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Integrated Curriculum for Primary Schools

Curriculum Specifications

MATHEMATICS YEAR 3

Curriculum Development CentreMinistry of Education Malaysia

2003

MINISTRY OF EDUCATION MALAYSIA


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Copyright (C) 2003 Curriculum Development CentreMinistry of Education MalaysiaPesiaran Duta Off Jalan Duta50604 Kuala Lumpur

First published 2003

Copyright reserved. Except for use in a review, thereproduction 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 forbiddenwithout the prior written permission from the Director of theCurriculum Development Centre, Ministry of Education Malaysia.


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CONTENTS

RUKUNEGARA vNATIONAL PHILOSOPHY OF EDUCATION viiPREFACE ixINTRODUCTION xi

WHOLE NUMBERS Numbers to 10 000 1 Addition with the Highest Total of 10 000 7Subtraction within the Range of 10 000 9Multiplication within 6, 7, 8 and 9 Times-tables 12Multiplication with the Highest Product of 1000 16Division within 6, 7, 8 and 9 Times-tables 18Division with the Highest Dividend of 1000 22

FRACTIONS Introduction to Fractions 24

MONEY Money to RM100 25

TIME Reading and Writing Time 30Relationship between Units of Time 33

Addition, Subtraction, Multiplication and 34Division involving TimeSolving Problems involving Time 36

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LENGTH Measuring and Comparing Lengths 37Relationship between Units of Lengths 39Addition, Subtraction, Multiplication and 40

Division involving LengthSolving Problems involving Length 42

MASS Measuring and Comparing Masses 43Relationship between Units of Lengths 45Addition, Subtraction, Multiplication and 46

Division involving MassSolving Problems involving Mass 48

VOLUME OF LIQUID Measuring and Comparing Volumes of Liquids 49Relationship between Units of Lengths 53Addition, Subtraction, Multiplication and 54

Division involving Volumes of LiquidsSolving Problems involving Volumes of Liquids 56

SHAPE AND SPACE Three-Dimensional Shapes 57Two-Dimensional Shapes 60Symmetry 62

DATA HANDLING Collecting and Organising Data 63

CONTRIBUTORS 65

PANEL OF WRITERS 66

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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


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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 whoare 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.

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Science and technology plays a crucial role inmeeting Malaysias aspiration to achieve developednation status. Since mathematics is instrumental indeveloping scientific and technological knowledge, theprovision of quality mathematics education from an

early age in the education process is critical.

The primary school Mathematics curriculum asoutlined in the syllabus has been designed to provideopportunities for pupils to acquire mathematicalknowledge and skills and develop the higher order problem solving and decision making skills that theycan apply in their everyday lives. But, more

importantly, together with the other subjects in theprimary school curriculum, the mathematicscurriculum seeks to inculcate noble values and lovefor the nation towards the final aim of developing theholistic person who is capable of contributing to theharmony and prosperity of the nation and its people.

Beginning in 2003, science and mathematics will be

taught in English following a phased implementationschedule, which will be completed by 2008.Mathematics education in English makes use of ICT in its delivery. Studying mathematics in themedium of English assisted by ICT will provide

greater opportunities for pupils to enhancetheir knowledge and skills because they are able tosource the various repositories of knowledge written inmathematical English whether in electronic or printforms. Pupils will be able to communicate

mathematically in English not only in the immediateenviroment but also with pupils from other countriesthus increasing their overall English proficiency andmathematical competence in the process.

The development of a set of Curriculum Specificationsas a supporting document to the syllabus is the workof many individuals and experts in the field. To those

who have contributed in one way or another to thiseffort, on behalf of the Ministry of Education, I wouldlike to thank them and express my deepestappreciation.

PREFACE

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(Dr. SHARIFAH MAIMUNAH SYED ZIN)Director Curriculum Development CentreMinistry of Education Malaysia


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Our nations vision can be achieved through a societythat is educated and competent in the application of mathematical knowledge. To achieve this vision,society must be inclined towards mathematics.Therefore, problem solving and communicational skills

in mathematics have to be nurtured so that decisionscan be made effectively.

Mathematics is integral in the development of scienceand technology. As such, the acquisition of mathematical knowledge must be upgradedperiodically to create a skilled workforce in preparingthe country to become a developed nation. In order to

create a K-based economy, research and developmentskills in Mathematics must be taught and instilled atschool level.

The Mathematics Curriculum has been designed toprovide knowledge and mathematical skills to pupilsfrom various backgrounds and levels of ability.

Acquisition of these skills will help them in their careers

INTRODUCTION

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Several factors have been taken into account whendesigning the curriculum and these are: mathematicalconcepts and skills, terminology and vocabulary used,and the level of proficiency of English among teachersand pupils.

The Mathematics Curriculum at the primary level(KBSR) emphasises the acquisition of basic conceptsand skills. The content is categorised into four interrelated areas, namely, Numbers, Measurement,Shape and Space and Statistics.

It is hoped that with the knowledge and skills acquiredin Mathematics, pupils will discover, adapt, modify andbe innovative in facing changes and future challenges.

The learning of mathematics at all levels involves morethan just the basic acquisition of concepts and skills. Itinvolves, more importantly, an understanding of theunderlying mathematical thinking, general strategies of problem solving, communicating mathematically andinculcating positive attitudes towards an appreciationof mathematics as an important and powerful tool ineveryday life.

Achieving this requires a sound mathematicscurriculum, competent and knowledgeable teacherswho can integrate instruction with assessment,classrooms with ready access to technology, and acommitment to both equity and excellence.

later in life and in the process, benefit the society andthe nation.


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The Primary School Mathematics Curriculum willenable pupils to:

1. know and understand the concepts,definition, rules sand principles related tonumbers, operations, space, measures anddata representation;

2. master the basic operations of mathematics:

4. master basic mathematical skills, namely:

5. use mathematical skills and knowledge tosolve problems in everyday life effectivelyand responsibly;

6. use the language of mathematics correctly;

7. use suitable technology in concept building,acquiring mathematical skills and solvingproblems;

8. apply the knowledge of mathematicssystematically, heuristically, accurately andcarefully;

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AIM

The Primary School Mathematics Curriculum aimsto build pupils understanding of number conceptsand their basic skills in computation that they canapply in their daily routines effectively and responsiblyin keeping with the aspirations of a developed societyand nation, and at the same time to use thisknowledge to further their studies.

3. master the skills of combined operations;

OBJECTIVES

9. participate in activities related to mathematics;and

10. appreciate the importance and beauty of mathematics.

addition, subtraction, multiplication, division;

making estimates and approximates, measuring, handling data representing information in the form

of graphs and charts;


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CONTENT ORGANISATION

The Mathematics Curriculum at the primary levelencompasses four main areas, namely, Numbers,Measures, Shape and Space and Statistics. Thetopics for each area have been arranged from thebasic 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. Num bers

2. Measures

3. Shape and Space

4. Statistics

The Learning Areas outline the breadth and depth of

the scope of knowledge and skills that have to bemastered during the allocated time for learning. Theselearning areas are, in turn, broken down into moremanageable objectives. Details as to teaching-learningstrategies, vocabulary to be used and points to noteare set out in five columns as follows:

Column 1:

Column 2:

Column 3:Column 4:Column 5:

Learning Objectives.

Suggested Teaching andLearning Activities.Learning Outcomes.Points To Note.Vocabulary.

Whole Numbers; Fractions; Decimals; Money; Percentage.

Time; Length; Mass; Volume of Liquid.

Two-dimensional Shapes; Three-dimensional Shapes.

Average; Data Representation.

The purpose of these columns is to illustrate, for aparticular teaching objective, a list of what pupilsshould know, understand and be able to do by theend of each respective topic.


