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# MATHEMATICS YEAR 6

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### MATHEMATICS YEAR 6

1. 1. Ministry of Education MalaysiaIntegrated Curriculum for Primary Schools CURRICULUM SPECIFICATIONSMATHEMATICS Curriculum Development Centre Ministry of Education Malaysia 2006
2. 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. 3. CONTENTRUKUNEGARA v MONEY 14National Philosophy of Education vii Money up to RM10 million 14Preface ix TIME 15Introduction xi Duration 15 LENGTH 17 Computation of Length 17WHOLE NUMBERS 1Numbers up to Seven Digits 1 MASS 18Basic Operations with Numbers up to Seven Digits 3 Computation of Mass 18Mixed Operations with Numbers up to Seven Digits 6 VOLUME OF LIQUID 19FRACTIONS 7 Computation of Volume of Liquid 19Addition of Fractions 7Subtraction of Fractions 8 SHAPE AND SPACE 20Multiplication of Fractions 9 Two-Dimensional Shapes 20Division of Fractions 10 Three-Dimensional Shapes 22DECIMALS 11 DATA HANDLING 24Mixed Operations with Decimals 11 Average 24 Organising and Interpreting Data 26PERCENTAGE 12Relationship between Percentage, Fraction and Decimal 12 Contributors 28
4. 4. 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)
5. 5. 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)
6. 6. 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)
7. 7. 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)
8. 8. 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)
9. 9. 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)
10. 10. 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)
11. 11. 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)
12. 12. 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)
13. 13. 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)
14. 14. Learning Area: NUMBERS UP TO SEVEN DIGITS Year 6LEARNING 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 millionup to seven digits. numerals, pupils name the up to seven digits. numerals. digits respective numbers and write Seven-digit numbers are the number words. conversion numbers from 1 000 000 up • Teacher says the number to 9 999 999. place value names and pupils show the Emphasise reading and explore numbers using the calculator or writing numbers in extended the abacus, then, pupils write notation for example number patterns the numerals. multiple of 10 5 801 249 = 5 000 000 • Provide suitable number line + 800 000 + 1 000 + 200 simplest form scales and ask pupils to mark + 40 + 9 the positions that represent a extended notation set of given numbers. or round off 5 801 249 = 5 millions + 8 hundred thousands + 1 thousands + 2 hundreds + 4 tens + 9 ones. • Given a set of numbers, pupils (ii) Determine the place value To avoid confusion, initials represent each number using of the digits in any whole for place value names may the number base blocks or the number of up to seven be written in upper cases. abacus. Pupils then state the digits. place value of every digit of the given number. 1
15. 15. Learning Area: NUMBERS UP TO SEVEN DIGITS Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to… (iii) Express whole numbers in Write numbers in partial words and numerals, for a) decimals example a) 800 000 is 0.8 million b) fractions b) 6 320 000 is 6.32 million of a million and vice versa. c) 1.4 million is 1 400 000 d) 5.602 million is 5 602 000 1 e) 3 500 000 is 3 2 million f) 8 3 million is 8 750 000 4 For fractional number words, denominators are in multiples of 10 (10 to 90, 100 and 1000) and reduce fractional terms to its simplest form. Limit decimal terms up to 3 decimal places. • Given a set of numerals, pupils (iv) Compare number values compare and arrange the up to seven digits. numbers in ascending then descending order. (v) Round off numbers to the Explain to pupils that nearest tens, hundreds, numbers are rounded off to thousands, ten thousands, get an approximate. hundred thousands and millions. 2
16. 16. Learning Area: BASIC OPERATIONS WITH NUMBERS UP TO SEVEN DIGITS Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…2 Add, subtract, multiply • Pupils practice addition, (i) Add any two to five Addition exercises include simplerand divide numbers subtraction, multiplication and numbers to 9 999 999. addition of two numbers to simulatinginvolving numbers up to division using the four-step four numbers with andseven digits. algorithm of without regrouping. analogy 1) Estimate the solution. Provide mental addition sequences practice either using the 2) Arrange the numbers abacus-based technique or involved according to place using quick addition values. strategies such as estimating 3) Perform the operation. total by rounding, simplifying addition by pairs of tens, 4) Check the reasonableness doubles, etc. of the answer. (ii) Subtract Limit subtraction problems to subtracting from a bigger a) one number from a number. bigger number less than Provide mental subtraction 10 000 000 practice either using the abacus-based technique or b) successively from a using quick subtraction bigger number less than strategies. 10 000 000. Quick subtraction strategies to be implemented are a) estimating the sum by rounding numbers b) counting up and counting down (counting on and counting back). 3
