MINISTRY OF EDUCATION MALAYSIAIntegrated Curriculum for Primary Schools           Curriculum Specifications              M...
MINISTRY OF EDUCATION MALAYSIAIntegrated Curriculum for Primary Schools           Curriculum Specifications              M...
Copyright (C) 2003 Curriculum Development CentreMinistry of Education MalaysiaPesiaran Duta Off Jalan Duta50604 Kuala Lump...
CONTENTSRUKUNEGARA                                                             vNATIONAL PHILOSOPHY OF EDUCATION          ...
RUKUNEGARA                                   DECLARATIONOUR NATION, MALAYSIA, being dedicatedto achieving a greater unity ...
NATIONAL PHILOSOPHY OF EDUCATIONEducation in Malaysia is an on-going effort towards developing the potential ofindividuals...
PREFACEScience and technology plays a crucial role in                greater opportunities for pupils to enhancemeeting Ma...
INTRODUCTIONOur nation’s vision can be achieved through a society          later in life and in the process, benefit the s...
AIMThe Primary School Mathematics Curriculum aims                4.   master basic mathematical skills, namely:to build pu...
CONTENT ORGANISATIONThe Mathematics Curriculum at the primary level              4.   Statisticsencompasses four main area...
The Learning Objectives define clearly what should          The Vocabulary column consists of standardbe taught. They cove...
EMPHASIS IN TEACHING AND LEARNING                                1.       Problem Solving in MathematicsThe Mathematics Cu...
•   Trying a simple case;                             and concise mathematical terms during oral     •   Trial and improve...
•   Stimulating meta-cognitive skills;                     Written communication is the process whereby    •   Inculcating...
3.   Mathematical Reasoning                                   The mathematics curriculum consists of several              ...
The use of teaching resources is very important in          attitudes and personalities, the intrinsic mathematicalmathema...
The choice of an approach that is suitable will stimulatethe teaching and learning environment in the classroomor outside ...
CONTRIBUTORSAdvisors    Dr. Sharifah Maimunah bt Syed Zin      Director                                                   ...
PANEL OF WRITERSRusnani Mohd Sirin                                          Sugara Abd LatifAssistant Director            ...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:           NUMBERS TO 1000LEARNING OBJECTIVES              SUGGESTED TEACHING AND ...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:         NUMBERS TO 1000LEARNING OBJECTIVES             SUGGESTED TEACHING AND    ...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:         NUMBERS TO 1000LEARNING OBJECTIVES             SUGGESTED TEACHING AND    ...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        NUMBERS TO 1000LEARNING OBJECTIVES              SUGGESTED TEACHING AND    ...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        NUMBERS TO 1000LEARNING OBJECTIVES             SUGGESTED TEACHING AND     ...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        NUMBERS TO 1000LEARNING OBJECTIVES             SUGGESTED TEACHING AND     ...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        NUMBERS TO 1000LEARNING OBJECTIVES             SUGGESTED TEACHING AND     ...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        ADDITION WITH THE HIGHEST TOTAL OF 1000 LEARNING OBJECTIVES             SU...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        ADDITION WITH THE HIGHEST TOTAL OF 1000LEARNING OBJECTIVES             SUG...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        ADDITION WITH THE HIGHEST TOTAL OF 1000LEARNING OBJECTIVES             SUG...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:         ADDITION WITH THE HIGHEST TOTAL OF 1000LEARNING OBJECTIVES             SU...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        ADDITION WITH THE HIGHEST TOTAL OF 1000LEARNING OBJECTIVES             SUG...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        SUBTRACTION WITHIN THE RANGE OF 1000LEARNING OBJECTIVES              SUGGE...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        SUBTRACTION WITHIN THE RANGE OF 1000LEARNING OBJECTIVES             SUGGES...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        SUBTRACTION WITHIN THE RANGE OF 1000LEARNING OBJECTIVES             SUGGES...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        SUBTRACTION WITHIN THE RANGE OF 1000LEARNING OBJECTIVES             SUGGES...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        SUBTRACTION WITHIN THE RANGE OF 1000LEARNING OBJECTIVES              SUGGE...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        SUBTRACTION WITHIN THE RANGE OF 1000LEARNING OBJECTIVES              SUGGE...