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The Learning Objectives define clearly what shouldbe taught. They cover all aspects of the Mathematicscurriculum and are presented in a developmentalsequence to enable pupils to grasp concepts andmaster skills essential to a basic understanding of mathematics.

The Suggested Teaching and Learning Activitieslist some examples of teaching and learning activities.These include methods, techniques, strategies andresources useful in the teaching of a specificconcepts and skills. These are however not the onlyapproaches to be used in classrooms.

The Learning Outcomes define specifically whatpupils should be able to do. They prescribe theknowledge, skills or mathematical processes andvalues that should be inculcated and developed atthe appropriate levels. These behavioural objectivesare measurable in all aspects.

In Points To Note, attention is drawn to the more

significant aspects of mathematical concepts andskills. These aspects must be taken into accountsso as to ensure that the concepts and skills are taughtand learnt effectively as intended.

The Vocabulary column consists of standardmathematical terms, instructional words and phrasesthat are relevant when structuring activities, askingquestions and in setting tasks. It is important to paycareful 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 knowof their meaning and learn how to usethem appropriately.

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The teaching and learning processes emphasiseconcept building, skill acquisition as well as the

inculcation of positive values. Besides these, thereare other elements that need to be taken into accountand learnt through the teaching and learningprocesses in the classroom. The main emphasis areas follows:

The Mathematics Curriculum is ordered in such a wayso as to give flexibility to the teachers to create anenvironment that is enjoyable, meaningful, useful andchallenging for teaching and learning. At the same timeit is important to ensure that pupils show progressionin acquiring the mathematical concepts and skills.

On completion of a certain topic and in deciding toprogress to another learning area or topic, the followingneed to be taken into accounts:

EMPHASIS IN TEACHING AND LEARNING

The skills or concepts acquired in the newlearning area or topics;

Ensuring that the hierarchy or relationshipbetween learning areas or topics have beenfollowed through accordingly; and

Ensuring the basic learning areas have or skills have been acquired or mastered beforeprogressing to the more abstract areas.

Problem solving is the main focus in the teaching andlearning of mathematics. Understanding mathematicalprocedures and solving problemsare two skills that emerge naturally when relationalunderstanding is focussed upon. As a result, problemsolving approaches should be used to investigate andunderstand mathematical content. The teaching-learning process must include exercises on problemsolving skills which are comprehensive and cover thewhole curriculum. The development of these skillsmust to be emphasised so that pupils are able to solvevarious problems effectively. The skillsinvolved are:

Various strategies and steps are used to solveproblems and these can be applied to other learningareas. In solving these problems, pupils learn to applymathematics and gradually become confident in facingnew challenging situations. Among the problem solvingstrategies to consider are:

1. Problem Solving in Mathematics

Interpreting problems; Planning the strategy; Carrying out the strategy; and Looking back at the solutions.

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2. Communication in Mathematics

Communication is one way to share ideas and clarifythe understanding of Mathematics. Through talkingand questioning, mathematical ideas can be reflectedupon, discussed and modified. The process of reasoning analytically and systematically can helpreinforce and strengthen pupils knowledge andunderstanding of mathematics to a deeper level.Through effective communications pupils will becomeefficient in problem solving and be able to explainconcepts and mathematical skills to their peers andteachers.

Pupils who have developed the above skills willbecome more inquisitive gaining confidence in theprocess. Communicational skills in mathematicsinclude reading and understanding problems,interpreting diagrams and graphs, and using correct

and concise mathematical terms during oralpresentation and written work. This is also expandedto the listening skills involved.

Communication in mathematics through the listeningprocess occurs when individuals respond to whatthey hear and this encourages them to think using

their mathematical knowledge in making decisions.Communication in mathematics through the readingprocess takes place when an individual collectsinformation or data and rearranges the relationshipbetween ideas and concepts.

Communication in mathematics through the

visualization process takes place when an individualmakes observation, analyses it, interprets andsynthesises the data into graphic forms, such aspictures, diagrams, tables and graphs.

The following methods can create an effectivecommunication environment:

Trying a simple 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.

Identifying relevant contexts associatedwith environment and everyday lifeexperiences of pupils;

Identifying interests of pupils; Identifying teaching materials; Ensuring active learning;


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Oral communication is an interactive process thatinvolves activities like listening, speaking, reading andobserving. 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 aboutmathematics and to tell others the results of their thinking, they learn to be clear and convincing. Listeningto others explanations gives pupils the opportunitiesto develop their own understanding. Conversations inwhich mathematical ideas are explored from multipleperspectives help sharpen pupils thinking and help

make connections between ideas. Such activity helpspupils develop a language for expressing mathematicalideas and appreciation of the need for precision in thelanguage. Some effective and meaningful oralcommunication techniques in mathematics are asfollows:

Stimulating meta-cognitive skills; Inculcating positive attitudes; and Creating a conducive learning environment.

Written communication is the process wherebymathematical ideas and information areshared with others through writing. The written workis usually the result of discussions, contributions andbrain-storming activities when working onassignments. Through writing, the pupils will beencouraged to think more deeply about themathematics content and observe the relationshipsbetween 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 amathematical problem and interpreting it from onemode to another. Mathematical representation enablespupils to find relationship between mathematical ideasthat are informal, intuitive and abstract using their everyday language. Pupils will realise that somemethods of representation are more effective anduseful if they know how to use the elements of mathematical representation.

Story-telling, question and answer sessionsusing own words;

Asking and answering questions; Structured and unstructure interviews; Discussions during forums, seminars

debates and brain-storming sessions; and Presentation of findings of assignments.


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3. Mathematical Reasoning

Logical reasoning or thinking is the basis for understanding and solving mathematical problems.The development of mathematical reasoning is closelyrelated to the intellectual and communicativedevelopment of the pupils. Emphasis on logical

thinking during mathematical activities opens up pupilsminds to accept mathematics as a powerful tool inthe world today.

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Pupils are encouraged to predict and do guess workin the process of seeking solutions. Pupils at alllevels have to be trained to investigate their predictions or guesses by using concrete

materials, calculators, computers, mathematicalrepresentation and others. Logical reasoning has tobe infused in the teaching of mathematics so thatpupils can recognise, construct and evaluatepredictions and mathematical arguments.

4. Mathematical Connections

In the mathematics curriculum, opportunities for making connections must be created so that pupilscan link conceptual to procedural knowledge andrelate topics in mathematics with other learningareas in general.

The mathematics curriculum consists of severalareas such as arithmetic, geometry, measures andproblem solving. Without connections between theseareas, pupils will have to learn and memorise too manyconcepts and skills separately. By making connectionspupils are able to see mathematics as an integratedwhole rather than a jumble of unconnected ideas.Teachers can foster connections in a problem-orientedclassrooms by having pupils to communicate, reasonand present their thinking. When these mathematicalideas are connected with real life situations and thecurriculum, pupils will become more conscious in theapplication of mathematics. They will also be able touse mathematics contextually in different learningareas in real life.

5. Application of Technology

The application of technology helps pupils tounderstand mathematical concepts in depth,meaningfully and precisely enabling them to exploremathematical concepts. The use of calculators,

computers, educational software, websites in theinternet and available learning packages can help toupgrade the pedagogical skills in the teaching andlearning of mathematics.


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The use of teaching resources is very important inmathematics. This will ensure that pupils absorbabstract ideas, be creative, feel confident and be ableto work independently or in groups. Most of theseresources are designed for self-access learning.Through self-access learning, pupils will be able toaccess knowledge or skills and informationsindependently according to their pace. This will serveto stimulate pupils interests and responsibility inlearning mathematics.

