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- 1. Ministry of Education MalaysiaIntegrated Curriculum for Primary Schools CURRICULUM SPECIFICATIONSMATHEMATICS Curriculum Development Centre Ministry of Education Malaysia 2006
- 2. Copyright © 2006 Curriculum Development CentreMinistry of Education MalaysiaKompleks Kerajaan Parcel EPusat Pentadbiran Kerajaan Persekutuan62604 PutrajayaFirst published 2006Copyright reserved. Except for use in a review, the reproductionor utilisation of this work in any form or by any electronic,mechanical, or other means, now known or hereafter invented,including photocopying, and recording is forbidden without theprior written permission from the Director of the CurriculumDevelopment Centre, Ministry of Education Malaysia.
- 3. RUKUNEGARA RUKUNEGARA DECLARATION DECLARATIONOUR NATION, MALAYSIA, beingbeing dedicated achieving a OUR NATION, MALAYSIA, dedicated togreater unity of all her peoples; • to achieving a greater unity of all her peoples;• to maintaining a democratic way of life; of life; • to maintaining a democratic way• to creating creating a just society in which the wealth of nation • to a just society in which the wealth of the the shall be equitably shared; nation shall be equitably shared; • to a liberal approach to her rich and diverse cultural• to ensuring ensuring a liberal approach to her rich and diverse cultural traditions; traditions; • to building a progressive society which shall be oriented• to building a progressive society which shall be orientated to to modern science and technology; modern science and technology;WE, herWE, her peoples, pledge our united efforts to attain these peoples, pledge our united efforts to attain these endsguided by these principles: these principles: ends guided by • BELIEF IN GOD• Belief in God • LOYALTY TO KING AND COUNTRY• Loyalty to King and Country • UPHOLDING THE CONSTITUTION• Upholding the Constitution • RULE OF LAW• Rule • Law of GOOD BEHAVIOUR AND MORALITY• Good Behaviour and Morality (v)
- 4. NATIONAL PHILOSOPHY OF EDUCATIONEducation in Malaysia is an on-going effort towards developingthe potential of individuals in a holistic and integrated manner, soas to produce individuals who are intellectually, spiritually, Education in Malaysia is an ongoing effortemotionally and physically balanced and harmonious based on afirm belief in and devotion to God. Such an effort is designed of towards further developing the potential toproduce Malaysian citizens in a holistic and integrated individuals who are knowledgeable andcompetent, who possess as to moral standards and who are manner so high produce individuals who areresponsible andintellectually, spiritually, emotionally and capable of achieving a high level of personalwell being as well as being able to contribute to the harmony and physically balanced and harmonious, basedbetterment of the family, society and the nation at large. on a firm belief in God. Such an effort is designed to produce Malaysian citizens who are knowledgeable and competent, who possess high moral standards, and who are responsible and capable of achieving a high level of personal well-being as well as being able to contribute to the betterment of the family, the society and the nation at large. (vi)
- 5. PREFACE The development of a set of Curriculum Specifications as a supporting document to the syllabus is the work of many individuals and expertsScience and technology plays a crucial role in meeting Malaysia’s in the field. To those who have contributed in one way or another toaspiration to achieve developed nation status. Since mathematics is this effort, on behalf of the Ministry of Education, I would like to thankinstrumental in developing scientific and technological knowledge, the them and express my deepest appreciation.provision of quality mathematics education from an early age in theeducation process is critical.The primary school Mathematics curriculum as outlined in the syllabushas been designed to provide opportunities for pupils to acquiremathematical knowledge and skills and develop the higher orderproblem solving and decision making skills that they can apply in theireveryday lives. But, more importantly, together with the other subjectsin the primary school curriculum, the mathematics curriculum seeks to (DR. HAILI BIN DOLHAN)inculcate noble values and love for the nation towards the final aim ofdeveloping the holistic person who is capable of contributing to the Directorharmony and prosperity of the nation and its people. Curriculum Development Centre Ministry of EducationBeginning in 2003, science and mathematics will be taught in English Malaysiafollowing a phased implementation schedule, which will be completedby 2008. Mathematics education in English makes use of ICT in itsdelivery. Studying mathematics in the medium of English assisted byICT will provide greater opportunities for pupils to enhance theirknowledge and skills because they are able to source the variousrepositories of knowledge written in mathematical English whether inelectronic or print forms. Pupils will be able to communicatemathematically in English not only in the immediate environment butalso with pupils from other countries thus increasing their overallEnglish proficiency and mathematical competence in the process. (vii)
