 2 41 × 1 thousand =
2 88 × 1 000 = 3 × 100 = 47 000
3 × 10 = 40 300 4 1 432 × 8 =
4 × 580 = 58 000 5 77 × 43 =
5 2 735 × 7 = 6 89 × 24 =
6 1 295 × 36 = 7 Find the product of 594 and 27.
7 Multiply 27 by 68.
18

Name: Class: Date:

1

1 Diagram 1 shows a spike abacus that represents a number.

PENERBIT ILMUTen thousands Thousands HundredsTens Ones
BAKTI SDN. BHD.
Diagram 1

(a) Write the number in numerals and words.
35 419. [ 1 mark]
Thirty-five thousand four hundred and nineteen. [ 1 mark]

[2 marks] PL1

(b) Partition the number in 1(a) according to digit value.
30 000 + 5 000 + 400 + 10 + 9

[1 mark] PL2

2 There are five lorries carrying some watermelons from Kangar to Ipoh. Each lorry
can carry 100 baskets of watermelons. There are 25 watermelons in each basket.
(a) How many baskets of watermelons are carried altogether?

100 ϫ 5 = 500 baskets

[1 mark] PL3

(b) Find the total number of watermelons carried by all the lorries.

Total number of watermelons

= 25 ϫ 500 [1 mark]

= 12 500 [1 mark]

[2 marks] PL3

(c) The watermelons are divided equally among four wholesalers.
How many watermelons are received by each wholesaler?

Number of watermelons

= 12 500 ÷ 4 [1 mark]

= 3 125 [1 mark]

[2 marks] PL3
31

Unit Learning Area: Numbers and Operations Digital File
Unit 2
2 Fractions, Decimals and
Percentages

Express Notes

1 An improper fraction is a fraction where 5 Before adding or subtracting two or
the denominator is smaller than the more fractions, make sure that the
numerator.
denominators of the fractions are the
same.
PENERBIT ILMUEXAMPLE 4
BAKTI SDN. BHD.3Numerator EXAMPLES
Denominator
2 5 2ϫ3 5
2 A mixed number is a combination of a (a) 3 + 9 = 3ϫ3 + 9
whole number and a proper fraction.
= 6 + 5
9 9
EXAMPLE 11
2 Proper fraction = 9
Whole number 3
6 = 1 2
9

3 A fraction that is larger than 1 can (b) 7 – 1 = 7 – 1ϫ2
be written as a mixed number or an 8 4 8 4ϫ2
improper fraction. 7 2
= 8 – 8
EXAMPLE
5
1 11 1 = 8
2 22 2
1 2 3 1
5 10 2
1 3 (c) + –
2 2
1 Improper fraction = 2ϫ2 + 3 – 1ϫ5
5ϫ2 10 2ϫ5
Mixed number

4 An improper fraction can be converted = 4+3–5
to a mixed number and vice versa. 10
2
EXAMPLES = 10

(a) 9 = 2 1 2 Whole = 1
4 4 49 number 5

Denominator –8 Numerator 6 A fraction of a quantity is determined
1 by multiplying the fraction by the whole
quantity to give the required quantity.
2
(b) 3 5 = 17 EXAMPLE
5
3 of 20 pens = 15 pens
3 2 = (3 ϫ 5) + 2 4
5 5 3
17 4 ϫ 250 =3ϫ5
= 5 = 15
1

35

Name: Class: Date:

4 Table 1 shows the quiz marks obtained by four pupils that are divided into two groups.

Group Pupils Marks
A Lim 88.654
Sue 90.35
B 89.339
Joseph 91.53
Rani PdPc

Table 1 Extra
PENERBIT ILMU
BAKTI SDN. BHD. Practice

(a) Calculate the total marks obtained by group A. PdPc

Total Quiz
= 88.654 + 90.35
= 179.004

[1 mark] PL3
(b) What is the difference in marks obtained by group A and group B?

Total marks of group B

= 89.339 + 91.53

= 180.869 [1 mark]

Difference

= 180.869 – 179.004 [1 mark]

= 1.865 [1 mark]

[3 marks] PL4

Extra Quiz
Practice

51

Unit Learning Area: Numbers and Operations Digital File
Unit 3
3 Money

Express Notes

1 The calculations of addition, subtraction, 4 Budget planning can help us to manage
multiplication and division involving our money well and to achieve our
short-term goals. For example, we may
money are similar to the basic want to save up to buy a watch.
operations involving decimals.
PENERBIT ILMU
BAKTI SDN. BHD.2 The calcualtion involving mixed5 Every country has its own currency.
operations are carried out starting from
left to right. 6 The table below shows the currencies
of several major countries.
EXAMPLES
(a) RM5 563.70 + RM3 842.20 Country Currency
China Renminbi
= RM9 405.90 Australia
United States of Dollar
11 America
Canada Dollar
RM 5 5 6 3 . 7 0 France
+ RM 3 8 4 2 . 2 0 Russia Dollar
Japan Euro
RM 9 4 0 5 . 9 0 Bangladesh Ruble
India Yen
(b) RM432.50 ϫ 28 Saudi Arabia Taka
= RM12 110 Great Britain Rupee
South Korea Riyal
RM 1 2 decimal Pound Sterling
ϫ 2 24 places Won
2 decimal
432.50 places
28