APPROACHES IN TEACHING AND LEARNING

Various changes occur that influence the content and

pedagogy in the teaching of mathematics in primaryschools. These changes require variety in the way of teaching mathematics in schools. The use of teachingresources is vital in forming mathematical concepts.Teachers can use real or concrete objects in teachingand learning to help pupils gain experience, constructabstract ideas, make inventions, build self confidence,encourage independence and inculcate cooperation.

The teaching and learning materials that are usedshould contain self-diagnostic elements so that pupilscan know how far they have understood the conceptsand skills. To assist the pupils in having positive

attitudes and personalities, the intrinsic mathematicalvalues of exactness, confidence and thinkingsystematically have to be absorbed through thelearning areas.

A mong the approaches that can be given consideration

are:

Good moral values can be cultivated through suitablecontext. For example, learning in groups can help

pupils develop social skills and encourage cooperationand self-confidence in the subject. The element of patriotism can also be inculcated throughthe teaching-learning process in the classroom using plannedtopics. These values should be imbibed throughoutthe process of teaching and learning mathematics.

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.


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The choice of an approach that is suitable will stimulatethe teaching and learning environment in the classroomor outside it. The approaches that are suitable includethe following:

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Cooperative learning; Contextual learning; Mastery learning; Constructivism; Enquiry-discovery; and Futures Study.

ASSESSMENT

Assessment is an integral part of the teaching and learningprocess. It has to be well-structured and carried out

continuously as part of the classroom activities. Byfocusing on a broad range of mathematical tasks, thestrengths and weaknesses of pupils can be assessed.Different methods of assessment can be conducted usingmultiple assessment techniques, including written andoral work as well as demonstration. These may be inthe form of interviews, open-ended questions,observations and assignments. Based on the results,

the teachers can rectify the pupils misconceptions andweaknesses and at the same time improve their teachingskills. As such, teachers can take subsequent effectivemeasures in conducting remedial and enrichmentactivities to upgrade pupils performance.


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Year 3

1

TOPIC: WHOLE NUMBERS

LEARNING AREA: NUMBERS TO 10 000

LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIES

LEARNING OUTCOMES POINTS TO NOTE VOCABULARY

Pupils will be taught to: Pupils will be able to:

1. Say and use the

number names infamiliar contexts.

Pupils recite number

sequence in tens, hundredsand thousands up to 10 000.

Pupils sing number song tocount systematically.e.g. From 5000 to 5100.

Teacher shows differentrepresentation of numbers upto 10 000 using multi-basedblocks or Cuisenaire rods andpupils say the numbers.

Pupils count up to 10 000using concrete andmanipulative materials suchas Cuisenaire rods or multi-based blocks.

i. Say the number names

to 10 000.

ii. Recognise numerals to10 000.

iii. Count up to 10 000objects by groupingthem in thousands,hundreds and tens.

Encourage pupils to pronounce

the number names correctly.

Check on pronunciation of number names.

Overcome difficulties andrecognise recitation errors.

Pupils should countsystematically to keep track of the count.

Count a larger collection of objects by grouping them inthousands, hundreds, and tens.

Emphasise skip counting inthousands, hundreds, tens, fives,twos and ones.

Check for accuracy.

number

numeralsrecite

one thousand,one thousandand one, onethousand andtwo, ten

thousandcount

thousandshundreds


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Year 3

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2. Read and write

numbers to 10 000.

Teacher says a number,

pupils write the numerals. Pupils fill in the missing

numbers in a sequence or missing digits in a number.

Pupils write numerals for given number words or viceversa.

Teacher flashes number wordcards and pupils read thenumber words.

Pupils read and spell thenumber words to tenthousand.

Pupils match numerals withnumber words.

i. Write numerals to

10 000.ii. Read number words to

10 000.

iii. Write number words to10 000.

Check on pronunciation of

number names.Overcome difficulties inspelling and check for accuracy.

numerals

number namesnumber words

one thousandand one, onethousand andtwo, ninethousand nine

hundred andninety-nine andten thousand


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Year 3

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3. Know what each digit

in a number represents.

Represent numbers with

manipulatives such asCuisenaire rods, multi-basedblocks or place value material.

e.g. 8069

In 8069, 0 representshundreds.

Pupils partition three-digit or four-digit numbers intothousands, hundreds, tensand ones.

e.g.1: 34503450 is 3 thousands, 4hundreds, 5 tens and 0 ones.

e.g.2:1258 = 1000 + 200 + 50 + 8

Pupils recompose numbers.e.g. 9000 + 600 + 5 = 9605

i. Recognise the place

value of numbers.

Emphasise the place value of

numbers.Emphasise zero as a placeholder.

number

digitthousandshundredstensonesfour-digit

three-digittwo-digitone-digitplace valueplace holder partition

Thousands Hundreds Tens Ones

8 0 6 9


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Year 3

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4. Understand and use

the vocabulary of comparing andarranging numbersor quantities to10 000.

Pupils count on and countback in thousands.

e.g. 4000, 5000, 6000, 8240, 7240, 6240,

i. Arrange numbers to

10 000:a. count on in ones,

twos, fives, tens,hundreds andthousands.

b. count back in ones,twos, fives, tens,hundreds andthousands.

Arrange in order a complete set

of numbers.Emphasise that a number following another number in thecounting on sequence is larger.

Emphasise that a number following another number in thecounting back sequence issmaller.

numberscount oncount backnextbeforeafter between


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Year 3

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Pupils compare two numbers

using concrete andmanipulative materials suchas Cuisenaire rods or multi-based blocks.

e.g. Which is more?7823 or 7238

Pupils compare two numbersbased on place value.e.g. 3652 and 3552.

36523552

3652 is more than 3552.

Pupils position a set of

numbers on a number line.e.g. 1500, 500, 1000

ii. Compare two numbers

and say which is moreor less.

iii. Position numbers inorder on a number line.

Check for accuracy in

positioning the numbers.Emphasise comparing twonumbers based on place value.

compare

morelessarrangeorder positionnumber line

smaller smallestlarger largestascendingdescendingsequence

0 2000


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Year 3

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5. Understand and use the

vocabulary of estimationand approximation.

Pupils dip into a bag of beans

and take a handful andestimate.

Pupils estimate the number of objects in a transparentcontainer.

Using number lines, pupilsround numbers up or down tothe nearest 10.

Pupils play games or simulate situations toenhance their understandingof the concepts.

i. Estimate quantities of

objects up to 1000.ii. Round whole numbers

less than 10 000 to thenearest 10.

Estimation should be done from

smaller number of objects tolarger number.

Record estimates and find thedifference between the estimateand the actual number to ensurethe reasonableness of estimation.

If the ones in the number is lessthan 5, round down to the lower 10. If the ones in the number is 5or greater, round up to the higher 10.

estimate

estimationquantitiesactualdifferenceobjectshandful

approximationroundwhole numbers

nearestless thanlower greater higher


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Year 3

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LEARNING AREA: ADDITION WITH THE HIGHEST TOTAL OF 10 000




1. Understand addition

as combining twogroups of objects.

Pupils model concept of

addition using concrete andmanipulative materials suchas multi-based blocks andCuisenaire rods.

Pupils add up to threenumbers with and withoutregrouping.

e.g. 516 + 29 =

i. Add up to three numbers

without regrouping,involving up to 4-digitnumbers.

ii. Add two numbers up to4-digit, with regrouping.

iii. Add three numbers upto 4-digit, with regrouping.

Emphasise that adding zero to a

number leaves the number unchanged.

Emphasise mental calculation.

