Ministry of Education Malaysia launches new integrated primary school mathematics curriculum

Ministry of Education
Malaysia

Integrated Curriculum for Primary Schools
CURRICULUM SPECIFICATIONS

MATHEMATICS

Curriculum Development Centre
Ministry of Education Malaysia
2006

Copyright © 2006 Curriculum Development Centre
Ministry of Education Malaysia
Kompleks Kerajaan Parcel E
Pusat Pentadbiran Kerajaan Persekutuan
62604 Putrajaya

First published 2006

Copyright reserved. Except for use in a review, the reproduction
or utilisation of this work in any form or by any electronic,
mechanical, or other means, now known or hereafter invented,
including photocopying, and recording is forbidden without the
prior written permission from the Director of the Curriculum
Development Centre, Ministry of Education Malaysia.

CONTENT

RUKUNEGARA v MONEY 14
National Philosophy of Education vii Money up to RM10 million 14
Preface ix TIME 15
Introduction xi Duration 15

LENGTH 17
Computation of Length 17
WHOLE NUMBERS 1
Numbers up to Seven Digits 1
MASS 18
Basic Operations with Numbers up to Seven Digits 3
Computation of Mass 18
Mixed Operations with Numbers up to Seven Digits 6
VOLUME OF LIQUID 19
FRACTIONS 7
Computation of Volume of Liquid 19
Addition of Fractions 7
Subtraction of Fractions 8 SHAPE AND SPACE 20
Multiplication of Fractions 9 Two-Dimensional Shapes 20
Division of Fractions 10 Three-Dimensional Shapes 22

DECIMALS 11 DATA HANDLING 24
Mixed Operations with Decimals 11 Average 24
Organising and Interpreting Data 26
PERCENTAGE 12
Relationship between Percentage, Fraction and Decimal 12 Contributors 28

RUKUNEGARA
RUKUNEGARA
DECLARATION
DECLARATION
OUR NATION, MALAYSIA, beingbeing dedicated achieving a
OUR NATION, MALAYSIA, dedicated to
greater unity of all her peoples;
• to achieving a greater unity of all her peoples;
• to maintaining a democratic way of life; of life;
• to maintaining a democratic way
• to creating creating a just society in which the wealth of nation
• to a just society in which the wealth of the the
shall be equitably shared;
nation shall be equitably shared;
• to a liberal approach to her rich and diverse cultural
• to ensuring ensuring a liberal approach to her rich and diverse
cultural traditions;
traditions;
• to building a progressive society which shall be oriented
• to building a progressive society which shall be orientated to
to modern science and technology;
modern science and technology;
WE, herWE, her peoples, pledge our united efforts to attain these
peoples, pledge our united efforts to attain these ends
guided by these principles: these principles:
ends guided by
• BELIEF IN GOD
• Belief in God
• LOYALTY TO KING AND COUNTRY
• Loyalty to King and Country
• UPHOLDING THE CONSTITUTION
• Upholding the Constitution
• RULE OF LAW
• Rule • Law
of GOOD BEHAVIOUR AND MORALITY
• Good Behaviour and Morality

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NATIONAL PHILOSOPHY OF EDUCATION
Education in Malaysia is an on-going effort towards developing
the potential of individuals in a holistic and integrated manner, so
as to produce individuals who are intellectually, spiritually,
Education in Malaysia is an ongoing effort
emotionally and physically balanced and harmonious based on a
firm belief in and devotion to God. Such an effort is designed of
towards further developing the potential to
produce Malaysian citizens in a holistic and integrated
individuals who are knowledgeable and
competent, who possess as to moral standards and who are
manner so high produce individuals who are
responsible andintellectually, spiritually, emotionally and
capable of achieving a high level of personal
well being as well as being able to contribute to the harmony and
physically balanced and harmonious, based
betterment of the family, society and the nation at large.
on a firm belief in God. Such an effort is
designed to produce Malaysian citizens who
are knowledgeable and competent, who
possess high moral standards, and who are
responsible and capable of achieving a high
level of personal well-being as well as being
able to contribute to the betterment of the
family, the society and the nation at large.