17. 17. Learning Area: BASIC OPERATIONS WITH NUMBERS UP TO SEVEN DIGITS Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to… (iii) Multiply up to six-digit Limit products to less than numbers with 10 000 000. Provide mental multiplication a) a one-digit number practice either using the abacus-based technique or b) a two-digit number other multiplication strategies. c) 10, 100 and 1000. Multiplication strategies to be implemented include factorising, completing 100, lattice multiplication, etc. (iv) Divide numbers of up to Division exercises include seven digits by quotients with and without remainder. Note that “r” is a) a one-digit number used to signify “remainder”. Emphasise the long division b) 10, 100 and 1000 technique. c) two-digit number. Provide mental division practice either using the abacus-based technique or other division strategies. Exposed pupils to various division strategies, such as a) divisibility of a number b) divide by 10, 100 and 1 000. 4
18. 18. Learning Area: BASIC OPERATIONS WITH NUMBERS UP TO SEVEN DIGITS Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to… • Pose to pupils problems in (v) Solve Use any of the common numerical form, simple strategies of problem sentences, tables and pictures. a) addition, solving, such as • Pupils create stories from given a) Try a simpler case b) subtraction, number sentences. b) Trial and improvement • Teacher guides pupils to solve c) multiplication, c) Draw a diagram problems following Polya’s four- step model of d) division d) Identifying patterns and sequences 1) Understanding the problem problems involving e) Make a table, chart or a 2) Devising a plan numbers up to seven digits. systematic list 3) Implementing the plan f) Simulation 4) Looking back. g) Make analogy h) Working backwards. 5
19. 19. Learning Area: MIXED OPERATIONS WITH NUMBERS UP TO SEVEN DIGITS Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…3 Perform mixed • Explain to pupils the conceptual (i) Compute mixed operations Mixed operations are limited computeoperations with whole model of mixed operations then problems involving addition to not more than two mixed operationsnumbers. connect the concept with the and multiplication. operators, for example procedures of performing bracket a) 427 890 − 15 600 ÷ 25 = operations according to the horizontal form order of operations. b) 12 745 + 20 742 × 56 = vertical form • Teacher pose problems (ii) Compute mixed operations Order of operations verbally, i.e., in the numerical problems involving B – brackets form or simple sentences. subtraction and division. O – of D – division M – multiplication A – addition S – subtraction • Teacher guides pupils to solve (iii) Compute mixed operations Examples of mixed problems following Polya’s four- problems involving operations with brackets step model of brackets. a) (1050 + 20 650) × 12 = 1) Understanding the problem b) 872 ÷ (8 − 4) = 2) Devising a plan c) (24 + 26) × (64 − 14) = 3) Implementing the plan 4) Looking back. (iv) Solve problems involving mixed operations on numbers of up to seven digits. 6
20. 20. Learning Area: ADDITION OF FRACTIONS Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…1 Add three mixed • Demonstrate addition of mixed (i) Add three mixed numbers An example of addition of mixed numbersnumbers with denominators numbers through with the same denominator three mixed numbers with equivalent fractionsof up to 10. of up to 10. the same denominator of up 1) paper folding activities to 10. simplest form 2) fraction charts 3 1 7 +17 2 +2 3 7 = multiplication tables 3) diagrams 4) number lines 5) multiplication tables • Pupils create stories from given (ii) Add three mixed numbers An example of addition of number sentences involving with different denominators three mixed numbers with mixed numbers. of up to 10. different denominators of up to 10. 2 3 +16 + 2 4 = 1 1 1 Write answers in its simplest form. • Teacher guides pupils to solve (iii) Solve problems involving problems following Polya’s four- addition of mixed numbers. step model of 1) Understanding the problem 2) Devising a plan 3) Implementing the plan 4) Looking back. 7