11

3460 00
+ 8650 00

RM12110 .00

3 A budget is the estimation of income
and expenditure for a certain period.

7 Besides cash, other payment instruments include cheque, credit card, prepaid card,
debit card, internet banking, postal order and e-wallet.

EXAMPLE

SPECIMEN

Cash Debit card Credit card Prepaid card Cheque

52

Unit Learning Area: Measurement and Geometry Digital File
Unit 4
4 Time

Express Notes 5 Conversion of units of time:

1 Time can be stated in two systems, ϫ 24 ϫ7
12-hour system and 24-hour system.
PENERBIT ILMU
BAKTI SDN. BHD.2 The relationship between the 12-hour Day Hour Week Day
system and the 24-hour sytem is shown
by a time-loop below. ÷ 24 ϫ 12 ÷7

Year Month

5:00 a.m. 6:00 a.m. 7:00 a.m. ϫ 10 ÷ 12 ϫ 100

4:00 a.m. 8:00 a.m. Decade Year Century Year

3:00 a.m. 0400 0500 0600 0700 0800 9:00 a.m. ÷ 10 ÷ 100
2:00 a.m. 0300 0900 10:00 a.m.

1:00 a.m. 0200 midnight 1000 11:00 a.m. 6 Basic operations involving units of time:
0100 1100 11:59 a.m.
12:01 a.m. 00000010 12:00 EXAMPLES
12:00 2359 noon 11125090 12:01 p.m.
2300 1201
11:59 p.m. 1300 1:00 p.m.

11:00 p.m. 2200 1400

10:00 p.m. 2100 1500 2:00 p.m. (a) 5 days 9 hours + 2 days 17 hours

9:00 p.m. 2000 1900 1800 1700 1600 3:00 p.m. =

8:00 p.m. 4:00 p.m. Days Hours
7:00 p.m. 6:00 p.m. 5:00 p.m. 5 19
17
3 When converting a time between +2
1:00 p.m. and 11:59 p.m. from the
12-hour system to the 24-hour system, 7 26
add 12 hours to the hour digits.
+1 –24
EXAMPLE
82
Convert 4:20 p.m. to the 24-hour
system. (b) 5 weeks 4 days – 1 week 5 days
=
420
+ 1 200 Weeks Days
54 4 11
1 6 2 0 o 1620 hours 5
–1
6
3

4 When converting a time between 1300 (c) 3 ϫ 7 years 6 months =
hours and 2359 hours from the 24-hour
system to the 12-hour system, subtract Years Months
12 hours from the hour digits. 7 6
3
EXAMPLE ϫ
21 18
Convert 2110 hours to the 12-hour
system. +1 –1 2

1 11 22 6

2 110
– 1 200

9 1 0 o 9:10 p.m.

67

Name: Class: Date:

(d) 27 centuries 12 years ÷ 4 = PdPc Tutorial Video

6 centuries 7 8 years Scan the QR or visit https://youtu.
be/02w1yI9y8dY to watch a tutorial video
4 2 7 centuries 1 2 years solving problems involving time
in daily situations involving
– 24 +300 addition and subtraction.

3 312 UFonrtuekdtuucjuaationnpaelmpubreplaojsaeraonnly

–28

32

–32

0

PENERBIT ILMUDSKP Practice
BAKTI SDN. BHD.
4.1 12-Hour System and 24-Hour System Textbook Pages: 139 – 142

Convert the following time to the 12-hour system or 24-hour system. L.S 4.1.1 PL1

PdPc

Tutorial 12-hour system 24-hour system

Video 10: 30 a.m.
1 12: 01 a.m. 1030 hours
PdPc 2 0001 hours
Website
3 3:25 p.m. 1525 hours

4 8:55 p.m. 2055 hours

5 7:50 a.m. 0750 hours

6 4:40 a.m. 0440 hours

7 11:20 p.m. 2320 hours

8 5:10 p.m. 1710 hours

9 10:45 p.m. 2245 hours

10 11: 15 a.m. 1115 hours

PdPc Website
Scan the QR code or visit https://www.freecodecamp.org/news/mathematics-
converting-am-pm-to-24-hour-clock/ for additional notes converting time
from the12-hour system to the 24-hour system and vice versa.

