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MATEMATIK

TAHUN 4

KEMENTERIAN PENDIDIKAN MALAYSIA

KURIKULUM STANDARD SEKOLAH RENDAH

(EDISI BAHASA INGGERIS)

DOKUMEN STANDARD KURIKULUM DAN PENTAKSIRAN

DRAF

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STANDARD DOCUMENT

KURIKULUM STANDARD SEKOLAH RENDAH

(PRIMARY SCHOOL CURRICCULUM STANDARD)

(KSSR)

MATHEMATICS YEAR FOUR

CURRICULUM DEVELOPMENT DIVISION

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Copyright © 2008 Curriculum Development Centre First published 2012 Second published 2013 © Ministry of Education Malaysia Copyright reserved. Except for use in a review, the reproduction or utilisation of this work in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, and recording is forbidden without the prior written permission from the Director of the Curriculum Development Division, Ministry of Education Malaysia, Level 4-8, Block E9, Parcel E, Kompleks Kerajaan Parcel E,Pusat Pentadbiran Kerajaan Persekutuan, 62604 Putrajaya

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CONTENTS

CONTENTS iii

RUKUN NEGARA v

NATIONAL PHILOSOPHY OF EDUCATION vi

INTRODUCTION 1

THE RATIONALE OF MATHEMATICS EDUCATION 1

AIMS 1

FOCUS 2

NATIONAL CURRICULUM’S FRAMEWORK 2

STRUCTURE OF PRIMARY SCHOOL 3 MATHEMATICS EDUCATION

OBJECTIVES 3

MATHEMATICS CURRICULUM’S FRAMEWORK 3

CONTENT STANDARD AND LEARNING STANDARD 10

STRATEGIES IN TEACHING AND LEARNING 10

HIGHER ORDER THINKING SKILLS (HOTS) 11

21st CENTURY SKILLS 13

ELEMENTS OF ADDED VALUES 14

ASSESSMENT 16

SCHOOL BASED ASSESSMENT 16

NUMBERS AND OPERATIONS WHOLE NUMBERS UP TO 100 000 25 ADDITION IN THE RANGE OF 100 000 26 SUBTRACTION IN THE RANGE OF 100 000 27 MULTIPLICATION 28 DIVISION 29 MIXED OPERATIONS 30 FRACTIONS 31 DECIMALS 32 PERCENTAGE 34 MONEY 35 MEASUREMENT AND GEOMETRY TIME 37 13 LENGTH 39 14 MASS 41 15 VOLUME OF LIQUID 42 SPACE 43 RELATIONSHIP AND ALGEBRA COORDINATE 44 RATIO AND PROPORTION 45 STATISTIC AND PROBABILITY DATA HANDLING 46

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RUKUN NEGARA

BAHAWASANYA negara kita Malaysia mendukung cita-

cita untuk mencapai perpaduan yang lebih erat

dalam kalangan seluruh masyarakatnya; memelihara

satu cara hidup demokratik; mencipta masyarakat

yang adil bagi kemakmuran negara yang akan

dapat dinikmati bersama secara adil dan saksama;

menjamin satu cara yang liberal terhadap tradisi-

tradisi kebudayaannya yang kaya dan berbagai-

bagai corak; membina satu masyarakat progresif

yang akan menggunakan sains dan teknologi

moden;

MAKA KAMI, rakyat Malaysia, berikrar akan

menumpukan seluruh tenaga dan usaha kami untuk

mencapai cita-cita tersebut berdasarkan atas prinsip-

prinsip yang berikut:

• KEPERCAYAAN KEPADA TUHAN

• KESETIAAN KEPADA RAJA DAN NEGARA

• KELUHURAN PERLEMBAGAAN

• KEDAULATAN UNDANG-UNDANG

• KESOPANAN DAN KESUSILAAN

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RUKUNEGARA DECLARATION

OUR NATION, MALAYSIA, being dedicated

to achieving a greater unity of all her peoples;

to maintaining a democratic way of life;

to creating a just society in which the wealth of the nation shall be equitably shared;

to ensuring a liberal approach to her rich and diverse cultural traditions;

to building a progressive society which shall be orientated to modern science and technology;

WE, her peoples, pledge our united efforts to attain these ends guided by these principles:

Belief in God

Loyalty to King and Country

Upholding the Constitution

Rule of Law

Good Behaviour and Morality

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Pendidikan di Malaysia adalah suatu usaha

berterusan ke arah memperkembangkan lagi

potensi individu secara menyeluruh dan

bersepadu untuk mewujudkan insan yang

seimbang dan harmonis dari segi intelek,

rohani, emosi dan jasmani berdasarkan

kepercayaan dan kepatuhan kepada Tuhan.

Usaha ini adalah bagi melahirkan rakyat

Malaysia yang berilmu pengetahuan,

berketerampilan, berakhlak mulia,

bertanggungjawab dan berkeupayaan

mencapai kesejahteraan diri serta

memberikan sumbangan terhadap

keharmonian dan kemakmuran keluarga,

masyarakat dan negara.

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INTRODUCTION “Sekolah Unggul Penjana Generasi Terbilang” (“Ideal Schools Generating an Illustrious Generation”) is the vision of the Malaysian Ministry of Education. The education purpose in Malaysia is to develop individual potential through quality education by preparing committed citizens and a generation that has the ability to think. Ministry Of Education continuously reviews the curriculum to ensure that the implementation of the curriculum in schools equips pupils with knowledge, skills and values to face current and future challenges.

Mathematics is a discipline that trains the mind to think logically and systematically in problem solving and decision making. Inherently, mathematical nature promotes meaningful learning and challenge the mind. Due to this, mathematics is one of the most important disciplines in any endeavor for human development. Based on the National Philosophy of Education and to ensure the relevancy of the curriculum, the Primary School Standard Curriculum for Mathematics is adapted and restructured. This restructuring takes into account the ongoing continuity to the next level. Measures taken are consistent with the need to provide the knowledge and mathematical skills to pupils from various backgrounds and abilities. With the knowledge and skills, they are able to explore the knowledge, make adaptations, modifications and innovations in managing changes and dealing with future challenges.

