Math yr5

Ministry of Education
Malaysia
Integrated Curriculum for Primary Schools
CURRICULUM SPECIFICATIONS
MATHEMATICS
Curriculum Development Centre
Ministry of Education Malaysia
2006

Copyright © 2006 Curriculum Development Centre
Ministry of Education Malaysia
Kompleks Kerajaan Parcel E
Pusat Pentadbiran Kerajaan Persekutuan
62604 Putrajaya
First published 2006
Copyright reserved. Except for use in a review, the reproduction
or utilisation of this work in any form or by any electronic,
mechanical, or other means, now known or hereafter invented,
including photocopying, and recording is forbidden without the
prior written permission from the Director of the Curriculum
Development Centre, Ministry of Education Malaysia.

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

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

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PREFACE
Science and technology plays a crucial role in meeting Malaysia’s
aspiration to achieve developed nation status. Since mathematics is
instrumental in developing scientific and technological knowledge, the
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
inculcate noble values and love for the nation towards the final aim of
developing the holistic person who is capable of contributing to the
harmony and prosperity of the nation and its people.
Beginning in 2003, science and mathematics will be taught in English
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.
The development of a set of Curriculum Specifications as a supporting
document to the syllabus is the work of many individuals and experts
in the field. To those who have contributed in one way or another to
this effort, on behalf of the Ministry of Education, I would like to thank
them and express my deepest appreciation.
(DR. HAILI BIN DOLHAN)
Director
Curriculum Development Centre
Ministry of Education
Malaysia

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INTRODUCTION
Our nation’s vision can be achieved through a society that is educated
and competent in the application of mathematical knowledge. To
realise this vision, society must be inclined towards mathematics.
Therefore, problem solving and communicational skills in mathematics
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
become a developed nation. In order to create a K-based economy,
research and development skills in Mathematics must be taught and
instilled at school level.
Achieving this requires a sound mathematics curriculum, competent
and knowledgeable teachers who can integrate instruction with
assessment, classrooms with ready access to technology, and a
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
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.
Several factors have been taken into account when designing the
curriculum and these are: mathematical concepts and skills,
terminology and vocabulary used, and the level of proficiency of
English among teachers and pupils.
The Mathematics Curriculum at the primary level (KBSR) emphasises
the acquisition of basic concepts and skills. The content is categorised
into four interrelated areas, namely, Numbers, Measurement, Shape
and Space and Statistics.
The learning of mathematics at all levels involves more than just the
basic acquisition of concepts and skills. It involves, more importantly,
an understanding of the underlying mathematical thinking, general
strategies of problem solving, communicating mathematically and
inculcating positive attitudes towards an appreciation of mathematics
as an important and powerful tool in everyday life.
It is hoped that with the knowledge and skills acquired in Mathematics,
pupils will discover, adapt, modify and be innovative in facing changes
and future challenges.
AIM
The Primary School Mathematics Curriculum aims to build pupils’
understanding of number concepts and their basic skills in
computation that they can apply in their daily routines effectively and
responsibly in keeping with the aspirations of a developed society and
nation, and at the same time to use this knowledge to further their
studies.
OBJECTIVES
The Primary School Mathematics Curriculum will enable pupils to:
1 know and understand the concepts, definition, rules sand
principles related to numbers, operations, space, measures and
data representation;
2 master the basic operations of mathematics:
• addition,
• subtraction,
• multiplication,
• division;
3 master the skills of combined operations;

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

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The purpose of these columns is to illustrate, for a particular teaching
objective, a list of what pupils should know, understand and be able to
do by the end of each respective topic.
The Learning Objectives define clearly what should be taught. They
cover all aspects of the Mathematics curriculum and are presented in
a developmental sequence to enable pupils to grasp concepts and
master skills essential to a basic understanding of mathematics.
The Suggested Teaching and Learning Activities list some
examples of teaching and learning activities. These include methods,
techniques, strategies and resources useful in the teaching of a
specific concepts and skills. These are however not the only
approaches to be used in classrooms.
The Learning Outcomes define specifically what pupils should be
able to do. They prescribe the knowledge, skills or mathematical
processes and values that should be inculcated and developed at the
appropriate levels. These behavioural objectives are measurable in all
aspects.
In Points To Note, attention is drawn to the more significant aspects
of mathematical concepts and skills. These aspects must be taken into
accounts so as to ensure that the concepts and skills are taught and
learnt effectively as intended.
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
careful attention to the use of correct terminology. These terms need
to be introduced systematically to pupils and in various contexts so
that pupils get to know of their meaning and learn how to use them
appropriately.
EMPHASES IN TEACHING AND LEARNING
The Mathematics Curriculum is ordered in such a way so as to give
flexibility to the teachers to create an environment that is enjoyable,
meaningful, useful and challenging for teaching and learning. At the
same time it is important to ensure that pupils show progression in
acquiring the mathematical concepts and skills.
On completion of a certain topic and in deciding to progress to another
learning area or topic, the following need to be taken into accounts:
• The skills or concepts acquired in the new learning area or
topics;
• Ensuring that the hierarchy or relationship between learning
areas or topics have been followed through accordingly; and
• Ensuring the basic learning areas have or skills have been
acquired or mastered before progressing to the more
abstract areas.
The teaching and learning processes emphasise concept building, skill
acquisition as well as the inculcation of positive values. Besides these,
there are other elements that need to be taken into account and learnt
through the teaching and learning processes in the classroom. The
main emphasis are as follows:
1. Problem Solving in Mathematics
Problem solving is a dominant element in the mathematics curriculum
for it exists in three different modes, namely as content, ability, and
learning approach.