Year 2TOPIC: WHOLE NUMBERSLEARNING AREA:        MULTIPLICATION WITHIN 2, 3, 4 AND 5 TIMES-TABLESLEARNING OBJECTIVES       ...
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  1. 1. MINISTRY OF EDUCATION MALAYSIAIntegrated Curriculum for Primary Schools Curriculum Specifications MATHEMATICS YEAR 2 Curriculum Development Centre Ministry of Education Malaysia 2003
  2. 2. MINISTRY OF EDUCATION MALAYSIAIntegrated Curriculum for Primary Schools Curriculum Specifications MATHEMATICS YEAR 2 Curriculum Development Centre Ministry of Education Malaysia 2003
  3. 3. Copyright (C) 2003 Curriculum Development CentreMinistry of Education MalaysiaPesiaran Duta Off Jalan Duta50604 Kuala LumpurFirst published 2003Copyright reserved. Except for use in a review, thereproduction or utilisation of this work in any form or by anyelectronic, mechanical, or other means, now known or hereafterinvented, including photocopying, and recording is forbiddenwithout the prior written permission from the Director of theCurriculum Development Centre, Ministry of Education Malaysia.
  4. 4. CONTENTSRUKUNEGARA vNATIONAL PHILOSOPHY OF EDUCATION viiPREFACE ixINTRODUCTION xiWHOLE 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 24MONEY Money to RM50 28TIME Reading and Writing Time 32 Relationship between Units of Time 34 Solving Problems involving Time 35LENGTH Introduction to Length 36 Measuring and Comparing Lengths 37MASS Introduction to Mass 39 Measuring and Comparing Masses 40VOLUME OF LIQUID Introduction to Volume of Liquid 42 Measuring and Comparing Volumes of Liquids 43SHAPE AND SPACE Three-Dimensional Shapes 45 Two-Dimensional Shapes 48CONTRIBUTORS 51PANEL OF WRITERS 52 iii
  5. 5. RUKUNEGARA DECLARATIONOUR NATION, MALAYSIA, being dedicatedto 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 GodLoyalty to King and CountryUpholding the ConstitutionRule of LawGood Behaviour and Morality v
  6. 6. NATIONAL PHILOSOPHY OF EDUCATIONEducation in Malaysia is an on-going effort towards developing the potential ofindividuals in a holistic and integrated manner, so as to produce individuals whoare intellectually, spiritually, emotionally and physically balanced and harmoniousbased on a firm belief in and devotion to God. Such an effort is designed to produceMalaysian citizens who are knowledgeable and competent, who possess highmoral standards and who are responsible and capable of achieving a high level ofpersonal well being as well as being able to contribute to the harmony andbetterment of the family, society and the nation at large. vii
  7. 7. PREFACEScience and technology plays a crucial role in greater opportunities for pupils to enhancemeeting Malaysia’s aspiration to achieve developed their knowledge and skills because they are able tonation status. Since mathematics is instrumental in source the various repositories of knowledge written indeveloping scientific and technological knowledge, the mathematical English whether in electronic or printprovision of quality mathematics education from an forms. Pupils will be able to communicateearly age in the education process is critical. mathematically in English not only in the immediate enviroment but also with pupils from other countriesThe primary school Mathematics curriculum as thus increasing their overall English proficiency andoutlined in the syllabus has been designed to provide mathematical competence in the process.opportunities for pupils to acquire mathematicalknowledge and skills and develop the higher order The development of a set of Curriculum Specificationsproblem solving and decision making skills that they as a supporting document to the syllabus is the workcan apply in their everyday lives. But, more of many individuals and experts in the field. To thoseimportantly, together with the other subjects in the who have contributed in one way or another to thisprimary school curriculum, the mathematics effort, on behalf of the Ministry of Education, I wouldcurriculum seeks to inculcate noble values and love like to thank them and express my deepestfor the nation towards the final aim of developing the appreciation.holistic person who is capable of contributing to theharmony and prosperity of the nation and its people.Beginning in 2003, science and mathematics will betaught in English following a phased implementationschedule, which will be completed by 2008. (Dr. SHARIFAH MAIMUNAH SYED ZIN)Mathematics education in English makes use of DirectorICT in its delivery. Studying mathematics in the Curriculum Development Centremedium of English assisted by ICT will provide Ministry of Education Malaysia ix