Emphasise addition usingstandard written method.

e.g. 687+ 25

e.g. 3159+ 406

numbers

addadditionplustotalsumgroup

regroupwithoutregrouping

with regroupingzerodigitstandard-

writtenmethod

one-digittwo-digitthree-digitfour-digit


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Year 3

8


LEARNING AREA: ADDITION WITH THE HIGHEST TOTAL OF 10 000




2. Use and applyknowledge of additionin real life.

Pupils solve problems by

simulating or modellingsituation.

Pupils pose problems basedon given informationinvolving addition.

i. Solve problems involving

addition in real life situations.

Use and apply knowledge of

addition in a variety of contextsEmphasise mental calculation.

Select problems according topupils ability and proficiency inlanguage.

Encourage pupils to expressideas and opinions clearly.

add

plussumtotalnumber sentencesolve

problemsmodelling


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Year 3

9


LEARNING AREA: SUBTRACTION WITHIN THE RANGE OF 10 000




1. Understandsubtraction as takeaway or differencebetween two groups of objects.

Model concepts of subtraction

using concrete andmanipulative materials suchas chips, multi-based blocksand Cuisenaire rods.

Pupils subtract two numberswith regrouping.

i. Subtract two numbers up

to 4-digit, withoutregrouping.

ii. Subtract two numbers upto 4-digit, with regrouping.

Emphasise that subtracting zero

from a number leaves thenumber unchanged.

Emphasise mental calculation

Emphasise subtraction usingstandard written method.

e.g. 7896- 1253

e.g. 648- 59

subtract

take awayminusHow many left?What is left?regroupingzero

digitmultiplesstandardwritten methodone-digittwo-digitthree-digit

four-digit


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Year 3

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Pupils subtract three numberswithout regrouping and withregrouping.

iii. Subtract three numbersup to 4-digit, withoutregrouping.

iv. Subtract three numbersup to 4-digit, withregrouping.

Emphasise subtraction usingstandard written method.

e.g. 7859 231 304 =

7859 7628 231 304

7628 7324

e.g. 95 6 7 =

95 89 6 7

89 82


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Year 3

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2. Use and applyknowledge of subtraction in real life.

Develop the concept of subtraction as the inverse of addition by doing thesenumber sentences.

e.g3000 + 4000 = 70004000 + 3000 = 70007000 4000 = 30007000 3000 = 4000

Pupils write as many number sentences as they can usinga set of three numbers.Discuss further and acceptcomments from pupils.

Pupils solve problems by

simulating or modellingsituations.

Pupils pose problems basedon given information involvingsubtraction.

i. Recognise subtraction asthe inverse of addition.

ii. Solve problems involvingsubtraction in real lifesituations.

Use and apply knowledge of subtraction in a variety of contexts.

Continue to develop theunderstanding of subtraction astaking away and finding thedifference between twonumbers.



subtract

subtractiontake awayminusdifferenceHow many left?What is left?regroupingstandard writtenmethod

one-digittwo-digitthree-digitfour-digit

additioninversesolveproblemsmodelling


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Year 3

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LEARNING AREA: MULTIPLICATION WITHIN 6, 7, 8 AND 9 TIMES-TABLES




1. Understandmultiplication asrepeated addition(6, 7, 8 and 9times-tables).

Pupils model concept of multiplication as repeatedaddition using concrete andmanipulative materials.

e.g.Pupils form 3 groups of 6books.Pupils count the number of groups and the number of

books in each group.

Pupils write the number sentences to find the totalnumber of books in 3 groups.6 + 6 + 6 = 183 x 6 = 18

Relate multiplication torepeated addition.

i. Recognise multiplicationas repeated addition.

Emphasise multiplication asrepeated addition.

equals

timesmultiplymultiplied byskip countingtimes-tablesmultiplicationtablesrepeated addition


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Year 3

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Pupils write number sentences for multiplication.

e.g.1

2 x 7 = 14

e.g.23 x 6 = 18

Pupils build up multiplicationtables of 6, 7, 8 and 9 usingconcrete objects, manipulativematerials or pictorialrepresentations.

1 x 8 = 8

2 x 8 = 16

3 x 8 = 24

ii. Write number sentencesfor multiplication.

iii. Build up themultiplication tables of 6, 7, 8 and 9.

iv. Multiply two 1-digitnumbers.

Emphasise x and = signs innumber sentences.

Relate x to times and multiply.

Read number sentence6 x 4 = 24 as six times four equals twenty-four or sixmultiplied by four is equal totwenty-four.

Include activities such as makingnumber patterns usingmanipulatives or ICT to build upmultiplication tables.

Emphasise multiplication usingstandard written method.

e.g. 7x 6

times

multiplymultiplied byequalsis equal toskip countingtimes-tablesnumber sentencemultiplicationmultiplicationtablesbuild upstandard writtenmethod

one-digit number

6 12 240 18


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Year 3

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2. Know by heart themultiplication tables of 6, 7, 8 and 9.

Pupils list all possiblecombinations of two numbersthat equals to a given product.

e.g. Product is 7212 x 6 = 729 x 8 = 728 x 9 = 726 x 12 = 72

Pupils use flash cards and sayaloud multiplication facts.

Pupils memorise multiplicationtables by singing or chanting.

Pupils respond rapidly to oraland written questions such as:

e.g. 8 times 7.Multiply 9 by 6.

i. Recall rapidly themultiplication facts of 6,7, 8 and 9 times-tables.

Pupils should know by heart thebasic facts of multiplicationinvolving 6, 7, 8 and 9 times-tables.

Relate skip counting by sixes,sevens, eights and nines tomultiplication.


times

multiplymultiplied byequalsis equal tomultiplicationrecallskip count


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Year 3

15






3. Use and applyknowledge of multiplication in reallife.

Pupils find unknown numbersin number sentences.

e.g. x 8 = 56

x = 81

Pupils solve problems bysimulating or modelling

situations. Pupils pose problems based

on given information involvingmultiplication.

i. Find unknown numbersin number sentences.

ii. Solve problems involvingmultiplication in real lifesituations.

Use and apply knowledge of multiplication in a variety of contexts.

Emphasise finding unknownnumbers in number sentencesas follows:

a. 2 x 6 =

a. 9 x = 63

b. x 8 = 24

c. x = 49

d. = = 8 x 7

e. 72 = 9 x

f. 64 = x 8

g. 54 = x



unknownnumberstimesmultiplymultiplied by

equalsis equal tonumber sentencesolve


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Year 3

16


LEARNING AREA: MULTIPLICATION WITH THE HIGHEST PRODUCT OF 1000




1. Understand and usethe operation of multiplication.

Pupils use concrete materialsand pictorial representationsto develop the concept of multiplication.

Pupils multiply two numberswithout regrouping.

e.g.1. 14 x 2 = 282. 80 x 10 = 8003. 213 x 3 = 639

Pupils multiply two numberswith regrouping.

e.g.1. 57 x 6 = 3422. 438 x 4 = 1752

Pupils multiply two numbersmentally by partitioning themultiplier.

e.g. 23 x 4 =20 x 4 = 80

3 x 4 = 1223 x 4 = 92

i. Multiply 2-digit numbersby 1-digit numberswithout regrouping.

ii. Multiply 2-digit numbersby 10.

iii. Multiply 2-digit numbersby 1-digit numbers withregrouping.

iv. Multiply 3-digit numbersby 1-digit numberswithout regrouping.

v. Multiply 3-digit numbersby 1-digit numbers withregrouping.

Emphasise that any number multiplied by zero results in zero.e.g.6 x 0 = 00 x 6 = 0

Emphasise that a number multiplied by one will give ananswer the same as the number.e.g.18 x 1 = 181 x 18 = 18

Emphasise multiplication usingstandard written method.


times

multiplymultiplied byequalsis equal towithoutregroupingwith regroupingmultiplicationproduct


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Year 3

17


LEARNING AREA: MULTIPLICATION WITH THE HIGHEST PRODUCT OF 1000




Pupils solve problems bysimulating or modellingsituations.