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

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

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

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

Learning Area : NUMBERS TO 1 000 000 Year 5
1
LEARNING OBJECTIVES
Pupils will be taught to…
SUGGESTED TEACHING AND
LEARNING ACTIVITIES
LEARNING OUTCOMES
Pupils will be able to…
POINTS TO NOTE VOCABULARY
1 Develop number sense
up to 1 000 000
• Teacher pose numbers in
numerals, pupils name the
respective numbers and write
the number words.
• Teacher says the number
names and pupils show the
numbers using the calculator or
the abacus, then pupils write
the numerals.
• Provide suitable number line
scales and ask pupils to mark
the positions that representt a
set of given numbers.
(i) Name and write numbers
up to 1 000 000.
Write numbers in words and
numerals.
Emphasise reading and
writing numbers in extended
notation for example :
801 249 = 800 000 + 1 000
+ 200 + 40 + 9
or
801 249 = 8 hundred
thousands + 1 thousands + 2
hundreds + 4 tens + 9 ones.
• Given a set of numbers, pupils
represent each number using
the number base blocks or the
abacus. Pupils then state the
place value of every digit of the
given number.
(ii) Determine the place value
of the digits in any whole
number up to 1 000 000.
• Given a set of numerals, pupils
compare and arrange the
numbers in ascending then
descending order.
(iii) Compare value of numbers
up to 1 000 000.
(iv) Round off numbers to the
nearest tens, hundreds,
thousands, ten thousands
and hundred thousands.
Explain to pupils that
numbers are rounded off to
get an approximate.
numbers
numeral
count
place value
value of the digits
partition
decompose
estimate
check
compare
count in …
hundreds
ten thousands
thousands
round off to the
nearest…
tens
hundreds
thousands
ten thousands
hundred thousands

Learning Area : ADDITION WITH THE HIGHEST TOTAL OF 1 000 000 Year 5
2
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
2 Add numbers to the
total of 1 000 000
• Pupils practice addition using
the four-step algorithm of:
1) Estimate the total.
2) Arrange the numbers
involved according to place
values.
3) Perform the operation.
4) Check the reasonableness of
the answer.
• Pupils create stories from given
addition number sentences.
(i) Add any two to four
numbers to 1 000 000.
Addition exercises include
addition of two numbers to
four numbers
• without trading (without
regrouping).
• with trading (with
regrouping).
Provide mental addition
practice either using the
abacus-based technique or
using quick addition
strategies such as estimating
total by rounding, simplifying
addition by pairs of tens and
doubles, e.g.
Rounding
410 218 → 400 000
294 093 → 300 000
68 261 → 70 000
Pairs of ten
4 + 6, 5 + 5, etc.
Doubles
3 + 3, 30 + 30, 300 + 300,
3000 + 3000, 5 + 5, etc.
number sentences
vertical form
without trading
with trading
quick calculation
pairs of ten
doubles
estimation
range

Learning Area : ADDITION WITH THE HIGHEST TOTAL OF 1 000 000 Year 5
3
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
• Teacher pose problems
verbally, i.e., in the numerical
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.
(ii) Solve addition problems. Before a problem solving
exercise, provide pupils with
the activity of creating stories
from number sentences.
A guide to solving addition
problems:
Understanding the
problem
Extract information from
problems posed by drawing
diagrams, making lists or
tables. Determine the type of
problem, whether it is
addition, subtraction, etc.
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.
total
sum of
numerical
how many
number sentences
create
pose problem
tables
modeling
simulating

Learning Area : SUBTRACTION WITHIN THE RANGE OF 1 000 000 Year 5
4
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
3 Subtract numbers from
a number less than
1 000 000.
subtraction number sentences.
• Pupils practice subtraction
using the four-step algorithm of:
1) Estimate the sum.
values.
the answer.
(i) Subtract one number from
a bigger number less than
1 000 000.
Subtraction refers to
a) taking away,
b) comparing differences
c) the inverse of addition.
Limit subtraction problems to
subtracting from a bigger
number.
Provide mental sutraction
using quick subtraction
strategies.
Quick subtraction strategies
to be implemented:
a) Estimating the sum by
rounding numbers.
b) counting up and
counting down
(counting on and
counting back)
number sentence
vertical form
without trading
with trading
quick calculation
pairs of ten
counting up
counting down
estimation
range
modeling
successively
• Pupils subtract successively by
writing the number sentence in
the
a) horizontal form
b) vertical form
(ii) Subtract successively from
a bigger number less than
1 000 000.
Subtract successively two
numbers from a bigger
number

Learning Area : SUBTRACTION WITHIN THE RANGE OF 1 000 000 Year 5
5
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
step model of:
2) Devising a plan
4) Looking back.
(iii) Solve subtraction
problems.
Also pose problems in the
form of pictorials and stories.
create
pose problems
tables