- 6. INTRODUCTION strategies of problem solving, communicating mathematically and inculcating positive attitudes towards an appreciation of mathematicsOur nation’s vision can be achieved through a society that is educated as an important and powerful tool in everyday life.and competent in the application of mathematical knowledge. To It is hoped that with the knowledge and skills acquired in Mathematics,realise this vision, society must be inclined towards mathematics. pupils will discover, adapt, modify and be innovative in facing changesTherefore, problem solving and communicational skills in mathematics and future challenges.have to be nurtured so that decisions can be made effectively.Mathematics is integral in the development of science and technology.As such, the acquisition of mathematical knowledge must be upgradedperiodically to create a skilled workforce in preparing the country to AIMbecome a developed nation. In order to create a K-based economy,research and development skills in Mathematics must be taught and The Primary School Mathematics Curriculum aims to build pupils’ understanding of number concepts and their basic skills ininstilled at school level. computation that they can apply in their daily routines effectively andAchieving this requires a sound mathematics curriculum, competent responsibly in keeping with the aspirations of a developed society andand knowledgeable teachers who can integrate instruction with nation, and at the same time to use this knowledge to further theirassessment, classrooms with ready access to technology, and a studies.commitment to both equity and excellence.The Mathematics Curriculum has been designed to provide knowledgeand mathematical skills to pupils from various backgrounds and levels OBJECTIVESof ability. Acquisition of these skills will help them in their careers laterin life and in the process, benefit the society and the nation. The Primary School Mathematics Curriculum will enable pupils to:Several factors have been taken into account when designing the 1 know and understand the concepts, definition, rules sandcurriculum and these are: mathematical concepts and skills, principles related to numbers, operations, space, measures andterminology and vocabulary used, and the level of proficiency of data representation;English among teachers and pupils.The Mathematics Curriculum at the primary level (KBSR) emphasises 2 master the basic operations of mathematics:the acquisition of basic concepts and skills. The content is categorised • addition,into four interrelated areas, namely, Numbers, Measurement, Shapeand Space and Statistics. • subtraction,The learning of mathematics at all levels involves more than just the • multiplication,basic acquisition of concepts and skills. It involves, more importantly, • division;an understanding of the underlying mathematical thinking, general 3 master the skills of combined operations; (viii)
- 7. 4 master basic mathematical skills, namely: • Decimals; • making estimates and approximates, • Money; • measuring, 2 Measures • handling data • Time; • representing information in the form of graphs and charts; • Length; 5 use mathematical skills and knowledge to solve problems in • Mass; everyday life effectively and responsibly; • Volume of Liquid. 6 use the language of mathematics correctly; 3 Shape and Space 7 use suitable technology in concept building, acquiring • Two-dimensional Shapes; mathematical skills and solving problems; • Three-dimensional Shapes; 8 apply the knowledge of mathematics systematically, heuristically, • Perimeter and Area. accurately and carefully; 4 Statistics 9 participate in activities related to mathematics; and • Data Handling10 appreciate the importance and beauty of mathematics. The Learning Areas outline the breadth and depth of the scope of knowledge and skills that have to be mastered during the allocated time for learning. These learning areas are, in turn, broken down intoCONTENT ORGANISATION more manageable objectives. Details as to teaching-learning strategies, vocabulary to be used and points to note are set out in fiveThe Mathematics Curriculum at the primary level encompasses four columns as follows:main areas, namely, Numbers, Measures, Shape and Space, and Column 1: Learning Objectives.Statistics. The topics for each area have been arranged from the basicto the abstract. Teachers need to teach the basics before abstract Column 2: Suggested Teaching and Learning Activities.topics are introduced to pupils. Column 3: Learning Outcomes.Each main area is divided into topics as follows: Column 4: Points To Note. 1 Numbers Column 5: Vocabulary. • Whole Numbers; • Fractions; (ix)
