Integrated Curriculum for Primary Schools CURRICULUM SPECIFICATIONS
Integrated Curriculum for Primary Schools CURRICULUM SPECIFICATIONS
MATHEMATICS
Curriculum Development Centre Ministry of Education Malaysia
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.
RUKUNEGARA DECLARATION DECLARATION
OUR NATION, MALAYSIA, being dedicated to achieving a OUR NATION, MALAYSIA, being dedicated greater unity of all her peoples; • to achieving a greater unity of all her peoples;
• to maintaining a democratic way of life; • to maintaining a democratic way of life; • to creating a just society in which the wealth of the nation • to creating a just society in which the wealth of the
shall be equitably shared; nation shall be equitably shared; • to ensuring a liberal approach to her rich and diverse cultural • to ensuring a liberal approach to her rich and diverse
traditions; cultural traditions; • to building a progressive society which shall be orientated to • to building a progressive society which shall be oriented
modern science and technology; to modern science and technology; WE, her peoples, pledge our united efforts to attain these ends WE, her peoples, pledge our united efforts to attain these
guided by these principles: ends guided by these principles: • 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 of Law • GOOD BEHAVIOUR AND MORALITY
• Good Behaviour and Morality
N AT I ON AL PH I LOSOPH Y OF EDU CAT I ON
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, emotionally and physically balanced and harmonious based on a Education in Malaysia is an ongoing effort firm belief in and devotion to God. Such an effort is designed to towards further developing the potential of produce Malaysian citizens who are knowledgeable and individuals in a holistic and integrated competent, who possess high moral standards and who are manner so as to produce individuals who are responsible and capable of achieving a high level of personal intellectually, spiritually, emotionally and well being as well as being able to contribute to the harmony and betterment of the family, society and the nation at large. physically balanced and harmonious, based
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.
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.
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
AI M
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’ instilled at school level.
understanding of number concepts and their basic skills in 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
OBJ ECT I V ES
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,
• multiplication,
The learning of mathematics at all levels involves more than just the
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;
• 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
1 0 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
CON T EN T ORGAN I SAT I ON
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; • Whole Numbers; • Fractions;
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 . Proble m Solving in M a t he m a t ic s
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.
step algorithm, expressed as follows:- mathematical concept and ability to be acquired by students during the • Understanding the problem; particular lesson. As students go through the process of solving the 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 • Carrying out the plan; and end of the lesson to assess the learning that has taken place.
• Looking back at the solution.
2 . Com m unic a t ion in M a t he m a t ic s
In the course of solving a problem, one or more strategies can be employed to lead up to a solution. Some of the common strategies of
Communication is one way to share ideas and clarify the 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 • Trial and improvement; reinforce and strengthen pupils’ knowledge and understanding of 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 • Simulation; in mathematics include reading and understanding problems, interpreting diagrams and graphs, and using correct and concise • Make analogy; and
mathematical terms during oral presentation and written work. This is • Working also expanded to the listening skills involved.
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.
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 • Identifying teaching materials; content and observe the relationships between concepts.
• Ensuring Examples of written communication activities are: active learning;
• Stimulating exercises; meta-cognitive skills;
• Doing • Keeping scrap books;
• Inculcating positive attitudes; and
• Keeping folios;
• Creating a conducive learning environment. Oral communication is an interactive process that involves activities
• Undertaking projects; and
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 . M a t he m a t ic a l Re a soning
communication techniques in mathematics are as follows: • Story-telling, question and answer sessions using own words; Logical reasoning or thinking is the basis for understanding and 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 • Asking and answering questions; reasoning is closely related to the intellectual and communicative development of the pupils. Emphasis on logical thinking during
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 . M a t he m a t ic a l Conne c t ions
In the mathematics curriculum, opportunities for making connections must be created so that pupils can link conceptual to procedural
APPROACH ES I N T EACH I N G AN D LEARN I N G
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 communicate, reason and present their thinking. When these
The teaching and learning materials that are used should contain self- mathematical ideas are connected with real life situations and the
diagnostic elements so that pupils can know how far they have understood the concepts and skills. To assist the pupils in having
curriculum, pupils will become more conscious in the application of mathematics. They will also be able to use mathematics contextually
positive
in different learning areas in real life. attitudes and personalities, the intrinsic mathematical values of exactness, confidence and thinking systematically have to be
5 . Applic a t ion of T e c hnology
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- element of patriotism can also be inculcated through the teaching-
take subsequent effective measures in conducting remedial and • The learning ability and styles of learning; enrichment activities to upgrade pupils’ performance.
