Integrated Curriculum for Primary Schools
MINISTRY OF EDUCATION MALAYSIA
Integrated Curriculum for Primary Schools
Curriculum Specifications MATHEMATICS YEAR 2
Curriculum Development Centre Ministry of Education Malaysia
MINISTRY OF EDUCATION MALAYSIA
Integrated Curriculum for Primary Schools
Curriculum Specifications MATHEMATICS YEAR 2
Curriculum Development Centre Ministry of Education Malaysia
Copyright (C) 2003 Curriculum Development Centre Ministry of Education Malaysia Pesiaran Duta Off Jalan Duta 50604 Kuala Lumpur
First published 2003
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.
PREFACE ix INTRODUCTION
xi
WHOLE NUMBERS
Numbers to 1000
1 Addition with the Highest Total of 1000
8 Subtraction within the Range of 1000
13 Multiplication within 2, 3, 4 and 5 Times-tables
19 Division within 2, 3, 4 and 5 Times-tables
24 MONEY
28 TIME
Money to RM50
Reading and Writing Time
32 Relationship between Units of Time
35 LENGTH
Solving Problems involving Time
Introduction to Length
36 Measuring and Comparing Lengths
37 MASS
Introduction to Mass
39 Measuring and Comparing Masses
40 VOLUME OF LIQUID
Introduction to Volume of Liquid
42 Measuring and Comparing Volumes of Liquids
43 SHAPE AND SPACE Three-Dimensional Shapes
48 CONTRIBUTORS
Two-Dimensional Shapes
51 PANEL OF WRITERS
DECLARATION
O UR 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;
W E, 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
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.
meeting Malaysia’s aspiration to achieve developed their knowledge and skills because they are able to nation status. Since mathematics is instrumental in
source the various repositories of knowledge written in developing scientific and technological knowledge, the
mathematical English whether in electronic or print provision of quality mathematics education from an
forms. Pupils will be able to communicate early age in the education process is critical.
mathematically in English not only in the immediate enviroment but also with pupils from other countries
The primary school Mathematics curriculum as thus increasing their overall English proficiency and outlined in the syllabus has been designed to provide
mathematical competence in the process. opportunities for pupils to acquire mathematical knowledge and skills and develop the higher order
The development of a set of Curriculum Specifications problem solving and decision making skills that they
as a supporting document to the syllabus is the work can apply in their everyday lives. But, more
of many individuals and experts in the field. To those importantly, together with the other subjects in the
who have contributed in one way or another to this primary school curriculum, the mathematics
effort, on behalf of the Ministry of Education, I would curriculum seeks to inculcate noble values and love
like to thank them and express my deepest for the nation towards the final aim of developing the
appreciation.
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.
(Dr. SHARIFAH MAIMUNAH SYED ZIN) Mathematics education in English makes use of
Director
ICT in its delivery. Studying mathematics in the
Curriculum Development Centre
medium of English assisted by ICT will provide
Ministry of Education Malaysia
Our nation’s vision can be achieved through a society that is educated and competent in the application of
the nation.
mathematical knowledge. To achieve this vision, society must be inclined towards mathematics.
Several factors have been taken into account when designing the curriculum and these are: mathematical
Therefore, problem solving and communicational skills concepts and skills, terminology and vocabulary used, in mathematics have to be nurtured so that decisions
can be made effectively. and the level of proficiency of English among teachers and pupils.
Mathematics is integral in the development of science The Mathematics Curriculum at the primary level and technology. As such, the acquisition of
mathematical knowledge must be upgraded (KBSR) emphasises the acquisition of basic concepts periodically to create a skilled workforce in preparing
and skills. The content is categorised into four interrelated areas, namely, Numbers, Measurement,
the country to become a developed nation. In order to Shape and Space and Statistics. create a K-based economy, research and development
skills in Mathematics must be taught and instilled at The learning of mathematics at all levels involves more school level.
than just the basic acquisition of concepts and skills. It involves, more importantly, an understanding of the
Achieving this requires a sound mathematics curriculum, competent and knowledgeable teachers
underlying mathematical thinking, general strategies of who can integrate instruction with assessment,
problem solving, communicating mathematically and inculcating positive attitudes towards an appreciation
classrooms with ready access to technology, and a of mathematics as an important and powerful tool in commitment to both equity and excellence.
everyday life.
The Mathematics Curriculum has been designed to It is hoped that with the knowledge and skills acquired provide knowledge and mathematical skills to pupils in Mathematics, pupils will discover, adapt, modify and from various backgrounds and levels of ability.
be innovative in facing changes and future challenges. Acquisition of these skills will help them in their careers
The Primary School Mathematics Curriculum aims
4. master basic mathematical skills, namely: to build pupils’ understanding of number concepts
• making estimates and approximates, and their basic skills in computation that they can
• measuring,
apply in their daily routines effectively and responsibly
• handling data
in keeping with the aspirations of a developed society • representing information in the form and nation, and at the same time to use this
of graphs and charts; knowledge to further their studies.