- 8. The purpose of these columns is to illustrate, for a particular teaching EMPHASES IN TEACHING AND LEARNINGobjective, a list of what pupils should know, understand and be able todo by the end of each respective topic. The Mathematics Curriculum is ordered in such a way so as to giveThe Learning Objectives define clearly what should be taught. They flexibility to the teachers to create an environment that is enjoyable,cover all aspects of the Mathematics curriculum and are presented in meaningful, useful and challenging for teaching and learning. At thea developmental sequence to enable pupils to grasp concepts and same time it is important to ensure that pupils show progression inmaster skills essential to a basic understanding of mathematics. acquiring the mathematical concepts and skills.The Suggested Teaching and Learning Activities list some On completion of a certain topic and in deciding to progress to anotherexamples of teaching and learning activities. These include methods, learning area or topic, the following need to be taken into accounts:techniques, strategies and resources useful in the teaching of a • The skills or concepts acquired in the new learning area orspecific concepts and skills. These are however not the only topics;approaches to be used in classrooms. • Ensuring that the hierarchy or relationship between learningThe Learning Outcomes define specifically what pupils should be areas or topics have been followed through accordingly; andable to do. They prescribe the knowledge, skills or mathematicalprocesses and values that should be inculcated and developed at the • Ensuring the basic learning areas have or skills have beenappropriate levels. These behavioural objectives are measurable in all acquired or mastered before progressing to the moreaspects. abstract areas. In Points To Note, attention is drawn to the more significant aspects The teaching and learning processes emphasise concept building, skillof mathematical concepts and skills. These aspects must be taken into acquisition as well as the inculcation of positive values. Besides these,accounts so as to ensure that the concepts and skills are taught and there are other elements that need to be taken into account and learntlearnt effectively as intended. through the teaching and learning processes in the classroom. The main emphasis are as follows:The Vocabulary column consists of standard mathematical terms,instructional words and phrases that are relevant when structuringactivities, asking questions and in setting tasks. It is important to pay 1. Problem Solving in Mathematicscareful attention to the use of correct terminology. These terms needto be introduced systematically to pupils and in various contexts so Problem solving is a dominant element in the mathematics curriculumthat pupils get to know of their meaning and learn how to use them for it exists in three different modes, namely as content, ability, andappropriately. learning approach. (x)
- 9. Over the years of intellectual discourse, problem solving has People learn best through experience. Hence, mathematics is bestdeveloped into a simple algorithmic procedure. Thus, problem solving learnt through the experience of solving problems. Problem-basedis taught in the mathematics curriculum even at the primary school learning is an approach where a problem is posed at the beginning oflevel. The commonly accepted model for problem solving is the four- a lesson. The problem posed is carefully designed to have the desiredstep algorithm, expressed as follows:- mathematical concept and ability to be acquired by students during the particular lesson. As students go through the process of solving the • Understanding the problem; problem being posed, they pick up the concept and ability that are built • Devising a plan; into the problem. A reflective activity has to be conducted towards the end of the lesson to assess the learning that has taken place. • Carrying out the plan; and • Looking back at the solution. 2. Communication in MathematicsIn the course of solving a problem, one or more strategies can be Communication is one way to share ideas and clarify theemployed to lead up to a solution. Some of the common strategies of understanding of Mathematics. Through talking and questioning,problem solving are:- mathematical ideas can be reflected upon, discussed and modified. • Try a simpler case; The process of reasoning analytically and systematically can help reinforce and strengthen pupils’ knowledge and understanding of • Trial and improvement; mathematics to a deeper level. Through effective communications • Draw a diagram; pupils will become efficient in problem solving and be able to explain concepts and mathematical skills to their peers and teachers. • Identifying patterns and sequences; Pupils who have developed the above skills will become more • Make a table, chart or a systematic list; inquisitive gaining confidence in the process. Communicational skills in mathematics include reading and understanding problems, • Simulation; interpreting diagrams and graphs, and using correct and concise • Make analogy; and mathematical terms during oral presentation and written work. This is also expanded to the listening skills