Pupils pose problems basedon given information involvingmultiplication.

vi. Solve problems involvingmultiplication in real lifesituations.

Use and apply knowledge of multiplication in a variety of contexts.

Continue to develop theunderstanding of multiplicationas repeated addition.



times

multiplymultiplied byequalsis equal towithoutregroupingwith regroupingmultiplicationproduct

solveproblems

Y 3


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Year 3

18


LEARNING AREA: DIVISION WITHIN 6, 7, 8 AND 9 TIMES-TABLES




1. Understand division assharing equally or grouping.(Corresponding to 6, 7,8 and 9 times-tables)

Pupils model the concept of division using concrete andmanipulative materials.

a: Sharing equally

e.g.14 flowers are shared equallybetween 7 girls. Each girl gets2 flowers.

14 7 = 2

i. Recognise division assharing equally.

Relate division as sharingequally or grouping.

Use and = signs in number sentences.

Relate to sharing equally or grouping in sixes, sevens, eightsand nines.

Read number sentence21 7 = 3 as twenty-one dividedby seven equals three or twenty-one divided by seven isequal to three.

Use manipulatives to help pupilssee the relationship betweendivision and multiplication.

e.g. 72 9 = 89 x 8 = 72

Use multiplication tables todevelop division skills.

share

sharing equallygroupingtimes-tablesdivideequalsis equal todivision

Y 3


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Year 3

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b. Grouping

e.g. 12 6 = 2

Pupils write number sentences for division.

e.g.

24 8 = 3

ii. Recognise division asgrouping.

iii. Write number sentencesfor division.

iv. Divide numbers withinthe multiplication tables.

Emphasise division usingstandard written method.

e.g. 8 24

Exclude division withremainders.

share equally

group in sixesgroup in sevensgroup in eightsgroup in ninesdividedivisiondivided byequalsis equal tostandard writtenmethodmultiplicationtables

number sentence

Year 3


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2. Derive quickly divisionfacts.(Corresponding to 6, 7,8 and 9 times-tables)

Pupils use flash cards andsay division facts aloud.

Pupils respond rapidly to oraland written questions.

e.g. Share 25 among 5.Divide 30 by 6.

i. Derive quickly divisionfacts of 6, 7, 8 and 9times-tables.

Pupils should know by heart thedivision facts of 6, 7, 8 and 9times-tables.


divide

divisionshare equallygroupnumber sentencederive

Year 3


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Year 3

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3. Use and applyknowledge of divisionin real life.


e.g.Jeya has made a patternusing 12 tiles. One tile inevery four is red. How manytiles are red?

Pupils pose problems basedon given information involvingdivision.

e.g. 30 5 = 6

I have 30 cakes. One boxholds 5 cakes. So I need 6

boxes to hold all the cakes.

Pupils find unknown numbersin number sentences.

e.g. 48 = 8

i. Find unknown numbersin number sentences.

ii. Solve problems involvingdivision in real lifesituations.


Use and apply knowledge of division in a variety of contexts.

Emphasise finding unknownnumbers in number sentencesas follows.

e.g:

a. 40 8 =b. 49 = 7

a. 9 = 3

b. = 9

c. = 36 9

d. 4 = 32

e. 9 = 7

f. 8 =

divide

share equallynumber sentencedivideunknownnumbersmodelingsimulating

equalsis equal to

with remainder withoutremainderssolve

problems

Year 3


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Year 3

22


LEARNING AREA: DIVISION WITH THE HIGHEST DIVIDEND OF 1000




1. Understand and usethe operation of division.

Pupils use concrete materialsand pictorial representationsto develop the concept of division.

Pupils divide two numberswithout remainders.

e.g.1. 35 7 = 52. 60 10 = 63. 408 2 = 204

Pupils divide two numberswith remainders.

e.g.1. 37 6 = 6 remainder 1

2. 525 10 = 52 remainder 53. 106 4 = 26 remainder 2

i. Divide 2-digit numbersby 1-digit numberswithout remainders.

ii. Divide 2-digit numbersby 10 without remainders.

iii. Divide 2-digit number by 1-digit numbers withremainders.

iv. Divide 2-digit numbersby 10 with remainders.

v. Divide 3-digit numbersby 1-digit numberswithout remainders.

vi. Divide 3-digit numbersby 1-digit numbers withremainders.

Exclude zero as divisor.

Emphasise that a number divided by one will give ananswer the same as the number.

Emphasise division usingstandard written method.


Continue to develop theunderstanding of division assharing equally and grouping.


divide

divided bydivisionsharing equallyequalsis equal towith remainder withoutremainders

Year 3


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Year 3

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LEARNING AREA: DIVISION WITH THE HIGHEST DIVIDEND OF 1000





Pupils pose problems basedon given information involvingdivision.

vii. Solve problems involvingdivision in real lifesituations.

Use and apply knowledge of division in a variety of contexts.

Continue to develop theunderstanding of division assharing equally and grouping.



divide

divided bydivisionequalsis equal towith remainder withoutremainders

solvepose

problems

Year 3


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Year 3

24

TOPIC: FRACTIONS

LEARNING AREA: INTRODUCTION TO FRACTIONS




1. Understand and usethe vocabulary relatedto fractions.

Teacher introduces theconcept of fractions usingconcrete objects andmanipulative materials.

Use ICT/ graphic to modelfractions.

Discuss by showing what isnot one half or one quarter and explain why.

e.g.1. These shapes are not

divided into halves.

2. This jar is not half full.

i. Recognise one whole,one half, one quarter and three quarters.

ii. Say fractions, parts,one whole, one half,one quarter and threequarters in context.

iii. Read fractions, parts,one whole, one half,one quarter and threequarters in context.

iv. Write21 ,

41 and

43 in

context.

v. Recognise 42

= 21

and

144

= .

vi. Recognise fractions asequal shares of a wholeset.

Emphasise fractions as:a. equalled size portions of a

whole.b. Equal shares of a whole set:

one half and one quarter.

Limit fractions to21 ,

41 and

43 .

is written as21 and

pronounced as half, one halfor one over two.

Introduce the terms, numerator and denominator. For example in

21 , 1 is the numerator and 2 is the

denominator.

fractions

partsone wholeone half one quarter two quartersthree quartersnumerator denominator equal partsequal sharesportionsover

Year 3


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25

TOPIC: MONEY

LEARNING AREA: MONEY TO RM100




1. Understand and usethe vocabulary relatedto money.

Pupils show differentcombinations of notes torepresent a given amount of money.e.g. RM 57.00

Pupils show differentcombinations of notes andcoins to represent a givenamount of money.e.g. RM 68.55

i. Represent the value of money in RM and sen.

Emphasise stating the value of money correctly.

Introduce genuine RM100 note.

ringgit

senRMcoinsnotesvalueHow much?combinationmoney

RM50

RM50

RM 2

RM1RM5

RM 1

or

RM5

RM50 RM10

20sen

RM5

RM1 RM1 RM1

10sen

20sen

5sen

Year 3


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26

TOPIC: MONEY





Provide notes and coins(toy-money) of differentdenominations to show thedifferent combinations for acertain amount of money.

Encourage pupils to usemental addition to convertringgit to sen.

e.g.RM52.80 = 5200 sen + 80 sen4635 sen = RM46.00 + RM0.35

Pupils do conversion usingtoy money.

ii. Exchange:

a. coins up to RM10;and

b. notes up to RM100.

iii. Convert ringgit to senand vice versa.

Check for accurate amountexchanged.

Provide pupils with sufficientamount of toy money to carryout conversion activity.