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PREFACE The development of a set of Curriculum Specifications as a supporting
document to the syllabus is the work of many individuals and experts
Science and technology plays a crucial role in meeting Malaysia’s in the field. To those who have contributed in one way or another to
aspiration to achieve developed nation status. Since mathematics is this effort, on behalf of the Ministry of Education, I would like to thank
instrumental in developing scientific and technological knowledge, the them and express my deepest appreciation.
provision of quality mathematics education from an early age in the
education process is critical.
The primary school Mathematics curriculum as outlined in the syllabus
has been designed to provide opportunities for pupils to acquire
mathematical knowledge and skills and develop the higher order
problem solving and decision making skills that they can apply in their
everyday lives. But, more importantly, together with the other subjects
in the primary school curriculum, the mathematics curriculum seeks to (DR. HAILI BIN DOLHAN)
inculcate noble values and love for the nation towards the final aim of
developing the holistic person who is capable of contributing to the Director
harmony and prosperity of the nation and its people. Curriculum Development Centre
Ministry of Education
Beginning in 2003, science and mathematics will be taught in English Malaysia
following a phased implementation schedule, which will be completed
by 2008. Mathematics education in English makes use of ICT in its
delivery. Studying mathematics in the medium of English assisted by
ICT will provide greater opportunities for pupils to enhance their
knowledge and skills because they are able to source the various
repositories of knowledge written in mathematical English whether in
electronic or print forms. Pupils will be able to communicate
mathematically in English not only in the immediate environment but
also with pupils from other countries thus increasing their overall
English proficiency and mathematical competence in the process.

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INTRODUCTION strategies of problem solving, communicating mathematically and
inculcating positive attitudes towards an appreciation of mathematics
Our nation’s vision can be achieved through a society that is educated as an important and powerful tool in everyday life.
and competent in the application of mathematical knowledge. To It is hoped that with the knowledge and skills acquired in Mathematics,
realise this vision, society must be inclined towards mathematics. pupils will discover, adapt, modify and be innovative in facing changes
Therefore, problem solving and communicational skills in mathematics and future challenges.
have to be nurtured so that decisions can be made effectively.
Mathematics is integral in the development of science and technology.
As such, the acquisition of mathematical knowledge must be upgraded
periodically to create a skilled workforce in preparing the country to AIM
become a developed nation. In order to create a K-based economy,
research and development skills in Mathematics must be taught and The Primary School Mathematics Curriculum aims to build pupils’
understanding of number concepts and their basic skills in
instilled at school level.
computation that they can apply in their daily routines effectively and
Achieving this requires a sound mathematics curriculum, competent responsibly in keeping with the aspirations of a developed society and
and knowledgeable teachers who can integrate instruction with nation, and at the same time to use this knowledge to further their
assessment, classrooms with ready access to technology, and a studies.
commitment to both equity and excellence.
The Mathematics Curriculum has been designed to provide knowledge
and mathematical skills to pupils from various backgrounds and levels OBJECTIVES
of ability. Acquisition of these skills will help them in their careers later
in life and in the process, benefit the society and the nation. The Primary School Mathematics Curriculum will enable pupils to:
Several factors have been taken into account when designing the
1 know and understand the concepts, definition, rules sand
curriculum and these are: mathematical concepts and skills,
principles related to numbers, operations, space, measures and
terminology and vocabulary used, and the level of proficiency of
data representation;
English among teachers and pupils.
The Mathematics Curriculum at the primary level (KBSR) emphasises 2 master the basic operations of mathematics:
the acquisition of basic concepts and skills. The content is categorised • addition,
into four interrelated areas, namely, Numbers, Measurement, Shape
and Space and Statistics. • subtraction,

The learning of mathematics at all levels involves more than just the • multiplication,
basic acquisition of concepts and skills. It involves, more importantly, • division;
an understanding of the underlying mathematical thinking, general
3 master the skills of combined operations;

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4 master basic mathematical skills, namely: • Decimals;
• making estimates and approximates, • Money;
• measuring, 2 Measures
• handling data • Time;
• representing information in the form of graphs and charts; • Length;
5 use mathematical skills and knowledge to solve problems in • Mass;
everyday life effectively and responsibly; • Volume of Liquid.
6 use the language of mathematics correctly; 3 Shape and Space
7 use suitable technology in concept building, acquiring • Two-dimensional Shapes;
mathematical skills and solving problems;
• Three-dimensional Shapes;
8 apply the knowledge of mathematics systematically, heuristically, • Perimeter and Area.
accurately and carefully;
4 Statistics
9 participate in activities related to mathematics; and
• Data Handling
10 appreciate the importance and beauty of mathematics.
The Learning Areas outline the breadth and depth of the scope of
knowledge and skills that have to be mastered during the allocated
time for learning. These learning areas are, in turn, broken down into
CONTENT ORGANISATION more manageable objectives. Details as to teaching-learning
strategies, vocabulary to be used and points to note are set out in five
The Mathematics Curriculum at the primary level encompasses four columns as follows:
main areas, namely, Numbers, Measures, Shape and Space, and Column 1: Learning Objectives.
Statistics. The topics for each area have been arranged from the basic
to the abstract. Teachers need to teach the basics before abstract Column 2: Suggested Teaching and Learning Activities.
topics are introduced to pupils. Column 3: Learning Outcomes.
Each main area is divided into topics as follows: Column 4: Points To Note.
1 Numbers Column 5: Vocabulary.
• Whole Numbers;
• Fractions;