  8. 8. INTRODUCTIONOur nation’s vision can be achieved through a society later in life and in the process, benefit the society andthat 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 whenTherefore, problem solving and communicational skills designing the curriculum and these are: mathematicalin mathematics have to be nurtured so that decisions concepts and skills, terminology and vocabulary used,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 leveland technology. As such, the acquisition of (KBSR) emphasises the acquisition of basic conceptsmathematical knowledge must be upgraded and skills. The content is categorised into fourperiodically to create a skilled workforce in preparing 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 developmentskills in Mathematics must be taught and instilled at The learning of mathematics at all levels involves moreschool level. than just the basic acquisition of concepts and skills. It involves, more importantly, an understanding of theAchieving this requires a sound mathematics underlying mathematical thinking, general strategies ofcurriculum, competent and knowledgeable teachers problem solving, communicating mathematically andwho can integrate instruction with assessment, inculcating positive attitudes towards an appreciationclassrooms with ready access to technology, and a of mathematics as an important and powerful tool incommitment to both equity and excellence. everyday life.The Mathematics Curriculum has been designed to It is hoped that with the knowledge and skills acquiredprovide knowledge and mathematical skills to pupils in Mathematics, pupils will discover, adapt, modify andfrom various backgrounds and levels of ability. be innovative in facing changes and future challenges.Acquisition of these skills will help them in their careers xi
  9. 9. AIMThe 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 datain keeping with the aspirations of a developed society • representing information in the formand nation, and at the same time to use this of graphs and charts;knowledge to further their studies. 5. use mathematical skills and knowledge toOBJECTIVES solve problems in everyday life effectively and responsibly;The Primary School Mathematics Curriculum willenable 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. xii
  10. 10. CONTENT ORGANISATIONThe Mathematics Curriculum at the primary level 4. Statisticsencompasses four main areas, namely, Numbers, • Average;Measures, Shape and Space and Statistics. The • Data Representation.topics for each area have been arranged from thebasic to the abstract. Teachers need to teach the The Learning Areas outline the breadth and depth ofbasics before abstract topics are introduced to pupils. the scope of knowledge and skills that have to beEach main area is divided into topics as follows: mastered during the allocated time for learning. These learning areas are, in turn, broken down into more1. 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 and2. 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 a3. 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. xiii
  11. 11. The Learning Objectives define clearly what should The Vocabulary column consists of standardbe taught. They cover all aspects of the Mathematics mathematical terms, instructional words and phrasescurriculum and are presented in a developmental that are relevant when structuring activities, askingsequence to enable pupils to grasp concepts and questions and in setting tasks. It is important to paymaster 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 knowThe Suggested Teaching and Learning Activities of their meaning and learn how to uselist some examples of teaching and learning activities. them appropriately.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 moresignificant 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. xiv
  12. 12. EMPHASIS IN TEACHING AND LEARNING 1. Problem Solving in MathematicsThe Mathematics Curriculum is ordered in such a way Problem solving is the main focus in the teaching andso as to give flexibility to the teachers to create an learning of mathematics. Understanding mathematicalenvironment that is enjoyable, meaningful, useful and procedures and solving problemschallenging for teaching and learning. At the same time are two skills that emerge naturally when relationalit is important to ensure that pupils show progression understanding is focussed upon. As a result, problemin acquiring the mathematical concepts and skills. solving approaches should be used to investigate and understand mathematical content. The teaching-On completion of a certain topic and in deciding to learning process must include exercises on problemprogress to another learning area or topic, the following solving skills which are comprehensive and cover theneed to be taken into accounts: whole curriculum. The development of these skills • The skills or concepts acquired in