THE RATIONALE OF MATHEMATICS EDUCATION Mathematics is the best platform to develop individual intellectual proficiency in making logical reasoning, space visualization, abstract thinking skills and analyzing. Pupils develop numeracy skills, reasoning, thinking and problem solving ways of thinking through learning and application of mathematics. Mathematics provides opportunities for students to perform creative tasks and experience the fun and excitement of learning something new. Such experiences increase interest and are the driving forces for students to learn mathematics outside the classroom and at the higher level of education.

AIMS

The Aim of the Primary School Standard Curriculum for Mathematics is to develop pupils’ understanding on the concept of numbers, basic calculation skills, understanding simple mathematical ideas and are competent in applying mathematical knowledge and skills effectively and responsibly in everyday life.

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FOCUS

NATIONAL CURRICULUM’S FRAMEWORK

STRUCTURE OF PRIMARY SCHOOL MATHEMATICS EDUCATION

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Mathematical teaching and learning process gives priority to mastering knowledge and understanding to enable pupils to apply concepts, principles and the mathematical processes they have learned. Emphasis on the development of mathematical thinking is built and developed through the teaching and learning in the classroom based on the following principles, which are, problem solving, communication, reasoning, making connections, making representations and the application of technology in mathematics.

The Standard curriculum is based on six pillars, namely Communication; Spiritual, Attitudes and Values; Humanity; Physical Development and Aesthetic; Personal Experience; and Science and Technology. The six pillars are the main domain that supports each other and are integrated with critical thinking, creative and innovative thinking. This integration aims to develop balanced, knowledgeable and competent human capital as shown in the adjacent figure.

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PRIMARY SCHOOL MATHEMATICS EDUCATION STRUCTURE

LEVEL AIMS

I Primary School Mathematics Curriculum Level I aims to build understanding, mathematics and basic application skills.

II

Primary Mathematics Curriculum Level II aims to build understanding, mathematical skills and more complex application skills that can be used in effectively overcoming the challenges in the pupils’ daily life.

OBJECTIVES

The primary school mathematics curriculum will enable pupils to:

Understand and apply the concepts and mathematical skills in various contexts.

Expand the use of basic operations of addition, subtraction, multiplication and division basic skills related to Numbers and Operations, Measurement and Geometry, Relationship and Algebra, and Statistic and Probability.

Identify and use the relationship in mathematical ideas, between mathematical fields with other fields and with daily life.

Communicate using mathematical ideas clearly and use correct symbols and terminologies.

Use mathematical knowledge and skills to be applied and adapted to various strategies to solve problems.

Think, reason, and explore mathematically in daily life.

Use various representations to deliver mathematical ideas and associations.

Appreciate and internalise the beauty of mathematics.

Use various mathematical instruments effectively including ICT to build conceptual understanding and apply mathematical knowledge.

MATHEMATICS CURRICULUM FRAMEWORK The Mathematics curriculum framework shows a mathematical programme that could be utilized at the primary level. Mathematical Learning is planned with the aim of moulding pupils’ mathematical thoughtful learning. MATHEMATICAL THOUGHTFUL LEARNING The definition of “fikrah” (thoughtful learning) according to the fourth edition of the Kamus Dewan (2005) has the same meaning with thinking and reasoning. In the context of mathematics education, thoughtful learning refers to the desired quality of pupils to be delivered through the national mathematics education system. Pupils who are mathematically inclined are those capable of doing mathematics and understanding mathematical ideas, and responsibly applying the mathematical knowledge and skills in their daily lives based on attitudes and values of mathematics.

Each pupil in Malaysia has the opportunity to go through at least six years of basic education in schools. This includes three years of Level I studies and three years of Level II studies. Subsequently, pupils can pursue education at a higher level of education.

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MATHEMATICS CURRICULUM DESIGN

CONTENT ORGANISATION The Mathematics Curriculum encompasses four learning areas:

Numbers and Operations

Measurement and Geometry

Relationship and Algebra

Statistics and Probability The contents of the KSSR Mathematics are as follows:

NUMBERS AND OPERATIONS MEASUREMENT AND GEOMETRY

Whole Numbers

Addition

Subtraction

Multiplication

Division

Mixed Operations

Fractions

Decimals

Percentage

Money

Time

Length

Mass

Volume of Liquid

Three Dimensional Shapes

Two Dimensional Shapes

RELATIONSHIP AND ALGEBRA STATISTICS AND PROBABILITY

Coordinates

Ratio and Proportion Data Handling

Likelihood

Perception, interest, appreciation, confidently resilient and perseverance.

Personality, interaction, procedure, intrinsic.

Numbers and Operations

Measurement and Geometry

Relationship and Algebra

Statistics and Probability

Communicating

Reasoning

Relating

Problem Solving

Representing

Mathematical skills

Analytical skills

Problems solving skills

Research skills

Communication skills

Information Communication Technology skills

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Pupils should develop and explore mathematical ideas in depth through various learning opportunities and experiences. Awareness should be fostered and developed among pupils that mathematical ideas are intertwined, and mathematics is comprehensive; not isolated bits of knowledge. With such awareness and understanding, comprehending of mathematical ideas become more meaningful, and thus can enhance the capability of pupils to apply mathematics. Opportunities and a variety of learning experiences provided should actively engage the pupils in learning mathematics, help them to form a deep understanding of mathematical concepts, and establish a more meaningful understanding of various mathematical ideas. Based on the understanding and comprehension developed, pupils are able to relate and apply mathematical ideas, and subsequently, make pupils more confident in exploring and applying mathematics. The use of teaching aids, technological equipment and the implementation of assignments / practical / project work should be encompassed in the learning experiences provided for pupils. SKILLS Skills in mathematics that should be developed and instilled in pupils including numeracy, measuring and constructing, data handling and interpretation, arithmetic manipulation, algebra manipulation, using alogarithm, and using mathematical instruments and ICT. Mathematics Skills Mathematical skills refer to the following abilities:

• Using correct standard mathematical language and applying

logical reasoning.

• Stating mathematical ideas concisely.

• Creating, testing, and proving conjecture.

• Extracting meaning from a mathematical writing.

• Using mathematics to explain physical world.

Analysing Skills Analysing skills refer to the following abilities:

• Thinking clearly.

• Giving attention and concentrating to each aspect.

• Manipulating precise, concise and detail ideas.