• 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;
• Futures Study.
ASSESSM EN T
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
Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
(i) Name and write numbers Write numbers in words and numbers up to 1 000 000
1 Develop number sense
• Teacher pose numbers in
numerals, pupils name the
up to 1 000 000.
numerals.
numeral
respective numbers and write the number words. Emphasise reading and
writing numbers in extended
count
• Teacher says the number
notation for example :
place value
names and pupils show the
value of the digits
numbers using the calculator or
the abacus, then pupils write
or
partition
the numerals.
801 249 = 8 hundred
decompose
• Provide suitable number line
thousands + 1 thousands + 2 estimate
scales and ask pupils to mark
hundreds + 4 tens + 9 ones.
the positions that representt a
check
set of given numbers.
compare
• Given a set of numbers, pupils
(ii) Determine the place value
count in …
represent each number using
of the digits in any whole
the number base blocks or the
number up to 1 000 000.
hundreds
abacus. Pupils then state the
ten thousands
place value of every digit of the
thousands
given number.
round off to the
• Given a set of numerals, pupils
(iii) Compare value of numbers
nearest…
compare and arrange the
up to 1 000 000.
tens
numbers in ascending then
hundreds
descending order.
thousands
(iv) Round off numbers to the Explain to pupils that
ten thousands
nearest tens, hundreds,
numbers are rounded off to
thousands, ten thousands
get an approximate.
hundred thousands
and hundred thousands.
number sentences total of 1 000 000
2 Add numbers to the
• Pupils practice addition using
(i) Add any two to four Addition exercises include
the four-step algorithm of:
numbers to 1 000 000.
addition of two numbers to four numbers
vertical form
1) Estimate the total.
• without trading (without
without trading
2) Arrange the numbers
regrouping).
with trading
involved according to place values.
• with trading (with
quick calculation
3) Perform the operation.
regrouping).
pairs of ten
4) Check the reasonableness of
Provide mental addition practice either using the
doubles
the answer.
abacus-based technique or
estimation
• Pupils create stories from given
using quick addition
range
addition number sentences.
strategies such as estimating total by rounding, simplifying
addition by pairs of tens and doubles, e.g.
Pairs of ten
4 + 6, 5 + 5, etc.
Doubles
3 + 3, 30 + 30, 300 + 300, 3000 + 3000, 5 + 5, etc.
• Teacher pose problems
(ii) Solve addition problems. Before a problem solving
total
verbally, i.e., in the numerical
exercise, provide pupils with
sum of
form or simple sentences.
the activity of creating stories from number sentences.
• Teacher guides pupils to solve numerical
problems following Polya’s four-
A guide to solving addition
how many
step model of:
problems:
number sentences
1) Understanding the problem
Understanding the problem
create
2) Devising a plan
Extract information from
pose problem
3) Implementing the plan
problems posed by drawing diagrams, making lists or
tables
4) Looking back.
tables. Determine the type of modeling problem, whether it is addition, subtraction, etc.
simulating
Devising a plan
Translate the information into a number sentence. Determine what strategy to use to perform the operation.
Implementing the plan
Perform the operation conventionally, i.e. write the number sentence in the vertical form.
Looking back
Check for accuracy of the solution. Use a different startegy, e.g. calculate by using the abacus.
3 Subtract numbers from
• Pupils create stories from given
(i) Subtract one number from Subtraction refers to
number sentence
a number less than
subtraction number sentences.
a bigger number less than
a) taking away,
vertical form
• Pupils practice subtraction 1 000 000.
b) comparing differences
without trading
using the four-step algorithm of:
c) the inverse of addition.
with trading
1) Estimate the sum.
