Integrated Curriculum for Primary Schools CURRICULUM SPECIFICATIONS
Integrated Curriculum for Primary Schools CURRICULUM SPECIFICATIONS
MATHEMATICS
Curriculum Development Centre Ministry of Education Malaysia
Copyright © 2006 Curriculum Development Centre Ministry of Education Malaysia Kompleks Kerajaan Parcel E Pusat Pentadbiran Kerajaan Persekutuan 62604 Putrajaya
First published 2006
Copyright reserved. Except for use in a review, the reproduction or utilisation of this work in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, and recording is forbidden without the prior written permission from the Director of the Curriculum Development Centre, Ministry of Education Malaysia.
CON T EN T
14 National Philosophy of Education
Money up to RM10 million
15 Introduction
Preface ix
WHOLE NUMBERS
17 Numbers up to Seven Digits
1 Computation of Length
18 Basic Operations with Numbers up to Seven Digits
MASS
18 Mixed Operations with Numbers up to Seven Digits
Computation of Mass
19
VOLUME OF LIQUID
FRACTIONS
19 Addition of Fractions
7 Computation of Volume of Liquid
20 Multiplication of Fractions
Subtraction of Fractions 8 SHAPE AND SPACE
20 Division of Fractions
9 Two-Dimensional Shapes
10 Three-Dimensional Shapes 22
24 Mixed Operations with Decimals
DECIMALS
11 DATA HANDLING
Organising and Interpreting Data
Relationship between Percentage, Fraction and Decimal
12 Contributors
RU K U N EGARA
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.
PREFACE
The development of a set of Curriculum Specifications as a supporting document to the syllabus is the work of many individuals and experts
Science and technology plays a crucial role in meeting Malaysia’s in the field. To those who have contributed in one way or another to aspiration to achieve developed nation status. Since mathematics is
this effort, on behalf of the Ministry of Education, I would like to thank instrumental in developing scientific and technological knowledge, the
them and express my deepest appreciation.
provision of quality mathematics education from an early age in the
education process is critical.
The primary school Mathematics curriculum as outlined in the syllabus has been designed to provide opportunities for pupils to acquire
mathematical knowledge and skills and develop the higher order
problem solving and decision making skills that they can apply in their everyday lives. But, more importantly, together with the other subjects
in the primary school curriculum, the mathematics curriculum seeks to
(DR. HAILI BIN DOLHAN)
inculcate noble values and love for the nation towards the final aim of developing the holistic person who is capable of contributing to the
Director
harmony and prosperity of the nation and its people.
Curriculum Development Centre Ministry of Education
Beginning in 2003, science and mathematics will be taught in English
Malaysia
following a phased implementation schedule, which will be completed by 2008. Mathematics education in English makes use of ICT in its delivery. Studying mathematics in the medium of English assisted by ICT will provide greater opportunities for pupils to enhance their knowledge and skills because they are able to source the various repositories of knowledge written in mathematical English whether in electronic or print forms. Pupils will be able to communicate mathematically in English not only in the immediate environment but also with pupils from other countries thus increasing their overall English proficiency and mathematical competence in the process.
I N T RODU CT I ON
strategies of problem solving, communicating mathematically and inculcating positive attitudes towards an appreciation of mathematics
Our nation’s vision can be achieved through a society that is educated as an important and powerful tool in everyday life. and competent in the application of mathematical knowledge. To
It is hoped that with the knowledge and skills acquired in Mathematics, realise this vision, society must be inclined towards mathematics.
pupils will discover, adapt, modify and be innovative in facing changes Therefore, problem solving and communicational skills in mathematics
and future challenges.
have to be nurtured so that decisions can be made effectively.
Mathematics is integral in the development of science and technology. As such, the acquisition of mathematical knowledge must be upgraded periodically to create a skilled workforce in preparing the country to
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;
4 master basic mathematical skills, namely:
• Decimals;
• making estimates and approximates,
• Money;
• measuring,
2 Measures
• handling data
• Time;
• representing information in the form of graphs and charts;
• Length;
5 use mathematical skills and knowledge to solve problems in
• Mass;
everyday life effectively and responsibly;
• Volume of Liquid.