• Understanding complex reasoning.

• Constructing and persevering logical arguments.

• Debating illogical arguments.

Problem Solving Skills Problem solving skills refer to following abilities:

• Construct problems precisely and identify the main issues.

• Present solutions clearly and explicate assumptions.

• Solving difficult problems by analysing simple and specific

problems.

• Open-minded and using different approaches in solving the same

problem.

• Solving problems confidently even though the solutions are not

envisioned

• Asking for assistance if required.

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Research Skills Research skills refer to the following abilities:

• Refering to notes, textbooks and other sources.

• Accessing books in the library.

• Using database.

• Gaining information from various individuals.

• Thinking.

Communication Skills

Communication skills referring to the following abilities:

• Listening effectively.

• Writing mathematical ideas clearly and precisely.

• Writing essays and reports.

• Doing presentations.

Information Communication Technology Skills

Information communication technology skills refer to the ability in

using and handling mathematical instruments such as abacus,

calculators, computers, educational software, websites on the internet

and educational packages for:

• Developing and understanding mathematical concepts in-depth.

• Doing, testing and proving conjecture.

• Exploring mathematical ideas.

• Solving problems.

PROCESS

Communicating

Communication about mathematical ideas can help pupils clarify and strengthen the understanding of mathematics. By sharing the understanding of mathematics in writing and orally with classmates, teachers and parents, pupils will be able to increase their confidence and facilitate their teachers in monitoring the progress of their mathematics skills. Communication plays a vital role in ensuring the meaningful learning of mathematics. Through communication, mathematical ideas can be expressed and understood better. Mathematical communication, whether oral, written, in symbols and visual representations (using charts, graphs, diagrams etc), can help pupils understand and apply mathematics more effectively. Communication among themselves or with peers, parents, adults and teachers can help pupils to reflect, clarify and strengthen their ideas and understanding on mathematics. To ensure the process of generating, sharing and increasing understanding, pupils should be given the opportunity to debate their mathematical ideas analytically and systematically. Communication involves a variety of perspectives and these points of view can help pupils to increase their understanding of mathematics. An important aspect of effective communication in mathematics is the ability to provide information effectively, understand and apply the correct mathematical notation. Pupils need to use mathematical language and symbols correctly to ensure that mathematical ideas can be explained accurately. Mathematical communication also involves the use of the various media like charts, graphs

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manipulatives, calculators, computers and others. Pupils should be able to use the various different media to explain mathematical ideas and solve mathematical problems. Effective communication requires a sensitive environment towards the pupils’ needs to feel comfortable in a conversation, ask questions, answer questions and explain the statements to classmates and teachers. Pupils should be given the opportunity to communicate actively in various situations, for example communicating during activities in pairs, groups or providing explanations to the entire class. Assessment of the ability of pupils to communicate in mathematics effectively should show evidence that they are able to generate, explain and share their mathematical ideas through various forms of communication in various environments. Pupils, who are always given opportunities and encouragement to speak, read, write and listen during the teaching and learning of mathematics will be able to communicate to learn mathematics and learn to communicate mathematically. Reasoning Reasoning is fundamental in understanding mathematics more effectively and making the delineation of mathematics more meaningful. The development of mathematical reasoning is closely related to intellectual development and communication of the pupils. Reasoning has the ability to expand not only the capacity of logical thinking but also increase the capacity of critical thinking, which is also the basis for a deeper and meaningful and in-depth understanding of mathematics. To achieve this objective, pupils should be trained and guided to make a conjecture, prove the conjecture, give a logical explanation, analyse, consider, evaluate,

and justify all mathematic activities. In addition, teachers need to provide space and opportunities for the discussion of mathematics which is not only engaging but also allows each pupil to be involved well. Reasoning can be done inductively through mathematical activities that involve the identification of mathematical patterns and making conclusions based on the patterns. Reasoning element in teaching and learning prevents pupils from assuming mathematics as only one set of procedures or algorithms that need to be followed to obtain a solution, without actually understanding the true concepts of mathematics. Reasoning does not only change the paradigm of pupils from just learning to thinking, but also gives an intellectual empowerment when pupils are guided and trained to make a conjecture, prove the conjecture, provide a logical explanation, analyse, evaluate and justifiy all mathematic activities. This training will produce pupils who are self-confident and resilient in line with the aspiration to mould mathematics thinkers with high capabilities.

Relating

In implementing the mathematics curriculum, the opportunities for making connections need to be established so that pupils can link conceptual and procedural knowledge and also able to relate topics in mathematics particularly and mathematics in other areas in general. This will enhance the pupils’ understanding of mathematics and makes mathematics clearer, more meaningful and interesting to them.

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Mathematics curriculum generally consists of several discrete areas such as calculation, geometry, algebra, measurement and problem solving. Without relating these areas, pupils will have to learn and remember too many concepts and skills separately. Instead, recognizing how the concepts or skills in different fields relate to each other, mathematics will be seen and studied as a disciplined and comprehensive knowledge and can be easily understood. When these mathematical ideas are related with everyday experience inside and outside the school, pupils will be more aware of the use, importance, strength and beauty of mathematics. In addition, pupils have the opportunity to use mathematics contextually in other fields and in their daily lives. Mathematical models are used to describe real life situations mathematically. Pupils will find this method can be used to find solutions to problems or to predict the likelihood of a situation based on the mathematical model.

Problem Solving Problem solving is the main focus in the teaching and learning of mathematics. Thus, teaching and learning need to involve problem solving skills comprehensively and across the whole curriculum. The development of problem solving skills needs to be given due emphasis so that pupils are able to solve various problems effectively. These skills involve the following steps:

Understanding and interpreting problems;

Planning the strategy;

Carrying out the strategy; and

Checking the solutions.