Limit subtraction problems to quick calculation
2) Arrange the numbers
subtracting from a bigger
involved according to place
number.
pairs of ten
values.
Provide mental sutraction
counting up
3) Perform the operation.
practice either using the
counting down
4) Check the reasonableness of
abacus-based technique or
the answer.
using quick subtraction
Quick subtraction strategies
modeling
to be implemented:
successively
a) Estimating the sum by rounding numbers.
b) counting up and counting down (counting on and counting back)
• Pupils subtract successively by
(ii) Subtract successively from Subtract successively two
writing the number sentence in
a bigger number less than
numbers from a bigger
a) horizontal form
b) vertical form
• Teacher pose problems
(iii) Solve subtraction
Also pose problems in the
create
verbally, i.e., in the numerical
problems.
form of pictorials and stories. pose problems
form or simple sentences.
• Teacher guides pupils to solve tables
problems following Polya’s four- step model of:
1) Understanding the problem
2) Devising a plan
3) Implementing the plan
4) Looking back.
times numbers with the highest
4 Multiply any two
• Pupils create stories from given
(i) Multiply up to five digit Limit products to less than
multiply product of 1 000 000.
multplication number
numbers with
sentences.
Provide mental multiplication
e.g. 40 500 × 7 = 283 500
a) a one-digit number,
practice either using the abacus-based technique or
multiplied by
multiple of
“A factory produces 40 500
b) a two-digit number,
other multiplication
batteries per day. 283 500
strategies.
various
batteries are produced in 7
c) 10, 100 and 1000.
estimation
days”
Multiplication strategies to be implemented:
• Pupils practice multiplication lattice
using the four-step algorithm of:
1) Estimate the product.
2) Arrange the numbers
involved according to place
3) Perform the operation.
Check the reasonableness of
the answer.
Lattice multiplication
• Teacher pose problems
(ii) Solve problems involving A guide to solving addition
Times
verbally, i.e., in the numerical
form or simple sentences.
Understanding the
• Teacher guides pupils to solve multiplied by problem
problems following Polya’s four-
Extract information from
multiple of
step model of:
problems posed by drawing diagrams, making lists or
estimation
1) Understanding the problem
tables. Determine the type of lattice
2) Devising a plan
problem, whether it is addition, subtraction, etc.
multiplication
3) Implementing the plan
Devising a plan
4) Looking back.
Translate the information into a number sentence.
(Apply some of the common
Determine what strategy to
strategies in every problem
use to perform the operation.
solving step.)
Implementing the plan
Perform the operation conventionally, i.e. write the number sentence in the vertical form.
Looking back
Check for accuracy of the solution. Use a different startegy, e.g. calculate by using the abacus.
divide than 1 000 000 by a two-
5 Divide a number less
• Pupils create stories from given
(i) Divide numbers up to six Division exercises include
dividend digit number.
division number sentences.
digits by
quptients
• Pupils practice division using
a) without remainder,
a) one-digit number,
quotient
the four-step algorithm of:
b) with remainder.
divisor
1) Estimate the quotient.
b) 10, 100 and 1000,
Note that “r” is used to
2) Arrange the numbers
signify “remainder”.
remainder
involved according to place
c) two-digit number,
Emphasise the long division
3) Perform the operation.
Provide mental division
4) Check the reasonableness of
practice either using the
the answer.
abacus-based technique or other division strategies.
Example for long division
Exposed pupils to various
1 3 5 6 2 r 20
division strategies, such as,
35 4 7 4 6 9 0 a) divisibility of a number
3 5 b) divide by 10, 100 and
• Teacher pose problems
(ii) Solve problems involving
verbally, i.e., in the numerical
division.
form or simple sentences. • Teacher guides pupils to solve
problems following Polya’s four- step model of:
1) Understanding the problem
2) Devising a plan
3) Implementing the plan
4) Looking back.
(Apply some of the common
strategies in every problem solving step.)
