MATHEMATICS YEAR 5

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1

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

2

Learning Area : ADDITION WITH THE HIGHEST TOTAL OF 1 000 000 Year 5
• Teacher pose problems (ii) Solve addition problems. Before a problem solving total
verbally, i.e., in the numerical exercise, provide pupils with
sum of
form or simple sentences. the activity of creating stories
from number sentences. numerical
• Teacher guides pupils to solve
problems following Polya’s four- A guide to solving addition how many
step model of: problems:
number sentences
1) Understanding the problem Understanding the
problem create
2) Devising a plan Extract information from pose problem
3) Implementing the plan
problems posed by drawing
diagrams, making lists or tables
4) Looking back. tables. Determine the type of modeling
problem, whether it is
addition, subtraction, etc. simulating
Devising a plan
Translate the information
into a number sentence.
Determine what strategy to
use to perform the operation.
Implementing the plan
Perform the operation
conventionally, i.e. write the
number sentence in the
vertical form.
Looking back
Check for accuracy of the
solution. Use a different
startegy, e.g. calculate by
using the abacus.

3

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

4

Learning Area : SUBTRACTION WITHIN THE RANGE OF 1 000 000 Year 5
• Teacher pose problems (iii) Solve subtraction Also pose problems in the create
verbally, i.e., in the numerical problems. form of pictorials and stories.
pose problems
form or simple sentences.
tables
problems following Polya’s four-
step model of:
1) Understanding the problem
2) Devising a plan
4) Looking back.

5

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

1 6 5 7 2 ×
0 1 1 2 0
3
3 8 5 1 6
0 3 3 4 1
5 6
6 6 0 2 2
9 6 5 9 2

6

Learning Area : MULTIPLICATION WITH THE HIGHEST PRODUCT OF 1 000 000 Year 5
• Teacher pose problems (ii) Solve problems involving A guide to solving addition Times
verbally, i.e., in the numerical multiplication. problems:
Multiply
form or simple sentences. Understanding the
problem multiplied by
problems following Polya’s four- Extract information from multiple of
step model of: problems posed by drawing
diagrams, making lists or estimation
1) Understanding the problem tables. Determine the type of lattice
2) Devising a plan
problem, whether it is
addition, subtraction, etc. multiplication
3) Implementing the plan Devising a plan
4) Looking back. Translate the information
into a number sentence.
(Apply some of the common Determine what strategy to
strategies in every problem use to perform the operation.
solving step.)
Implementing the plan
Perform the operation
conventionally, i.e. write the
number sentence in the
vertical form.
Looking back
Check for accuracy of the
solution. Use a different
startegy, e.g. calculate by
using the abacus.

7

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

Learning Area : DIVISION WITH THE HIGHEST DIVIDEND OF 1 000 000 Year 5
• Teacher pose problems (ii) Solve problems involving
verbally, i.e., in the numerical division.
form or simple sentences.
problems following Polya’s four-
step model of:
1) Understanding the problem
2) Devising a plan
4) Looking back.
(Apply some of the common
strategies in every problem
solving step.)

9

Learning Area : MIXED OPERATIONS Year 5
6 Perform mixed • Pupils create stories from given (i) Calculate mixed operation For mixed operations Mixed operations
operations involving number sentences involving on whole numbers involving multiplication and
multiplication and division. mixed operations of division involving multiplication and division, calculate from left to
and multiplication. division. right.
• Pupils practice calculation Limit the result of mixed
involving mixed operation using operation exercises to less
the four-step algorithm of: than 100 000, for example
1) Estimate the quotient. a) 24 × 10 ÷ 5 =
b) 496 ÷ 4 × 12 =
involved according to place c) 8 005 × 200 ÷ 50 =
values. Avoid problems such as
3) Perform the operation. a) 3 ÷ 6 x 300 =
4) Check the reasonableness of b) 9 998 ÷ 2 × 1000 =
the answer. c) 420 ÷ 8 × 12 =

• Teacher guides pupils to solve (ii) Solve problems involving Pose problems in simple
problems following Polya’s four- mixed operations of sentences, tables or
step model of: division and multiplication.. pictorials.
1) Understanding the problem Some common problem
solving strategies are
2) Devising a plan
a) Drawing diagrams
b) Making a list or table
4) Looking back.
c) Using arithmetic
(Apply appropriate strategies in formula
every problem solving step.)
d) Using tools.

10

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

1 1 1 1 1
3 3 3 3 3

The fraction reperesented by
the diagram is “five thirds”
and is written as 5 . It is
3
commonly said as “five over
three”.

11

Learning Area : MIXED NUMBERS Year 5
2 Understand mixed • Teacher demonstrates mixed (i) Name and write mixed A mixed number consists of fraction
numbers. numbers by partitioning real numbers with denominators a whole number and a
proper fraction
objects or manipulative. up to 10. proper fraction.
improper fraction
• Pupils perform activities such e.g.
as
(ii) Convert improper fractions mixed numbers
to mixed numbers and vice- 21
2
a) paper folding and shading versa.
Say as ‘two and a half’ or
b) pouring liquids into
‘two and one over two’.
containers
To convert improper
c) marking number lines
fractions to mixed numbers,
to represent mixed numbers. use concrete representations
to verify the equivalence,
e.g. then compare with the
procedural calculation.
e.g.

2 3 shaded parts.
4

7 1 2R 1
=2
3 3 3 7
6
3 1 beakers full.
2 1

12

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

13

Learning Area : SUBTRACTION OF FRACTIONS Year 5
4 Subtract mixed • Demonstrate subtraction of (i) Subtract two mixed Some examples of simplest form
numbers. mixed numbers through numbers with the same subtraction problems:
multiply
denominator up to 10.
a) paper folding activities 3
a) 2 − 2 = fraction chart
b) fraction charts 5
mixed numbers
c) diagrams 4 3
b) 2 − = multiplication tables.
d) number lines 7 7
e) multiplication tables. 3 1
c) 2 −1 =
• Pupils create stories from given 4 4
number sentences involving
1
mixed numbers. d) 3 − 1 =
9
1 3
e) 2 −1 =
8 8
Emphasise answers in
simplest form.

14

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

15

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

1
b) × 70 =
5
1
c) × 648 =
8
1 6
×6= =3
2 2

16

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

17

MATHEMATICS YEAR 5

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