5. use mathematical skills and knowledge to
OBJECTIVES
solve problems in everyday life effectively and responsibly;
The Primary School Mathematics Curriculum will enable pupils to:
6. use the language of mathematics correctly;
1. know and understand the concepts,
7. use suitable technology in concept building, definition, rules sand principles related to acquiring mathematical skills and solving numbers, operations, space, measures and
problems;
data representation;
8. apply the knowledge of mathematics
2. master the basic operations of mathematics: systematically, heuristically, accurately and
• addition,
carefully;
• subtraction, • multiplication,
9. participate in activities related to mathematics; • division;
and
3. master the skills of combined operations;
10. appreciate the importance and beauty of
mathematics.
encompasses four main areas, namely, Numbers,
• Average;
Measures, Shape and Space and Statistics. The • Data Representation. topics for each area have been arranged from the basic to the abstract. Teachers need to teach the
The Learning Areas outline the breadth and depth of basics before abstract topics are introduced to pupils.
the scope of knowledge and skills that have to be Each main area is divided into topics as follows:
mastered during the allocated time for learning. These learning areas are, in turn, broken down into more
1. Numbers manageable objectives. Details as to teaching-learning
• Whole Numbers; strategies, vocabulary to be used and points to note • Fractions;
are set out in five columns as follows: • Decimals;
• Money; Column 1: Learning Objectives. • Percentage.
Column 2: Suggested Teaching and
2. Measures
Learning Activities.
• Time; Column 3: Learning Outcomes. • Length;
Column 4: Points To Note.
• Mass;
Column 5: Vocabulary.
• Volume of Liquid. The purpose of these columns is to illustrate, for a
3. Shape and Space particular teaching objective, a list of what pupils • Two-dimensional Shapes;
should know, understand and be able to do by the • Three-dimensional Shapes.
end of each respective topic.
curriculum and are presented in a developmental that are relevant when structuring activities, asking sequence to enable pupils to grasp concepts and
questions and in setting tasks. It is important to pay master skills essential to a basic understanding of
careful attention to the use of correct terminology. mathematics.
These terms need to be introduced systematically to pupils and in various contexts so that pupils get to know
The Suggested Teaching and Learning Activities of their meaning and learn how to use list some examples of teaching and learning activities.
them appropriately.
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 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:
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.
Problem solving is the main focus in the teaching and learning of mathematics. Understanding mathematical procedures and solving problems are two skills that emerge naturally when relational understanding is focussed upon. As a result, problem solving approaches should be used to investigate and understand mathematical content. The teaching- learning process must include exercises on problem solving skills which are comprehensive and cover the whole curriculum. The development of these skills must to be emphasised so that pupils are able to solve various problems effectively. The skills involved are:
Various strategies and steps are used to solve problems and these can be applied to other learning areas. In solving these problems, pupils learn to apply mathematics and gradually become confident in facing new challenging situations. Among the problem solving strategies to consider are:
• Interpreting problems; • Planning the strategy; • Carrying out the strategy; and • Looking back at the solutions.
• Draw a diagram;
to the listening skills involved.
• Identifying patterns and sequences; Communication in mathematics through the listening • Make a table, chart or a systematic list; process occurs when individuals respond to what • Simulation; they hear and this encourages them to think using • Make analogy; and their mathematical knowledge in making decisions. • Working backwards.
Communication in mathematics through the reading
2. Communication in Mathematics
process takes place when an individual collects information or data and rearranges the relationship
Communication is one way to share ideas and clarify
between ideas and concepts.
the understanding of Mathematics. Through talking and questioning, mathematical ideas can be reflected
Communication in mathematics through the upon, discussed and modified. The process of
visualization process takes place when an individual reasoning analytically and systematically can help
makes observation, analyses it, interprets and reinforce and strengthen pupils’ knowledge and
synthesises the data into graphic forms, such as understanding of mathematics to a deeper level.
pictures, diagrams, tables and graphs. Through effective communications pupils will become
efficient in problem solving and be able to explain The following methods can create an effective concepts and mathematical skills to their peers and
communication environment:
teachers. • Identifying relevant contexts associated
Pupils who have developed the above skills will with environment and everyday life become more inquisitive gaining confidence in the
experiences of pupils;
process. Communicational skills in mathematics • Identifying interests of pupils; include reading and understanding problems,
• Identifying teaching materials; interpreting diagrams and graphs, and using correct
• Ensuring active learning;
• Creating a conducive learning environment. shared with others through writing. The written work is usually the result of discussions, contributions and
Oral communication is an interactive process that brain-storming activities when working on involves activities like listening, speaking, reading and assignments. Through writing, the pupils will be observing. It is a two-way interaction that takes place encouraged to think more deeply about the between teacher-pupil, pupil-pupil, and pupil-object. mathematics content and observe the relationships When pupils are challenged to think and reason about
between concepts.
mathematics and to tell others the results of their thinking, they learn to be clear and convincing. Listening
Examples of written communication activities are: to others’ explanations gives pupils the opportunities • to develop their own understanding. Conversations in Doing exercises;
• Keeping scrap books;
which mathematical ideas are explored from multiple
• Keeping folios;
perspectives help sharpen pupils thinking and help
make connections between ideas. Such activity helps • Undertaking projects; and
• Doing written tests.
pupils develop a language for expressing mathematical
ideas and appreciation of the need for precision in the language. Some effective and meaningful oral
Representation is a process of analysing a mathematical problem and interpreting it from one
communication techniques in mathematics are as mode to another. Mathematical representation enables follows: pupils to find relationship between mathematical ideas
• Story-telling, question and answer sessions that are informal, intuitive and abstract using their using own words;
everyday language. Pupils will realise that some • Asking and answering questions;
methods of representation are more effective and • Structured and unstructure interviews;
useful if they know how to use the elements of • Discussions during forums, seminars
mathematical representation.
debates and brain-storming sessions; and • Presentation of findings of assignments.