involved. • Working backwards. Communication in mathematics through the listening process occursProblem solving is the ultimate of mathematical abilities to be when individuals respond to what they hear and this encourages themdeveloped amongst learners of mathematics. Being the ultimate of to think using their mathematical knowledge in making decisions.abilities, problem solving is built upon previous knowledge andexperiences or other mathematical abilities which are less complex in Communication in mathematics through the reading process takesnature. It is therefore imperative to ensure that abilities such as place when an individual collects information or data and rearrangescalculation, measuring, computation and communication are well the relationship between ideas and concepts.developed amongst students because these abilities are thefundamentals of problem solving ability. (xi)
- 10. Communication in mathematics through the visualization process • Structured and unstructured interviews;takes place when an individual makes observation, analyses it,interprets and synthesises the data into graphic forms, such as • Discussions during forums, seminars, debates and brain-pictures, diagrams, tables and graphs. storming sessions; andThe following methods can create an effective communication • Presentation of findings of assignments.environment: Written communication is the process whereby mathematical ideas • Identifying relevant contexts associated with environment and and information are shared with others through writing. The written everyday life experiences of pupils; work is usually the result of discussions, contributions and brain- storming activities when working on assignments. Through writing, the • Identifying interests of pupils; pupils will be encouraged to think more deeply about the mathematics content and observe the relationships between concepts. • Identifying teaching materials; Examples of written communication activities are: • Ensuring active learning; • Doing exercises; • Stimulating meta-cognitive skills; • Keeping scrap books; • Inculcating positive attitudes; and • Keeping folios; • Creating a conducive learning environment. • Undertaking projects; andOral communication is an interactive process that involves activitieslike listening, speaking, reading and observing. It is a two-way • Doing written tests.interaction that takes place between teacher-pupil, pupil-pupil, andpupil-object. When pupils are challenged to think and reason about Representation is a process of analysing a mathematical problem andmathematics and to tell others the results of their thinking, they learn interpreting it from one mode to another. Mathematical representationto be clear and convincing. Listening to others’ explanations gives enables pupils to find relationship between mathematical ideas thatpupils the opportunities to develop their own understanding. are informal, intuitive and abstract using their everyday language.Conversations in which mathematical ideas are explored from multiple Pupils will realise that some methods of representation are moreperspectives help sharpen pupils thinking and help make connections effective and useful if they know how to use the elements ofbetween ideas. Such activity helps pupils develop a language for mathematical representation.expressing mathematical ideas and appreciation of the need forprecision in the language. Some effective and meaningful oral 3. Mathematical Reasoningcommunication techniques in mathematics are as follows: Logical reasoning or thinking is the basis for understanding and • Story-telling, question and answer sessions using own words; solving mathematical problems. The development of mathematical • Asking and answering questions; reasoning is closely related to the intellectual and communicative development of the pupils. Emphasis on logical thinking during (xii)
- 11. mathematical activities opens up pupils’ minds to accept mathematics educational software, websites in the internet and available learningas a powerful tool in the world today. packages can help to upgrade the pedagogical skills in the teaching and learning of mathematics.Pupils are encouraged to predict and do guess work in the process ofseeking solutions. Pupils at all levels have to be trained to investigate The use of teaching resources is very important in mathematics. Thistheir predictions or guesses by using concrete materials, calculators, will ensure that pupils absorb abstract ideas, be creative, feelcomputers, mathematical representation and others. Logical reasoning confident and be able to work independently or in groups. Most ofhas to be infused in the teaching of mathematics so that pupils can these resources are designed for self-access learning. Through self-recognise, construct and evaluate predictions and mathematical access learning, pupils will be able to access knowledge or skills andarguments. information independently according to their pace. This will serve to stimulate pupils’ interests and responsibility in learning mathematics.4. Mathematical