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The purpose of these columns is to illustrate, for a particular teaching EMPHASES IN TEACHING AND LEARNING
objective, a list of what pupils should know, understand and be able to
do by the end of each respective topic. The Mathematics Curriculum is ordered in such a way so as to give
The Learning Objectives define clearly what should be taught. They flexibility to the teachers to create an environment that is enjoyable,
cover all aspects of the Mathematics curriculum and are presented in meaningful, useful and challenging for teaching and learning. At the
a developmental sequence to enable pupils to grasp concepts and same time it is important to ensure that pupils show progression in
master skills essential to a basic understanding of mathematics. acquiring the mathematical concepts and skills.

The Suggested Teaching and Learning Activities list some On completion of a certain topic and in deciding to progress to another
examples of teaching and learning activities. These include methods, learning area or topic, the following need to be taken into accounts:
techniques, strategies and resources useful in the teaching of a • The skills or concepts acquired in the new learning area or
specific concepts and skills. These are however not the only topics;
approaches to be used in classrooms.
• Ensuring that the hierarchy or relationship between learning
The Learning Outcomes define specifically what pupils should be areas or topics have been followed through accordingly; and
able to do. They prescribe the knowledge, skills or mathematical
processes and values that should be inculcated and developed at the • Ensuring the basic learning areas have or skills have been
appropriate levels. These behavioural objectives are measurable in all acquired or mastered before progressing to the more
aspects. abstract areas.
In Points To Note, attention is drawn to the more significant aspects The teaching and learning processes emphasise concept building, skill
of mathematical concepts and skills. These aspects must be taken into acquisition as well as the inculcation of positive values. Besides these,
accounts so as to ensure that the concepts and skills are taught and there are other elements that need to be taken into account and learnt
learnt effectively as intended. through the teaching and learning processes in the classroom. The
main emphasis are as follows:
The Vocabulary column consists of standard mathematical terms,
instructional words and phrases that are relevant when structuring
activities, asking questions and in setting tasks. It is important to pay 1. Problem Solving in Mathematics
careful attention to the use of correct terminology. These terms need
to be introduced systematically to pupils and in various contexts so Problem solving is a dominant element in the mathematics curriculum
that pupils get to know of their meaning and learn how to use them for it exists in three different modes, namely as content, ability, and
appropriately. learning approach.

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Over the years of intellectual discourse, problem solving has People learn best through experience. Hence, mathematics is best
developed into a simple algorithmic procedure. Thus, problem solving learnt through the experience of solving problems. Problem-based
is taught in the mathematics curriculum even at the primary school learning is an approach where a problem is posed at the beginning of
level. The commonly accepted model for problem solving is the four- a lesson. The problem posed is carefully designed to have the desired
step algorithm, expressed as follows:- mathematical concept and ability to be acquired by students during the
particular lesson. As students go through the process of solving the
• Understanding the problem; problem being posed, they pick up the concept and ability that are built
• Devising a plan; into the problem. A reflective activity has to be conducted towards the
end of the lesson to assess the learning that has taken place.
• Carrying out the plan; and
• Looking back at the solution. 2. Communication in Mathematics
In the course of solving a problem, one or more strategies can be
Communication is one way to share ideas and clarify the
employed to lead up to a solution. Some of the common strategies of
understanding of Mathematics. Through talking and questioning,
problem solving are:-
mathematical ideas can be reflected upon, discussed and modified.
• Try a simpler case; The process of reasoning analytically and systematically can help
reinforce and strengthen pupils’ knowledge and understanding of
• Trial and improvement; mathematics to a deeper level. Through effective communications
• Draw a diagram; pupils will become efficient in problem solving and be able to explain
concepts and mathematical skills to their peers and teachers.
• Identifying patterns and sequences;
Pupils who have developed the above skills will become more
• Make a table, chart or a systematic list; inquisitive gaining confidence in the process. Communicational skills
in mathematics include reading and understanding problems,
• Simulation;
interpreting diagrams and graphs, and using correct and concise
• Make analogy; and mathematical terms during oral presentation and written work. This is
also expanded to the listening skills involved.
• Working backwards.
Communication in mathematics through the listening process occurs
Problem solving is the ultimate of mathematical abilities to be when individuals respond to what they hear and this encourages them
developed amongst learners of mathematics. Being the ultimate of to think using their mathematical knowledge in making decisions.
abilities, problem solving is built upon previous knowledge and
experiences or other mathematical abilities which are less complex in Communication in mathematics through the reading process takes
nature. It is therefore imperative to ensure that abilities such as place when an individual collects information or data and rearranges
calculation, measuring, computation and communication are well the relationship between ideas and concepts.
developed amongst students because these abilities are the
fundamentals of problem solving ability.