Emphasise 0 in the sen value.

e.g. RM69. 05

RM14.7 0

ringgit

senRMcoinsnotesvalueHow much?combinationsmoney

Year 3


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TOPIC: MONEY





2. Use and applyknowledge of moneyin real life.

Set up bargain counters withitems priced up to RM100 for buying and selling activities.

i. Add money up to RM100.

ii. Subtract money up toRM100.

Limit:a. addition to the highest total of

RM100; andb. subtraction within the range

of RM100.

Emphasise addition andsubtraction of money usingstandard written method.

e.g. 1. RM 32.45+ RM 17.05________

e.g. 2. RM 80.00- RM 20.00

_______

Check for accuracy in additionand subtraction.

money

ringgitsenRMcoinsnotesvalueaddsubtractHow much more?How much less?balancetotal

Year 3


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28

TOPIC: MONEY





Pupils model concept of multiplication and divisionusing toy money.

Pupils multiply and dividemoney in:a. RM only; andb. sen only.

e.g.

1. RM7 x 3 =

2. 50 sen x 7 =

3. RM45 9 =

4. 85 sen 5 =

iii. Multiply money to thehighest product of RM100.

iv. Divide money withdividend not more thanRM100.

Limit:a. multiplicand to 1-digit;b. divisor to 1-digit; andc. exclude remainders.

Provide pupils with sufficientamount of toy money.

Multiplication and division of money involves:a. RM only; andb. sen only.

Emphasise multiplication anddivision of money using standardwritten method.

e.g.1. RM 14

x 8

2. RM306

Exclude division with remainders.

moneyringgitsenRMcoinsnotesvalueamount

multiplymultiplied bymultiplicationrepeatedadditiondividedivided by

divisionsharesharingequallystandard writtenmethod

Year 3


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29

TOPIC: MONEY





Use any of the four operationsto solve story problemsinvolving money in real life.

e.g.1

My mother gives me RM52.40and my father gives meRM20.20. How much would Ihave?

e.g.2

Three boys share RM36equally. How much moneydoes each boy get?

Pupils pose problems relatedto the four operations involvingmoney.

v. Solve problems involvingmoney in real lifesituations.

Select problems according topupils ability and proficiency inthe language.

Encourage pupils to explainmethods used.

money

RinggitcoinsnotessenRMvalueamounthow much?solveproblems

Year 3


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30

TOPIC: TIME

LEARNING AREA: READING AND WRITING TIME




1. Understand, read andwrite the vocabulary

related to time.

Teacher uses a clock face toshow half hour and quarter

hour. Pupils say timeaccordingly after teacher.

i. Read time to the half or quarter hour on a clock.

Use analogue and digital clocks.

Emphasise the correct ways of reading time.

e.g.1: 4:15a. Quarter past four.b. Fifteen minutes past four.c. Fifteen past four.d. Four fifteen.

e.g.2: 10:45a. Quarter to eleven.b. Fifteen minutes to eleven.c. Fifteen to eleven.d. Ten forty-five.

e.g.3: 2:30a. Half past two.

b. Thirty minutes past two.c. Two thirty.

half quarter hour

quarter pastquarter tohalf past minutes past past

minutes to to

Year 3


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31

TOPIC: TIME

LEARNING AREA: READING AND WRITING TIMELEARNING OBJECTIVES SUGGESTED TEACHING AND

LEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY


Pupils write time to the half and quarter hour based ontimes shown on clock faces.

Pupils read the classtimetable, bus schedules,radio or televisionprogrammes.

ii. Write the time to the half and quarter hour.

iii. Read simple timetables.

Emphasise the correct ways of writing time.

e.g.1: 2:45a. Quarter to three.b. Fifteen minutes to three.c. Fifteen to three.d. Two forty-five.

e.g.2: 7.15

a. Quarter past seven.b. Fifteen minutes past seven.c. Fifteen past sevend. Seven fifteen.

e.g.3: 11.30a. Half past eleven.b. Thirty minutes past eleven.

c. Eleven thirty.Check on the correct spelling.

half

quarter hour quarter pastquarter tohalf past minutes past past minutes to to

Year 3


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32

TOPIC: TIME

LEARNING AREA: READING AND WRITING TIMELEARNING OBJECTIVES SUGGESTED TEACHING AND



Pupils read calendars. iv. Read calendars. Emphasise the correct ways of reading dates.

e.g.1. 1 April 1st of April

First of April.2. 2 May 2nd of May

Second of May.3. 3 June 3rd of June

Third of June.

4. 4 July 4th

of JulyFourth of July.

rows

columnsdate

calendars

month

day

week

Year 3


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33

TOPIC: TIME

LEARNING AREA: RELATIONSHIP BETWEEN UNITS OF TIMELEARNING OBJECTIVES SUGGESTED TEACHING AND



1. Understand therelationshipbetween units of time.

Teacher uses clocks with thesecond hand to show therelationship between minutesand seconds.

Teacher uses calendar toengage pupils in activities tounderstand the relationshipbetween:a. week and days; and

b. year and months.

Pupils convert larger units tosmaller units and vice versa.

e.g. 5 weeks = 35 days28 days = 4 weeks

Pupils respond rapidly to oraland written questionsinvolving conversion.

i. Use units of time andknow the relationshipbetween:

a. minute and seconds;b. week and days; andc. year and months.

ii. Convert weeks to daysand vice versa.

Emphasise the standard units for time and show the relationshipbetween them.

1 minute = 60 seconds1 week = 7 days1 year = 12 months

Start conversion from larger tosmaller units.

minute

minutessecondsecondsdaydaysweekweeksmonthmonthsyear yearssecond handminute hand

hour handunitsconvert

Year 3


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34

TOPIC: TIME

LEARNING AREA: ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION INVOLVING TIMELEARNING OBJECTIVES SUGGESTED TEACHING AND



1. Add, subtract, multiplyand divide units of

time.

Pupils add and subtract unitsof time in:a. hours; andb. minutes.

e.g.1. 3 hours + 2 hours = 5 hours

2. 20 minutes + 10 minutes +35 minutes = 65 minutes

3. 14 hours 9 hours = 5 hours

4. 130 minutes 45 minutes =85 minutes

i. Add units of time in:

a. hours; andb. minutes.

ii. Subtract units of time in:


Exclude compound units.

Exclude conversion of units.


Include addition and subtractionof time using standard writtenmethod.

e.g.

1. 15 minutes30 minutes

+ 25 minutes

2. 14 hours- 8 hours

hour

hoursminuteminutesaddplustotalsumequalsis equal toaltogether subtractminustake away

hours left? minutes left?

Year 3


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35

TOPIC: TIME

LEARNING AREA: ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION INVOLVING TIMELEARNING OBJECTIVES SUGGESTED TEACHING AND



Pupils multiply and divideunits of time in:a. hours;b. minutes.

e.g.1. 15 hours x 4 = 60 hours

2. 49 minutes x 3 =147 minutes

3. 18 hours 9 = 2 hours

4. 240 minutes 6 =40 minutes

iii. Multiply units of time in:


iv. Divide units of time in:


Limit:a. multiplicand to 1-digit;b. divisor to 1-digit; and

exclude remainders.



Include multiplication and

division of time using standardwritten method.

e.g.

1. 13 hoursx 7

2. minutes426

hour

hoursminuteminutestimesmultiplymultiplied byshare

share equallydivisiondividedivided byrecalltimes- tables

equalsis equal to

Year 3


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36

TOPIC: TIME

LEARNING AREA: SOLVING PROBLEMS INVOLVING TIMELEARNING OBJECTIVES SUGGESTED TEACHING AND



1. Use and applyknowledge of time in

real life.