6 use the language of mathematics correctly;
3 Shape and Space
7 use suitable technology in concept building, acquiring
• Two-dimensional Shapes;
mathematical skills and solving problems;
• Three-dimensional Shapes;
8 apply the knowledge of mathematics systematically, heuristically,
• Perimeter and Area.
accurately and carefully;
4 Statistics
9 participate in activities related to mathematics; and
• Data Handling
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;
The purpose of these columns is to illustrate, for a particular teaching
EM PH ASES I N T EACH I N G AN D LEARN I N G
objective, a list of what pupils should know, understand and be able to do by the end of each respective topic.
The Mathematics Curriculum is ordered in such a way so as to give The Learning Objectives define clearly what should be taught. They
flexibility to the teachers to create an environment that is enjoyable, cover all aspects of the Mathematics curriculum and are presented in
meaningful, useful and challenging for teaching and learning. At the
a developmental sequence to enable pupils to grasp concepts and same time it is important to ensure that pupils show progression in master skills essential to a basic understanding of mathematics.
acquiring the mathematical concepts and skills.
The Suggested Teaching and Learning Activities list some On completion of a certain topic and in deciding to progress to another examples of teaching and learning activities. These include methods,
learning area or topic, the following need to be taken into accounts: techniques, strategies and resources useful in the teaching of a
• The skills or concepts acquired in the new learning area or specific concepts and skills. These are however not the only
topics;
approaches to be used in classrooms. • Ensuring that the hierarchy or relationship between learning The Learning Outcomes define specifically what pupils should be
areas or topics have been followed through accordingly; and able to do. They prescribe the knowledge, skills or mathematical
processes and values that should be inculcated and developed at the • Ensuring the basic learning areas have or skills have been appropriate levels. These behavioural objectives are measurable in all
acquired or mastered before progressing to the more aspects.
abstract areas.
In Points To Note, attention is drawn to the more significant aspects The teaching and learning processes emphasise concept building, skill of mathematical concepts and skills. These aspects must be taken into
acquisition as well as the inculcation of positive values. Besides these, accounts so as to ensure that the concepts and skills are taught and
there are other elements that need to be taken into account and learnt learnt effectively as intended.
through the teaching and learning processes in the classroom. The main emphasis are as follows:
The Vocabulary column consists of standard mathematical terms, instructional words and phrases that are relevant when structuring activities, asking questions and in setting tasks. It is important to pay
1 . 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.
Over the years of intellectual discourse, problem solving has People learn best through experience. Hence, mathematics is best developed into a simple algorithmic procedure. Thus, problem solving
learnt through the experience of solving problems. Problem-based is taught in the mathematics curriculum even at the primary school
learning is an approach where a problem is posed at the beginning of level. The commonly accepted model for problem solving is the four-
a lesson. The problem posed is carefully designed to have the desired step algorithm, expressed as follows:-
mathematical concept and ability to be acquired by students during the • 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.
Communication in mathematics through the visualization process • Structured and unstructured interviews; takes place when an individual makes observation, analyses it, interprets and synthesises the data into graphic forms, such as
• Discussions during forums, seminars, debates and brain- pictures, diagrams, tables and graphs.
storming sessions; and
The following methods can create an effective communication • Presentation of findings of assignments.
environment: Written communication is the process whereby mathematical ideas • Identifying relevant contexts associated with environment and
and information are shared with others through writing. The written everyday life experiences of pupils;
work is usually the result of discussions, contributions and brain- storming activities when working on assignments. Through writing, the
• Identifying interests of pupils; pupils will be encouraged to think more deeply about the mathematics • 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
packages can help to upgrade the pedagogical skills in the teaching and learning of mathematics.
Pupils are encouraged to predict and do guess work in the process of seeking solutions. Pupils at all levels have to be trained to investigate
The use of teaching resources is very important in mathematics. This their predictions or guesses by using concrete materials, calculators,
will ensure that pupils absorb abstract ideas, be creative, feel computers, mathematical representation and others. Logical reasoning
confident and be able to work independently or in groups. Most of has to be infused in the teaching of mathematics so that pupils can
these resources are designed for self-access learning. Through self- recognise, construct and evaluate predictions and mathematical
access learning, pupils will be able to access knowledge or skills and arguments.
information independently according to their pace. This will serve to stimulate pupils’ interests and responsibility in learning mathematics.