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Communication in mathematics through the visualization process • Structured and unstructured interviews;
takes place when an individual makes observation, analyses it,
interprets and synthesises the data into graphic forms, such as • Discussions during forums, seminars, debates and brain-
pictures, diagrams, tables and graphs. storming sessions; and

The following methods can create an effective communication • Presentation of findings of assignments.
environment: Written communication is the process whereby mathematical ideas
• Identifying relevant contexts associated with environment and and information are shared with others through writing. The written
everyday life experiences of pupils; work is usually the result of discussions, contributions and brain-
storming activities when working on assignments. Through writing, the
• Identifying interests of pupils; pupils will be encouraged to think more deeply about the mathematics
content and observe the relationships between concepts.
• Identifying teaching materials;
Examples of written communication activities are:
• Ensuring active learning;
• Doing exercises;
• Stimulating meta-cognitive skills;
• Keeping scrap books;
• Inculcating positive attitudes; and
• Keeping folios;
• Creating a conducive learning environment.
• Undertaking projects; and
Oral communication is an interactive process that involves activities
like listening, speaking, reading and observing. It is a two-way • Doing written tests.
interaction that takes place between teacher-pupil, pupil-pupil, and
pupil-object. When pupils are challenged to think and reason about Representation is a process of analysing a mathematical problem and
mathematics and to tell others the results of their thinking, they learn interpreting it from one mode to another. Mathematical representation
to be clear and convincing. Listening to others’ explanations gives enables pupils to find relationship between mathematical ideas that
pupils the opportunities to develop their own understanding. are informal, intuitive and abstract using their everyday language.
Conversations in which mathematical ideas are explored from multiple Pupils will realise that some methods of representation are more
perspectives help sharpen pupils thinking and help make connections effective and useful if they know how to use the elements of
between ideas. Such activity helps pupils develop a language for mathematical representation.
expressing mathematical ideas and appreciation of the need for
precision in the language. Some effective and meaningful oral 3. Mathematical Reasoning
communication techniques in mathematics are as follows:
Logical reasoning or thinking is the basis for understanding and
• Story-telling, question and answer sessions using own words; solving mathematical problems. The development of mathematical
• Asking and answering questions; reasoning is closely related to the intellectual and communicative
development of the pupils. Emphasis on logical thinking during

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mathematical activities opens up pupils’ minds to accept mathematics educational software, websites in the internet and available learning
as a powerful tool in the world today. packages can help to upgrade the pedagogical skills in the teaching
and learning of mathematics.
Pupils are encouraged to predict and do guess work in the process of
seeking solutions. Pupils at all levels have to be trained to investigate The use of teaching resources is very important in mathematics. This
their predictions or guesses by using concrete materials, calculators, will ensure that pupils absorb abstract ideas, be creative, feel
computers, mathematical representation and others. Logical reasoning confident and be able to work independently or in groups. Most of
has to be infused in the teaching of mathematics so that pupils can these resources are designed for self-access learning. Through self-
recognise, construct and evaluate predictions and mathematical access learning, pupils will be able to access knowledge or skills and
arguments. information independently according to their pace. This will serve to
stimulate pupils’ interests and responsibility in learning mathematics.
4. Mathematical Connections
In the mathematics curriculum, opportunities for making connections
must be created so that pupils can link conceptual to procedural APPROACHES IN TEACHING AND LEARNING
knowledge and relate topics in mathematics with other learning areas
Various changes occur that influence the content and pedagogy in the
in general.
teaching of mathematics in primary schools. These changes require
The mathematics curriculum consists of several areas such as variety in the way of teaching mathematics in schools. The use of
arithmetic, geometry, measures and problem solving. Without teaching resources is vital in forming mathematical concepts.
connections between these areas, pupils will have to learn and Teachers can use real or concrete objects in teaching and learning to
memorise too many concepts and skills separately. By making help pupils gain experience, construct abstract ideas, make
connections pupils are able to see mathematics as an integrated inventions, build self confidence, encourage independence and
whole rather than a jumble of unconnected ideas. Teachers can foster inculcate cooperation.
connections in a problem oriented classrooms by having pupils to
The teaching and learning materials that are used should contain self-
communicate, reason and present their thinking. When these
diagnostic elements so that pupils can know how far they have
mathematical ideas are connected with real life situations and the
understood the concepts and skills. To assist the pupils in having
curriculum, pupils will become more conscious in the application of
positive
mathematics. They will also be able to use mathematics contextually
in different learning areas in real life. attitudes and personalities, the intrinsic mathematical values of
exactness, confidence and thinking systematically have to be
5. Application of Technology absorbed through the learning areas.
Good moral values can be cultivated through suitable context. For
The application of technology helps pupils to understand mathematical example, learning in groups can help pupils develop social skills and
concepts in depth, meaningfully and precisely enabling them to encourage cooperation and self-confidence in the subject. The
explore mathematical concepts. The use of calculators, computers, element of patriotism can also be inculcated through the teaching-