The various uses of general strategies in problem solving including steps in solving need to be expanded more in the use of this subject. In carrying out learning activities to build problem solving skills, problems based on human activities should be introdued. Through these activities, pupils can use mathematics when facing new situations and reinforce themselves in dealing with various challenges every day. Some of the problems solving strategies that can be considered are: 1. Try an easier problem;

2. Try and error;

3. Draw a diagram;

4. Identifying patterns

5. Create a table, chart or a systematic list;

6. Simulation;

7. Using analogy;

8. Work backwards;

9. Logically reasoning; and

10. Using algebra

Representing

Mathematics is often used to represent the world that we live in. Therefore, there must be similarities between aspects of the represented world and aspects that are represented by the world. The abstract relationship between these two worlds can be depicted as follows:

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Representation can be regarded as a facilitator that allows the relationship between the real world and the world of mathematics. Formula, table, graph, equation etc. are mathematical objects used to represent various conglomerates and real world relationships. Representation can be defined as any configuration of letters, images or concrete objects that can reflect or represent other delegates. The representation system is naturally divided into internal and external. The internal representation of the system exists in the mind of individual, whereas the external representation is easily shared and viewed by others. Internal representation consists of ideas that help in describing the human process of learning and solving problems in mathematics, and external representation consists of items such as diagrams, the formal language, and notational symbols. Using multiple representations in order to show a concept helps to develop better understanding and also to strengthen one's ability in solving problems.

Representation is necessary for pupils’ understanding in mathematical conceptual relationship. It allows pupils to communicate approaches, debates and understanding of mathematics to themselves and others. It also allows pupils to recognize the relationships between related concepts and apply mathematics to realistic problems. Representation is an important component in the development of mathematical understanding and quantitative thinking. As a whole, without representation, mathematics is an abstract, mostly philosophic, and unapproachable by most of the population. With the representation, ideas can be formed into a mathematical model, important relationship can be elaborated, understanding can be stimulated through a construction and sequencing of suitable experiences and observations.

ATTITUDES AND VALUES

The aim of the nurturing of values and attitudes in Mathematics curriculum is to produce competent individuals with virtuous moral standards. In addition, the appreciation of attitudes and values can shape a well mannered and noble younger generation. Understanding and awareness of the attitudes and values in the Malaysian society should be directly or indirectly fostered in line with universal values. Values and attitudes are instilled through learning experiences provided by teachers. It involves an element of trust, interest, appreciation, confidence, efficiency and endurance. Instilling of values and attitudes also include personal aspects, interaction, procedural and intrinsic.

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In mathematics, attitudes and values need to be mould through appropriate context. Attitudes in mathematics refer to the affective aspects of mathematical learning that covers, among others: • positive response towards mathematics and the usefulness

of mathematics • Interest and joy in learning mathematics. • Appreciation of the beauty and mathematical ability. • Confidence in using and applying mathematics. • Steadfast and perseverance in solving problems related to

mathematics. Personal values refer to the values that are related with the formation of individual traits and personality such as honesty, systematic, perserverence, hardworking and steadfast, creative, confidence, conscientious, good time managers, independent, trustworthy, efficient, responsible, patience and dedication. Interaction values are related with the instillation of good behavior in the classroom context. The value refers to theemphasized values in the interaction during mathematical activities such as appreciation for mathematics, teamwork, discussion and sharing of ideas, tolerance, fair, open minded, and respect. Procedural values associated with specific activities in mathematics such as reasoning, making representations, solving problems, communication, making connection, and using technology. Intrinsic values associated with the formation of mathematical content and its discipline such as the epistemology, cultural and historical values.

CONTENT STANDARD AND LEARNING STANDARD

Primary School Mathematics Standard Curriculum is formulated with emphasis on Content Standards and Learning Standards should be known and can be done by pupils. This standard is presented in modular form divided into topics based on areas of learning. Content Standard

General statements of the cognitive domain (knowledge) and affective (attitudes and values) can be achieved by pupils through a subtopic. Learning Standard

Specific statement of what pupils should know and do in terms of knowledge or concepts and the ability in order to show their proficiency in measureable knowledge acquisition, skills and values. Learning Standard does not show the steps of teaching and learning. It gives teachers space and opportunity to prepare a condusive learning environment creatively. Thus, pupils are able to form concepts and develop skills, attitudes and values in mathematics.

STRATEGIES IN TEACHING AND LEARNING Mathematical thoughtful learning is transferred into teaching and learning practices. Teaching and learning is guided by the principle of mastery learning and the learning occurs in access and self-directed and in accordance with its own pace.

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Teaching and learning strategies should be pupil-centred to enable them to interact and master the learning skills through their own experience. Pupils-centered inquiry or discovery approach with the aid of appropriate technology is comprehensively and effectively used to make the experience of learning mathematics fun, meaningful, useful and challenging. Teaching and learning of primary school mathematics encourage the use of diverse methods. Teachers can choose appropriate teaching and learning approach and methods depending on pupils’ abilities. The effectiveness of teaching and learning depends on the processing techniques and the use of teaching aids and technology that can stimulate and encourage pupils to think critically and creatively, innovative, communicate, and interact. The inculcation of attitudes and values should be considered when planning the teaching and learning of a distinctive skill. Moral values could be instilled appropriately according to the well planned lesson. Elements of history, patriotism, environmental and science can be applied accordingly to the appropriate topics to allow pupils to appreciate mathematics and encourage their interest on a particular topic. Elements of this history can be a specific event about a mathematician or a brief history of a concept or symbol. Problem solving is an important aspect that must be embedded in teaching and learning of mathematics to enhance pupils’ analytical thinking and creative. Solutions presented for problems should be appropriate with the pupils’ level. In addition, pupils are also encouraged to communicate and courageously make decisions.

HIGHER ORDER THINKING SKILLS (HOTS) The National Curriculum aims to produce pupils who are well balance, resilient, curious, principled, informed and patriotism with thinking skills, communication skills and teamwork. 21st century skills in line with the six aspirations required by each pupils to be able to compete at a global level outlined in the National Education Blueprint that every pupils will have leadership skills, bilingual proficiency, ethics and spiritual, social identity, knowledge and thinking skills. Thinking skills were emphasized in the curriculum since 1994 to introduce Critical and Creative Thinking Skills (CCTS). This thinking skills focuses from lower level to higher level of thinking. Beginning in 2011 the Standard Curriculum for Primary School (KSSR) has emphasis on Higher Order Thinking Skills (HOTS). Higher Order Thinking Skills (HOTS) is the ability to apply knowledge, skills and value in creating reasoning and reflection to solve problems, make decisions, innovate and create something. HOTS is referring to applying skills, analyze, evaluate and create as the following table.