4 . 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-
demonstration. These may be in the form of interviews, open-ended mathematics.
questions, observations and assignments. Based on the results, the Among the approaches that can be given consideration are:
teachers can rectify the pupils’ misconceptions and weaknesses and at the same time improve their teaching skills. As such, teachers can
• Pupil centered learning that is interesting; take subsequent effective measures in conducting remedial and • 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
Year 6
Lear n i n g Ar e a: NUMBERS UP TO SEVEN DIGITS
LEARN I N G OBJ ECT I V ES
SU GGEST ED T EACH I N G AN D
LEARN I N G OU T COM ES
POI N T S T O N OT E
V OCABU LARY
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 million up to seven digits.
1 develop number sense
• Teacher pose numbers in
numerals, pupils name the
up to seven digits.
numerals.
digits
respective numbers and write
Seven-digit numbers are
the number words.
conversion
numbers from 1 000 000 up
• Teacher says the number
to 9 999 999.
place value
names and pupils show the
Emphasise reading and
explore
numbers using the calculator or
writing numbers in extended
the abacus, then, pupils write
notation for example
number patterns
the numerals.
multiple of 10
• Provide suitable number line
simplest form
scales and ask pupils to mark
the positions that represent a
extended notation
set of given numbers.
or
round off
5 801 249 = 5 millions + 8 hundred thousands + 1 thousands + 2 hundreds + 4 tens + 9 ones.
• Given a set of numbers, pupils
(ii) Determine the place value To avoid confusion, initials
represent each number using
of the digits in any whole
for place value names may
the number base blocks or the
number of up to seven
be written in upper cases.
abacus. Pupils then state the
digits.
place value of every digit of the given number.
Year 6
Lear n i n g Ar e a: NUMBERS UP TO SEVEN DIGITS
LEARN I N G OBJ ECT I V ES
SU GGEST ED T EACH I N G AN D
LEARN I N G OU T COM ES
POI N T S T O N OT E
V OCABU LARY
Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
(iii) Express whole numbers in Write numbers in partial words and numerals, for
a) decimals
example
a) 800 000 is 0.8 million
b) fractions
b) 6 320 000 is 6.32 million
of a million and vice versa.
c) 1.4 million is 1 400 000
d) 5.602 million is 5 602 000
e) 3 500 000 is 3 2 1 million
f) 8 3 4 million is 8 750 000 For fractional number words,
denominators are in multiples of 10 (10 to 90, 100 and 1000) and reduce fractional terms to its simplest form.
Limit decimal terms up to 3 decimal places.
• Given a set of numerals, pupils
(iv) Compare number values
compare and arrange the
up to seven digits.
numbers in ascending then descending order.
(v) Round off numbers to the Explain to pupils that
nearest tens, hundreds,
numbers are rounded off to
thousands, ten thousands,
get an approximate.
hundred thousands and millions.
Year 6
Lear n i n g Ar e a: BASIC OPERATIONS WITH NUMBERS UP TO SEVEN DIGITS
LEARN I N G OBJ ECT I V ES
SU GGEST ED T EACH I N G AN D
LEARN I N G OU T COM ES
POI N T S T O N OT E
V OCABU LARY
Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
simpler and divide numbers
2 Add, subtract, multiply
• Pupils practice addition,
(i) Add any two to five
Addition exercises include
subtraction, multiplication and
numbers to 9 999 999.
addition of two numbers to four numbers with and
simulating involving numbers up to
division using the four-step
seven digits.
algorithm of
without regrouping.
analogy
1) Estimate the solution.
Provide mental addition
sequences
practice either using the
2) Arrange the numbers
abacus-based technique or
involved according to place values. using quick addition
strategies such as estimating
3) Perform the operation.
total by rounding, simplifying addition by pairs of tens,
4) Check the reasonableness
doubles, etc.
of the answer.
(ii) Subtract Limit subtraction problems to subtracting from a bigger
a) one number from a
number.
bigger number less than Provide mental subtraction
practice either using the abacus-based technique or
b) successively from a
using quick subtraction
bigger number less than strategies.
10 000 000. Quick subtraction strategies
to be implemented are
a) estimating the sum by rounding numbers
b) counting up and counting down (counting on and counting back).
Year 6
Lear n i n g Ar e a: BASIC OPERATIONS WITH NUMBERS UP TO SEVEN DIGITS
LEARN I N G OBJ ECT I V ES
SU GGEST ED T EACH I N G AN D
LEARN I N G OU T COM ES
POI N T S T O N OT E
V OCABU LARY
Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
(iii) Multiply up to six-digit
Limit products to less than
numbers with
10 000 000. Provide mental multiplication
a) a one-digit number
practice either using the abacus-based technique or
b) a two-digit number
other multiplication strategies.
c) 10, 100 and 1000. Multiplication strategies to be
implemented include factorising, completing 100, lattice multiplication, etc.