Learning Area : MULTIPLICATION WITH THE HIGHEST PRODUCT OF 1 000 000 Year 5
6
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
4 Multiply any two
numbers with the highest
product of 1 000 000.
multplication number
sentences.
e.g. 40 500 × 7 = 283 500
“A factory produces 40 500
batteries per day. 283 500
batteries are produced in 7
days”
• Pupils practice multiplication
using the four-step algorithm of:
1) Estimate the product.
values.
the answer.
(i) Multiply up to five digit
numbers with
a) a one-digit number,
b) a two-digit number,
c) 10, 100 and 1000.
Limit products to less than
1 000 000.
Provide mental multiplication
other multiplication
strategies.
Multiplication strategies to be
implemented:
Factorising
16 572 × 36
= (16 572 × 30)+(16 572 × 6)
= 497 160 + 99 432
= 596 592
Completing 100
99 × 4982
= 4982 × 99
= (4982 × 100) – (4982 × 1)
= 498 200 – 4982
= 493 218
Lattice multiplication
times
multiply
multiplied by
multiple of
various
estimation
lattice
multiplication
1 6 5 7 2 ×
0
3
1
8
1
5
2
1
0
6
3
5
0
6
3
6
3
0
4
2
1
2
6
9 6 5 9 2

Learning Area : MULTIPLICATION WITH THE HIGHEST PRODUCT OF 1 000 000 Year 5
7
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
step model of:
2) Devising a plan
4) Looking back.
(Apply some of the common
strategies in every problem
solving step.)
(ii) Solve problems involving
multiplication.
A guide to solving addition
problems:
Understanding the
problem
Extract information from
problems posed by drawing
diagrams, making lists or
tables. Determine the type of
problem, whether it is
addition, subtraction, etc.
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
vertical form.
Looking back
Check for accuracy of the
solution. Use a different
startegy, e.g. calculate by
using the abacus.
Times
Multiply
multiplied by
multiple of
estimation
lattice
multiplication

Learning Area : DIVISION WITH THE HIGHEST DIVIDEND OF 1 000 000 Year 5
8
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
5 Divide a number less
than 1 000 000 by a two-
digit number.
division number sentences.
• Pupils practice division using
1) Estimate the quotient.
values.
the answer.
Example for long division
(i) Divide numbers up to six
digits by
a) one-digit number,
b) 10, 100 and 1000,
c) two-digit number,
Division exercises include
quptients
a) without remainder,
b) with remainder.
Note that “r” is used to
signify “remainder”.
Emphasise the long division
technique.
Provide mental division
other division strategies.
Exposed pupils to various
division strategies, such as,
a) divisibility of a number
b) divide by 10, 100 and
1 000.
divide
dividend
quotient
divisor
remainder
divisibility
1 3 5 6 2 r 20
35 4 7 4 6 9 0
3 5
1 2 4
1 0 5
1 9 6
1 7 5
2 1 9
2 1 0
9 0
7 0
2 0

Learning Area : DIVISION WITH THE HIGHEST DIVIDEND OF 1 000 000 Year 5
9
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
step model of:
2) Devising a plan
4) Looking back.
(Apply some of the common
strategies in every problem
solving step.)
division.

Learning Area : MIXED OPERATIONS Year 5
10
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
6 Perform mixed
operations involving
multiplication and division.
number sentences involving
mixed operations of division
and multiplication.
• Pupils practice calculation
involving mixed operation using
1) Estimate the quotient.
values.
the answer.
(i) Calculate mixed operation
on whole numbers
involving multiplication and
division.
For mixed operations
involving multiplication and
division, calculate from left to
right.
Limit the result of mixed
operation exercises to less
than 100 000, for example
a) 24 × 10 ÷ 5 =
b) 496 ÷ 4 × 12 =
c) 8 005 × 200 ÷ 50 =
Avoid problems such as
a) 3 ÷ 6 x 300 =
b) 9 998 ÷ 2 × 1000 =
c) 420 ÷ 8 × 12 =
Mixed operations
step model of:
2) Devising a plan
4) Looking back.
(Apply appropriate strategies in
every problem solving step.)
mixed operations of
division and multiplication..
Pose problems in simple
sentences, tables or
pictorials.
Some common problem
solving strategies are
a) Drawing diagrams
b) Making a list or table
c) Using arithmetic
formula
d) Using tools.

Learning Area : IMPROPER FRACTIONS Year 5
11
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
1 Understand improper
fractions.
• Demonstrate improper fractions
using concrete objects such as
paper cut-outs, fraction charts
and number lines.
• Pupils perform activities such
as paper folding or cutting, and
marking value on number lines
to represent improper fractions.
(i) Name and write improper
fractions with denominators
up to 10.
(ii) Compare the value of the
two improper fractions.
Revise proper fractions
before introducing improper
fractions.
Improper fractions are
fractions that are more than
one whole.
“three halves” 2
3
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 3
5
. It is
commonly said as “five over
three”.
improper fraction
numerator
denominator
three over two
three halves
one whole
quarter
compare
partition
2
1
2
1
2
1
3
1
3
1
3
1
3
1
3
1

Learning Area : MIXED NUMBERS Year 5
12
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
2 Understand mixed
numbers.
• Teacher demonstrates mixed
numbers by partitioning real
objects or manipulative.
• Pupils perform activities such
as
a) paper folding and shading
b) pouring liquids into
containers
c) marking number lines
to represent mixed numbers.
e.g.
4
3
2 shaded parts.
2
1
3 beakers full.
(i) Name and write mixed
numbers with denominators
up to 10.
(ii) Convert improper fractions
to mixed numbers and vice-
versa.
A mixed number consists of
a whole number and a
proper fraction.
e.g.
2
1
2
Say as ‘two and a half’ or
‘two and one over two’.
To convert improper
fractions to mixed numbers,
use concrete representations
to verify the equivalence,
then compare with the
procedural calculation.
e.g.
3
1
2
3
7
=
12
1
6
73
R
fraction
proper fraction
improper fraction
mixed numbers