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HOTS Description

Application Using knowledge, skills and values in different situations to complete a piece of work.

Analysis Ability to break down information into smaller parts in order to understand and make connections between these parts.

Evaluation Ability to consider, make decisions using knowledge, experience, skills, and values and justify decisions made.

Creation Produce an idea or product using creative and innovative methods.

Proficiency is written explicitly in the curriculum of each subject. HOTS can be applied in the classroom through activities in the form of reasoning, inquiry learning, problem solving and projects. Teachers and pupils have to use their thinking tools such as thinking maps, mind maps and Thingking Hats and high level of questioning inside and outside of the classroom to encourage pupils to think. Higher order questions promote learning because it requires pupils to apply, analyze, synthesize and evaluate information not merely memorizing facts. There are two kinds of questions in mathematics that is the routine and the non-routine questions. Routine questions are problems that can be solve with methods that are commonly used by pupils by replicating the steps that are learned

before. Routine problem solving emphasize the use of a set of prosedures known or determine to solve the problem. The non-routine problem requires analysis and mathematical reasoning; many non-routine problem can be solve by more than one solution. The balance of mathematical problem solving should be implemented for both type of questions to ensure that every pupils can complete well and effectively. Routine and non-routine problems can be explained as follows:

ROUTINE QUESTION NON-ROUTINE QUESTION

• Does not require

students to use

higher order

thinking skills.

• Operation that should be used is clear

• Requires higher order thinking skills • Improves reasoning skills • Responses and procedures to be used are

not immediately obvious • Encourages more than one solution and

strategy • There is more than one answer • More challenges • Capable of producing pupils who are

creative and innovative • Solution requires more than just making

decisions and choosing mathematical operations

• Need more time to resolve • Encourage group discussion in finding

solution

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21st CENTURY SKILLS;

A student must be equipped with skills, knowledge and values that need to be mastered to survive in life and career of the 21st century.

The Ministry of Education Malaysia (MOE) has identified the skills and values that each student needs to have to face the 21st century. Skills and values are split into 3 aspects: Thinking skills: Prepares pupils to face life that is becoming more challenging as well as the current working environment. The skills are:

Creativity

Critical thinking

Reasoning

Innovative

Problem solving

Making decisions

Career and Life Skills: Needs more than thinking skills and knowledge. Students develop life and career skills to face life that is complex and working environment in a world that is becoming more challenging. These are:

Communication Skills

Information and Communication Technology

Cooperation

Entrepreneurship

Leadership

Lifelong learning

Flexibility

Ability to Adapt

Initiative and Self-direction

Values: Is the guideline for students to become individuals that have noble characters and are capable of making decisions and actions like carrying out responsibilities to family, society and country encompass:

Spirituality

Humanity

Patriotism

Integrity

Responsibility

Oneness

STUDENT PROFILE The critical factor that contributes to social growth, culture and economy of a country is the development of model individuals that are innovative and highly skilled. With that, each student that is produced must be balanced physically, emotionally, spiritually and intellectually as is stated in the National Education Philosophy. MOE has outlined 10 Student Profiles that each student needs to have to compete at a global stage. Student Profiles are characteristics that each student has: Balanced: They are balanced physically, emotionally, spiritually and intellectually to achieve personal satisfaction, as well as show empathy, compassion, and respect for others. Able to contribute towards the harmony of family, community and country. Thinker: They think critically, creatively and innovatively; able to handle complex problems and make ethical decisions. They think about learning and themselves as students. They come up with questions and are open to perspective, values and individual

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traditions and societal traditions. They are confident and creative in handling new learning fields. Resistant: They are able to face and overcome difficulties, challenges with wisdom, confidence, tolerance and empathy. Communicator: They confidently voice and express their thoughts, ideas and information. The though and idea are conveyed verbally, in written form or using various media and technology in a creative manner. Teamwork: They can work together effectively and harmoniously with others. They take on responsibility while respecting and appreciating the contributions given by all team members. They obtain interpersonal skills through collaborative activities, and make them better leaders and team mates. Curious: They develop natural curiosity to explore strategies and new ideas. They learn skills that are needed to carry out inquiry and research, as well as behave independently in learning. They enjoy continuous lifelong learning experiences. Principled: They are honest and have integrity, equality, fair and respect individual, group and community dignity. They are responsible for their actions, consequences and decisions. Informative: They gain knowledge and form wide and balanced understanding across various knowledge disciplines. They explore knowledge effectively and efficiently in the context of local and global issues. They understand ethical issues/laws related to the information that was gained. Caring: They show empathy, compassion and respect towards needs and feelings of others.

Attentive: They are committed to the country and ensure the sustainability of nature. Patriotism: They portray love, support and respect towards the country.

ELEMENTS OF ADDED VALUES CREATIVITY AND INNOVATION There are many definitions of creativity. According to the Kamus Dewan, 1997 creativity means the capability or the ability to create. Whereas according to PPK, 1999 creativity means the ability to digest and produce new and original ideas. The idea is developed through inspiration or combination of existing ideas. Creativity should be embedded effectively in teaching and learning in which teachers need to be creative and innovative in their role as triggers of ideas and produce pupils who are knowledgeable, able to master and practice the good attitudes and values as well as to expand pupils’ creativity and innovation. This is important as creativity and innovations need to be developed among pupils at an early stage of schooling. This is to enable them to know their potential and personal preferences as well as trigger the hidden potential in themselves. Creative and innovative teaching and learning can be applied through problem solving, logical reasoning, communication, making connections and the use of technology, where pupils:

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Build a mathematical model through the patterns and relationships.

Apply mathematical skills in estimation, measurement and visualization of data in everyday situations.

Make interconnections between mathematics skills with other disciplines of knowledge.

Apply mathematical knowledge to find solutions to routine and non-routine problems.

Make a conjecture (extrapolation, projections, cause and effect). The process of building creatively and innovatively can be initiated from the preparation phase, imagination, development and action in planning a preparation of teaching and learning in the classroom. Through this process, pupil-centered teaching and learning is formed to instigate the creative skills among pupils.