Pupils solve problemsinvolving time in real life

situations.

e.g.1. Shanti got into the pool at

3 oclock. She came outat 5 oclock. How long didshe swim?

2. Hon Meng takes 15minutes to answer 5questions. How long doeshe take to answer 1question?

Pupils pose problems relatedto the four operationsinvolving time.

i. Solve problems involvingtime in real life situations.

Select problems according topupils ability and proficiency in

language.


hour

hoursminute

minutes

addplus

take away

minustimesmultiply

multiplied byshare

share equally

dividedivided by

equalsis equal to

solvepose

Year 3


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37

TOPIC: LENGTH

LEARNING AREA: MEASURING AND COMPARING LENGTHSLEARNING OBJECTIVES SUGGESTED TEACHING AND



1. Measure andcompare lengths

using standard units.

Teacher shows and explainsreading of scales to the

nearest division. Pupils read scales on metre

and centimetre rulers.

Pupils measure and recordlengths of objects usingmetre or centimetre rulers.

Pupils measure and comparelengths of objects usingstandard units.

e.g.

The pencil is 15 cm long.The crayon is 10 cm long.The pencil is 5 cm longer thanthe crayon.

i. Read scales to thenearest division.

ii. Measure and recordlengths of objects usingthe standard units

a. metres; andb. centimetres.

iii. Compare the lengths of two objects usingstandard units


Emphasise that measuringshould start from the 0 mark of

the ruler.

Introduce the abbreviations:a. m for metre; andb. cm for centimetre.

Ensure that diagrams or picturesgiven are of exact measurements,

for example 3 m, 10 cm and18 cm.


Measurements are made tothe nearest metre andcentimetre.

Emphasise that depth isequivalent to height.

read

scalesmeasuremetresmcentimetrescmlength

heightwidthdepthmeasurecomparemeasurement

I I I I I I I I I I I I I I I I I I I I0 5 10 15 20

Year 3


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38

TOPIC: LENGTH

LEARNING AREA: MEASURING AND COMPARING LENGTHSLEARNING OBJECTIVES SUGGESTED TEACHING AND



Pupils estimate lengths of objects then check with the

actual measurements.Objects Estimate Actual Difference

Height of door

Length of pupils arm

Width of room

Depth of pail

iv. Estimate the lengths of objects in:


Emphasise choosing suitableunits for estimations.

Encourage pupils to analyse howclose their estimates were.

estimateestimationactualmeasuremeasurements

metresmcentimetres

cmheightlengthdepthwidthrecord

checkdifference

Year 3


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39

TOPIC: LENGTH

LEARNING AREA: RELATIONSHIP BETWEEN UNITS OF LENGTHLEARNING OBJECTIVES SUGGESTED TEACHING AND



2. Understand therelationship between

units of length.

Engage pupils in activitiesthat will create an awareness

of relationship.

e.g. How many teddies needto join hands to make ametre-long line?

i. Know and use therelationship between

metres and centimetres.

Emphasise the standard units for lengths and show the

relationship between metres andcentimetres.

1 m = 100 cm450 cm = 4 m 50 cm


measure

metresmcentimetrescmlengthwidthheight

depthrelationshipunits

20cm

Year 3


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40

TOPIC: LENGTH

LEARNING AREA: ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION INVOLVING LENGTH




1. Add, subtract, multiply

and divide units of length.

Pupils add units of length in

metres and centimetres.

Pupils subtract units of lengthin metres and centimetres.

i. Add units of length in:


ii. Subtract units of length in:

a. metres; and

b. centimetres.


Include addition and subtractionof lengths using standard writtenmethod.

e.g.

1. 12 m

+ 13 m

2. 150 cm 80 cm

metres

mcentimetrescmaddsubtract

units

lengthstake awayminustotalsum

altogether

differenceWhat is left?standardwritten method

Year 3


59/83

41

TOPIC: LENGTH

LEARNING AREA: ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION INVOLVING LENGTHLEARNING OBJECTIVES SUGGESTED TEACHING AND



Pupils multiply units of lengthin metres and centimetres.

e.g. 78 m x 5 =

Pupils divide units of length inmetres and centimetres.

e.g. 200 cm 4 =

iii. Multiply units of lengthin:


iv. Divide units of length in:

a. metres; and

b. centimetres.


Limit multiplicand to 1-digit.

Limit divisor to 1-digit andexclude remainders.

Include multiplication anddivision of lengths usingstandard written method.

e.g.

1. 37 mx 4

2. cm728

metres

mcentimetrescmmultiplydividelengthsunits

standardwritten method

Year 3


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42

TOPIC: LENGTH

LEARNING AREA: SOLVING PROBLEMS INVOLVING LENGTHLEARNING OBJECTIVES SUGGESTED TEACHING AND



1. Use and applyknowledge of length

in real life.

Pupils solve problems bysimulating and modelling the

situation.

e.g. A child throws a bean bag.1st throw = 3 m2nd throw = 5 mWhat is the differencebetween the two throws?

Pupils pose problems relatedto the four operationsinvolving length.

i. Solve problems involvinglength in real life

situations.


language.


solve

problemslengthHow many left?add

plus

take away

minus

times

multiplymultiplied by

shareshare equally

divide

divided by

pose

Year 3


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43

TOPIC: MASS

LEARNING AREA: MEASURING AND COMPARING MASSESLEARNING OBJECTIVES SUGGESTED TEACHING AND



1. Measure and comparemasses using

standard units.

Pupils read scales usingweighing scales.

Teacher shows and explainsreading of scales to thenearest division.

Pupils measure masses of objects such as a book, anegg or an empty box usingweighing scales and record

them in kilograms and grams. Pupils measure and compare

masses of objects usingstandard units in kilogramsand grams.

e.g. An apple weighs 180 g. An orange weighs 200 g.The orange is 20 g heavier than the apple.


ii. Measure and recordmasses of objects usingthe standard units:

a. kilograms; andb. grams.

iii. Compare the masses of two objects usingstandard units:

a. kilograms, andb. grams.


the weighing scale.

Introduce the abbreviations:a. kg for kilogram; andb. g for gram.


Measurements are made to thenearest kilogram and gram.

mass

kilogramskggramsgweighweightweighing scale

measurecompareheavyheavier lightlighter

Year 3


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44

TOPIC: MASS

LEARNING AREA: MEASURING AND COMPARING MASSESLEARNING OBJECTIVES SUGGESTED TEACHING AND



Pupils estimate masses andcheck with the actual

measurements.

e.g.

iv. Estimate masses of objects in


Emphasise choosing suitableunits for estimations.

Encourage pupils to use try,check and improve procedure tonarrow down differencesbetween estimates and actualmeasurements.

weigh

massestimateestimationkilogramskggramsg

nearest

Objects Estimate Actual Difference

marbles

plasticine

box

Year 3


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45

TOPIC: MASS

LEARNING AREA: RELATIONSHIP BETWEEN UNITS OF MASSLEARNING OBJECTIVES SUGGESTED TEACHING AND




units of mass .

Teacher prepares a few 1 kgand 100 g sand bags. Using

the equal arm balance, pupilsbalance a 1 kg sand bag withthe equivalent number of 100 g sandbags.

Pupils then weigh the sandbags on weighing scale tosee the relationship betweenkilograms and grams.


kilograms and grams.

Emphasise the standard units for mass and show the relationship

between kilograms and grams.

1 kg = 1000 g2 kg = 2000 g


measure

kilogramskggramsgweighing balanceweighscales

unitsmassrelationshipspring balanceequal armbalance

1 kg

100g 100g 100g

100g 100g 100g

100g 100g

100g

100g

Year 3

TOPIC MASS


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TOPIC: MASS

LEARNING AREA: ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION INVOLVING MASSLEARNING OBJECTIVES SUGGESTED TEACHING AND




mass .

