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