ENTREPRENEURSHIP IN MATHEMATICS An effort to build the entrepreneurship characteristic and practice until it becomes a culture among pupils. The entrepreneurship characteristic and practice can be formed by:

Practicing the entrepreneur’s attitude

Applying the entrepreneur’s thinking

Applying the knowledge and skills of business management

Formulating either entrepreneurship concept, process or product

Practice moral values and good ethics in entrepreneurship

Therefore, this element can be applied in the appropriate learning areas of mathematics such as in numbers and operations, measurement and geometry, statistic and probability in primary schools. INFORMATION COMMUNICATION AND TECHNOLOGY (ICT) Explosion of progress in various technologies now and in future make this element important in classroom teaching and learning. Exposure of ICT application in Mathematics teaching and learning can be applied successfully in:

Learning about ICT

Pupils are taught about ICT knowledge and skills in handling

hardware and software.

Learning through ICT

Use ICT to access information and knowledge through media

such as CD-Rom, DVD-Rom, Internet and etc.

Learning with ICT

Teachers and pupils use ICT as their teaching and learning aids

ICT teaching and learning

This can be as an access to make learning more interesting and

fun. Pupils can be exposed to various kinds of latest

communication information and the effective use will produce a

quality teaching and learning.

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ASSESSMENT Assessment is an integral part of the teaching and learning process. It has to be well-planned and carried out continuously as part of classroom activities. By focusing on a broad range of mathematical activities, the strengths and weaknesses of pupils can be assessed. Different methods of assessment can be conducted using various assessment techniques including oral and written work as well as demonstrations. These may be carried out in the form of interviews, open-ended questions, observations and research. Based on the results, teachers can rectify the pupils’ misconception and weaknesses and at the same time improve their teaching skills. As such, teachers can take subsequent effective measures in conducting remedial and enrichment activities to upgrade pupils’ performance.

SCHOOL BASED ASSESSMENT School Based Assessment (SBA) is a major component of the learning process (T&L) that it served to enhance student learning,improve teaching and be able to give valid information about what has been done or archieved in aprocess of (T&L) .SBA carried out by the teacher and the school completely starting from the planning, construction items and instruments. SBA carried out by the teacher and the school completely starting from the planning, construction items and assessment instruments,administration,inspection or scoring,recording and reporting. SBA is important to determine the effectiveness of teachers and schools in an effort to produce a balanced and harmonious human.SBA is an ongoing activity that charge high commitment and clear direction from the teacher and the school for each student to develop potential to its maximum. SBA has the following characteristic:-

Holistic which can provide overall information on he achievement of knowledge,skills and practice of virtue.

Namely continuous assessment activities go hand in hand with (T&L) process.

Flexible assessment methods varied according to suitability and readiness of pupils.

Referring to the performance standards developed by standard curriculum.

17

SBA can be carried out:-

Formative assessment carried out in line with (T&L)process.

Sumative assessment conducted at the end of the laerning unit,semester or year.

STANDARD ASSESSMENT REFERENCE Standard Assessment Reference was introduced, namely the Standard Performance to see the progress and growth of learning and pupil’s achievement. It is the process of obtaning information about the extent of student’s knowing,understanding and can do or mastered what is learned based on the performance standards established in accordance with the stages in achievement in standard based curriculum and assessment document. Standard Assessment Reference does not compare the performance of a student by another student but reports student’s performance in learning and to highlight the progress and growth of students in learning refers to the standard statement. Students are assessed fairly and equitably as individuals in society based on ability, capability, talent, skills and potential without comparison to others.The school was able to obtain a complete response in the form of qualitative and quantitative data that covers all aspects of a person’s pupils to enable those responsible to identify, understand,appreciate, recognize and honour the students as individuals who are useful,important and has the potential to contribute to national development and nation according to their respective capabilities and abilities.

PERFORMANCE STANDARDS Performance standard is a statement of the level of development of pupil’s learning as measured based on the standard and indicates the position of the pupil in the development or progression of learning. Developments in the standard is divided into two, that is, horizontal development (construct) and vertical development (performance level). The performance of pupil is indicated by one or more qualifiers using the words or phrases that correctly describe the standards in the form of the learning outcomes. PERFORMANCE STANDARD FRAMEWORK

PERFORMANCE

LEVEL DESCRIPTOR

1 Know

2 Know and understand

3 Know,understand and able to do.

4 Know,understand and able to do with good manner.

5 Know,understand and able to do with admirable manner.

6 Know,understand and able to do with exemplery manner.

Performance level is a label used to indicate benchmarks which are arranged in a hierarchy used for individual report purposes. Standard is a statement about a domain which refers to specific benchmarks and is generic in nature to provide a holistic picture of the individual .

18

THE GENERAL DESCRIPTOR OF PERFORMANCE LEVEL

Performance

Level DESCRIPTOR

1 Pupils know the basics or can perform basic skills or to respond to the basic subject matter.

2

Pupils demonstrate an understanding of the changing forms of communication or translate and explain what they have learned.

3

Pupils use knowledge to perform a skill in a particular situation.

4

Pupils carry out a civilized skills with procedure or systematically.

5

Pupils perform a skill in a new situation following the procedure systematically and consistently with a positive attitude.

6

Pupils are able to use existing knowledge and skills to use in a new situation in a systematic, positive,creative and innovative and exemplary.

INTERPRETATION OF PERFORMANCE FOR MATHEMATICS There are 3 groups should be evaluated to determine the level of students as follows :- 1. Knowledge 2. Skills and Process 3. Attitudes and values in mathematics.