Mixed operations operations involving
6 Perform mixed
• Pupils create stories from given
(i) Calculate mixed operation For mixed operations
number sentences involving
on whole numbers
involving multiplication and
multiplication and division.
mixed operations of division
involving multiplication and
division, calculate from left to
and multiplication.
division.
right.
• Pupils practice calculation
Limit the result of mixed
involving mixed operation using
operation exercises to less
the four-step algorithm of:
than 100 000, for example
a) 24 × 10 ÷ 5 =
1) Estimate the quotient.
b) 496 ÷ 4 × 12 =
2) Arrange the numbers
involved according to place
c) 8 005 × 200 ÷ 50 =
values.
Avoid problems such as
3) Perform the operation.
a) 3 ÷ 6 x 300 =
4) Check the reasonableness of
b) 9 998 ÷ 2 × 1000 =
the answer.
c) 420 ÷ 8 × 12 =
• Teacher guides pupils to solve
(ii) Solve problems involving
Pose problems in simple
problems following Polya’s four-
mixed operations of
sentences, tables or
step model of:
division and multiplication..
pictorials.
1) Understanding the problem
Some common problem solving strategies are
2) Devising a plan
a) Drawing diagrams
3) Implementing the plan
b) Making a list or table
4) Looking back.
c) Using arithmetic
(Apply appropriate strategies in
formula
every problem solving step.)
d) Using tools.
improper fraction fractions.
1 Understand improper
• Demonstrate improper fractions
(i) Name and write improper
Revise proper fractions
using concrete objects such as
fractions with denominators before introducing improper
fractions.
numerator
paper cut-outs, fraction charts
up to 10.
and number lines.
Improper fractions are
denominator
• Pupils perform activities such
(ii) Compare the value of the fractions that are more than
three over two
as paper folding or cutting, and
two improper fractions.
one whole.
three halves
marking value on number lines
to represent improper fractions.
1 1 one whole
quarter compare
“three halves” 3 2 partition
The numerator of an improper fraction has a higher value than the denominator.
The fraction reperesented by the diagram is “five thirds”
and is written as 5 3 . It is commonly said as “five over
three”.
fraction numbers.
2 Understand mixed
• Teacher demonstrates mixed
(i) Name and write mixed A mixed number consists of
numbers by partitioning real
numbers with denominators
a whole number and a
proper fraction
objects or manipulative.
up to 10.
proper fraction.
• Pupils perform activities such improper fraction
e.g.
as
(ii) Convert improper fractions
mixed numbers
to mixed numbers and vice- 2 1
a) paper folding and shading
versa.
Say as ‘two and a half’ or
b) pouring liquids into
‘two and one over two’.
containers To convert improper
c) marking number lines
fractions to mixed numbers,
to represent mixed numbers.
use concrete representations to verify the equivalence,
e.g.
then compare with the procedural calculation.
e.g.
4 shaded parts.
1 7= R 2
3 1 2 beakers full.
mixed numbers numbers.
3 Add two mixed
• Demonstrate addition of mixed
(i) Add two mixed numbers
Examples of mixed numbers
numbers through
with the same
addition exercise:
equivalent
denominators up to 10.
a) paper folding activities
a) 2 + = simplest form
b) fraction charts
(ii) Add two mixed numbers 3 denominators
c) diagrams
with different denominators
up to 10.
b) 2 + = multiples
d) number lines.
number lines
e.g.
(iii) Solve problems involving
addition of mixed numbers.
c) 1 + 2 = diagram
1 + 1 = 2 fraction charts
4 2 4 The following type of
problem should also be included:
a) 1 + 3 = 8 9 1 3 1 + 3
b) 1 + 1 = = × 1 + 2 3 2
Emphasise answers in
• Create stories from given
simplest form.
number sentences involving
mixed numbers.
simplest form numbers.