(iv) Divide numbers of up to
Division exercises include
seven digits by
quotients with and without remainder. Note that “r” is
a) a one-digit number
used to signify “remainder”. Emphasise the long division
b) 10, 100 and 1000
technique.
c) two-digit number.
Provide mental division practice either using the abacus-based technique or other division strategies.
Exposed pupils to various division strategies, such as
a) divisibility of a number
b) divide by 10, 100 and
Year 6
Lear n i n g Ar e a: BASIC OPERATIONS WITH NUMBERS UP TO SEVEN DIGITS
LEARN I N G OBJ ECT I V ES
SU GGEST ED T EACH I N G AN D
LEARN I N G OU T COM ES
POI N T S T O N OT E
V OCABU LARY
Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
• Pose to pupils problems in
(v) Solve Use any of the common
numerical form, simple
strategies of problem solving, such as
sentences, tables and pictures.
a) addition,
• Pupils create stories from given
a) Try a simpler case
number sentences.
b) subtraction,
b) Trial and improvement
• Teacher guides pupils to solve
c) multiplication,
c) Draw a diagram
problems following Polya’s four-
step model of
d) division
d) Identifying patterns and
sequences
1) Understanding the problem
problems involving
e) Make a table, chart or a
2) Devising a plan
numbers up to seven digits.
systematic list
3) Implementing the plan
f) Simulation
4) Looking back.
g) Make analogy
h) Working backwards.
Year 6
Lear n i n g Ar e a: MIXED OPERATIONS WITH NUMBERS UP TO SEVEN DIGITS
LEARN I N G OBJ ECT I V ES
SU GGEST ED T EACH I N G AN D
LEARN I N G OU T COM ES
POI N T S T O N OT E
V OCABU LARY
Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
(i) Compute mixed operations Mixed operations are limited compute operations with whole
3 Perform mixed
• Explain to pupils the conceptual
mixed operations numbers.
model of mixed operations then
problems involving addition
to not more than two
connect the concept with the
and multiplication.
operators, for example
procedures of performing
a) 427 890 − 15 600 ÷ 25 =
bracket
operations according to the
order of operations.
b) 12 745 + 20 742 × 56 =
horizontal form
vertical form
• Teacher pose problems
(ii) Compute mixed operations Order of operations
verbally, i.e., in the numerical
problems involving
B – brackets
form or simple sentences.
subtraction and division.
O – of
D – division M – multiplication
A – addition S – subtraction
• Teacher guides pupils to solve
(iii) Compute mixed operations Examples of mixed
problems following Polya’s four-
problems involving
operations with brackets
step model of
brackets.
a) (1050 + 20 650) × 12 =
1) Understanding the problem
b) 872 ÷ (8 − 4) =
2) Devising a plan
c) (24 + 26) × (64 − 14) =
3) Implementing the plan
4) Looking back.
(iv) Solve problems involving
mixed operations on numbers of up to seven
digits.
Year 6
Lear n i n g Ar e a: ADDITION OF FRACTIONS
LEARN I N G OBJ ECT I V ES
SU GGEST ED T EACH I N G AN D
LEARN I N G OU T COM ES
POI N T S T O N OT E
V OCABU LARY
Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
mixed numbers numbers with denominators
1 Add three mixed
• Demonstrate addition of mixed
(i) Add three mixed numbers An example of addition of
numbers through
with the same denominator
three mixed numbers with the same denominator of up
equivalent fractions of up to 10.
1) paper folding activities
of up to 10.
to 10.
simplest form
2) fraction charts
3 1 7 + 1 2 7 + 2 3 7 = multiplication tables
3) diagrams
4) number lines
5) multiplication tables
• Pupils create stories from given
(ii) Add three mixed numbers
An example of addition of
number sentences involving
with different denominators
three mixed numbers with
mixed numbers.
of up to 10.
different denominators of up to 10.
2 1 3 + 1 1 6 1 + 2 4 = Write answers in its simplest
form.
• Teacher guides pupils to solve
(iii) Solve problems involving
problems following Polya’s four-
addition of mixed numbers.
step model of
1) Understanding the problem
2) Devising a plan
3) Implementing the plan
4) Looking back.