Logical reasoning or thinking is the basis for problem solving. Without connections between these understanding and solving mathematical problems. areas, pupils will have to learn and memorise too many
The development of mathematical reasoning is closely concepts and skills separately. By making connections related to the intellectual and communicative
pupils are able to see mathematics as an integrated development of the pupils. Emphasis on logical
whole rather than a jumble of unconnected ideas. thinking during mathematical activities opens up pupils’ Teachers can foster connections in a problem-oriented minds to accept mathematics as a powerful tool in classrooms by having pupils to communicate, reason the world today.
and present their thinking. When these mathematical ideas are connected with real life situations and the
Pupils are encouraged to predict and do guess work curriculum, pupils will become more conscious in the in the process of seeking solutions. Pupils at all application of mathematics. They will also be able to levels have to be trained to investigate their use mathematics contextually in different learning predictions or guesses by using concrete
areas in real life.
materials, calculators, computers, mathematical representation and others. Logical reasoning has to
be infused in the teaching of mathematics so that
5. Application of Technology
pupils can recognise, construct and evaluate predictions and mathematical arguments.
The application of technology helps pupils to understand mathematical concepts in depth,
4. Mathematical Connections
meaningfully and precisely enabling them to explore mathematical concepts. The use of calculators,
In the mathematics curriculum, opportunities for computers, educational software, websites in the making connections must be created so that pupils
internet and available learning packages can help to can link conceptual to procedural knowledge and
upgrade the pedagogical skills in the teaching and relate topics in mathematics with other learning
learning of mathematics.
areas in general.
abstract ideas, be creative, feel confident and be able systematically have to be absorbed through the to work independently or in groups. Most of these
learning areas.
resources are designed for self-access learning. Through self-access learning, pupils will be able to
Good moral values can be cultivated through suitable access knowledge or skills and informations
context. For example, learning in groups can help independently according to their pace. This will serve
pupils develop social skills and encourage cooperation to stimulate pupils’ interests and responsibility in
and self-confidence in the subject. The element of learning mathematics.
patriotism can also be inculcated through the teaching- learning process in the classroom using planned topics. These values should be imbibed throughout
APPROACHES IN TEACHING AND LEARNING
the process of teaching and learning mathematics. Various changes occur that influence the content and
A mong the approaches that can be given consideration pedagogy in the teaching of mathematics in primary
are:
schools. These changes require variety in the way of teaching mathematics in schools. The use of teaching
• Pupil centered learning that is interesting; resources is vital in forming mathematical concepts.
• The learning ability and styles of learning; Teachers can use real or concrete objects in teaching
• The use of relevant, suitable and effective and learning to help pupils gain experience, construct
teaching materials; and
abstract ideas, make inventions, build self confidence, • Formative evaluation to determine the encourage independence and inculcate cooperation.
effectiveness of teaching and learning. 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 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
• 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.
Advisors
Dr. Sharifah Maimunah bt Syed Zin
Director Curriculum Development Centre
Dr. Rohani Abdul Hamid Deputy Director Curriculum Development Centre
Editorial
Rusnani Mohd Sirin Assistant Director
Advisors
(Head of Mathematics Unit) Curriculum Development Centre
S. Sivagnanachelvi Assistant Director (Head of English Language Unit) Curriculum Development Centre
Editors
Sugara Abd Latif Curriculum Officer (Mathematics Unit) Curriculum Development Centre
B. Jagdeesh Kaur Gill Curriculum Officer (English LanguageUnit) Curriculum Development Centre
Helen Henry Sarjit SK Bukit Damansara, Kuala Lumpur Lee Tan Yen Peng
SK St. Anthony, Penampang, Sabah
(Head of Mathematics Unit) Curriculum Development Centre
Dr. Lim Chap Sum
Universiti Sains Malaysia, Pulau Pinang
Wan Yusof Wan Ngah
Maktab Perguruan Perempuan Melayu, Melaka
Jeya Velu
Institut Bahasa Melayu Malaysia, Kuala Lumpur
Repiah Singah
Maktab Perguruan Temenggong Ibrahim, Johor
Tan Swee Hong
SK Convent St. Jesus (2), Melaka
Ragu Ramasamy
SK Bukit Bandaraya, Kuala Lumpur
Balkis Ahmad
SMK Sultan Sallahuddin Abdul Aziz Shah, Selangor
(Mathematics Unit) Curriculum Development Centre
Shanti Periasamy
Maktab Perguruan Ilmu Khas, Kuala Lumpur
Maimunah Tahir
Maktab Perguruan Kota Bahru, Kelantan
Abdul Razak Salleh
Maktab Perguruan Batu Rakit, Terengganu
Lee Gik Lean
SK (P) Treacher Methodist, Perak
Katherine Tan
SK Convent St. Jesus (1), Melaka
Latiff Darus
Pejabat Pendidikan Daerah, Pulau Pinang
LAYOUT & ILLUSTRATIONS Sugara Abd Latif
Mohd Razif Hashim
Mathematics Unit Curriculum Development Centre
Pupils will be taught to:
Pupils will be able to:
1. Say and use the
• Teacher show s picture cards or
i. Say the number names to
Encourage pupils to
number
num ber names in
number cards. Pupils listen and
pronounce the number
numerals
fam iliar contexts.