the new must to be emphasised so that pupils are able to solve learning area or topics; various problems effectively. The skills • Ensuring that the hierarchy or relationship involved are: between learning areas or topics have been followed through accordingly; and • Interpreting problems; • Ensuring the basic learning areas have or • Planning the strategy; skills have been acquired or mastered before • Carrying out the strategy; and progressing to the more abstract areas. • Looking back at the solutions.The teaching and learning processes emphasise Various strategies and steps are used to solveconcept building, skill acquisition as well as the problems and these can be applied to other learninginculcation of positive values. Besides these, there areas. In solving these problems, pupils learn to applyare other elements that need to be taken into account mathematics and gradually become confident in facingand learnt through the teaching and learning new challenging situations. Among the problem solvingprocesses in the classroom. The main emphasis are strategies to consider are:as follows: xv
  13. 13. • Trying a simple case; and concise mathematical terms during oral • Trial and improvement; presentation and written work. This is also expanded • 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 reading2. Communication in Mathematics process takes place when an individual collects information or data and rearranges the relationshipCommunication is one way to share ideas and clarify between ideas and concepts.the understanding of Mathematics. Through talkingand questioning, mathematical ideas can be reflected Communication in mathematics through theupon, discussed and modified. The process of visualization process takes place when an individualreasoning analytically and systematically can help makes observation, analyses it, interprets andreinforce and strengthen pupils’ knowledge and synthesises the data into graphic forms, such asunderstanding of mathematics to a deeper level. pictures, diagrams, tables and graphs.Through effective communications pupils will becomeefficient in problem solving and be able to explain The following methods can create an effectiveconcepts and mathematical skills to their peers and communication environment:teachers. • Identifying relevant contexts associatedPupils who have developed the above skills will with environment and everyday lifebecome 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; xvi
  14. 14. • Stimulating meta-cognitive skills; Written communication is the process whereby • Inculcating positive attitudes; and mathematical ideas and information are • Creating a conducive learning environment. shared with others through writing. The written work is usually the result of discussions, contributions andOral communication is an interactive process that brain-storming activities when working oninvolves activities like listening, speaking, reading and assignments. Through writing, the pupils will beobserving. It is a two-way interaction that takes place encouraged to think more deeply about thebetween teacher-pupil, pupil-pupil, and pupil-object. mathematics content and observe the relationshipsWhen pupils are challenged to think and reason about between concepts.mathematics and to tell others the results of theirthinking, they learn to be clear and convincing. Listening Examples of written communication activities are:to others’ explanations gives pupils the opportunities • Doing exercises;to develop their own understanding. Conversations in • Keeping scrap books;which mathematical ideas are explored from multiple • Keeping folios;perspectives help sharpen pupils thinking and help • Undertaking projects; andmake connections between ideas. Such activity helps • Doing written tests.pupils develop a language for expressing mathematicalideas and appreciation of the need for precision in thelanguage. Some effective and meaningful oral Representation is a process of analysing acommunication techniques in mathematics are as mathematical problem and interpreting it from onefollows: mode to another. Mathematical representation enables 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. xvii