Learning Area : ADDITION OF FRACTIONS Year 5
13
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
3 Add two mixed
numbers.
• Demonstrate addition of mixed
numbers through
a) paper folding activities
b) fraction charts
c) diagrams
d) number lines.
e.g.
4
3
2
2
1
1
4
1
1 =+
• Create stories from given
mixed numbers.
(i) Add two mixed numbers
with the same
denominators up to 10.
(ii) Add two mixed numbers
with different denominators
up to 10.
(iii) Solve problems involving
addition of mixed numbers.
Examples of mixed numbers
addition exercise:
a) =+
3
1
2
b) =+
5
4
5
3
2
c) =+
7
4
2
7
2
1
The following type of
problem should also be
included:
a) =+
3
1
3
9
8
1
b) =+
2
1
1
2
1
1
Emphasise answers in
simplest form.
mixed numbers
equivalent
simplest form
denominators
multiples
number lines
diagram
fraction charts
9
2
5
9
11
4
9
3
3
9
8
1
33
31
3
9
8
1
3
1
3
9
8
1
=
=
+=
×
×
+=
+

Learning Area : SUBTRACTION OF FRACTIONS Year 5
14
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
4 Subtract mixed
numbers.
• Demonstrate subtraction of
mixed numbers through
a) paper folding activities
b) fraction charts
c) diagrams
d) number lines
e) multiplication tables.
mixed numbers.
(i) Subtract two mixed
numbers with the same
denominator up to 10.
Some examples of
subtraction problems:
a) =− 2
5
3
2
b) =−
7
3
7
4
2
c) =−
4
1
1
4
3
2
d) =−
9
1
13
e) =−
8
3
1
8
1
2
simplest form.
simplest form
multiply
fraction chart
mixed numbers
multiplication tables.

Learning Area : SUBTRACTION OF FRACTIONS Year 5
15
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
(ii) Subtract two mixed
numbers with different
denominators up to 10.
subtraction of mixed
numbers.
Include the following type of
problems, e.g.
4
1
1
4
1
4
2
1
4
1
22
21
1
4
1
2
1
1
=
−=
−
×
×
=
−
Other examples
a) =−
2
1
8
7
1
b) =−
10
7
5
4
3
c) =−
3
2
4
1
2
d) =−
4
3
3
6
1
5
simplest form.
simplest form
equivalent
multiples
number sentences
mixed numbers
equivalent fraction

Learning Area : MULTIPLICATION OF FRACTIONS Year 5
16
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
5 Multiply any proper
fractions with a whole
number up to 1 000.
• Use groups of concrete
materials, pictures and number
lines to demonstrate fraction as
equal share of a whole set.
• Provide activities of comparing
equal portions of two groups of
objects.
e.g.
2
1
of 6 = 3
2
1
of 6 pencils is 3 pencils.
3
2
6
6
2
1
==×
(i) Multiply whole numbers
with proper fractions.
Emphasise group of objects
as one whole.
Limit whole numbers up to 3
digits in mulplication
exercises of whole numbers
and fractions.
Some examples
multiplication exercise for
fractions with the numerator
1 and denominator up to 10.
a) 2
1
of 8
b) =× 70
5
1
c) =× 648
8
1
Simplest form
Fractions
Denominator
Numerator
Whole number
Proper fractions
Divisible

Learning Area : MULTIPLICATION OF FRACTIONS Year 5
17
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
2
1
6× or six halves.
6 × ½ of an orange is…
33
1
3
1
3
1
3
1
3
1
3
1
=+++++ oranges.
• Create stories from given
number sentences.
multiplication of fractions.
Some multiplication
examples for fractions with
the numerator more than 1
and denominator up to 10.
e.g.
a)
3
2
of 9
b)
7
5
49×
c) 136
8
3
×
Multiply
fractions
Whole number
Divisible
Denominator
Numerator
Proper fractions

Learning Area : DECIMAL NUMBERS Year 5
18
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
1 Understand and use
the vocabulary related to
decimals.
• Teacher models the concept of
decimal numbers using number
lines.
e.g.
8 parts out of 1 000 equals
0.008
23 parts out of 1 000 is equal to
0.023.
100 parts out of 1 000 is 0.100
• Compare decimal numbers
using thousand squares and
number line.
• Pupils find examples that use
decimals in daily situation.
(i) Name and write decimal
numbers to three decimal
places.
(ii) Recognise the place value
of thousandths.
(iii) Convert fractions of
thousandths to decimal
numbers and vice versa.
(iv) Round off decimal numbers
to the nearest
a) tenths,
b) hundredths.
Decimals are fractions of
tenths, hundredths and
thousandths.
e.g
0.007 is read as “seven
thousandths” or ‘zero point
zero zero seven’.
12.302 is read as “twelve
and three hundred and two
thousandths” or ‘twelve point
three zero two’.
Emphasise place value of
thousandths using the
thousand squares.
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.
decimals
place value chart
thousandths
thousand squares
decimal point
decimal place
decimal fraction
mixed decimal
convert