For educational purpose only

68

Unit Learning Area: Measurement and Geometry Digital File
Unit 5
5 Length, Mass and
Volume of Liquid

Express Notes

1 The lengths of small and short objects, 6 Relationship between units of volume
such as the length of a needle or the of liquid:
thickness of a book, can be measured
in the unit millimetre (mm). ϫ 1 000

EXAMPLE

Length of safety pin
= 25 mm
PENERBIT ILMU litre (ᐉ) millilitre (mᐉ)
BAKTI SDN. BHD.
÷ 1 000

mm 7 For mixed operations involving
0 10 20 30 40 50 60 addition and subtraction of mass, or
multiplication and division of mass,
2 The lengths of the distance that are calculate from left to right.
far apart such as the distance between
two cities can be measured in the unit EXAMPLE
kilometre (km). 3 kg 960 g + 4 kg 150 g – 2 kg 520 g

3 Relationship between units of length: = 5 kg 590 g

ϫ 1 000 ϫ 100 ϫ 10

km m cm mm 1 91 6 0 g 78 kg 1 110

3 kg 110 g

+ 4 kg 1 5 0 g – 2 kg 5 2 0 g

÷ 1 000 ÷ 100 ÷ 10 8 kg 1 1 0 g 5 kg 5 9 0 g

4 The calculations of addition, subtraction, EXAMPLE
multiplication and division of lengths in 15 kg 776 g ÷ 8 ϫ 3 = 5 kg 916 g
the same units are similar to the basic
operations of whole numbers. 1 kg 972 g 1 kg 2
8 15 kg 776 g
EXAMPLE 972 g
– 8 + 7 000
12 cm 7 mm + 5 cm 4 mm 7 7 776 ϫ3
–7 2
57 3 kg 2 91 6 g
– 56
= 18 cm 1 mm 16 + 2 – 2 000
– 16
cm mm 0 5 kg 91 6 g
12 7
+5 4 EXAMPLE

17 11 8 ᐉ 90 mᐉ – 5 ᐉ 450 mᐉ + 860 mᐉ

+1 – 10 = 3 ᐉ 500 mᐉ

18 1

5 Relationship between units of mass: 7 1 090 2ᐉ 61 4 0 mᐉ
+ 8 6 0 mᐉ
ϫ 1 000 8ᐉ 9 0 mᐉ 1 5 0 0 mᐉ
– 5ᐉ 4 5 0 mᐉ 2ᐉ –1 000
kg g 6 4 0 mᐉ +1 5 0 0 mᐉ
2ᐉ
3ᐉ
÷ 1 000

79

Unit Learning Area: Measurement and Geometry Digital File
Unit 6
6 Space

Express Notes 7 An area is the total surface covered by
a shape.
1 Types of angles:
Area of a square and a rectangle
Acute angle Right angle Obtuse angle = length ϫ width
PENERBIT ILMU
2 Right angles are formed at the corners BAKTI SDN. BHD. Square Width Rectangle Width
of a square or a rectangle.
Length Length
3 The acute angle is smaller than the right
angle, meanwhile the obtuse angle is Area of a triangle
bigger than the right angle. 1
= 2 ϫ base ϫ height
4 The distance between two parallel lines
is always the same. Height Height

5 Two perpendicular lines intersect at the
right angle.

Base Base

Parallel lines Perpendicular lines 8 A volume is the total of space taken up
by a three-dimensional shape.

6 A perimeter of a shape is the sum of Volume of a cube and a cuboid
the lengths of all the outer sides of the = length ϫ width ϫ height
shape.
EXAMPLE
EXAMPLE Find the volume of the cuboid below.
Find the perimeter of the triangle below.

3 cm 5 cm 6 cm

4 cm 5 cm
8 cm
Perimeter
= 3 cm + 4 cm + 5 cm Volume = 8 cm ϫ 5 cm ϫ 6 cm
= 12 cm = 240 cm3

92

Unit Learning Area: Relationship and Algebra Digital File
Unit 7
7 Coordinates, Ratio and
Proportion

Express Notes

1 The coordinates of a point are stated by Place Coordinates
writing the x-coordinate first, followed by
the y-coordinate in brackets, (x, y).

Vertical axis

y
PENERBIT ILMU Zoo (0, 2)
BAKTI SDN. BHD.
Mosque (2, 2)

Post office (3, 1)

5 School (4, 2)
4 First quadrant
3 Hospital (4, 4)
2
1 Market (1, 4)

O 1 234 567 x PdPc Tutorial

2 The ratio of two quantities is the Video
comparison of two quantities measured
in the same unit.

Origin Horizontal axis 3 A ratio is written as x : y.