repeat each number after teacher.
names correctly.
ii. Recognise numerals to 1000.
one hundred,
• Pupils recite the number sequence
Pupils should count
one hundred
to 1000.
systematically to keep track
and one, one
iii. Count up to 1000 objects by
of the count.
hundred and
grouping them in hundreds,
• Pupils count to 1000 using objects
tw o, …, nine-
tens, fives, tw os and ones.
such as ice-cream sticks, straw s,
Count a larger collection of
hundred and
chips, multi-based blocks and
objects by grouping them in
ninety-nine,
Cuisenaire rods.
hundreds, tens, fives, tw os
one thousand
and ones.
count
Overcome difficulties and
tens
recognise recitation errors.
fives tw os
Check on pronunciation of number names.
ones
Check for accuracy.
Pupils will be taught to:
Pupils will be able to:
2. Read and w rite
• Teacher says a number, pupils
i. Write numerals to 1000.
Overcome difficulties in
number names
num bers to 1000.
w rite the numeral.
spelling.
ii. Read number w ords to one
number w ords
• Teacher flashes a number w ord
thousand.
Check on pronunciation of
one hundred,
card, pupils read the number
number names.
one hundred
w ord:
iii. Write number w ords to one
and one, one
thousand.
Check for accuracy in
hundred and
e.g.
spelling.
tw o, …, nine hundred and
Six hundred and forty-two.
ninety-nine, one thousand
• Pupils read and spell the number w ords to one thousand.
• Pupils match numerals w ith number w ords up to one thousand.
• Pupils w rite the number w ords.
Pupils will be taught to:
Pupils will be able to:
3. Know w hat each
• Represent 568 w ith objects such
i. Recognise the place value of
Emphasise the place value of number
digit in a number
as Cuisenaire rods or multi-based
numbers.
each digit in tw o-digit and
three-digit numbers.
place holder tw o-digit
Hundreds T ens On es
5 hundreds
three-digit partition
The digit 5 in 568 represents 500,
Emphasise the use of zero as
6 represents 60 and 8 represents
a place holder.
e.g. In 406, 0 represents • Pupils partition tw o-digit or three- tens. digit numbers into hundreds, tens
and ones.
e.g. 702
702 is 7 hundreds,
0 tens and 2 ones.
Pupils will be taught to:
Pupils will be able to:
4. Understand and use • Pupils count on and count back
i. Arrange numbers to 1000:
Arrange in order a complete number names
the vocabulary of
in ones:
a. count on and count back
set of numbers.
number w ords
comparing and
e.g. 300, 301, 302 …
in ones.
arranging num bers
e.g. 241, 240, 239 …
Include counting on and back one hundred,
or quantities to
b. count on and count back
in multiples of 10 and 100.
one hundred
• Pupils count on and count back
in tw os.
e.g: 10, 20, 30 …
and one, one
in tw os:
hundred and
c. count on and count back
tw o, …, nine
e.g. 0, 2, 4, …
in fives.
Emphasise that a number
hundred and
e.g. 122, 120, 118 …
follow ing another number in
ninety-nine,
d. count on and count back
• Pupils count on and count back
the counting on sequence is one thousand
in fives:
in tens.
larger.
arrange
e.g. 30, 35, 40, …
e. count on and count back
count on
e.g 570, 565, 555 …
in hundreds.
Emphasise that a number
count back
follow ing another number in
• Pupils count on and count back
the counting back sequence next
in tens:
is smaller.
e.g. 283, 293, 303 …
before
e.g. 600, 590, 580 …
after
Check for accuracy in
• Pupils count on and count back
counting on and counting
betw een
in hundreds:
back.
e.g. 418, 518, 618 …
e.g. 1000, 900, 800 …
Pupils will be taught to:
Pupils will be able to:
• Pupils locate the correct position
Use hundred grids for
of a number on a hundred grid
counting on and back in tens
by counting on or back in tens
and hundreds.
or hundreds.
e.g. Write 670 on the grid.
Pupils will be taught to:
Pupils will be able to:
• Pupils compare tw o numbers
ii. Compare tw o numbers and
Arrange numbers in
more
using concrete or manipulative
say w hich is more or less.
sequence of ones, tw os,
less
mater ials such as Cuisenaire
fives and tens.
rods or multi-based blocks.
iii. Arrange numbers in order:
arrange
a. compare the numbers;
order
e.g. Which is more, 217 or
and
number line
b. position the numbers on a
smaller
• Pupils arrange a group of
number line.
numbers in order.
ascending descending
Ascending order:
31, 33, 35, 37, 39, 41 Descending order:
41, 39, 37, 35, 33, 31 • Pupils use number line to arrange
numbers in order.
e.g. 65, 40, 80, 25
Pupils will be taught to:
Pupils will be able to:
5. Understand and use • Teacher introduces ordinal
i. Say ordinal numbers from
Pupils recall ordinal numbers arrange
ordinal num bers in
numbers eleventh to tw entieth
eleventh to tw entieth.
from first to tenth to denote order
different contexts.
through activities.
position.
first, second,
e.g. 20 pupils line up in a
third, fourth
ii. Use ordinal numbers in
Emphasise the relationship
straight line. Each pupil
fifth, sixth,
different contexts.
betw een cardinal and ordinal
says his/her number:
seventh, eighth
numbers up to tw entieth.