Learning Area : ADDITION OF DECIMAL NUMBERS Year 5
19
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
2 Add decimal numbers
up to three decimal places.
• Pupils practice adding decimals
using the four-step algorithm of
values.
the answer.
number sentences.
(i) Add any two to four
decimal numbers up to
three decimal places
involving
a) decimal numbers and
decimal numbers,
b) whole numbers and
decimal numbers,
addition of decimal
numbers.
Add any two to four decimals
given number sentences in
the horizontal and vertical
form.
Emphasise on proper
positioning of digits to the
corresponding place value
when writng number
sentences in the vertical
form.
6.239 + 5.232 = 11.471
decimal numbers
vertical form
place value
decimal point
estimation
horizontal form
total
addend
addend
sum

Learning Area : SUBTRACTION OF DECIMAL NUMBERS Year 5
20
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
3 Subtract decimal
numbers up to three
decimal places.
• Pupils subtract decimal
numbers, given the number
sentences in the horizontal and
vertical form.
• Pupils practice subtracting
decimals using the four-step
algorithm of
values.
the answer.
• Pupils make stories from given
number sentences.
(i) Subtract a decimal number
from another decimal up to
three decimal places.
(ii) Subtract successively any
two decimal numbers up to
three decimal places.
subtraction of decimal
numbers.
Emphasise performing
subtraction of decimal
numbers by writing the
vertical form.
Emphasise the alignment of
place values and decimal
points.
Emphasise subtraction using
the four-step algorithm.
The minuend should be of a
bigger value than the
subtrahend.
8.321 – 4.241 = 4.080
vertical
place value
decimal point
estimation
range
decimal numbers
difference
subtrahend
minuend

Learning Area : MULTIPLICATION OF DECIMAL NUMBERS Year 5
21
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
4 Multiply decimal
numbers up to three
decimal places with a
whole number.
• Multiply decimal numbers with
a number using horizontal and
vertical form.
algorithm
values.
the answer.
number sentences.
(i) Multiply any decimal
numbers up to three
decimal places with
b) a two-digit number,
c) 10, 100 and 1000.
multiplication of decimal
numbers.
Emphasise performing
multiplication of decimal
numbers by writing the
vertical form.
Emphasise the alignment of
place values and decimal
points.
Apply knowledge of decimals
in:
a) money,
b) length,
c) mass,
d) volume of liquid.
vertical form
decimal point
estimation
range
product
horizontal form

Learning Area : DIVISION OF DECIMAL NUMBERS Year 5
22
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
5 Divide decimal
numbers up to three
decimal places by a whole
number.
algorithm of
values.
the answer.
number sentences.
(i) Divide a whole number by
a) 10
b) 100
c) 1 000
(ii) Divide a whole number by
b) a two-digit whole
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.
Emphasise division using the
four-steps algorithm.
Quotients must be rounded
off to three decimal places.
Apply knowledge of decimals
in:
a) money,
b) length,
c) mass,
d) volume of liquid.
divide
quotient
decimal places
rounded off
whole number

Learning Area : PERCENTAGE Year 5
23
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
percentage.
• Pupils represent percentage
with hundred squares.
• Shade parts of the hundred
squares.
• Name and write the fraction of
the shaded parts to percentage.
(i) Name and write the symbol
for percentage.
(ii) State fraction of hundredths
in percentage.
(iii) Convert fraction of
hundredths to percentage
and vice versa.
The symbol for percentage is
% and is read as ‘percent’,
e.g. 25 % is read as ‘twenty-
five percent’.
The hundred squares should
be used extensively to easily
convert fractions of
hundredths to percentage.
e.g.
a)
100
16
= 16%
b) 42% =
100
42
percent
percentage

Learning Area : CONVERT FRACTIONS AND DECIMALS TO PERCENTAGE Year 5
24
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
2 Relate fractions and
decimals to percentage.
• Identify the proper fractions
with the denominators given.
(i) Convert proper fractions of
tenths to percentage.
(ii) Convert proper fractions
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.
e.g.
%50
100
50
10
10
10
5
10
5
→=×→
%28
100
28
4
4
25
7
25
7
→=×→
20
7
5
5
100
35
100
35
%35 →÷=→

Learning Area : MONEY TO RM100 000 Year 5
25
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
money.
• Pupils show different
combinations of notes and
coins to represent a given
amount of money.
(i) Read and write the value of
money in ringgit and sen up
to RM100 000.
RM
sen
note
value
2 Use and apply
mathematics concepts
when dealing with money
up to RM100 000.
• Pupils perform basic and mixed
operations involving money by
writing number sentences in
the horizontal and vertical form.
money in real context, for
example,
a) Profit and loss in trade
b) Banking transaction
c) Accounting
d) Budgeting and finance
management
(i) Add money in ringgit and
sen up to RM100 000.
(ii) Subtract money in ringgit
and sen within the range of
RM100 000.
(iii) Multiply money in ringgit
and sen with a whole
number, fraction or decimal
with products within
RM100 000.
(iv) Divide money in ringgit and
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.
When performing mixed
operations, the order of
operations should be
observed.
Example of mixed operation
involving money,
RM62 000 ÷ 4 × 3 = ?
Avoid problems with
remainders in division, e.g.,
RM75 000.10 ÷ 4 × 3 = ?
total
amount
range
dividend
combination