EXAMPLE EXAMPLE

y State the ratio of the number of blue
pens to the number of red pens.
5
Market Blue pens Red pens

4 Hospital

3 Mosque Ratio = 3 : 5

2 School 4 Problems involving proportions in daily
Zoo situations can be solved by the unitary
Post office method, that is by determining the
1 x value of a single unit first.

O1 234 5 EXAMPLE
There is 700 mᐉ of water in 4 glasses.
PdPc Tutorial Video Each glass contains the same volume
of water. Calculate the volume of water
Scan the QR code or visit https://youtu.be/ in 3 glasses.
XvjIrfbJ7CM to watch a tutorial video
on determining the coordinates Number of Volume of
of a point in the first quadrant. glasses water

For educational purpose only 4 700 mᐉ

1 700 mᐉ ÷ 4 = 175 mᐉ

3 175 mᐉ ϫ 3 = 525 mᐉ

101

Unit Learning Area: Statistics and Probability Digital File
Unit 8
8 Data Handling

Express Notes

1 A pictograph uses pictures to represent 7 There are two types of bar charts:
the data. (a) vertical bar chart
(b) horizontal bar chart
EXAMPLE
(a) Vertical bar chart

Title Storybooks Read in a Month
2 Each pictograph has title and key to NumberBAKTofIbooksSDN. BHD.
represent the symbol used.

EXAMPLE

Title Sales of Noodles for Symbol 10
4 Days 8
PdPc Monday 6 Bar
4
Tutorial Tuesday 2
0
Video Wednesday Alia

Thursday Vertical axis Edi Ravi Weng
label
Key represents 10 bowls of noodles Pupils
ILMU
3 A bar chart uses bars to represent the Horizontal
data. axis label

4 The width of all bars in the bar chart (b) Horizontal bar chart
are the same. Favourite Colours of a Group of Pupils

5 The length or height of each bar
depends on the frequency of the data.

6 The bar chart has title and consists of
the data at the horizontal axis and data
on the vertical axis.
PENERBIT Yellow

Colour Green
Blue
PdPc Tutorial Video
Red
Scan the QR code or visit
https://youtu.be/J2DKgCf353k to watch 0 5 10 15 20 25
a tutorial video constructing
and interpreting pictographs Number of pupils
and bar charts.

For educational purpose only

112

Name: Class: Date:

4 Find the difference between the number of pupils who score 30 marks and the number
of pupils who score 40 marks.

12 – 3 = 9 pupils

5 Calculate the total number of pupils who obtained scores of 20 and 50.
5 + 11 = 16 pupils

6 What is the total number of pupils in class 4 Bijak?PENERBIT ILMU
8 + 5 + 12 + 3 + 11 = 39 pupilsBAKTI SDN. BHD.

PdPc Pelibatan Ibu Bapa (PIB) Activity PdPc

Favourite Holiday Activities PIB
Travelling
Watching movies
Picnic
Cooking
Shopping

represents 1 vote

115

Name: Class: Date:

5 Calculate the total number of fish caught on Monday and Wednesday.

Total = (5 ϫ 20) + (4 ϫ 20)
= 100 + 80
= 180 fish

PENERBIT ILMU6 Represent the pictograph on page 116 in a vertical bar chart.
BAKTI SDN. BHD. Number of Fish Caught in 4 Days

Number of fish

120

100

80

60

40

20

0 Monday Tuesday Wednesday Thursday Day

PdPc

PdPc PAK-21 Activity PAK-21

117

Ujian Akhir Sesi Akademik Performance Marks
Level

1 Diagram 1 shows a number card. For
70 965 Examiner’s

Use

Diagram 1

(a) State the digit in the hundreds place.
9
PENERBIT ILMU 1(a)
BAKTI SDN. BHD. [1 mark] PL2
1
(b) Round off the number in Diagram 1 to the nearest hundred. 1(b)

70 965 = 71 000 1
Total
+1
1
[1 mark] PL3 2

2 Diagram 2 shows five similar circles.

Diagram 2 2(a)
1
(a) State the fraction that represents the shaded parts of the whole
2(b)
diagram. 1

3 Total
2
5 [1 mark] PL1 2
(b) Convert the answer in 2(a) to a percentage.
3(a)
3 ϫ 100% = 60% 2
5

[1 mark] PL3

3 (a) Diagram 3 shows three number cards of different shapes.

12 360 4

Diagram 3

The cards are arranged as below. Find the answer.

+

= 12 + 360 – 4 [1 mark]
= 372 – 4 [1 mark]

= 368

[2 marks] PL3

121