  15. 15. 3. Mathematical Reasoning The mathematics curriculum consists of several areas such as arithmetic, geometry, measures andLogical reasoning or thinking is the basis for problem solving. Without connections between theseunderstanding and solving mathematical problems. areas, pupils will have to learn and memorise too manyThe development of mathematical reasoning is closely concepts and skills separately. By making connectionsrelated to the intellectual and communicative pupils are able to see mathematics as an integrateddevelopment 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-orientedminds to accept mathematics as a powerful tool in classrooms by having pupils to communicate, reasonthe world today. and present their thinking. When these mathematical ideas are connected with real life situations and thePupils are encouraged to predict and do guess work curriculum, pupils will become more conscious in thein the process of seeking solutions. Pupils at all application of mathematics. They will also be able tolevels have to be trained to investigate their use mathematics contextually in different learningpredictions or guesses by using concrete areas in real life.materials, calculators, computers, mathematicalrepresentation and others. Logical reasoning has tobe infused in the teaching of mathematics so that 5. Application of Technologypupils can recognise, construct and evaluatepredictions 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 themaking connections must be created so that pupils internet and available learning packages can help tocan link conceptual to procedural knowledge and upgrade the pedagogical skills in the teaching andrelate topics in mathematics with other learning learning of mathematics.areas in general. xviii
  16. 16. The use of teaching resources is very important in attitudes and personalities, the intrinsic mathematicalmathematics. This will ensure that pupils absorb values of exactness, confidence and thinkingabstract ideas, be creative, feel confident and be able systematically have to be absorbed through theto 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 suitableaccess knowledge or skills and informations context. For example, learning in groups can helpindependently according to their pace. This will serve pupils develop social skills and encourage cooperationto stimulate pupils’ interests and responsibility in and self-confidence in the subject. The element oflearning mathematics. patriotism can also be inculcated through the teaching- learning process in the classroom using planned topics. These values should be imbibed throughoutAPPROACHES IN TEACHING AND LEARNING the process of teaching and learning mathematics.Various changes occur that influence the content and Among the approaches that can be given considerationpedagogy in the teaching of mathematics in primary are:schools. These changes require variety in the way ofteaching 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 effectiveand learning to help pupils gain experience, construct teaching materials; andabstract ideas, make inventions, build self confidence, • Formative evaluation to determine theencourage independence and inculcate cooperation. effectiveness of teaching and learning.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 xix
  17. 17. 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: • Cooperative learning; • Contextual learning; • Mastery learning; • Constructivism; • Enquiry-discovery; and • Futures Study.ASSESSMENTAssessment is an integral part of the teaching and learningprocess. It has to be well-structured and carried outcontinuously 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. xx
  18. 18. CONTRIBUTORSAdvisors Dr. Sharifah Maimunah bt Syed Zin Director Curriculum Development Centre Dr. Rohani Abdul Hamid Deputy Director Curriculum Development CentreEditorial Rusnani Mohd Sirin Assistant DirectorAdvisors (Head of Mathematics Unit) Curriculum Development Centre S. Sivagnanachelvi Assistant Director (Head of English Language Unit) Curriculum Development CentreEditors 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 51
  19. 19. PANEL OF WRITERSRusnani Mohd Sirin Sugara Abd LatifAssistant Director Curriculum Officer(Head of Mathematics Unit) (Mathematics Unit)Curriculum Development Centre Curriculum Development CentreDr. Lim Chap Sum Shanti PeriasamyUniversiti Sains Malaysia, Pulau Pinang Maktab Perguruan Ilmu Khas, Kuala LumpurWan Yusof Wan Ngah Maimunah TahirMaktab Perguruan Perempuan Melayu, Melaka Maktab Perguruan Kota Bahru, KelantanJeya Velu Abdul Razak SallehInstitut Bahasa Melayu Malaysia, Kuala Lumpur Maktab Perguruan Batu Rakit, TerengganuRepiah Singah Lee Gik LeanMaktab Perguruan Temenggong Ibrahim, Johor SK (P) Treacher Methodist, PerakTan Swee Hong Katherine TanSK Convent St. Jesus (2), Melaka SK Convent St. Jesus (1), MelakaRagu Ramasamy Latiff DarusSK Bukit Bandaraya, Kuala Lumpur Pejabat Pendidikan Daerah, Pulau PinangBalkis AhmadSMK Sultan Sallahuddin Abdul Aziz Shah, Selangor LAYOUT & ILLUSTRATIONS Sugara Abd Latif Mohd Razif Hashim Mathematics Unit Curriculum Development Centre 52