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learning process in the classroom using planned topics. These values assessment techniques, including written and oral work as well as
should be imbibed throughout the process of teaching and learning demonstration. These may be in the form of interviews, open-ended
mathematics. questions, observations and assignments. Based on the results, the
teachers can rectify the pupils’ misconceptions and weaknesses and
Among the approaches that can be given consideration are:
at the same time improve their teaching skills. As such, teachers can
• Pupil centered learning that is interesting; take subsequent effective measures in conducting remedial and
enrichment activities to upgrade pupils’ performance.
• The learning ability and styles of learning;
• The use of relevant, suitable and effective teaching materials;
and
• Formative evaluation to determine the effectiveness of
teaching and learning.
The choice of an approach that is suitable will stimulate the teaching
and learning environment in the classroom or outside it. The
approaches that are suitable include the following:
• Cooperative learning;
• Contextual learning;
• Mastery learning;
• Constructivism;
• Enquiry-discovery; and
• Futures Study.

ASSESSMENT
Assessment is an integral part of the teaching and learning process. It
has to be well-structured and carried out continuously as part of the
classroom activities. By focusing on a broad range of mathematical
tasks, the strengths and weaknesses of pupils can be assessed.
Different methods of assessment can be conducted using multiple

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Learning Area: NUMBERS UP TO SEVEN DIGITS Year 6
LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARY
Pupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…
1 develop number sense • Teacher pose numbers in (i) Name and write numbers Write numbers in words and million
up to seven digits. numerals, pupils name the up to seven digits. numerals.
digits
respective numbers and write
Seven-digit numbers are
the number words. conversion
numbers from 1 000 000 up
• Teacher says the number to 9 999 999. place value
names and pupils show the Emphasise reading and explore
numbers using the calculator or writing numbers in extended
the abacus, then, pupils write notation for example number patterns
the numerals.
multiple of 10
5 801 249 = 5 000 000
• Provide suitable number line + 800 000 + 1 000 + 200 simplest form
scales and ask pupils to mark + 40 + 9
the positions that represent a extended notation
set of given numbers. or
round off
5 801 249 = 5 millions
+ 8 hundred thousands
+ 1 thousands
+ 2 hundreds + 4 tens
+ 9 ones.
• Given a set of numbers, pupils (ii) Determine the place value To avoid confusion, initials
represent each number using of the digits in any whole for place value names may
the number base blocks or the number of up to seven be written in upper cases.
abacus. Pupils then state the digits.
place value of every digit of the
given number.

1

Learning Area: NUMBERS UP TO SEVEN DIGITS Year 6
(iii) Express whole numbers in Write numbers in partial
words and numerals, for
a) decimals example
a) 800 000 is 0.8 million
b) fractions
b) 6 320 000 is 6.32 million
of a million and vice versa. c) 1.4 million is 1 400 000
d) 5.602 million is 5 602 000
1
e) 3 500 000 is 3 2 million
f) 8 3 million is 8 750 000
4
For fractional number words,
denominators are in
multiples of 10 (10 to 90, 100
and 1000) and reduce
fractional terms to its
simplest form.
Limit decimal terms up to 3
decimal places.
• Given a set of numerals, pupils (iv) Compare number values
compare and arrange the up to seven digits.
numbers in ascending then
descending order.
(v) Round off numbers to the Explain to pupils that
nearest tens, hundreds, numbers are rounded off to
thousands, ten thousands, get an approximate.
hundred thousands and
millions.
2