One, tw o, … tw enty. The
ninth, tenth,
pupil w ho says ‘eleven’ is
eleventh, Check pupils’ pronunciation
the ‘eleventh’ in the line.
tw elfth,
and spelling of ordinal
thirteenth,
numbers.
• Pupils respond to questions in
fourteenth,
different contexts such as:
fifteenth,
a. Who is the eleventh, tw elfth, sixteenth,
… in this queue?
seventeenth, eighteenth,
b. What is the tw elfth month of
nineteenth,
the year?
tw entieth.
c. Point to the thirteenth bead
last
from the right.
next before
d. What position is the eleventh
after
boy in the row ?
Pupils will be taught to:
Pupils will be able to:
1. Understand
• Model concept of addition
i. Add tw o numbers w ithout
Emphasise that adding zero numbers
addition as
using concrete and manipulative
regrouping:
to a number leaves the
add
combining tw o
mater ials such as chips, multi-
number unchanged.
groups of objects.
based blocks and Cuisenaire rods.
a. tw o 1-digit numbers;
plus
e.g: 768 + 0 = 768
total
• Pupils carry out addition mentally
b. a 2-digit number and a
involving:
1-digit number; and
Emphasise mental
sum
a. 1-digit numbers and multiples
c. tw o 2-digit numbers.
e.g. 3 + 50 =
Include addition using
regrouping
standard w ritten method.
zero
b. 1-digit numbers and multiples of 100.
e.g.
digit
e.g. 400 + 7 =
multiples
c. pairs of multiples of 10 to
standard
make 100.
w ritten method
e.g. 20 + = 100
one-digit
• Pupils add tw o numbers up to tw o
tw o-digit
digits w ithout regrouping.
e.g.
Tens Ones T O 5 1 + 4 3
Pupils will be taught to:
Pupils will be able to:
• Pupils add tw o numbers up to tw o
ii. Add tw o numbers w ith
Emphasise that adding zero numbers
digits w ith regrouping.
regrouping:
to a number leaves the
add
number unchanged.
e.g.
a. a 2-digit number and a
plus
1-digit number; and
Emphasise mental
b. tw o 2-digit numbers.
sum
Include addition using
groups
T ens On es
standard w ritten method.
regrouping
iii. Add tw o numbers w ithout
a. a 3-digit number and a
1-digit number;
multiples standard
• Pupils add tw o numbers up to
b. a 3-digit number and a
w ritten method
three digits w ithout regrouping.
2-digit number; and
c. tw o 3-digit numbers.
tw o-digit
three-digit
Pupils will be taught to:
Pupils will be able to:
• Pupils add three 1-digit numbers;
iv. Add three 1-digit numbers.
Emphasise that adding zero numbers
a. w ithout regrouping:
to a number leaves the
add
e.g. 4 + 3 + 2 =
number unchanged.
plus
b. w ith regrouping:
Emphasise mental
total
e.g. 5 + 7 + 6 =
calculation.
sum
Include addition using
groups
standard w ritten method.
multiples standard
w ritten method
one-digit
Pupils will be taught to:
Pupils will be able to:
2. Use and apply
• Pupils find unknow n numbers in
i. Find unknow n numbers in
Use and apply know ledge of add
knowledge of
number sentences.
number sentences.
addition in a variety of contexts including real life
plus
addition in real life.
situations.
sum Emphasise finding unknow n total
numbers in number
unknow n
sentences as follow s:
number
a. 16 + 5 =
sentence regrouping
digit multiples
tw o-digit three-digit
f. 519 = 300 +
g. 600 = + 200
h. 463 = + Emphasise mental
calculation.
Pupils will be taught to:
Pupils will be able to:
• Pupils solve problems by
ii. Solve problems involving
Use and apply know ledge of add
simulating or modelling the
addition in real life situations.
addition in a variety of
plus
situation.
contexts including real life situations.
Mat has 23 chickens.
Select problems according to
He buys 6 more chickens.
pupils’ ability and proficiency number
How many chickens has he now ?
in language.
sentence regrouping
• Pupils make up a number story to
zero
a given number sentence.
digit
multiples one-digit
e.g.
I have 46 stickers and Kumar has
tw o-digit
12 stickers. Altogether w e have
three-digit
58 stickers.
Pupils will be taught to:
Pupils will be able to:
1. Understand
• Model concept of subtraction
i. Subtract tw o numbers w ithout
Emphasise that subtracting subtract
subtraction as
using concrete and manipulative
regrouping:
zero leaves a number
take aw ay
“take aw ay” or
mater ials such as, chips, multi-
unchanged.
“difference”
based blocks and Cuisenaire rods.
a. a 1-digit number from a
minus
e.g. 415 – 0 = 415
between two
1-digit number;
How many
groups of objects.
• Pupils carry out subtraction
left?
mentally involving:
Emphasise mental
b. a 1-digit number from a
calculation.