21. 21. Learning Area: SUBTRACTION OF FRACTIONS Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…2 Subtract mixed • Demonstrate subtraction of (i) Subtract involving three An example of subtraction mixed numbersnumbers with denominators mixed numbers through mixed numbers with the involving three mixed equivalent fractionsof up to 10. same denominator of up to numbers with the same 1) paper holding activities denominator of up to 10. 10. simplest form 2) fractions charts 5 4 5 −15 2 −15 1 = multiplication tables 3) diagrams 4) number lines 5) multiplication tables • Pupils create stories from given (ii) Subtract involving three An example of subtraction number sentences involving mixed numbers with involving three mixed mixed numbers. different denominators of numbers with different up to 10. denominators of up to 10. 7 8 − 3 4 −12 = 7 1 1 Write answers in its simplest form. • Pose to pupils, problems in the (iii) Solve problems involving real context in the form of subtraction of mixed numbers. 1) words, 2) tables, 3) pictorials. 8
22. 22. Learning Area: MULTIPLICATION OF FRACTIONS Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…3 Multiply any mixed • Use materials such as the (i) Multiply mixed numbers Model multiplication of mixed mixed numbersnumbers with a whole hundred squares to model with a whole number. numbers with whole portionsnumbers up to 1000. multiplication of mixed numbers as grouping sets of numbers. For example, objects, for example simplest form 2 2 × 100 = ? 1 3 × 300 means 3 1 3 1 3 groups of sets of 300. Suppose we have a set of 100 objects. Two groups or sets will contain 200 objects, i.e. 2 × 100 = 200 .Therefore, 1 2 2 groups will contain 2 2 × 100 = 250 objects. 1 Limit the whole number component of a mixed number, to three digits. The • Present calculation in clear and denominator of the fractional organised steps. part of the mixed number is limited to less than 10. 5 2 2 × 100 = 1 × 100 2 5 = × 50 1 = 250 9
23. 23. Learning Area: DIVISION OF FRACTIONS Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…4 Divide fractions with a • Teacher models the division of (ii) Divide fractions with Limit denominators for thewhole number and a fraction with another fraction as dividend to less than 10.fraction. sharing. The following a) a whole number Limit divisors to less than 10 illustrations demonstrate this for both the whole number idea… b) a fraction. and fraction. 1 2 ÷ 2 =1 1 Some models of division of a Half a vessel of liquid poured fraction with a fraction… into a half-vessel makes one full half-vessel. 1 4 ÷ 1 2 = ( 4 × 2) ÷ (2 × 2) 1 1 1 = ( 4 × 2) ÷ 1 1 3 4 = 1 2 ÷1 1 2 = 1 2 1 4 or 0 1 ÷ 1 =2 (iii) Divide mixed numbers with 1 ×2 2 4 1 ÷ 1 = 4 Half a vessel of liquid poured 4 2 1 ×2 a) a whole number 2 into a quarter-vessel makes two 1 full quarter-vessels. b) a fraction. = 2 1 1 = 1 2 3 4 or 1 2 1 2 1 4 = 1 2 ×2 1 4 ×2 = 1 1 2 = 1 2 1 4 0 10
24. 24. Learning Area: MIXED OPERATIONS WITH DECIMALS Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…1 Perform mixed • Pupils add and/or subtract (i) Add and subtract three to Some examples of mixed decimal numberoperations of addition and three to four decimal numbers four decimal numbers of up operations with decimals. decimal placessubtraction of decimals of in parts, i.e. by performing one to 3 decimal places, 0.6 + 10.2 – 9.182 =up to 3 decimal places. operation at a time in the order involving of left to right. Calculation steps 8.03 – 5.12 + 2.8 = are expressed in the vertical a) decimal numbers only 126.6 + 84 - 3.29 = form. b) whole numbers and or • The abacus may be used to decimal numbers. verify the accuracy of the result 10 – 4.44 + 2.126 – 7 = of the calculation. 2.4 + 8.66 – 10.992 + 0.86 = 0.6 + 0.006 +3.446 – 2.189 = An example of how calculation for mixed operations with decimals is expressed. 126.6 – 84 + 3.29 = ? 1 2 6 . 6 + 8 4 2 1 0 . 6 − 3 . 2 9 2 0 7 . 3 1 11
25. 25. Learning Area: RELATIONSHIP BETWEEN PERCENTAGE, FRACTION AND DECIMAL Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…1 Relate fractions and • Use the hundred-squares to (i) Convert mixed numbers to Fractions can be modeled as simplest formdecimals to percentage. model conversion of mixed percentage. parts of a whole, groupings multiples numbers to percentage. For of sets of objects, or division. 3 example, convert 1 10 to To relate mixed numbers to percent percentages, the numbers percentage. percentage have to be viewed as fractions. Mixed numbers have to be converted to improper fractions first, to give meaning to the relationship mixed numbers with percentages. For example 1= 100 3 30 3 3 × 50 150 = 12 = 1 = = = 100% 100 10 100 2 2 × 50 100 100% 30% The shaded parts represent (ii) Convert decimal numbers Limit decimal numbers to 130% of the hundred-squares. of value more than 1 to values less than 10 and to percentage. two decimal places only. An example of a decimal number to percentage conversion 265 2.65 = = 265% 100 12