Year 6
Lear n i n g Ar e a: SUBTRACTION OF FRACTIONS
LEARN I N G OBJ ECT I V ES
SU GGEST ED T EACH I N G AN D
LEARN I N G OU T COM ES
POI N T S T O N OT E
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
mixed numbers numbers with denominators
2 Subtract mixed
• Demonstrate subtraction of
(i) Subtract involving three
An example of subtraction
mixed numbers through
mixed numbers with the
involving three mixed
equivalent fractions of up to 10.
1) paper holding activities
same denominator of up to
numbers with the same
10. denominator of up to 10.
simplest form
2) fractions charts
5 4 − 1 2 5 1 5 − 1 5 = multiplication tables
3) diagrams
4) number lines
5) multiplication tables • Pupils create stories from given
(ii) Subtract involving three
An example of subtraction
number sentences involving
mixed numbers with
involving three mixed
mixed numbers.
different denominators of
numbers with different
up to 10.
denominators of up to 10.
7 7 − 3 8 1 4 − 1 1 2 = Write answers in its simplest
form.
• Pose to pupils, problems in the
(iii) Solve problems involving
real context in the form of
subtraction of mixed
1) words,
numbers.
2) tables,
3) pictorials.
Year 6
Lear n i n g Ar e a: MULTIPLICATION OF FRACTIONS
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
(i) Multiply mixed numbers Model multiplication of mixed mixed numbers numbers with a whole
3 Multiply any mixed
• Use materials such as the
hundred squares to model
with a whole number.
numbers with whole
portions numbers up to 1000.
multiplication of mixed
numbers as grouping sets of
numbers. For example,
objects, for example
simplest form
3 1 × 300 means 3 3 1 3 groups
of sets of 300. Suppose we have a set of
100 objects. Two groups or sets will contain 200 objects,
i.e. 2 × 100 = 200 .Therefore,
2 1 2 groups will contain
2 1 2 × 100 = 250 objects. Limit the whole number
component of a mixed number, to three digits. The
• Present calculation in clear and
denominator of the fractional
organised steps.
part of the mixed number is
limited to less than 10.
Year 6
Lear n i n g Ar e a: DIVISION OF FRACTIONS
LEARN I N G OBJ ECT I V ES
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
4 Divide fractions with a
• Teacher models the division of
(ii) Divide fractions with Limit denominators for the
whole number and a
fraction with another fraction as
dividend to less than 10.
fraction.
sharing. The following
a) a whole number
illustrations demonstrate this
Limit divisors to less than 10 for both the whole number
idea…
b) a fraction.
and fraction.
2 2 = 1 Some models of division of a
Half a vessel of liquid poured
fraction with a fraction…
into a half-vessel makes one full half-vessel.
4 or
(iii) Divide mixed numbers with
Half a vessel of liquid poured
a) a whole number
into a quarter-vessel makes two
full quarter-vessels.
b) a fraction.
or
Year 6
Lear n i n g Ar e a: MIXED OPERATIONS WITH DECIMALS
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
decimal number operations of addition and
1 Perform mixed
• Pupils add and/or subtract
(i) Add and subtract three to
Some examples of mixed
three to four decimal numbers
four decimal numbers of up operations with decimals.
decimal places subtraction of decimals of
in parts, i.e. by performing one
to 3 decimal places,
operation at a time in the order
up to 3 decimal places.
involving
of left to right. Calculation steps
are expressed in the vertical
a) decimal numbers only
form.
126.6 + 84 - 3.29 =
• The abacus may be used to or
b) whole numbers and
verify the accuracy of the result
decimal numbers.
of the calculation.
0.6 + 0.006 +3.446 – 2.189 = An example of how
calculation for mixed operations with decimals is
expressed. 126.6 – 84 + 3.29 = ?
Year 6
Lear n i n g Ar e a: RELATIONSHIP BETWEEN PERCENTAGE, FRACTION AND DECIMAL
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
(i) Convert mixed numbers to Fractions can be modeled as simplest form decimals to percentage.