Connections In the mathematics curriculum, opportunities for making connectionsmust be created so that pupils can link conceptual to procedural APPROACHES IN TEACHING AND LEARNINGknowledge and relate topics in mathematics with other learning areas Various changes occur that influence the content and pedagogy in thein general. teaching of mathematics in primary schools. These changes require The mathematics curriculum consists of several areas such as variety in the way of teaching mathematics in schools. The use ofarithmetic, geometry, measures and problem solving. Without teaching resources is vital in forming mathematical concepts.connections between these areas, pupils will have to learn and Teachers can use real or concrete objects in teaching and learning tomemorise too many concepts and skills separately. By making help pupils gain experience, construct abstract ideas, makeconnections pupils are able to see mathematics as an integrated inventions, build self confidence, encourage independence andwhole rather than a jumble of unconnected ideas. Teachers can foster inculcate cooperation.connections in a problem oriented classrooms by having pupils to The teaching and learning materials that are used should contain self-communicate, reason and present their thinking. When these diagnostic elements so that pupils can know how far they havemathematical ideas are connected with real life situations and the understood the concepts and skills. To assist the pupils in havingcurriculum, pupils will become more conscious in the application of positivemathematics. They will also be able to use mathematics contextuallyin different learning areas in real life. attitudes and personalities, the intrinsic mathematical values of exactness, confidence and thinking systematically have to be5. Application of Technology absorbed through the learning areas. Good moral values can be cultivated through suitable context. ForThe application of technology helps pupils to understand mathematical example, learning in groups can help pupils develop social skills andconcepts in depth, meaningfully and precisely enabling them to encourage cooperation and self-confidence in the subject. Theexplore mathematical concepts. The use of calculators, computers, element of patriotism can also be inculcated through the teaching- (xiii)
- 12. learning process in the classroom using planned topics. These values assessment techniques, including written and oral work as well asshould be imbibed throughout the process of teaching and learning demonstration. These may be in the form of interviews, open-endedmathematics. questions, observations and assignments. Based on the results, the teachers can rectify the pupils’ misconceptions and weaknesses andAmong the approaches that can be given consideration are: at the same time improve their teaching skills. As such, teachers can • Pupil centered learning that is interesting; take subsequent effective measures in conducting remedial and enrichment activities to upgrade pupils’ performance. • The learning ability and styles of learning; • The use of relevant, suitable and effective teaching materials; and • Formative evaluation to determine the effectiveness of teaching and learning.The choice of an approach that is suitable will stimulate the teachingand learning environment in the classroom or outside it. Theapproaches that are suitable include the following: • Cooperative learning; • Contextual learning; • Mastery learning; • Constructivism; • Enquiry-discovery; and • Futures Study.ASSESSMENTAssessment is an integral part of the teaching and learning process. Ithas to be well-structured and carried out continuously as part of theclassroom activities. By focusing on a broad range of mathematicaltasks, the strengths and weaknesses of pupils can be assessed.Different methods of assessment can be conducted using multiple (xiv)
- 13. Learning Area : NUMBERS TO 1 000 000 Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…1 Develop number sense • Teacher pose numbers in (i) Name and write numbers Write numbers in words and numbersup to 1 000 000 numerals, pupils name the up to 1 000 000. numerals. numeral respective numbers and write Emphasise reading and the number words. count writing numbers in extended • Teacher says the number notation for example : place value names and pupils show the 801 249 = 800 000 + 1 000 value of the digits numbers using the calculator or + 200 + 40 + 9 the abacus, then pupils write partition or the numerals. 801 249 = 8 hundred decompose • Provide suitable number line thousands + 1 thousands + 2 estimate scales and ask pupils to mark hundreds + 4 tens + 9 ones. the positions that representt a check set of given numbers. compare • Given a set of numbers, pupils (ii) Determine the place value count in … represent each number using of the digits in any whole hundreds the number base blocks or the number up to 1 000 000. abacus. Pupils then state the ten thousands place value of every digit of the thousands given number. round off to the • Given a set of numerals, pupils (iii) Compare value of numbers nearest… compare and arrange the up to 1 000 000. tens numbers in ascending then hundreds descending order. thousands (iv) Round off numbers to the Explain to pupils that ten thousands nearest tens, hundreds, numbers are rounded off to hundred thousands thousands, ten thousands get an approximate. and hundred thousands. 1