4 Subtract mixed
• Demonstrate subtraction of
(i) Subtract two mixed Some examples of
mixed numbers through
numbers with the same
subtraction problems:
multiply
denominator up to 10.
a) paper folding activities
a) 2 −2 = fraction chart
b) fraction charts
mixed numbers
c) diagrams
b) 2 − = multiplication tables.
d) number lines
e) multiplication tables.
c) 2 − 1 =
• Pupils create stories from given
number sentences involving mixed numbers.
d) 3 − 1 =
e) 2 − 1 =
8 8 Emphasise answers in
simplest form.
(ii) Subtract two mixed
Include the following type of
simplest form
numbers with different
problems, e.g.
equivalent
denominators up to 10.
multiples (iii) Solve problems involving 2 4 number sentences
subtraction of mixed
numbers.
2 × 2 4 mixed numbers
2 1 equivalent fraction
4 Other examples
a) 1 − =
b) 3 −
c) 2 − =
d) 5 − 3 =
6 4 Emphasise answers in
simplest form.
Simplest form fractions with a whole
5 Multiply any proper
• Use groups of concrete
(i) Multiply whole numbers Emphasise group of objects
Fractions number up to 1 000.
materials, pictures and number
with proper fractions.
as one whole.
lines to demonstrate fraction as
Limit whole numbers up to 3
equal share of a whole set.
digits in mulplication
Denominator
• Provide activities of comparing
exercises of whole numbers
Numerator
equal portions of two groups of
and fractions.
Whole number
objects.
Some examples multiplication exercise for
Proper fractions
e.g.
fractions with the numerator
Divisible
2 of 6 = 3
1 and denominator up to 10.
a) 2 1 of 6 pencils is 3 pencils. 2 of 8
b)
c)
6 × or six halves.
1 (ii) Solve problems involving
Some multiplication
Multiply
2 multiplication of fractions.
examples for fractions with the numerator more than 1
fractions
and denominator up to 10.
Whole number
e.g.
Divisible
6 × ½ of an orange is…
2 Denominator
a)
of 9
3 + 3 + 3 + 3 + 3 = 3 oranges.
3 Numerator
5 • Create stories from given Proper fractions
b) 49 ×
number sentences.
c) 3× 136 c) 3× 136
1 Understand and use
• Teacher models the concept of
(i) Name and write decimal Decimals are fractions of
place value chart decimals.
decimal numbers using number
numbers to three decimal
tenths, hundredths and
(ii) Recognise the place value
thousand squares
8 parts out of 1 000 equals
of thousandths.
0.007 is read as “seven
thousandths” or ‘zero point
decimal point
zero zero seven’.
23 parts out of 1 000 is equal to
(iii) Convert fractions of
decimal place
thousandths to decimal
12.302 is read as “twelve
numbers and vice versa.
and three hundred and two
decimal fraction
100 parts out of 1 000 is 0.100
thousandths” or ‘twelve point mixed decimal
• Compare decimal numbers
(iv) Round off decimal numbers three zero two’.
convert
using thousand squares and
to the nearest
Emphasise place value of
number line.
a) tenths,
thousandths using the
• Pupils find examples that use
thousand squares.
decimals in daily situation.
b) hundredths.
Fractions are not required to
be expressed in its simplest form.
Use overlapping slides to compare decimal values of tenths, hundredths and thousandths.
The size of the fraction charts representing one whole should be the same for tenths, hundredths and thousandths.
2 Add decimal numbers • Pupils practice adding decimals (i) Add any two to four Add any two to four decimals decimal numbers up to three decimal places.
using the four-step algorithm of
decimal numbers up to
given number sentences in
three decimal places
the horizontal and vertical
vertical form
1) Estimate the total.
involving
form.
place value
2) Arrange the numbers
Emphasise on proper
decimal point
involved according to place
a) decimal numbers and
positioning of digits to the
values.
decimal numbers,
corresponding place value
estimation
3) Perform the operation.
when writng number
horizontal form
b) whole numbers and
sentences in the vertical
4) Check the reasonableness of
decimal numbers,
form.
total
the answer. • Pupils create stories from given 6.239 + 5.232 = 11.471 (ii) Solve problems involving
number sentences.
addition of decimal
numbers.
addend
sum
addend addend
3 Subtract decimal
• Pupils subtract decimal
(i) Subtract a decimal number Emphasise performing
place value decimal places.
numbers, given the number
from another decimal up to
subtraction of decimal
sentences in the horizontal and
three decimal places.
numbers by writing the
vertical form.
number sentence in the
decimal point
• Pupils practice subtracting
(ii) Subtract successively any vertical form.
estimation
decimals using the four-step
two decimal numbers up to
Emphasise the alignment of
algorithm of
three decimal places.
place values and decimal
range
points.
decimal numbers
1) Estimate the total.