1 Relate fractions and
• Use the hundred-squares to
model conversion of mixed
percentage.
parts of a whole, groupings
of sets of objects, or division. numbers to percentage. For multiples
example, convert 1 3 to
To relate mixed numbers to
percent
percentages, the numbers
percentage.
have to be viewed as
percentage
fractions. Mixed numbers have to be converted to improper fractions first, to give meaning to the relationship mixed numbers with percentages. For example
100% 30% The shaded parts represent
(ii) Convert decimal numbers
Limit decimal numbers to
130% of the hundred-squares.
of value more than 1 to
values less than 10 and to
percentage.
two decimal places only. An example of a decimal
number to percentage conversion
Year 6
Lear n i n g Ar e a: RELATIONSHIP BETWEEN PERCENTAGE, FRACTION AND DECIMAL
LEARN I N G OBJ ECT I V ES
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
• Demonstrate the concept of
(iii) Find the value for a given Finding values for
simplest form
percentage of a quantity using
percentage of a quantity.
percentage of a quantity, shall include the following,
multiple
the hundred-squares or multi- based blocks.
Quantity value of income
a) 100
expenses savings
b) less than 100
c) more than 100,
profit loss
Percentage value of
a) less than 100%
discount
The shaded parts of the two hundred-squares is 128% of
b) more than 100%.
dividend
Sample items for finding
interest
• Guide pupils to find the value
values for percentage of a
tax
for percentage of a quantity
quantity are as follows:
through some examples, such
commission
as
a) 9.8% of 3500
45% of 10
b) 114% of 100
c) 150% of 70
d) 160% of 120
• Pupils create stories from given
(iv) Solve problems in real
Solve problems in real life
percentage of a quantity.
context involving
involving percentage
• Pose to pupils, situational calculation of income and
relationships between
percentage, fractions and
expenditure, savings, profit
problems in the form of words,
decimals.
and loss, discount, dividend
tables and pictorials.
or interest, tax, commission, etc.
Year 6
Lear n i n g Ar e a: MONEY UP TO RM10 MILLION
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
mixed operation sense in real context
1 Use and apply number
• Provide to pupils a situation
(i) Perform mixed operations Mixed operations exercise
involving money where mixed
with money up to a value of may also include brackets,
bracket involving money.
operations need to be
RM10 million.
for example
performed. Then, demonstrate
savings
how the situation is
RM8000 + RM1254 – RM5555 =
transformed to a number
RM125.05 – RM21 – RM105.95 =
income
sentence of mixed operations.
(RM100 + RM50) ×5=
expenditure
• Pupils solve mixed operations
(RM125 × 8) – (RM40 × 8) =
investments
involving money in the usual
cost price
proper manner by writing
RM1200 – (RM2400 ÷ 6) =
number sentences in the
selling price
vertical form.
profit
• Pose problems involving
(ii) Solve problems in real
Discuss problems involving
loss
money in numerical form,
context involving
various situations such as savings, income,
discount
simple sentences, tables or
computation of money.
pictures.
expenditure, investments,
computation
• Teacher guides pupils to solve cost price, selling price, profit, loss and discount.
problems following Polya’s four- step model of
1) Understanding the problem
2) Devising a plan
3) Implementing the plan
4) Looking back.
Year 6
Lear n i n g Ar e a: DURATION
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
calculation knowledge of time to find
1 Use and apply
• Pupils find the duration from
(i) Calculate the duration of an Some basic ideas of points
the start to the end of an event
event in between
in time so that calculation of duration is possible, are as
compute the duration.
from a given situation with the aid of the calendar, schedules
a) months
follows:
date
and number lines.
For duration in months, “…
calendar
b) years
from March until October.”
schedule
c) dates.
For duration in years and months, “… from July 2006
duration
to September 2006.”
event
For duration in years,
month
months and days,
year
a) “… from 25th March 2004 up to 25th June 2004”, or
b) “… from 27th May 2005 till 29th June 2006.”
(ii) Compute time period from
An example of a situation
situations expressed in
expressed in a fraction of
fractions of duration.
time duration
57 … 2 3 of 2 years.
Year 6
Lear n i n g Ar e a: DURATION
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
• Pose problems involving
(iii) Solve problem in real Discuss problem involving
computation of time in
context involving
various situations such as
numerical form, simple
computation of time
event, calendar etc.
sentences, tables or pictures.
duration.
• Teacher guides pupils to solve
problems following Polya’s four-
step model of
1) Understanding the problem
2) Devising a plan
3) Implementing the plan
4) Looking back.