Pupils add and subtract unitsof masses in


e.g.a. 25 kg + 40 kg =b. 10 kg + 68 kg + 30 kg =c. 200g + 300 g =d. 500 g + 150 g + 70 g =

e.g.a. 75 kg 14 kg =b. 100 kg 80 kg 40 kg=c. 550 g 200 g =d. 780 g 150 g 200 g =

i. Add units of mass in:


ii. Subtract units of mass in:



Include addition and subtractionof masses using standard writtenmethod.

e.g.

1. 25 kg6 kg

+ 40 kg

2. 500 g 150 g

add

plustotalmassweightsubtracttake awaykilograms

kggramsgstandardwritten method

Year 3

TOPIC: MASS


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47

TOPIC: MASS

LEARNING AREA: ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION INVOLVING MASS




Pupils multiply and divideunits of masses in

a. kilogramsb. grams.

e.g.a. 25 kg x 5 =b. 120 g x 3 =

e.g.

a. 56 kg 7 =

b. 720 g 6 =

iii. Multiply units of mass in:


iv. Divide units of mass in:





Include multiplication anddivision of masses usingstandard written method.

e.g:

1. 84 kgx 4

2. g6408

multiplydivide

massweightkilogramskggrams

gstandardwritten method

Year 3

TOPIC: MASS


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48

TOPIC: MASS

LEARNING AREA: SOLVING PROBLEMS INVOLVING MASS




1. Use and applyknowledge of mass in

real life.

Pupils solve problems.

e.g. A book weighs 90 g?What is the weight of 6books?

Pupils pose problems relatedto the four operationsinvolving mass.

i. Solve problems involvingmass in real life

situations.


the language.Encourage pupils to explainmethods used.

solve

problemsmassweighweighsweightadd

plus

take awayminus

times

multiply

multiplied byshare

share equallydivide

divided by

pose

Year 3

TOPIC: VOLUME OF LIQUID


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LEARNING AREA: MEASURING AND COMPARING VOLUMES OF LIQUIDS




1. Measure and comparevolumes of liquid

using standard units.

Teacher shows picture of measuring jugs which are

calibrated at 100 lm division(with every division markedwith reading in lm ). Jugsshould contain water atdifferent levels. Pupils readscales to the nearest division.



the measuring cylinder.Introduce the abbreviations:b. l for litre; andb. lm for millilitre.


Measurements are made to thenearest litre and millilitre.

scalesmeasuringcylinder measuring jugwater level

volumeliquidlitres

l

millilitreslm

Year 3



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Pupils fill uncalibratedcontainers with water (up to

any level) and display their containers.

Teacher gives pupils 1 litremeasuring cylinders that arecalibrated into 10 divisionsand explain that each divisionrepresents 100 lm . Askpupils to pour water fromuncalibrated containers into1 l measuring cylinders in100 lm progressions.

For every 100 lm they sayout the volume.e.g. 100 lm , 200 lm ,

Teacher explains that the lastmarked division represents1000 lm or 1 l .

Pupils measure and recordvolumes of liquid.

ii. Measure and recordvolumes of liquids using

the standard units:a. litres; andb. millilitres.


Provide pupils with sufficientmaterials for activities.

litresl

millilitreslm

measuremeasuringcylinder capacityvolumesliquidsholdscontainscontainer

Year 3



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Q





Pupils compare the volumesof two liquids using standard

units.e.g.Pupils pour 1 l of water intothe first container and 2 l intothe second container.

1 l 2 l

Repeat activity with smaller containers and 100 lmmeasuring cylinders.

iii. Compare the volumes of two liquids using

standard units:a. litres; andb. millilitres.

Compare and record thevolumes of two liquids.

1 l measuring cylinders can bereplaced by any other containersthat would accurately contain thevolume of 1 l .

litresl

millilitreslm

measuringcylinder volumesliquidsmorelesslesser How much?

Year 3


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Pupils are given plastic cups

and rubber bands. Pupilsplace a rubber band aroundthe plastic cup and move it toestimate the line where thevolume of 100 lm wouldreach. Check the closestestimate.

Pupils are given a largeuncalibrated jug. Pupilsestimate the line where thevolume of 1 l would reach.Check the closest estimate.

iv. Estimate volumes of

liquids in

a. litres; andb. millilitres.

Emphasise choosing suitable

units for estimations.

Encourage pupils to analyse howclose their estimates were.

estimate

uncalibrated jugvolumescapacityliquidslitresl

millilitreslm

Year 3



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LEARNING AREA: RELATIONSHIP BETWEEN UNITS OF VOLUME OF LIQUID





units of volume of liquid.

Pupils are given containers of 100 lm and 1 l capacities.

Pupils fill up 100 lm container with water and pour it into the1 l container.(Do not reveal the capacitiesof the containers).

Pupils report how many100 lm containers are

needed to fill up the 1 lcontainer.

Pupils repeat activity for

2 l , l211 ,


litres and millilitres.

Emphasise the standard units for volume and show the

relationship between litres andmillilitres.

1 l = 1000 lm3 l = 3000 lm


litrel

millilitreslm

capacityvolumeliquid

Year 3



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LEARNING AREA: ADDITION, SUBTRACTION, MUTIPLICATION AND DIVISION INVOLVING VOLUME OF LIQUID





volume of liquid.

Pupils add and subtract unitsof volume of liquids in

a. litres; andb. millilitres

e.g.1a. 1 l + 2 l =b. 500 lm + 250 lm =

e.g.2

a. 60l

- 15l

=b. 750 lm - 30 lm =

i. Add units of volume of liquid in:


ii. Subtract units of volumeof liquid in:



Emphasise mental calculation.Check on accuracy in addingunits of volume of liquid.

Include addition and subtractionof volumes of liquid usingstandard written method.

e.g.

1. 14 l+ 5 l

2. 420 lm+ 280 lm

add

volume

capacityliquidlitrel

millilitreslm

subtractHow much?How much left?remainder

Year 3



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LEARNING AREA: ADDITION, SUBTRACTION, MUTIPLICATION AND DIVISION INVOLVING VOLUME OF LIQUID




Pupils multiply units volumeof liquid in:

a. litresb. millilitres

e.g.40 l x 2 =165 lm x 3 =

Pupils divide units of volumeof liquid:a. litresb. millilitres

e.g.60 l 3 =175 lm 5 =

iii. Multiply units of volumeof liquid in:


iv. Divide units of volumeof liquid in:




Emphasise on accuracy.

Encourage mental calculation.

Include multiplication anddivision of volumes of liquidusing standard written method.

e.g.

1. l603

2. lm1755

volume

capacity

liquidlitrel

millilitreslm

multiplication

Year 3



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LEARNING AREA: SOLVING PROBLEMS INVOLVING VOLUME OF LIQUID




1. Use and applyknowledge of volumeof liquid in real life.

Pupils solve problems.

e.g.

A bottle holds 1 l of mango juice. Imran and his 3 friendsshare the amount of mango

juice equally. How much doeseach one get to drink?

Pupils pose problems relatedto the four operationsinvolving volume of liquid.

i. Solve problems involvingvolume of liquid in real

life situations.

Check for accuracy incalculation.

Select problems according topupils ability and proficiency inthe language.


solve

problems

volumeliquidcapacityHow much?add

plus

take awayminus

times

multiply

multiplied byshare equally

dividedivided by

pose

Year 3

TOPIC: SHAPE AND SPACE


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TOPIC: SHAPE AND SPACE

LEARNING AREA: THREE-DIMENSIONAL SHAPES



Pupils will be taught to: Pupils will b

hsp maths y3 copy

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