26. 26. Learning Area: RELATIONSHIP BETWEEN PERCENTAGE, FRACTION AND DECIMAL Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to… • Demonstrate the concept of (iii) Find the value for a given Finding values for simplest form percentage of a quantity using percentage of a quantity. percentage of a quantity, multiple the hundred-squares or multi- shall include the following, based blocks. income Quantity value of expenses a) 100 savings b) less than 100 profit c) more than 100, loss Percentage value of discount The shaded parts of the two a) less than 100% hundred-squares is 128% of dividend b) more than 100%. 100. interest Sample items for finding • Guide pupils to find the value values for percentage of a tax for percentage of a quantity quantity are as follows: through some examples, such commission as a) 9.8% of 3500 45% of 10 b) 114% of 100 450 c) 150% of 70 × 10 = 45 100 d) 160% of 120 • Pupils create stories from given (iv) Solve problems in real Solve problems in real life percentage of a quantity. context involving involving percentage relationships between calculation of income and • Pose to pupils, situational expenditure, savings, profit percentage, fractions and problems in the form of words, and loss, discount, dividend decimals. tables and pictorials. or interest, tax, commission, etc. 13
27. 27. Learning Area: MONEY UP TO RM10 MILLION Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…1 Use and apply number • Provide to pupils a situation (i) Perform mixed operations Mixed operations exercise mixed operationsense in real context involving money where mixed with money up to a value of may also include brackets, bracketinvolving money. operations need to be RM10 million. for example performed. Then, demonstrate savings RM8000 + RM1254 – RM5555 = how the situation is income transformed to a number RM125.05 – RM21 – RM105.95 = sentence of mixed operations. expenditure (RM100 + RM50) × 5 = • Pupils solve mixed operations investments involving money in the usual (RM125 × 8) – (RM40 × 8) = cost price proper manner by writing RM1200 – (RM2400 ÷ 6) = number sentences in the selling price vertical form. profit • Pose problems involving (ii) Solve problems in real Discuss problems involving loss money in numerical form, context involving various situations such as discount simple sentences, tables or computation of money. savings, income, pictures. expenditure, investments, computation cost price, selling price, • Teacher guides pupils to solve profit, loss and discount. problems following Polya’s four- step model of 1) Understanding the problem 2) Devising a plan 3) Implementing the plan 4) Looking back. 14
28. 28. Learning Area: DURATION Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to…1 Use and apply • Pupils find the duration from (i) Calculate the duration of an Some basic ideas of points calculationknowledge of time to find the start to the end of an event event in between in time so that calculation of computethe duration. from a given situation with the duration is possible, are as aid of the calendar, schedules a) months follows: date and number lines. For duration in months, “… calendar b) years from March until October.” schedule c) dates. For duration in years and months, “… from July 2006 duration to September 2006.” event For duration in years, month months and days, year a) “… from 25th March 2004 up to 25th June 2004”, or b) “… from 27th May 2005 till 29th June 2006.” (ii) Compute time period from An example of a situation situations expressed in expressed in a fraction of fractions of duration. time duration 2 57 … 3 of 2 years. 15
29. 29. Learning Area: DURATION Year 6LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING OUTCOMES POINTS TO NOTE VOCABULARYPupils will be taught to… LEARNING ACTIVITIES Pupils will be able to… • Pose problems involving (iii) Solve problem in real Discuss problem involving computation of time in context involving various situations such as numerical form, simple computation of time event, calendar etc. sentences, tables or pictures. duration. • Teacher guides pupils to solve problems following Polya’s four- step model of 58 1) Understanding the problem 2) Devising a plan 3) Implementing the plan 4) Looking back. 16