(iii) Solve problems involving
2) Arrange the numbers
subtraction of decimal
Emphasise subtraction using the four-step algorithm.
involved according to place
numbers.
values.
The minuend should be of a bigger value than the
3) Perform the operation.
subtrahend.
4) Check the reasonableness of
the answer. • Pupils make stories from given
number sentences.
minuend difference
subtrahend subtrahend
4 Multiply decimal
• Multiply decimal numbers with
(i) Multiply any decimal Emphasise performing
decimal point decimal places with a
a number using horizontal and
numbers up to three
multiplication of decimal numbers by writing the
vertical form.
decimal places with
whole number.
• Pupils practice subtracting estimation
number sentence in the
a) a one-digit number,
vertical form.
decimals using the four-step
range
algorithm
Emphasise the alignment of
b) a two-digit number,
place values and decimal
product
1) Estimate the total.
points.
horizontal form
2) Arrange the numbers
c) 10, 100 and 1000.
Apply knowledge of decimals
involved according to place
(ii) Solve problems involving in:
values.
multiplication of decimal
a) money,
3) Perform the operation.
numbers.
b) length,
4) Check the reasonableness of
the answer.
c) mass,
• Pupils create stories from given
d) volume of liquid.
number sentences.
(i) Divide a whole number by Emphasise division using the divide numbers up to three
5 Divide decimal
• Pupils practice subtracting
quotient decimal places by a whole
decimals using the four-step
four-steps algorithm.
algorithm of
a) 10
Quotients must be rounded
number.
1) Estimate the total.
off to three decimal places.
decimal places
Apply knowledge of decimals Arrange the numbers rounded off involved according to place
whole number
values.
a) money,
3) Perform the operation.
(ii) Divide a whole number by
b) length,
4) Check the reasonableness of
a) a one-digit number,
c) mass,
the answer.
• Pupils create stories from given d) volume of liquid.
b) a two-digit whole
number sentences.
number,
(iii) Divide a decimal number of three decimal places by
a) a one-digit number
b) a two-digit whole number
c) 10
d) 100. (iv) Solve problem involving
division of decimal numbers.
(i) Name and write the symbol The symbol for percentage is percent percentage.
1 Understand and use
• Pupils represent percentage
with hundred squares.
for percentage.
% and is read as ‘percent’,
e.g. 25 % is read as ‘twenty- percentage
• Shade parts of the hundred
(ii) State fraction of hundredths five percent’.
squares.
• Name and write the fraction of
in percentage.
The hundred squares should
be used extensively to easily
the shaded parts to percentage. (iii) Convert fraction of
convert fractions of
hundredths to percentage
hundredths to percentage.
and vice versa.
e.g.
a)
b) 42% =
2 Relate fractions and
• Identify the proper fractions
(i) Convert proper fractions of
e.g.
decimals to percentage.
with the denominators given.
tenths to percentage.
(ii) Convert proper fractions 10 10 10 100 with the denominators of 2,
4, 5, 20, 25 and 50 to
percentage.
(iii) Convert percentage to
fraction in its simplest form.
(iv) Convert percentage to decimal number and vice versa.
RM the vocabulary related to
1 Understand and use
• Pupils show different
(i) Read and write the value of
sen money.
combinations of notes and
money in ringgit and sen up
coins to represent a given
to RM100 000.
amount of money.
note value
total mathematics concepts
2 Use and apply
• Pupils perform basic and mixed
(i) Add money in ringgit and When performing mixed
amount up to RM100 000.
operations involving money by
sen up to RM100 000.
operations, the order of
when dealing with money
writing number sentences in
operations should be
the horizontal and vertical form.