Learning Area: BASIC OPERATIONS WITH NUMBERS UP TO SEVEN DIGITS Year 6
2 Add, subtract, multiply • Pupils practice addition, (i) Add any two to five Addition exercises include simpler
and divide numbers subtraction, multiplication and numbers to 9 999 999. addition of two numbers to
simulating
involving numbers up to division using the four-step four numbers with and
seven digits. algorithm of without regrouping. analogy
1) Estimate the solution. Provide mental addition sequences
practice either using the
2) Arrange the numbers abacus-based technique or
involved according to place using quick addition
values. strategies such as estimating
3) Perform the operation. total by rounding, simplifying
addition by pairs of tens,
4) Check the reasonableness doubles, etc.
of the answer.
(ii) Subtract Limit subtraction problems to
subtracting from a bigger
a) one number from a number.
bigger number less than Provide mental subtraction
10 000 000 practice either using the
abacus-based technique or
b) successively from a using quick subtraction
bigger number less than strategies.
10 000 000.
Quick subtraction strategies
to be implemented are
a) estimating the sum by
rounding numbers
b) counting up and counting
down (counting on and
counting back).

3

(iii) Multiply up to six-digit Limit products to less than
numbers with 10 000 000.
Provide mental multiplication
a) a one-digit number practice either using the
b) a two-digit number other multiplication
strategies.
c) 10, 100 and 1000.
Multiplication strategies to be
implemented include
factorising, completing 100,
lattice multiplication, etc.
(iv) Divide numbers of up to Division exercises include
seven digits by quotients with and without
remainder. Note that “r” is
a) a one-digit number used to signify “remainder”.
Emphasise the long division
b) 10, 100 and 1000 technique.
c) two-digit number. Provide mental division
practice either using the
other division strategies.
Exposed pupils to various
division strategies, such as
a) divisibility of a number
b) divide by 10, 100 and
1 000.

4

• Pose to pupils problems in (v) Solve Use any of the common
numerical form, simple strategies of problem
sentences, tables and pictures. a) addition, solving, such as
• Pupils create stories from given a) Try a simpler case
b) subtraction,
number sentences. b) Trial and improvement
• Teacher guides pupils to solve c) multiplication, c) Draw a diagram
problems following Polya’s four-
step model of d) division d) Identifying patterns and
sequences
1) Understanding the problem
problems involving e) Make a table, chart or a
2) Devising a plan numbers up to seven digits. systematic list
3) Implementing the plan f) Simulation
4) Looking back. g) Make analogy
h) Working backwards.

5

Learning Area: MIXED OPERATIONS WITH NUMBERS UP TO SEVEN DIGITS Year 6
3 Perform mixed • Explain to pupils the conceptual (i) Compute mixed operations Mixed operations are limited compute
operations with whole model of mixed operations then problems involving addition to not more than two
mixed operations
numbers. connect the concept with the and multiplication. operators, for example
procedures of performing bracket
a) 427 890 − 15 600 ÷ 25 =
operations according to the
horizontal form
order of operations. b) 12 745 + 20 742 × 56 =
vertical form
• Teacher pose problems (ii) Compute mixed operations Order of operations
verbally, i.e., in the numerical problems involving
B – brackets
form or simple sentences. subtraction and division.
O – of
D – division
M – multiplication
A – addition
S – subtraction
• Teacher guides pupils to solve (iii) Compute mixed operations Examples of mixed
problems following Polya’s four- problems involving operations with brackets
step model of brackets.
a) (1050 + 20 650) × 12 =
b) 872 ÷ (8 − 4) =
2) Devising a plan
c) (24 + 26) × (64 − 14) =
3) Implementing the plan
4) Looking back.
(iv) Solve problems involving
mixed operations on
numbers of up to seven
digits.

6

Learning Area: ADDITION OF FRACTIONS Year 6
1 Add three mixed • Demonstrate addition of mixed (i) Add three mixed numbers An example of addition of mixed numbers
numbers with denominators numbers through with the same denominator three mixed numbers with
equivalent fractions
of up to 10. of up to 10. the same denominator of up
1) paper folding activities to 10. simplest form
2) fraction charts
3 1
7
+17
2
+2 3
7
= multiplication tables
3) diagrams
4) number lines
5) multiplication tables

• Pupils create stories from given (ii) Add three mixed numbers An example of addition of
number sentences involving with different denominators three mixed numbers with
mixed numbers. of up to 10. different denominators of up
to 10.

2 3 +16 + 2 4 =
1 1 1

Write answers in its simplest
form.
• Teacher guides pupils to solve (iii) Solve problems involving
problems following Polya’s four- addition of mixed numbers.
step model of
2) Devising a plan
4) Looking back.