  20. 20. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: NUMBERS TO 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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 1000. 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, twos and ones. such as ice-cream sticks, straws, Count a larger collection of hundred and chips, multi-based blocks and objects by grouping them in ninety-nine, Cuisenaire rods. hundreds, tens, fives, twos 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. 1
  21. 21. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: NUMBERS TO 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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. write the numeral. spelling. number w ords ii. Read number w ords to one • Teacher flashes a number w ord thousand. Check on pronunciation of one hundred, card, pupils read the number number names. one hundred word: 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 words to one thousand. • Pupils match numerals w ith number w ords up to one thousand. • Pupils w rite the number w ords. 2
  22. 22. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: NUMBERS TO 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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 digit represents. blocks. three-digit numbers. e.g. hundreds e.g. tens 1. 83 ones 2. 190 place holder tw o-digit Hundreds T ens On es 5 hundreds H T O three-digit partition 8 3 8 ones 1 9 0 6 tens The digit 5 in 568 represents 500, Emphasise the use of zero as 6 represents 60 and 8 represents a place holder. 8. 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. 3
  23. 23. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: NUMBERS TO 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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 1000. • Pupils count on and count back in tw os. e.g: 10, 20, 30 … and one, one in tw os: 100, 200, 300 … hundred and c. count on and count back tw o, …, nine e.g. 0, 2, 4, … in fives. hundred and Emphasise that a number e.g. 122, 120, 118 … ninety-nine, follow ing another number in d. count on and count back the counting on sequence is one thousand • Pupils count on and count back in fives: in tens. larger. arrange e.g. 30, 35, 40, … count on e. count on and count back e.g 570, 565, 555 … Emphasise that a number in hundreds. count back follow ing another number in • Pupils count on and count back next in tens: the counting back sequence is smaller. before e.g. 283, 293, 303 … 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 … 4
  24. 24. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: NUMBERS TO 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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. 10 1000 5
  25. 25. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: NUMBERS TO 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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, twos, 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 271? number line b. position the numbers on a smaller • Pupils arrange a group of number line. numbers in order. smallest e.g. larger 37 31 largest 39 41 35 33 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 0 25 40 65 80 100 6
  26. 26. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: NUMBERS TO 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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 elf th, 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 ? 7
  27. 27. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: ADDITION WITH THE HIGHEST TOTAL OF 1000 LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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 calculation. groups of 10. c. tw o 2-digit numbers. e.g. 3 + 50 = Include addition using regrouping standard written method. zero b. 1-digit numbers and multiples of 100. e.g. digit e.g. 400 + 7 = 1. 5 multiples + 8 c. pairs of multiples of 10 to standard make 100. written method e.g. 20 + = 100 one-digit 2. 62 • Pupils add tw o numbers up to tw o tw o-digit + 7 digits w ithout regrouping. e.g. Tens Ones T O 5 1 + 4 3 8
  28. 28. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: ADDITION WITH THE HIGHEST TOTAL OF 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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. 15 + 7 = 1-digit number; and Emphasise mental total calculation. 2. 76 + 29 = b. tw o 2-digit numbers. sum Include addition using groups T ens On es standard written method. T O regrouping iii. Add tw o numbers w ithout e.g. zero regrouping: 7 6 1. 49 + 38 digit + 2 9 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 written method three digits w ithout regrouping. 2-digit number; and 2. 502 + 61 one-digit e.g. c. tw o 3-digit numbers. tw o-digit 1. 521 + 6 = three-digit 2. 350 + 48 = 3. 647 + 102 = 9
  29. 29. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: ADDITION WITH THE HIGHEST TOTAL OF 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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 written method. regrouping e.g. zero 1. 5 1 digit + 2 multiples standard written method 2. 6 one-digit 3 + 8 10