(ii) Subtract money in ringgit
observed.
range
• Pupils create stories from given
and sen within the range of
Example of mixed operation
dividend
number sentences involving
RM100 000.
involving money,
combination
money in real context, for example,
(iii) Multiply money in ringgit
RM62 000 ÷ 4 ×3=?
and sen with a whole
Avoid problems with
a) Profit and loss in trade
number, fraction or decimal
remainders in division, e.g.,
b) Banking transaction
with products within
RM100 000.
RM75 000.10 ÷ 4 ×3=?
c) Accounting
d) Budgeting and finance
(iv) Divide money in ringgit and
management
sen with the dividend up to RM100 000.
(v) Perform mixed operation of
multiplication and division
involving money in ringgit
and sen up to RM100 000.
• Pupils solve problems following
(vi) Solve problems in real Pose problem in form of
Polya’s four-step algorithm and
context involving money in
numericals, simple
using some of the common
ringgit and sen up to
sentences, graphics and
problem solving strategies.
RM100 000.
stories. Polya’s four-step algorithm
1) Understanding the problem
2) Devising a plan
3) Implementing the plan
4) Checking the solution Examples of the common
problem solving strategies are
• Drawing diagrams • Making a list • Using formula • Using tools
Some common ways to read ante meridiem vocabulary related to time.
1 Understand the
• Pupils tell the time from the
(i) Read and write time in the
digital clock display.
24-hour system.
time in the 24-hour system.
post meridiem
• Design an analogue clock face
e.g.
showing time in the 24-hour
(ii) Relate the time in the 24-
analogue clock
system.
hour system to the 12-hour
digital clock.
system.
24-hour system
Say : Sixteen hundred hours
12-hour system
Write: 1600hrs
Say: Sixteen zero five hours Write: 1605hrs
Say: zero hundred hours Write: 0000hrs
• Pupils convert time by using
(iii) Convert time from the 24- Examples of time conversion a.m
hour system to the 12-hour
from the 24-hour system to
the number line
the 12-hour system.
p.m
system and vice-versa.
12 12 12 e.g.
a) 0400hrs ↔ 4.00 a.m.
b) 1130hrs ↔ 11.30 a.m.
c) 1200hrs ↔ 12.00 noon
d) 1905hrs ↔ 7.05 p.m.
e) 0000hrs ↔12.00 midnight
the clock face a.m.
ante meridiem refers to the time after midnight before
22 14 noon.
p.m.
21 15 post meridiem refers to the time after noon before
20 16 midnight.
2 Understand the
• Pupils convert from one unit of
(i) Convert time in fractions Conversion of units of time
decade of time.
time
and decimals of a minute to may involve proper fractions seconds.
• Pupils explore the relationship
and decimals.
between centuries, decades
a) 1 century = 100 years
and years by constructing a
(ii) Convert time in fractions
b) 1 century = 10 decade
time conversion table.
and decimals of an hour to
minutes and to seconds.
(iii) Convert time in fractions
and decimals of a day to
hours, minutes and
seconds.
(iv) Convert units of time from
a) century to years and
vice versa.
b) century to decades and
vice versa.
multiplier and divide units of time.
3 Add, subtract, multiply • Pupils add, subtract, multiply
(i) Add time in hours, minutes Practise mental calculation
and divide units of time by
and seconds.
for the basic operations
writing number sentences in
involving hours, minutes and
divisor
the horizontal and vertical form.
(ii) Subtract time in hours,
minutes and seconds.