2-digit number; and
What is left?
a. multiples of 10
regrouping
e.g. 70 – 40 =
Include subtraction using
c. a 2-digit number from a
standard w ritten method.
zero
b. multiples of 100
2-digit number.
e.g. 600 – 200 =
e.g.
digit
c. a 2-digit number and a
multiples
1-digit number.
standard
e.g. 15 – 3 =
w ritten method
• Pupils subtract tw o numbers
one-digit
w ithout regrouping:
tw o-digit
e.g. 54 – 31 =
T ens On es T O
Pupils will be taught to:
Pupils will be able to:
• Pupils subtract tw o numbers
ii. Subtract tw o numbers w ith
Emphasise that subtracting subtract
w ith regrouping.
regrouping:
zero leaves a number
take aw ay
a. a 1-digit number from a
minus
2-digit number; and
Emphasise mental
How many
b. a 2-digit number from a
2-digit number.
Include subtraction using
What is left?
T ens On es T O
standard w ritten method.
regrouping
zero
iii. Subtract tw o numbers w ithout
a. a 1-digit number from a
3-digit number;
standard w ritten method
• Pupils subtract tw o numbers
w ithout regrouping.
b. a 2-digit number from a
3-digit number; and
tw o-digit
c. a 3-digit number from a
three-digit
3-digit number.
Pupils will be taught to:
Pupils will be able to:
• Pupils subtract three 1-digit
iv. Subtract three 1-digit numbers. Emphasise that subtracting subtract
numbers.
zero leaves a number
take aw ay
e.g. 9 – 1 – 3 =
unchanged.
minus
Emphasise mental
How many
calculation.
left?
Include subtraction using
What is left?
standard w ritten method.
standard w ritten method
e.g. 8 – 2 – 5 =
Use manipulatives to help
standard
pupils see the relationship
w ritten method
betw een addition and
one-digit
subtraction. e.g.
Pupils will be taught to:
Pupils will be able to:
2. Use and apply
• Pupils find unknow n numbers in
i. Find unknow n numbers in
Use and apply know ledge of subtract
knowledge of
number sentences.
number sentences.
subtraction in a variety of
take aw ay
subtraction in
contexts including real life
real life.
situations.
minus difference
Emphasise finding unknow n numbers in number
How many
sentences as follow s:
left? What is left?
multiples standard
e. = 149 – 25
w ritten method
f. 300 = 867 –
one-digit tw o-digit
g. 275 = – 43
three-digit
h. 180 = – Emphasise mental
calculation.
Pupils will be taught to:
Pupils will be able to:
• Pupils respond to questions
ii. Solve problems involving
Continue to develop the
subtract
phrased in a variety of w ays
subtraction in real life
understanding of subtraction take aw ay
such as:
situations.
as taking aw ay and finding the difference betw een tw o
minus
1. What is the difference
numbers.
difference
betw een 20 and 32?
Use and apply know ledge
betw een
2. What number must you take
of subtraction in a variety
How many
from 40 to leave 26?
of contexts including real life. left? What is left?
3. Find pairs of numbers w ith a
Select problems according
difference of 10.
to pupils’ ability and
regrouping
proficiency in language.
zero
• Pupils solve problems by
digit
simulating or modelling the situation.
multiples standard
e.g.
w ritten method
1. Hema buys 20 cards.
If she gives 6 cards to her
one-digit
sister, how many cards has
tw o-digit
she left?
three-digit
Pupils will be taught to:
Pupils will be able to:
2. Class Bestari has 45 pupils and Class Maju has 38 pupils. How many more pupils are there in Class Bestari?
• Pupils make up a number story to
a given number sentence. e.g.
50 - 12 = 38
There are 50 children in the bus.
12 are standing and 38 are sitting.
Pupils will be taught to:
Pupils will be able to:
1. Understand
• Pupils model concept of
i. Recognise multiplication as
Introduce multiplication as
add 2 and 2 …
m ultiplication as
multiplication as repeated
repeated addition.
repeated addition.
add 3 and 3 …
repeated addition.
addition using concrete and
add 4 and 4 … tables)
(2, 3, 4 and 5 times-
manipulative materials.
add 5 and 5 …
e.g. Pupils form 3 groups of 2
Pupils count the number of groups and the number of
multiply
cookies in each group.
multiplied by
Pupils w rite the number
double
sentences to find the total
skip counting
number of cookies in 3 groups.
times-tables multiplication
tables
2+2+2=6 3x2=6
Relate multiplication to repeated addition.
Pupils will be taught to:
Pupils will be able to:
• Pupils w rite number sentences
ii. Wr ite number sentences for
Use ‘x’ and ‘=’ signs in a
times
for multiplication.
multiplication.
number sentence.
multiply
e.g.