7

Learning Area: SUBTRACTION OF FRACTIONS Year 6
2 Subtract mixed • Demonstrate subtraction of (i) Subtract involving three An example of subtraction mixed numbers
numbers with denominators mixed numbers through mixed numbers with the involving three mixed
equivalent fractions
of up to 10. same denominator of up to numbers with the same
1) paper holding activities denominator of up to 10.
10. simplest form
2) fractions charts
5 4
5
−15
2
−15
1
= multiplication tables
3) diagrams
4) number lines
5) multiplication tables
• Pupils create stories from given (ii) Subtract involving three An example of subtraction
number sentences involving mixed numbers with involving three mixed
mixed numbers. different denominators of numbers with different
up to 10. denominators of up to 10.

7 8 − 3 4 −12 =
7 1 1

Write answers in its simplest
form.
• Pose to pupils, problems in the (iii) Solve problems involving
real context in the form of subtraction of mixed
numbers.
1) words,
2) tables,
3) pictorials.

8

Learning Area: MULTIPLICATION OF FRACTIONS Year 6
3 Multiply any mixed • Use materials such as the (i) Multiply mixed numbers Model multiplication of mixed mixed numbers
numbers with a whole hundred squares to model with a whole number. numbers with whole
portions
numbers up to 1000. multiplication of mixed numbers as grouping sets of
numbers. For example, objects, for example simplest form
2 2 × 100 = ?
1
3 × 300 means 3
1
3
1
3
groups
of sets of 300.
Suppose we have a set of
100 objects. Two groups or
sets will contain 200 objects,
i.e. 2 × 100 = 200 .Therefore,
1
2 2 groups will contain
2 2 × 100 = 250 objects.
1

Limit the whole number
component of a mixed
number, to three digits. The
• Present calculation in clear and denominator of the fractional
organised steps. part of the mixed number is
limited to less than 10.
5
2 2 × 100 =
1
× 100
2
5
= × 50
1
= 250

9

Learning Area: DIVISION OF FRACTIONS Year 6
4 Divide fractions with a • Teacher models the division of (ii) Divide fractions with Limit denominators for the
whole number and a fraction with another fraction as dividend to less than 10.
fraction. sharing. The following a) a whole number Limit divisors to less than 10
illustrations demonstrate this
for both the whole number
idea… b) a fraction. and fraction.
1
2
÷ 2 =1
1
Some models of division of a
Half a vessel of liquid poured fraction with a fraction…
into a half-vessel makes one full
half-vessel. 1
4
÷ 1
2
= ( 4 × 2) ÷ (2 × 2)
1 1

1 = ( 4 × 2) ÷ 1
1
3
4 = 1
2
÷1
1
2 = 1
2
1
4
or
0
1
÷ 1
=2 (iii) Divide mixed numbers with 1
×2
2 4 1
÷ 1
= 4
Half a vessel of liquid poured 4 2 1
×2
a) a whole number 2
into a quarter-vessel makes two 1
full quarter-vessels.
b) a fraction. = 2
1
1 = 1
2
3
4 or
1
2 1
2
1
4
= 1
2
×2 1
4
×2 = 1 1
2
= 1
2
1
4

0

10

Learning Area: MIXED OPERATIONS WITH DECIMALS Year 6
1 Perform mixed • Pupils add and/or subtract (i) Add and subtract three to Some examples of mixed decimal number
operations of addition and three to four decimal numbers four decimal numbers of up operations with decimals.
decimal places
subtraction of decimals of in parts, i.e. by performing one to 3 decimal places,
0.6 + 10.2 – 9.182 =
up to 3 decimal places. operation at a time in the order involving
of left to right. Calculation steps 8.03 – 5.12 + 2.8 =
are expressed in the vertical a) decimal numbers only
126.6 + 84 - 3.29 =
form.
b) whole numbers and or
• The abacus may be used to
decimal numbers.
verify the accuracy of the result 10 – 4.44 + 2.126 – 7 =
of the calculation.
2.4 + 8.66 – 10.992 + 0.86 =
0.6 + 0.006 +3.446 – 2.189 =
An example of how
calculation for mixed
operations with decimals is
expressed.
126.6 – 84 + 3.29 = ?