- 14. Learning Area : ADDITION WITH THE HIGHEST TOTAL OF 1 000 000 Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…2 Add numbers to the • Pupils practice addition using (i) Add any two to four Addition exercises include number sentencestotal of 1 000 000 the four-step algorithm of: numbers to 1 000 000. addition of two numbers to vertical form four numbers 1) Estimate the total. without trading • without trading (without 2) Arrange the numbers regrouping). with trading involved according to place values. • with trading (with quick calculation regrouping). 3) Perform the operation. pairs of ten Provide mental addition 4) Check the reasonableness of doubles practice either using the the answer. abacus-based technique or estimation • Pupils create stories from given using quick addition range addition number sentences. strategies such as estimating total by rounding, simplifying addition by pairs of tens and doubles, e.g. Rounding 410 218 → 400 000 294 093 → 300 000 68 261 → 70 000 Pairs of ten 4 + 6, 5 + 5, etc. Doubles 3 + 3, 30 + 30, 300 + 300, 3000 + 3000, 5 + 5, etc. 2
- 15. Learning Area : ADDITION WITH THE HIGHEST TOTAL OF 1 000 000 Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to… • Teacher pose problems (ii) Solve addition problems. Before a problem solving total verbally, i.e., in the numerical exercise, provide pupils with sum of form or simple sentences. the activity of creating stories from number sentences. numerical • Teacher guides pupils to solve problems following Polya’s four- A guide to solving addition how many step model of: problems: number sentences 1) Understanding the problem Understanding the problem create 2) Devising a plan Extract information from pose problem 3) Implementing the plan problems posed by drawing diagrams, making lists or tables 4) Looking back. tables. Determine the type of modeling problem, whether it is addition, subtraction, etc. simulating Devising a plan Translate the information into a number sentence. Determine what strategy to use to perform the operation. Implementing the plan Perform the operation conventionally, i.e. write the number sentence in the vertical form. Looking back Check for accuracy of the solution. Use a different startegy, e.g. calculate by using the abacus. 3
- 16. Learning Area : SUBTRACTION WITHIN THE RANGE OF 1 000 000 Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…3 Subtract numbers from • Pupils create stories from given (i) Subtract one number from Subtraction refers to number sentencea number less than subtraction number sentences. a bigger number less than a) taking away, vertical form1 000 000. 1 000 000. • Pupils practice subtraction b) comparing differences without trading using the four-step algorithm of: c) the inverse of addition. with trading 1) Estimate the sum. Limit subtraction problems to quick calculation 2) Arrange the numbers subtracting from a bigger involved according to place pairs of ten number. values. counting up Provide mental sutraction 3) Perform the operation. practice either using the counting down 4) Check the reasonableness of abacus-based technique or estimation the answer. using quick subtraction strategies. range Quick subtraction strategies modeling to be implemented: successively a) Estimating the sum by rounding numbers. b) counting up and counting down (counting on and counting back) • Pupils subtract successively by (ii) Subtract successively from Subtract successively two writing the number sentence in a bigger number less than numbers from a bigger the 1 000 000. number a) horizontal form b) vertical form 4
- 17. Learning Area : SUBTRACTION WITHIN THE RANGE OF 1 000 000 Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to… • Teacher pose problems (iii) Solve subtraction Also pose problems in the create verbally, i.e., in the numerical problems. form of pictorials and stories. pose problems form or simple sentences. tables • Teacher guides pupils to solve problems following Polya’s four- step model of: 1) Understanding the problem 2) Devising a plan 3) Implementing the plan 4) Looking back. 5
- 18. Learning Area : MULTIPLICATION WITH THE HIGHEST PRODUCT OF 1 000 000 Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…4 Multiply any two • Pupils create stories from given (i) Multiply up to five digit Limit products to less than timesnumbers with the highest multplication number numbers with 1 000 000. multiplyproduct of 1 000 000. sentences. Provide mental multiplication a) a one-digit number, multiplied by e.g. 40 500 × 7 = 283 500 practice either using the abacus-based technique or multiple of “A factory produces 40 500 b) a two-digit number, other multiplication batteries per day. 283 500 strategies. various batteries are produced in 7 c) 10, 100 and 1000. estimation days” Multiplication strategies to be implemented: lattice • Pupils practice multiplication using the four-step algorithm of: Factorising multiplication 16 572 × 36 1) Estimate the product. = (16 572 × 30)+(16 572 × 6) 2) Arrange the numbers = 497 160 + 99 432 involved according to place = 596 592 values. Completing 100 3) Perform the operation. 99 × 4982 = 4982 × 99 4) Check the reasonableness of the answer. = (4982 × 100) – (4982 × 1) = 498 200 – 4982 = 493 218 Lattice multiplication 1 6 5 7 2 × 0 1 1 2 0 3 3 8 5 1 6 0 3 3 4 1 5 6 6 6 0 2 2 9 6 5 9 2 6