Relate ‘x’ to times and
multiplied by
multiply.
double
Read number sentence,
skip counting
4 x 5 = 20 as “four times five times-tables equals tw enty” or “four
number multiplied by five is equal to
7 x 3 = 21
sentence
tw enty”.
multiplication
2. 3 x 4 = 12
3. 3 x 2 = 6
Pupils will be taught to:
Pupils will be able to:
• Pupils build up multiplication
iii. Build up the multiplication
Include activities such as
times
tables of 2, 3, 4 and 5 using
tables of 2, 3, 4 and 5.
making number patterns
multiply
concrete or manipulative
using manipulatives or ICT
mater ials or pictorial
to build up multiplication
by
representation.
iv. Multiply tw o 1-digit numbers.
tables.
multiplied by
e.g.
double skip counting times-tables build
Include standard w ritten method.
e.g. 8 x 3
Pupils will be taught to:
Pupils will be able to:
2. Know by heart the
• Pupils list all possible
i. Recall rapidly the
Pupils must know by heart
times
m ultiplication
combinations of tw o numbers that
multiplication tables of 2, 3, 4
the basic facts of
multiply
tables of 2, 3, 4,
equal to a given product.
and 5.
multiplication involving the 2,
and 5.
e.g. Product is 12
3, 4 and 5 times-tables.
times-tables
6 x 2 = 12
skip counting
4 x 3 = 12
Relate skip counting by tw os,
3 x 4 = 12
threes, fours and fives to
• Activities such as using flash
cards and saying aloud
Emphasise mental
multiplication facts can be carried
calculation.
out. • Pupils memorise multiplication
tables by singing or chanting. • Pupils respond rapidly to oral and
w ritten questions such as:
e.g. 6 times 2 equals …? Multiply 7 by 4.
Pupils will be taught to:
Pupils will be able to:
3. Use and apply
• Pupils find unknow n numbers in
i. Find the unknow n numbers in
Use and apply know ledge of unknow n
knowledge of
number sentences.
number sentences.
multiplication in a variety of
numbers
m ultiplication in
contexts including real life
times
real life.
e.g. x 3 = 15
situations.
x = 36
ii. Solve problems involving
multiply
multiplication in real life
Emphasise finding unknow n
multiplied by numbers in number sentences
• Pupils solve problems by
situations.
such as:
doubles
simulating or modelling the situation.
a. 4 x 2 =
times as many times-tables
e.g. b. 9 x = 18
1. A bicycle has 2 w heels. How
skip counting
c. x 3 = 9
many w heels are there on 7
2. Tina puts 5 buns each in 3
e. = 7 x 4
plates. Altogether there are …buns.
f. 32 = 8 x
• Pupils make up a number story
g. 30 = x 5
to a given number sentence.
Emphasise mental calculation.
Zam bought 9 packets of
Select problems according to
balloons. Each packet has 2
pupils’ ability and proficiency
balloons. Altogether he has 18
in language.
balloons.
Pupils will be taught to:
Pupils will be able to:
1. Understand division • Pupils model concept of division
i. Recognise division as sharing Relate division as sharing
share
as sharing equally
using concrete and manipulative
equally.
equally or grouping.
sharing equally
or grouping.
mater ials.
(Corresponding to
group
2, 3, 4 and 5
a. Sharing equally
ii. Recognise division as grouping.
grouping times- tables)
e g.
6 ice-creams are shared equally
times-tables
betw een 2 boys.
division
Each boy gets 3 ice-creams.
b. Grouping
e.g. There are 12 bottles. A box can be filled w ith 4 bottles. Therefore 3 boxes are needed.
y4=3 12
Pupils will be taught to:
Pupils will be able to:
• Pupils w rite number sentences
iii. Write number sentences for
Use ‘÷’ and ‘=’ signs in a number share equally
for division.
division.
sentence.
group in tw os
e.g.
Relate ‘÷’ to share equally, group group in threes in twos, group in threes, group
iv. Divide numbers w ithin the
in fours or group in fives and
group in fours
multiplication tables.
divide.
group in fives
• Pupils use concrete or
divide
manipulative materials or
Read number sentence,
divided by
pictorial representation to
24 ÷ 4 = 6 as “tw enty-four
divide numbers.
divided by four equals 6” or “tw enty-four divided by four is
standard
w ritten method
equal to six”. Use manipulatives to help pupils
see the relationship betw een division and multiplication.
e.g. 20 ÷ 4 =
4 x = 20 Use multiplication tables to
develop division skills. Include standard w ritten method.
e.g. 3 27 Exclude division w ith
remainders.
Pupils will be taught to:
Pupils will be able to:
2. Derive quickly
• Activities such as using flash
i. Derive quickly division facts
Pupils derive quickly the
share equally
division facts.
cards and saying aloud can be
of 2, 3, 4 and 5 times-tables.
division facts involving the group in tw os
(Corresponding to
carried out.
2, 3, 4 and 5 times-tables.
group in threes tables)
2, 3. 4 and 5 times-
• Pupils respond rapidly to oral
Emphasise mental
group in fours
and w ritten questions, such as:
calculation.
Share 18 betw een 2.
group in fives
Divide 32 by 4.
divide divided by derive
Pupils will be taught to:
Pupils will be able to:
3. Use and apply
• Pupils find unknow n numbers in
i. Find the unknow n numbers
Use and apply know ledge divide
knowledge of
number sentences.
in number sentences.
of division in a variety of
share equally
division in real life.
contexts including real life
e.g. 18 ÷ = 9
ii. Solve problems involving
situations.
group
• Pupils solve problems by simulating
division in real life situations.
number Emphasise finding unknow n
or modelling the situation.
sentence
numbers in number sentences as follow s:
e.g.