Limit
minutes
5 hr 20 min 30 s (iii) Multiply time in hours,
a) multiplier to a one-digit
hours
minutes and seconds.
b) divisor to a one-digit (iv) Divide time in hours, number and
days
minutes and seconds.
c) exclude remainders in
4 13 hours 13 minutes
(i) Identify the start and end Expose pupils to a variety of duration knowledge of time to find
4 Use and apply
• Pupils read and state
schedule the duration.
information from schedules
times of are event.
schedules.
such as:
Emphasise the 24-hour
a) class time-table,
(ii) Calculate the duration of an system.
event
event, involving
The duration should not be
start
b) fixtures in a tournament
longer than a week.
c) public transport, etc
a) hours, minutes and
end
• Pupils find the duration the start competition
seconds.
and end time from a given
b) days and hours
(iii) Determine the start or end time of an event from a
24-hour system
given duration of time.
period (iv) Solve problems involving fixtures
time duration in fractions
tournament
and/or decimals of hours, minutes and seconds.
1 Measure and compare • Teacher provides experiences (i) Describe by comparison Introduce the symbol ‘km’ for kilometre distances.
to introduce the idea of a
the distance of one
Relate the knowledge of
e.g.
data handling (pictographs)
places
(ii) Measure using scales for to the scales in a simple
points
Walk a hundred-metre track
distance between places.
map.
and explain to pupils that a
destinations
kilometre is ten times the distance.
d represents 10 pupils.
between
• Use a simple map to measure
represents 5 km
record
the distances to one place to
a) school
b) village
c) town c) town
2 Understand the
• Compare the length of a metre
(i) Relate metre and kilometre. Emphasise relationships.
relationship of length.
string and a 100-cm stick, then
1 km = 1000 m
write the relationship between
(ii) Convert metre to kilometre
the units.
and vice versa.
1 m = 100 cm
• Pupils use the conversion table
1 cm = 10 mm
for units of length to convert
Practice mental calculation
length from km to m and vice
giving answers in mixed
versa.
decimals.
add and divide units of length.
3 Add, subtract, multiply • Pupils demonstrate addition
(i) Add and subtract units of Give answers in mixed
and subtraction involving units
length involving conversion
decimals to 3 decimal
subtract
of length using number
of units in
places.
sentences in the usual
Check answers by
conversion
conventional manner.
a) kilometres ,
performing mental
mixed decimal
e.g.
calculation wherever
b) kilometres and metres.
appropriate.
multiply
a) 2 km + 465 m = ______ m
quotient
b) 3.5 km + 615 m = _____ km
c) 12.5 km – 625 m = _____ m
• Pupils multiply and divide
(ii) Multiply and divide units of
involving units of length.
length in kilometres
e.g.
involving conversion of units with
a) 7.215 m ×1 000 =______km
b) 2.24 km ÷ 3 = _____m
a) a one-digit number,
Create stories from given number
b) 10, 100, 1 000.
sentence.
(iii) Identify operations in a
given situation.
(iv) Solve problems involving
basic operations on length.
read objects.
1 Compare mass of
• Pupils measure, read and
(i) Measure and record Emphasise that measuring
record masses of objects in
masses of objects in
should start from the ‘0’ mark of the weighing scale.
weighing scale
kilograms and grams using the
kilograms and grams.
weighing scale and determine
Encourage pupils to check
divisions
how many times the mass of an
(ii) Compare the masses of
object as compared to another.
accuracy of estimates.
weight
two objects using kilogram and gram, stating the
weigh
comparison in multiples or
compare
fractions.
record (iii) Estimate the masses of compound
objects in kilograms and grams.
measurement relationship between units
2 Understand the
• Pupils make stories for a given
(i) Convert units of mass from Emphasise relationships.
relationship of mass.
measurement of mass.
fractions and decimals of a
1 kg = 1000 g
e.g.
kilogram to grams and vice versa.
Emphasise mental
Aminah bought 4 kg of
calculations.
cabbages and 500 g celery.
(ii) Solve problems involving
Emphasise answers in
Altogether, she bought a total
conversion of mass units in
mixed decimals up to 3
of 4.5 kg vegetables.
fraction and/or decimals.
decimal place. e.g.
a) 3 kg 200 g = 3.2 kg
b) 1 kg 450 g = 1.45 kg
c) 2 kg 2 g = 2.002 kg c) 2 kg 2 g = 2.002 kg
1 Measure and compare • Pupils measure, read and