- 19. Learning Area : MULTIPLICATION WITH THE HIGHEST PRODUCT OF 1 000 000 Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to… • Teacher pose problems (ii) Solve problems involving A guide to solving addition Times verbally, i.e., in the numerical multiplication. problems: Multiply form or simple sentences. Understanding the problem multiplied by • Teacher guides pupils to solve problems following Polya’s four- Extract information from multiple of step model of: problems posed by drawing diagrams, making lists or estimation 1) Understanding the problem tables. Determine the type of lattice 2) Devising a plan problem, whether it is addition, subtraction, etc. multiplication 3) Implementing the plan Devising a plan 4) Looking back. Translate the information into a number sentence. (Apply some of the common Determine what strategy to strategies in every problem use to perform the operation. solving step.) Implementing the plan Perform the operation conventionally, i.e. write the number sentence in the vertical form. Looking back Check for accuracy of the solution. Use a different startegy, e.g. calculate by using the abacus. 7
- 20. Learning Area : DIVISION WITH THE HIGHEST DIVIDEND OF 1 000 000 Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…5 Divide a number less • Pupils create stories from given (i) Divide numbers up to six Division exercises include dividethan 1 000 000 by a two- division number sentences. digits by quptients dividenddigit number. a) without remainder, • Pupils practice division using quotient a) one-digit number, the four-step algorithm of: b) with remainder. divisor 1) Estimate the quotient. b) 10, 100 and 1000, Note that “r” is used to remainder 2) Arrange the numbers signify “remainder”. c) two-digit number, divisibility involved according to place Emphasise the long division values. technique. 3) Perform the operation. Provide mental division 4) Check the reasonableness of practice either using the the answer. abacus-based technique or other division strategies. Example for long division Exposed pupils to various 1 3 5 6 2 r 20 division strategies, such as, 35 4 7 4 6 9 0 a) divisibility of a number 3 5 b) divide by 10, 100 and 1 2 4 1 000. 1 0 5 1 9 6 1 7 5 2 1 9 2 1 0 9 0 7 0 2 0 8
- 21. Learning Area : DIVISION WITH THE HIGHEST DIVIDEND OF 1 000 000 Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to… • Teacher pose problems (ii) Solve problems involving verbally, i.e., in the numerical division. form or simple sentences. • Teacher guides pupils to solve problems following Polya’s four- step model of: 1) Understanding the problem 2) Devising a plan 3) Implementing the plan 4) Looking back. (Apply some of the common strategies in every problem solving step.) 9
- 22. Learning Area : MIXED OPERATIONS Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…6 Perform mixed • Pupils create stories from given (i) Calculate mixed operation For mixed operations Mixed operationsoperations involving number sentences involving on whole numbers involving multiplication andmultiplication and division. mixed operations of division involving multiplication and division, calculate from left to and multiplication. division. right. • Pupils practice calculation Limit the result of mixed involving mixed operation using operation exercises to less the four-step algorithm of: than 100 000, for example 1) Estimate the quotient. a) 24 × 10 ÷ 5 = b) 496 ÷ 4 × 12 = 2) Arrange the numbers involved according to place c) 8 005 × 200 ÷ 50 = values. Avoid problems such as 3) Perform the operation. a) 3 ÷ 6 x 300 = 4) Check the reasonableness of b) 9 998 ÷ 2 × 1000 = the answer. c) 420 ÷ 8 × 12 = • Teacher guides pupils to solve (ii) Solve problems involving Pose problems in simple problems following Polya’s four- mixed operations of sentences, tables or step model of: division and multiplication.. pictorials. 1) Understanding the problem Some common problem solving strategies are 2) Devising a plan a) Drawing diagrams 3) Implementing the plan b) Making a list or table 4) Looking back. c) Using arithmetic (Apply appropriate strategies in formula every problem solving step.) d) Using tools. 10