1. A baker bakes 16 buns. She puts 2 buns in every box. How
a. 8 ÷ 2 =
many boxes can she fill?
b. 16 ÷ = 8
2. There are 36 books. Four
c. ÷ 3 = 5
children share them equally. How many books does each
d. ÷ = 9
child get?
e. = 32 ÷ 4 • Pupils make up a number story to
a given number sentence.
h. 8 = ÷ Mrs.Tan has 28 stamps. She has four children. Each child gets 7
Select problems according
stamps.
to pupils’ ability and proficiency in language.
Pupils will be taught to:
Pupils will be able to:
1. Understand and use • Pupils show enough coins to make
i. Represent the value of money
Encourage pupils to tell the money
the vocabulary
up a small amount.
in ‘RM’ and ‘sen’.
value of money correctly.
sen
related to money.
e.g. RM1.35
Introduce RM50 note.
ringgit RM
50sen
50sen
Show pupils genuine notes and coins.
coins notes
20sen 10sen 5sen
Pupils are aw are that RM1 value is available in both forms, coin and note.
amount
• Pupils show enough notes to make
up a given amount.
Emphasise ‘0’ in the ‘sen’ value.
e.g. RM31 e.g.
RM10
RM10
1. RM12.05
RM5
RM5
2. RM38.60
RM1
Pupils will be taught to:
Pupils will be able to:
• Understand that RM5.25 means
ii. Exchange:
Pupils check for accurate money
RM5 and 25 sen.
amount exchanged.
sen
a. coins up to RM5; and
• Pupils respond to questions such
ringgit
as:
b. notes up to RM50.
RM
1. How many sen are there in
RM1?
coins
2. Write 165 sen in RM and sen.
notes
3. Write in RM and sen the total
value
of tw o RM10 notes, three RM5 notes and six 10 sen coins.
How much?
• Provide coins of different denominations and pupils make up to RM5 using different combinations of coins.
• Provide notes of different denominations and pupils make up to RM50 using different combinations of notes.
Pupils will be taught to:
Pupils will be able to:
2. Use and apply
• Set up bargain counters w ith
i. Add money up to RM50.
Addition and subtraction
money
knowledge of
articles priced up to RM50 for
involves:
sen
m oney in real life.
practical buying and selling.
a. sen only;
Provide a box of coins and notes
ii. Subtract money up to RM50.
b. RM only; and
ringgit
of different denominations for
c. RM and sen.
RM
“shopkeeper” and provide “customers” w ith some
Limit:
coins
denominations of coins and notes.
a. addition to the highest
notes
Show transactions in w ritten
total of RM50; and
forms.
b. subtraction w ithin the
value
range of RM50.
add
• Create “ Card Shop” scenario.
Include addition and
subtract
Pupils bring old cards from home.
subtraction of money using
Each card is labelled w ith a price
How much?
standard w ritten method. tag. Pupils carry out buying and
selling activities.
e.g.
1. RM13.45
• Pupils use mental addition or
+ RM 6.10
subtraction to solve problems.
2. RM40 - RM10
Inculcate moral values involving money.
Pupils will be taught to:
Pupils will be able to:
• Pupils solve problems.
iii. Solve problems involving
Encourage pupils to
money
money in real life situations.
explain methods used.
sen
e.g.
1. I have RM6 and my mother
Emphasise the
ringgit
gives me RM2. How much
development of the ability
RM
do I have now ?
to choose the correct operation.
coins
2. A banana costs 10 sen less
notes
than a mango. A mango costs
Select problems according value
70 sen. How much does a
to pupils’ ability.
banana cost?
How much? solve
Pupils will be taught to:
Pupils will be able to:
1. Understand, read
• Teacher introduces the minute
i. Read time to five minutes.
Begin w ith analogue clock. time
and write the
hand using a clock face.
Use clock faces w hich
hour hand
vocabulary related
• Pupils count in fives from 0 to 60
show the numerals 1 to 12
to time.
ii. Wr ite the time to five
minute hand
as teacher moves the hand around
and have clearly mar ked
minutes.
minute intervals.
minutes
the clock face.
Emphasise the difference
o’clock
• Teacher marks 5, 10, 15 … 60
betw een the hour hand
clock face
(minutes) on the clock face and
and the minute hand.
pupils count in fives.
analogue clock
Emphasise each mark on
e.g. 25 minutes
the clock face means 1 minute.
Pupils read time in at least
tw o w ays.
e.g. 5:10
15 Five ten.
Ten minutes past five.
Write the time, for example, seven tw enty as 7:20.
Pupils will be taught to:
Pupils will be able to:
• Teacher uses a clock face to
Exclude cases w here the
clock
show various times.
minute hand is betw een
o’clock
tw o numbers.
e.g. “It’s one thirty.”
hour hand
“It’s three fifty-five.”
Check on pupils’
minute hand
“It’s ten minutes past six.”
pronunciation w hen reading time.
minutes
• Pupils w rite the given time.
b. Teacher says the time, for example nine fifteen and pupils w rite: 9:15.
• Pupils draw the hour and the minute hands to show time.
Pupils will be taught to:
Pupils will be able to:
1. Understand the
• Teacher explains the comparative
i. Use units of time and know the
Introduce standard units
minutes
relationship
order of units of time and that
relationship betw een:
for time and show the
hour
between units
there are 60 minutes in an hour
a. hour and minutes; and
relationship betw een them.