1. KNOWLEDGE (Overall interpretation of performance level of mathematics)

Performance

Level Interpretation

1 Know basic knowledge of mathematics.

2 Know and understand basic knowledge of mathematics.

3 Know and understand basic mathematical knowledge to perform basic mathematical operations and conversions.

4 Know and understand the mathematical knowledge and perform the calculation steps in daily routine problems.

5 Master and apply knowledge&skills of mathematics in solving daily routine problems using various strategies.

6 Master and apply knowledge&skills of mathematics in solving daily non- routine problems creatively and innovatively.

19

Note: There are 12 titles in year six. Each title has designed its own level of interpretation.The instructions below designed as example guide for each title of group knowledge. INDICATOR:

2. MATHEMATICAL SKILLS AND PROCESS

a. Problem Solving

Performance

Level DESCRIPTOR

1 Able to state the steps of problem solving without performing the process.

2 Able to solve routine problems with guidance.

3 Able to solve rotine problems involving one step calculation without guidance.

4 Able to solve complex routine problems.

5 Able to solve complex routine problems using various strategies.

6 Able to solve non routine problems creatively and innovatively

Content Standard

Learning Standard

Pupil’s Performance level (1 to 6)

Performance Standard

Learning Year

Topic

Learning Area

Performance level intrepretation

20

b. Reasoning

Performance

Level DESCRIPTOR

1 Able to give justification for mathematics activity logically and with guidance.

2 Able to give justification for mathematics activity logically without guidance.

3 Able to show the correct justification for mathematics activity involving one calculation.

4 Able to show the correct justification for mathematics activity involving more than one calculation.

5 Able to show the correct justification for mathematics activity involving routine problem solving.

6 Able to explain the correct justification for mathematics activity involving non routine problem solving creatively and innovatively.

c. Relationship

Performance

Level DESCRIPTOR

1 Able to relate skills learnt in other topics and daily life with guidance.

2 Able to relate skills learnt in other topics and daily life without guidance.

3 Able to relate concept and procedure to solve mathematical sentence.

4 Able to relate concept and procedure to solve daily routine problems.

5 Able to relate concept and procedure to solve daily routine problems using various strategies.

6 Able to relate concept and procedure to solve daily non routine problems creatively and innovatively.

21

d. Representation

Performance

Level DESCRIPTOR

1 Able to use representation with guidance.

2 Able to use representation to show mathematical understanding without guidance.

3 Able to explain mathematical concept and prosedures using representation.

4 Use representation to solve daily routine problems.

5 Use various representation to solve daily routine problems in various strategy.

6 Use representation to solve daily non routine problems creatively and innovatively.

e. Communication

Performance

Level DESCRIPTOR

1

Able to state mathematical idea verbally or in written using mathematical symbol or visual representation.

2 Able to explain mathematical idea verbally or in written using mathematical symbol or visual representation.

3 Able to use correct mathematical language, symbol or visual representation.

4 Able to explain mathematical idea systematically using correct mathematical language, symbol or visual representation.

5 Able to explain mathematical idea systematically using correct mathematical language, symbol or visual representation to solve routine problems.

6

Able to explain mathematical idea systematically using correct mathematical language, symbol or visual representation to solve non routine problems creatively and innovatively.

22

f. Thinking Skills Performance Level

DESCRIPTOR

1 Able to state mathematical knowledge and skills.

2 Able to explain mathematical knowledge and skills.

3 Able to use mathematical knowledge and skills in different situations to carry out a task.

4 Able to break down the information into small portion for better understanding about the relationship between the division.

5 Able to make judgements and decisions using the knowledge, experience, skills and give justification.

6 Able to produce a product or idea or creative and innovative methods.

g. Soft skills

Performance

Level DESCRIPTOR

1 Show interest and want to learn

2 Try to understand a problem

3 Can communicate and interested in learning

4 Can work in team to solve problems.

5 Able to lead and guide the peer.

6 Could become mentor and role-model to their peer

Note: Soft skills include aspects of generic skills that involve the psychomotor and effective elements related to non-academic skills such as positive values, leadership, teamwork, communication, continuous learning ability to work (employability) and preparation for the working world.

23

h. Skills in using technologies

Performance

Level DESCRIPTOR

1 Know and can state mathematical tools.

2 Ability to use and handle basic mathematical tools.

3 Ability to use and handle basic mathematical tools, establish and understand mathematical concepts and explore mathematical ideas.

4 Able to use mathematical tools to solve daily routine problems.

5 Able to use mathematical tools to solve routine problems using variety of strategies.

6 Able to use mathematical tools to solve non-routine problems creatively and innovatively.

3. Attitude and Value in Mathematics Attitude and Values

Performance

Level DESCRIPTOR

1 Pupils able to state one of the items of attitude and values in Mathematics with teacher’s guidance.

2 Pupils able to explain one of the items of attitude and values in Mathematics by giving reasonable example.

3 Pupils able to show attitude and values in Mathematics for a given situation with teacher’s guidance.

4 Pupils able to demonstrate attitude and values related to mathematics in various situation.

5 Pupils always practice attitude and values related to mathematics in teaching and learning process.

6 Pupils always practice attitude and values related to mathematics in daily life and become adviser and example to other peers.

Every mathematic teacher should implement a (T&L) process with reference to the content standard and standard learning content. Teachers’ wisdom is needed to determine (T&L) process implemented effectively and appropriately. In a similar situation, teachers should access students’ ability to determine the level and ability by a list of performance standards which have been prepared in accordance with topics of learning. Teachers should provide opportunities for every pupil to be able to achieve a better ability to carry out the guidance and strengthening process.

25

Year 4

CONTENT STANDARD

LEARNING STANDARD PERFORMANCE STANDARD

LEVEL DESCRIPTOR

1.1 Value of numbers.

1.2 Estimation of quantity.

1.3 Numbers in

pattern.

1.4 Application of numbers.

(i) Read, say and write any given numbers up to 100 000 in words and numerals.

(ii) Name the place value and digit value for any number.

(iii) Write any number in expanded notation according to place value and digit value.

(iv) Determine the value of numbers up to 100 000 by arranging numbers according to ascending and descending order.

(i) Estimate number of objects by stating the reasonable quantity based on a given set of references.

(i) Classify the pattern of a given

number sequence. (ii) Complete the given number pattern.

(i) Round off any numbers up to the nearest ten thousands.

(ii) Identify numbers that can represent a given number rounded off up to the nearest ten thousands.

1 State any numbers up to100 000.

2 Determine the place value and digit value of any numbers up to 100 000.

3 Estimate and round off any numbers to the nearest tens, hundreds, thousands and ten thousands.

4 Classify and complete the number pattern.

5 Solve routine problems for any number by using various strategies.

6 Solve daily non-routine problems for any numbers creatively and innovatively.

NUMBERS AND OPERATIONS

1. WHOLE NUMBERS UP TO 100 000

26

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

2.1 Addition of any two up to four numbers.

2.2 Problem solving. 2.3 Usage of

unknown in addition.