  30. 30. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: ADDITION WITH THE HIGHEST TOTAL OF 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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 follows: number a. 16 + 5 = sentence regrouping b. 34 + = 60 zero c. + 27 = 138 digit multiples d. + = 85 one-digit e. = 74 + 9 tw o-digit three-digit f. 519 = 300 + g. 600 = + 200 h. 463 = + Emphasise mental calculation. 11
  31. 31. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: ADDITION WITH THE HIGHEST TOTAL OF 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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. sum e.g. total 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 46 + 12 = 58 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. 12
  32. 32. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: SUBTRACTION WITHIN THE RANGE OF 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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 unchanged. take aw ay “take aw ay” or mater ials such as, chips, multi- “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 Emphasise mental left? mentally involving: b. a 1-digit number from a calculation. What is left? 2-digit number; and a. multiples of 10 regrouping e.g. 70 – 40 = Include subtraction using c. a 2-digit number from a zero standard written method. b. multiples of 100 2-digit number. e.g. 600 – 200 = e.g. digit c. a 2-digit number and a multiples 1. 6 1-digit number. – 2 standard e.g. 15 – 3 = written method • Pupils subtract tw o numbers one-digit 2. 47 w ithout regrouping: tw o-digit – 3 e.g. 54 – 31 = T ens On es T O 3. 98 –50 5 4 – 3 1 13
  33. 33. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: SUBTRACTION WITHIN THE RANGE OF 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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 e.g. unchanged. 1. 24 – 8 = a. a 1-digit number from a minus 2-digit number; and Emphasise mental How many 2. 71 – 53 = calculation. left? b. a 2-digit number from a 2-digit number. Include subtraction using What is left? T ens On es T O standard written method. regrouping 7 1 zero iii. Subtract tw o numbers w ithout e.g. – 5 3 regrouping: 1. 82 digit – 5 multiples a. a 1-digit number from a 3-digit number; standard written method • Pupils subtract tw o numbers w ithout regrouping. b. a 2-digit number from a 2. 639 one-digit e.g. 3-digit number; and –107 tw o-digit 1. 748 – 6 = c. a 3-digit number from a three-digit 2. 365 – 20 = 3-digit number. 3. 914 – 503 = 14
  34. 34. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: SUBTRACTION WITHIN THE RANGE OF 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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 written method. standard written method e.g. 8–2–5 = regrouping 8 6 zero – 2 – 5 digit 6 1 multiples Use manipulatives to help standard pupils see the relationship written method betw een addition and one-digit subtraction. e.g. 4+5=9 9–4=5 9–5=4 15
  35. 35. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: SUBTRACTION WITHIN THE RANGE OF 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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 follows: left? What is left? a. 8 – 6 = regrouping b. 45 – = 20 zero c. – 13 = 76 digit d. – = 58 multiples standard e. = 149 – 25 written method f. 300 = 867 – one-digit tw o-digit g. 275 = – 43 three-digit h. 180 = – Emphasise mental calculation. 16
  36. 36. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: SUBTRACTION WITHIN THE RANGE OF 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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 ways subtraction in real life understanding of subtraction take aw ay such as: situations. as taking aw ay and finding the difference between two 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. written 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 17
  37. 37. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: SUBTRACTION WITHIN THE RANGE OF 1000LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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. 18
  38. 38. Year 2TOPIC: WHOLE NUMBERSLEARNING AREA: MULTIPLICATION WITHIN 2, 3, 4 AND 5 TIMES-TABLESLEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NO TE VOCABULARY LEARNING ACTIVITIESPupils 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 (2, 3, 4 and 5 times- manipulative materials. add 4 and 4 … tables) add 5 and 5 … e.g. Pupils form 3 groups of 2 equals cookies. times 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 3x 2=6 Relate multiplication to repeated addition. 19

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