Year 6
Lear n i n g Ar e a: COMPUTATION OF LENGTH
LEARN I N G OBJ ECT I V ES
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
proper fraction fractional computation to
1 Use and apply
• Use scaled number lines or
(i) Compute length from a
The term fraction includes
paper strips to model situations
situation expressed in
mixed numbers.
length problems involving length.
expressed in fractions.
fraction.
An example of computing
measurement
2 of 4 km.
length from a situation
expressed in fraction is as
In this context, “of” is a multiplication operator, so,
• Pose problems involving
(ii) Solve problem in real
Problems involving
computation of length in
context involving
computation of length may
numerical form, simple
computation of length.
also include measuring,
sentences, tables or pictures.
conversion of units and/or
• Teacher guides pupils to solve calculation of length. 61
problems following Polya’s four-
The scope of units of
step model of
measurement for length involves cm, m and km.
1) Understanding the problem
2) Devising a plan
3) Implementing the plan
4) Looking back.
Year 6
Lear n i n g Ar e a: COMPUTATION OF MASS
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
proper fraction fractional computation to
1 Use and apply
• Use the spring balance,
(i) Compute mass from a
An example of computing
weights and an improvised
situation expressed in
mass from a situation expressed in fraction is as
mixed number problems involving mass.
fractional scale to verify
fraction.
computations of mass.
follows:
mass
62- proper fraction … 1 2 of 30 kg
conversion
weight
1 63 – mixed numbers In this context, “of” is a
multiplication operator, so,
• Pose problems involving
(ii) Solve problem in real
Problems involving
computation of mass in
context involving
computation of mass may
numerical form, simple
computation of mass.
also include measuring,
sentences, tables or pictures.
conversion of units and/or
• Teacher guides pupils to solve calculation of mass.
64 – without conversion
problems following Polya’s four-
The scope of units of
65 – with conversion
step model of
measurement for mass involves g and kg.
1) Understanding the problem
2) Devising a plan
3) Implementing the plan
4) Looking back.
Year 6
Lear n i n g Ar e a: COMPUTATION OF VOLUME OF LIQUID
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
proper fraction fractional computation to
1 Use and apply
• Use the measuring cylinder and
(i) Compute volume of liquid An example of computing
mixed number of liquid.
an improvised fractional scale
from a situation expressed
volume of liquid from a
problems involving volume
to verify computations of
in fraction.
situation expressed in
volumes of liquid.
fraction is as follows:
volume of liquid … 3 8 of 400 λ conversion
litre
In this context, “of” is a
millilitre
multiplication operator, so,
8 of 400 λ is 150 λ .
• Pose problems involving
(ii) Solve problem in real
Problems involving
volume of liquid in numerical
context involving
computation of volume of
form, simple sentences, tables
computation of volume of
liquid may also include
or pictures.
liquid.
measuring, conversion of
• Teacher guides pupils to solve units and/or calculation of volume of liquid.
problems following Polya’s four- step model of
The scope of units of measurement for volume of
1) Understanding the problem
liquid involves m λ and λ .
2) Devising a plan
3) Implementing the plan
4) Looking back.
Year 6
Le ar n i n g Ar e a: TWO-DIMENSIONAL SHAPES
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
perimeter area of composite two-
1 Find the perimeter and
• Pupils construct two-
(i) Find the perimeter of a two-
A perimeter is the total
dimensional composite shapes
dimensional composite
distance around the outside
square, dimensional shapes.
on the geo-board or graph
shape of two or more
edges of a shape.
paper. Pupils then measure the
quadrilaterals and triangles.
rectangle
perimeter of the shapes.
Limit quadrilaterals to squares and rectangles, and
triangle
• Teacher provides a two-
triangles to right-angled
triangles.
quadrilateral
dimensional composite shape
with given dimensions. Pupils
Given below are examples of composite
calculate the perimeter of the
2-D composite shapes of two two-dimensional
shape.
or more quadrilaterals and triangles.
geo-board length breadth area
Year 6
Le ar n i n g Ar e a: TWO-DIMENSIONAL SHAPES
LEARN I N G OBJ ECT I V ES
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POI N T S T O N OT E
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Pupils will be taught to…
LEARN I N G ACT I V I T I ES
Pupils will be able to…
• Pupils construct two-
(ii) Find the area of a two-
To calculate area of 2-D
quadrilateral
dimensional composite shapes
dimensional composite
shapes, use the following