Learning Area : MONEY TO RM100 000 Year 5
26
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
• Pupils solve problems following
Polya’s four-step algorithm and
using some of the common
problem solving strategies.
(vi) Solve problems in real
context involving money in
ringgit and sen up to
RM100 000.
Pose problem in form of
numericals, simple
sentences, graphics and
stories.
Polya’s four-step algorithm
1) Understanding the
problem
2) Devising a plan
4) Checking the solution
Examples of the common
problem solving strategies
are
• Drawing diagrams
• Making a list
• Using formula
• Using tools

Learning Area : READING AND WRITING TIME Year 5
27
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
1 Understand the
vocabulary related to time.
• Pupils tell the time from the
digital clock display.
• Design an analogue clock face
showing time in the 24-hour
system.
(i) Read and write time in the
24-hour system.
(ii) Relate the time in the 24-
hour system to the 12-hour
system.
Some common ways to read
time in the 24-hour system.
e.g.
Say : Sixteen hundred hours
Write: 1600hrs
Say: Sixteen zero five hours
Write: 1605hrs
Say: zero hundred hours
Write: 0000hrs
ante meridiem
post meridiem
analogue clock
digital clock.
24-hour system
12-hour system

Learning Area : READING AND WRITING TIME Year 5
28
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
• Pupils convert time by using
the number line
the clock face
(iii) Convert time from the 24-
hour system to the 12-hour
system and vice-versa.
Examples of time conversion
from the 24-hour system to
the 12-hour system.
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
a.m.
ante meridiem refers to the
time after midnight before
noon.
p.m.
post meridiem refers to the
time after noon before
midnight.
a.m
p.m
6
12 12 12
afternoonmorning evening
noon
0000 1200 0000
00
13
14
15
16
17
1819
20
21
22
23

Learning Area : RELATIONSHIP BETWEEN UNITS OF TIME Year 5
29
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
2 Understand the
relationship between units
of time.
• Pupils convert from one unit of
time
• Pupils explore the relationship
between centuries, decades
and years by constructing a
time conversion table.
(i) Convert time in fractions
and decimals of a minute to
seconds.
(ii) Convert time in fractions
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.
Conversion of units of time
may involve proper fractions
and decimals.
a) 1 century = 100 years
b) 1 century = 10 decade
century
decade

Learning Area : BASIC OPERATIONS INVOLVING TIME Year 5
30
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
3 Add, subtract, multiply
and divide units of time.
• Pupils add, subtract, multiply
and divide units of time by
writing number sentences in
the horizontal and vertical form.
e.g.
(i) Add time in hours, minutes
and seconds.
(ii) Subtract time in hours,
minutes and seconds.
(iii) Multiply time in hours,
(iv) Divide time in hours,
Practise mental calculation
for the basic operations
involving hours, minutes and
seconds.
Limit
a) multiplier to a one-digit
number,
b) divisor to a one-digit
number and
c) exclude remainders in
division.
multiplier
divisor
remainders
minutes
hours
seconds
days
years
months
5 hr 20 min 30 s
+ 2 hr 25 min 43 s
4 hr 45 min 12 s
- 2 hr 30 min 52 s
2 hr 15 min 9 s
× 7
4 13 hours 13 minutes

Learning Area : DURATION Year 5
31
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
4 Use and apply
knowledge of time to find
the duration.
• Pupils read and state
information from schedules
such as:
a) class time-table,
b) fixtures in a tournament
c) public transport, etc
• Pupils find the duration the start
and end time from a given
situation.
(i) Identify the start and end
times of are event.
(ii) Calculate the duration of an
event, involving
a) hours, minutes and
seconds.
b) days and hours
(iii) Determine the start or end
time of an event from a
given duration of time.
(iv) Solve problems involving
time duration in fractions
and/or decimals of hours,
Expose pupils to a variety of
schedules.
Emphasise the 24-hour
system.
The duration should not be
longer than a week.
duration
schedule
event
start
end
competition
hours
minutes
24-hour system
period
fixtures
tournament

Learning Area : MEASURING LENGTH Year 5
32
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
1 Measure and compare
distances.
• Teacher provides experiences
to introduce the idea of a
kilometre.
e.g.
Walk a hundred-metre track
and explain to pupils that a
kilometre is ten times the
distance.
• Use a simple map to measure
the distances to one place to
another.
e.g.
a) school
b) village
c) town
(i) Describe by comparison
the distance of one
kilometre.
(ii) Measure using scales for
distance between places.
Introduce the symbol ‘km’ for
kilometre.
Relate the knowledge of
data handling (pictographs)
to the scales in a simple
map.
represents 10 pupils.
represents 5 km
kilometre
distance
places
points
destinations
between
record
map
scale
1 cm

Learning Area : RELATIONSHIP BETWEEN UNITS OF LENGTH Year 5
33
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
2 Understand the
of length.
• Compare the length of a metre
string and a 100-cm stick, then
write the relationship between
the units.
• Pupils use the conversion table
for units of length to convert
length from km to m and vice
versa.
(i) Relate metre and kilometre.
(ii) Convert metre to kilometre
and vice versa.
Emphasise relationships.
1 km = 1000 m
1 m = 100 cm
1 cm = 10 mm
Practice mental calculation
giving answers in mixed
decimals.
measurement
relationship