- 23. Learning Area : IMPROPER FRACTIONS Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…1 Understand improper • Demonstrate improper fractions (i) Name and write improper Revise proper fractions improper fractionfractions. using concrete objects such as fractions with denominators before introducing improper numerator paper cut-outs, fraction charts up to 10. fractions. and number lines. denominator Improper fractions are • Pupils perform activities such (ii) Compare the value of the fractions that are more than three over two two improper fractions. one whole. as paper folding or cutting, and three halves marking value on number lines to represent improper fractions. 1 1 one whole 2 2 1 quarter 2 compare “three halves” 3 2 partition The numerator of an improper fraction has a higher value than the denominator. 1 1 1 1 1 3 3 3 3 3 The fraction reperesented by the diagram is “five thirds” and is written as 5 . It is 3 commonly said as “five over three”. 11
- 24. Learning Area : MIXED NUMBERS Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…2 Understand mixed • Teacher demonstrates mixed (i) Name and write mixed A mixed number consists of fractionnumbers. numbers by partitioning real numbers with denominators a whole number and a proper fraction objects or manipulative. up to 10. proper fraction. improper fraction • Pupils perform activities such e.g. as (ii) Convert improper fractions mixed numbers to mixed numbers and vice- 21 2 a) paper folding and shading versa. Say as ‘two and a half’ or b) pouring liquids into ‘two and one over two’. containers To convert improper c) marking number lines fractions to mixed numbers, to represent mixed numbers. use concrete representations to verify the equivalence, e.g. then compare with the procedural calculation. e.g. 2 3 shaded parts. 4 7 1 2R 1 =2 3 3 3 7 6 3 1 beakers full. 2 1 12
- 25. Learning Area : ADDITION OF FRACTIONS Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…3 Add two mixed • Demonstrate addition of mixed (i) Add two mixed numbers Examples of mixed numbers mixed numbersnumbers. numbers through with the same addition exercise: equivalent denominators up to 10. a) paper folding activities 1 a) 2 + = simplest form b) fraction charts (ii) Add two mixed numbers 3 denominators c) diagrams with different denominators 3 4 multiples up to 10. b) 2 + = d) number lines. 5 5 number lines e.g. (iii) Solve problems involving 2 4 addition of mixed numbers. c) 1 +2 = diagram 1 1 3 7 7 1 +1 = 2 fraction charts 4 2 4 The following type of problem should also be included: 8 1 a) 1 +3 = 8 1 9 3 1 +3 9 3 1 1 +1 = 8 1× 3 b) 1 =1 + 3 2 2 9 3× 3 Emphasise answers in 8 3 simplest form. =1 + 3 • Create stories from given 9 9 number sentences involving 11 mixed numbers. =4 9 2 =5 9 13
- 26. Learning Area : SUBTRACTION OF FRACTIONS Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…4 Subtract mixed • Demonstrate subtraction of (i) Subtract two mixed Some examples of simplest formnumbers. mixed numbers through numbers with the same subtraction problems: multiply denominator up to 10. a) paper folding activities 3 a) 2 − 2 = fraction chart b) fraction charts 5 mixed numbers c) diagrams 4 3 b) 2 − = multiplication tables. d) number lines 7 7 e) multiplication tables. 3 1 c) 2 −1 = • Pupils create stories from given 4 4 number sentences involving 1 mixed numbers. d) 3 − 1 = 9 1 3 e) 2 −1 = 8 8 Emphasise answers in simplest form. 14
- 27. Learning Area : SUBTRACTION OF FRACTIONS Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to… (ii) Subtract two mixed Include the following type of simplest form numbers with different problems, e.g. equivalent denominators up to 10. 1 1 multiples 1 − (iii) Solve problems involving 2 4 number sentences subtraction of mixed 1× 2 1 numbers. =1 − mixed numbers 2× 2 4 2 1 equivalent fraction =1 − 4 4 1 =1 4 Other examples 7 1 a) 1 − = 8 2 4 7 b) 3 − = 5 10 1 2 c) 2 − = 4 3 1 3 d) 5 −3 = 6 4 Emphasise answers in simplest form. 15
- 28. Learning Area : MULTIPLICATION OF FRACTIONS Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…5 Multiply any proper • Use groups of concrete (i) Multiply whole numbers Emphasise group of objects Simplest formfractions with a whole materials, pictures and number with proper fractions. as one whole. Fractionsnumber up to 1 000. lines to demonstrate fraction as Limit whole numbers up to 3 equal share of a whole set. Denominator digits in mulplication • Provide activities of comparing exercises of whole numbers Numerator equal portions of two groups of and fractions. Whole number objects. Some examples Proper fractions e.g. multiplication exercise for fractions with the numerator Divisible 1 2 of 6 = 3 1 and denominator up to 10. 1 of 6 pencils is 3 pencils. a) 1 2 of 8 2 1 b) × 70 = 5 1 c) × 648 = 8 1 6 ×6= =3 2 2 16
- 29. Learning Area : MULTIPLICATION OF FRACTIONS Year 5LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to… 1 (ii) Solve problems involving Some multiplication Multiply 6× or six halves. multiplication of fractions. examples for fractions with 2 fractions the numerator more than 1 and denominator up to 10. Whole number e.g. Divisible 6 × ½ of an orange is… 2 Denominator a) of 9 1 + 1 + 1 + 1 + 1 + 1 = 3 oranges. 3 Numerator 3 3 3 3 3 3 5 Proper fractions • Create stories from given b) 49 × number sentences. 7 3 c) × 136 8 17

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