1 2 6 . 6

+ 8 4

2 1 0 . 6

− 3 . 2 9

2 0 7 . 3 1

11

Learning Area: RELATIONSHIP BETWEEN PERCENTAGE, FRACTION AND DECIMAL Year 6
1 Relate fractions and • Use the hundred-squares to (i) Convert mixed numbers to Fractions can be modeled as simplest form
decimals to percentage. model conversion of mixed percentage. parts of a whole, groupings
multiples
numbers to percentage. For of sets of objects, or division.
3
example, convert 1 10 to To relate mixed numbers to percent
percentages, the numbers
percentage. percentage
have to be viewed as
fractions. Mixed numbers
have to be converted to
improper fractions first, to
give meaning to the
relationship mixed numbers
with percentages. For
example

1=
100 3 30 3 3 × 50 150
= 12 =
1
= = = 100%
100 10 100 2 2 × 50 100

100% 30%
The shaded parts represent (ii) Convert decimal numbers Limit decimal numbers to
130% of the hundred-squares. of value more than 1 to values less than 10 and to
percentage. two decimal places only.
An example of a decimal
number to percentage
conversion
265
2.65 = = 265%
100

12

Learning Area: RELATIONSHIP BETWEEN PERCENTAGE, FRACTION AND DECIMAL Year 6
• Demonstrate the concept of (iii) Find the value for a given Finding values for simplest form
percentage of a quantity using percentage of a quantity. percentage of a quantity,
multiple
the hundred-squares or multi- shall include the following,
based blocks. income
Quantity value of
expenses
a) 100
savings
b) less than 100
profit
c) more than 100,
loss
Percentage value of
discount
The shaded parts of the two a) less than 100%
hundred-squares is 128% of dividend
b) more than 100%.
100.
interest
Sample items for finding
• Guide pupils to find the value values for percentage of a tax
for percentage of a quantity quantity are as follows:
through some examples, such commission
as a) 9.8% of 3500
45% of 10 b) 114% of 100

450 c) 150% of 70
× 10 = 45
100 d) 160% of 120
• Pupils create stories from given (iv) Solve problems in real Solve problems in real life
percentage of a quantity. context involving involving percentage
relationships between calculation of income and
• Pose to pupils, situational expenditure, savings, profit
percentage, fractions and
problems in the form of words, and loss, discount, dividend
decimals.
tables and pictorials. or interest, tax, commission,
etc.

13

Learning Area: MONEY UP TO RM10 MILLION Year 6
1 Use and apply number • Provide to pupils a situation (i) Perform mixed operations Mixed operations exercise mixed operation
sense in real context involving money where mixed with money up to a value of may also include brackets,
bracket
involving money. operations need to be RM10 million. for example
performed. Then, demonstrate savings
RM8000 + RM1254 – RM5555 =
how the situation is
income
transformed to a number RM125.05 – RM21 – RM105.95 =
sentence of mixed operations. expenditure
(RM100 + RM50) × 5 =
• Pupils solve mixed operations investments
involving money in the usual (RM125 × 8) – (RM40 × 8) =
cost price
proper manner by writing RM1200 – (RM2400 ÷ 6) =
number sentences in the selling price
vertical form.
profit
• Pose problems involving (ii) Solve problems in real Discuss problems involving loss
money in numerical form, context involving various situations such as
discount
simple sentences, tables or computation of money. savings, income,
pictures. expenditure, investments, computation
cost price, selling price,
• Teacher guides pupils to solve profit, loss and discount.
step model of
2) Devising a plan
4) Looking back.

14

Learning Area: DURATION Year 6
1 Use and apply • Pupils find the duration from (i) Calculate the duration of an Some basic ideas of points calculation
knowledge of time to find the start to the end of an event event in between in time so that calculation of
compute
the duration. from a given situation with the duration is possible, are as
aid of the calendar, schedules a) months follows: date
and number lines.
For duration in months, “… calendar
b) years from March until October.”
schedule
c) dates. For duration in years and
months, “… from July 2006 duration
to September 2006.” event
For duration in years, month
months and days,
year
a) “… from 25th March 2004
up to 25th June 2004”, or
b) “… from 27th May 2005
till 29th June 2006.”
(ii) Compute time period from An example of a situation
situations expressed in expressed in a fraction of
fractions of duration. time duration
2
57 … 3 of 2 years.

15

Learning Area: DURATION Year 6
• Pose problems involving (iii) Solve problem in real Discuss problem involving
computation of time in context involving various situations such as
numerical form, simple computation of time event, calendar etc.
sentences, tables or pictures. duration.
• Teacher guides pupils to solve
step model of
58
2) Devising a plan
4) Looking back.

16

Ministry of Education Malaysia launches new integrated primary school mathematics curriculum

Ministry of Education Malaysia launches new integrated primary school mathematics curriculum

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Ministry of Education Malaysia launches new integrated primary school mathematics curriculum