Learning Area : BASIC OPERATIONS INVOLVING LENGTH Year 5
34
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
3 Add, subtract, multiply
and divide units of length.
• Pupils demonstrate addition
and subtraction involving units
of length using number
sentences in the usual
conventional manner.
e.g.
a) 2 km + 465 m = ______ m
b) 3.5 km + 615 m = _____ km
c) 12.5 km – 625 m = _____ m
(i) Add and subtract units of
length involving conversion
of units in
a) kilometres ,
b) kilometres and metres.
Give answers in mixed
decimals to 3 decimal
places.
Check answers by
performing mental
calculation wherever
appropriate.
add
subtract
conversion
mixed decimal
multiply
quotient
-
• Pupils multiply and divide
involving units of length.
e.g.
a) 7.215 m ×1 000 =______km
b) 2.24 km ÷ 3 = _____m
Create stories from given number
sentence.
(ii) Multiply and divide units of
length in kilometres
involving conversion of
units with
b) 10, 100, 1 000.
(iii) Identify operations in a
given situation.
(iv) Solve problems involving
basic operations on length.

Learning Area : COMPARING MASS Year 5
35
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
1 Compare mass of
objects.
• Pupils measure, read and
record masses of objects in
kilograms and grams using the
weighing scale and determine
how many times the mass of an
object as compared to another.
(i) Measure and record
masses of objects in
kilograms and grams.
(ii) Compare the masses of
two objects using kilogram
and gram, stating the
comparison in multiples or
fractions.
(iii) Estimate the masses of
objects in kilograms and
grams.
Emphasise that measuring
should start from the ‘0’ mark
of the weighing scale.
Encourage pupils to check
accuracy of estimates.
read
weighing scale
divisions
weight
weigh
compare
record
compound
2 Understand the
of mass.
• Pupils make stories for a given
measurement of mass.
e.g.
Aminah bought 4 kg of
cabbages and 500 g celery.
Altogether, she bought a total
of 4.5 kg vegetables.
(i) Convert units of mass from
fractions and decimals of a
kilogram to grams and vice
versa.
conversion of mass units in
fraction and/or decimals.
1 kg = 1000 g
Emphasise mental
calculations.
mixed decimals up to 3
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
measurement
relationship

Learning Area : COMPARING VOLUME Year 5
36
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
1 Measure and compare
volumes of liquid using
standard units.
• Pupils measure, read and
record volume of liquid in litres
and mililitres using beaker,
measuring cylinder, etc.
• Pupils measure and compare
volume of liquid stating the
comparison in multiples or
factors.
(i) Measure and record the
volumes of liquid in a
smaller metric unit given
the measure in fractions
and/or decimals of a larger
uniit.
(ii) Estimate the volumes of
liquid involving fractions
and decimals in litres and
mililitres.
(iii) Compare the volumes of
liquid involving fractions
and decimals using litres
and mililitres.
Capacity is the amount a
container can hold.
Emphasise that reading of
measurement of liquid
should be at the bottom of
the meniscus. 1ℓ = 1000 mℓ
2
1
ℓ = 0.5 ℓ = 500 mℓ
4
1
ℓ = 0.25 ℓ = 250 mℓ
4
3
ℓ = 0.75 mℓ = 750 mℓ
Encourage pupils to check
accuracy of estimates.
read
meniscus
record
capacity
measuring
cylinder
water level
beaker
measuring jug
divisions

Learning Area : RELATIONSHIP BETWEEN UNITS OF VOLUME Year 5
37
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
2 Understand the
of volume of liquid.
• Engage pupils in activities that
will create an awareness of
relationship.
• Pupils make stories from a
given number sentence
involving volume of lquid.
(i) Convert unit of volumes
involving fractions and
decimals in litres and vice-
versa.
(ii) Solve problem involving
volume of liquid.
1 l = 1 000 m l
Emphasise mental
calculations.
decimal places.
e.g.
a) 400 m l = 0.4 l
b) 250 m l =
4
1
l
c) 4750 m l = 4.75 l
=
4
3
4 l
d)
5
2
3 l = 3.4 l
= 3400 m l
= 3 l 400 m l
Include compound units.
measurement
relationship

Learning Area : OPERATIONS ON VOLUME OF LIQUID Year 5
38
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
3 Add and subtract units
of volume.
• Pupils carry out addition up to 3
numbers involving mixed
decimals in litres and millitres .
(i) Add units of volume
involving mixed decimals in
a) litres,
b) mililitres,
c) litres and mililitres.
(ii) Subtract units of volume
involving mixed decimals in
a) litres,
b) mililitres,
c) litres and mililitres.
decimals places.
e.g:
a) 0.607 l + 4.715 l =
b) 4.052 l + 5 l + 1.46 l =
c) 642 m l + 0.523 l +1.2 l =
Practice mental calculations.
measurement
relationship
4 Multiply and divide
units of volume.
• Pupils demonstrate division for
units of volume in the
conventional manner.
• Pupils construct stories about
volume of liquids from given
number sentences.
(iii) Multiply units of volume
involving mixed number
using:
b) 10, 100, 1000, involving
conversion of units.
(iv) Divide units of volume
using
a) up to 2 digit number,
b) 10, 100, 1000, involving
mixed decimals.
Give answers in mixed
decimals to 3 decimals
places, e.g. 0.0008 l round
off to 0.001 l.
Avoid division with
remainders.
Make sensible estimations to
check answers.

Learning Area : OPERATIONS ON VOLUME OF LIQUID Year 5
39
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
(v) Divide unit of volume using:
b) 10, 100, 1000,
involving conversion of
units.
(vi) Solve problems involving
computations for volume of
liquids.

Learning Area : COMPOSITE TWO-DIMENSIONAL SHAPES Year 5
40
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
1 Find the perimeter of
composite 2-D shapes.
• Use measuring tapes, rulers or
string to measure the perimeter
of event composite shapes.
(i) Measure the perimeter of
the following composite 2-D
shapes.
a) square and square,
b) rectangle and rectangle,
c) triangle and triangle,
d) square and rectangle,
e) square and triangle,
f) rectangle and triangle.
(ii) Calculate the perimeter of
the following composite 2-D
shapes. a) square and
square,
a) rectangle and rectangle,
b) triangle and triangle,
c) square and rectangle,
d) square and triangle,
e) rectangle and triangle.
perimeters of composite 2-
D shapes.
Emphasise using units in cm
and m.
e.g.
Emphasise using various
combination of 2-D shapes
to find the perimeter and
area.
shape,
combination,
square
rectangle,
triangle,
area,
calculate3 cm
5 cm
2 cm
4 cm

Learning Area : COMPOSITE TWO-DIMENSIONAL SHAPES Year 5
41
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
2 Find the area of
• Pupils count the unit squares to
find the area of composite 2-D
shape on the grid paper.
(i) Measure the area of the
following composite 2-D
shapes.
a) square and square,
b) rectangle and rectangle,
c) square and rectangle,
(ii) Calculate the area of the
shapes. square and
square,
a) rectangle and rectangle,
b) square and rectangle,
areas of composite 2-D
shapes.
The units of area should be
in cm² and m².
Limit shapes to a
combination of two basic
shapes.
combination,
square
rectangle,
triangle,
area,
calculate,
2-D shapes.

Learning Area : COMPOSITE THREE-DIMENSIONAL SHAPES Year 5
42
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
1 Find the volume of
• Use any combinations of 3-D
shapes to find the surface area
and volume.
(i) Measure the volume of the
shapes
a) cube and cube,
b) cuboid and cuboid,
c) cube and cuboid.
(ii) Calculate the volume of the
composite 3-D shapes
following
a) cube and cube,
b) cuboid and cuboid,
c) cube and cuboid.
volume of composite 3-D
shapes.
Volume of cuboid A
= 3 cm × 4 cm × 6 cm
Volume of cuboid B
= 2 cm × 4 cm × 8 cm
The combined volume of
cubiod A and B
= 72 cm3
+ 64 cm3
= 136 cm3
The units of area should be
in cm and m.
shape,
cube,
cuboid,
surface area,
volume
composite 3-D
shapes
A
B4 cm
3 cm
6 cm 8 cm
2 cm

Learning Area : AVERAGE Year 5
43
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
average.
• Prepare two containers of the
same size with different
volumes of liquid.
• Equal the volume of liquid from
the two containers.
e.g.
(i) Describe the meaning of
average.
(ii) State the average of two or
three quantities.
(iii) Determine the formula for
average.
The formula for average average
calculate
quantities
total of
quantity
number of
quantities
objects
liquids
volume
e.g.
• Relate the examples given to
determine the average using
the formula.
A B
A B
1
2
1 2
quantityofnumber
quantityoftotal
Average
=

Learning Area : AVERAGE Year 5
44
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
2 Use and apply
knowledge of average.
• Calculate the average of two
numbers.
• Calculate the average of three
numbers.
• Pose problems involving real
life situation.
(i) Calculate the average
using formula.
(ii) Solve problem in real life
situation.
Emphasise the calculation of
average without involving
remainders.
Emphasise the calculation of
average involving numbers,
money, time, length, mass,
volume of liquid and quantity
of objects and people.
e.g.
Calculate the average 25, 86
and 105.
72
3
216
3
1058625
==
++
remainders
number
money
time
length
mass
volume of liquid
people
quantity of objects

Learning Area : ORGANISING AND INTERPRETING DATA Year 5
45
LEARNING OBJECTIVES
LEARNING ACTIVITIES
LEARNING OUTCOMES
1 Understand the
vocabulary relating to data
organisation in graphs.
• Discuss a bar graph showing
the frequency, mode, range,
maximum and minimum value.
e.g.
Number of books read by five
pupils in February
(i) Recognise frequency,
mode, range, maximinum
and minimum value from
bar graphs.
Initiate discussion by asking
simple questions. Using the
example in the Suggested
Teaching and Learning
Activities column, ask
questions that introduce the
terms, e.g.
1) How many books did
Adam read?
(frequency)
2) What is the most
common number of
books read? (mode)
3) Who read the most
books? (maximum)
frequency
mode
range
maximum
minimum
data table
score
chart
graph
organise
interpret
2 Organise and interpret
data from tables and
charts.
• Pupils transform data tables to
bar graphs.
(ii) Construct a bar graph from
a given set of data.
(iii) Determine the frequency,
mode, range, average,
maximum and minimum
value from a given graph.
From the data table,
What is the most common
score? (mode)
Arrange the scores for one
of the tests in order, then
determine the maximum and
minimum score. The range is
the difference between the
two scores.
frequency
pupils
Adam Shiela Davin Nadia May
1
2
3
4
5
Name Reading
test
score
Mental
Arithmetic
test score
Adam 10 8
Davin 7 10
May 9 8

Math yr5

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