(i) Add any two, three and four numbers up to five digits with the total up to 100 000 including making estimation.

(i) Solve daily problems involving

addition up to three numbers. (i) Identify an unknown involving

addition of two numbers. (ii) Form number sentences involving

addition of two numbers.

1 Identify unknown and write number sentences.

2 Add any two up to four numbers up to five digits without regrouping.

3 Add any two up to four numbers up to five digits with regrouping.

4 Solve daily routine problems involving addition up to three numbers.

5 Solve daily routine problems involving addition using various strategies.

6 Solve daily non-routine problems involving addition creatively and innovatively.


2. ADDITION UP TO 100 000

27

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

3.1 Subtraction of any two numbers.

3.2 Subtraction of

two numbers consecutively from any number.

3.3 Problem solving. 3.4 Usage of

unknown in subtraction.

(i) Subtract any two numbers up to 100 000.

(i) Subtract consecutively two numbers

from any number up to 100 000. (i) Solve daily problems involving

subtraction of two numbers. (i) Identify unknown involving

subtraction of two numbers. (ii) Form number sentences involving

subtraction of two numbers.

1 Identify unknown and write number sentences.

2 Subtract any two numbers up to 100 000.

3 Subtract consecutively two numbers from any number up to 100 000.

4 Solve daily routine problems involving subtraction of two numbers.

5 Solve daily routine problems involving subtraction using various strategies.

6 Solve daily non-routine problems involving subtraction creatively and innovatively.


3. SUBTRACTION UP TO 100 000

28

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

4.1 Multiplication of two numbers.

4.2 Problem solving.

(i) Multiply any numbers up to four digits by one-digit number, and the product up to 100 000.

(ii) Multiply any numbers up to three digits by two-digit number, and the product up to 100 000.

(iii) Multiply any numbers with 100 and 1000, and the product up to 100 000.

(iv) Multiply any numbers with numbers up to two-digit, 100 and 1000, and the product up to 100 000 including making estimations.


multiplication of two numbers.

1 Multiply any numbers up to four digits with one-digit number without regrouping.

2 Multiply any numbers up to four digits with one-digit number with regrouping.

3 Multiply any numbers up to three digits with two-digit number, 100 and 1000.

4 Solve daily routine problems involving multiplication of two numbers.

5 Solve daily routine problems involving multiplication using various strategies.

6 Solve daily non-routine problems involving multiplication creatively and innovatively.


4. MULTIPLICATION UP TO 100 000

29

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

5.1 Division of two numbers.


(i) Divide any number up to 100 000 by one-digit number, two-digit number, 100, and 1000.


division of two numbers.

1 Divide any numbers up to 100 000 with one-digit number without remainder.

2 Divide any numbers up to 100 000 with one-digit number with remainder.

3 Divide any numbers up to 100 000 with two-digit number, 100 and 1000.

4 Solve daily routine problems involving division of two numbers.

5 Solve daily routine problems involving division using various strategies.

6 Solve daily non-routine problems involving division creatively and innovatively.


5. DIVISION UP TO 100 000

30

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

6.1 Addition and subtraction.

6.2 Multiplication

and division. 6.3 Problem solving.

(i) Add and subtract any numbers within 100 000.

(i) Multiply and divide any number by one-digit number and two digit number within 100 000.


addition and subtraction. (ii) Solve daily problems involving

multiplication and division.

1

Do mixed operations involving addition and subtraction without regrouping, multiplication and division of any numbers by one-digit number without remainder within 100 000.

2 Do mixed operations involving addition and subtraction with regrouping, multiplication and division of any numbers with one-digit number with remainder within 100 000.

3

Do mixed operations involving addition and subtraction without and with regrouping, and division of any numbers with numbers up to two-digit without and with remainders within 100 000.

4 Solve daily routine problems using mixed operations involving addition and subtraction, multiplication and division.

5 Solve daily routine problems using mixed operations involving addition and subtraction, multiplication and division with various strategies.

6 Solve daily routine problems using mixed operations involving addition and subtraction, multiplication and division creatively and innovatively.


6. MIXED OPERATIONS

31

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

7.1 Improper fraction and mixed number.

7.2 Addition of

fraction.

7.3 Subtraction of fraction.

7.4 Addition and subtraction of fraction.

7.5 Problem

solving involving fraction.

(i) Recognise, name and write improper fractions and mixed numbers with denominator up to 10 using: (a) Objects, (b) Diagrams.

(ii) Convert improper fractions with denominator up to 10 to mixed numbers and vice-versa.

(i) Add up to three proper fractions with: (a) same denominator up to 10, (b) different denominator up to 10.

(i) Subtract up to two proper fractions from a proper fraction with: (a) same denominator up to 10, (b) different denominator up to 10.

(i) Add and subtract proper fractions with: (a) same denominator up to 10, (b) different denominator up to 10.

(i) Solve daily problems involving addition and subtraction of two proper fractions.

1 State improper fractions and mixed numbers with denominator up to 10.

2 Convert improper fractions with denominator up to 10 to mixed numbers and vice-versa.

3 Add up to three proper fractions, subtract up to two fractions using mixed operations involving addition and subtraction with same denominator up to 10.

4 Add up to three proper fractions, subtract up to two fractions using mixed operations involving addition and subtraction with different denominator up to 10.

5 Solve daily routine problems involving fractions using various strategies.

6 Solve daily non-routine problems involving fractions creatively and innovatively.


7. FRACTIONS

32

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

8.1 Decimal numbers up to three decimal places.

8.2 Value of decimals.

8.3 Addition of decimal numbers.

8.4 Subtraction of decimal numbers.

8.5 Multiplication of decimal numbers.

(i) Recognise, name and write decimals using diagrams.

(ii) Say and write decimal numbers up to three decimal places in words and numerals.

(i) Convert fractions of thousandths to decimals and vice-versa.

(ii) Compare values of two decimal numbers up to three decimal places.

(i) Add two decimal numbers up to three decimal places.

(i) Subtract two decimal numbers up to three decimal places.

(i) Multiply decimal numbers by one-digit number, and the product up to three decimal places.

(ii) Multiply decimal numbers up to three decimal places by 10, 100 and 1000.

1 State any decimal numbers based on concrete materials and diagrams.

2 Convert fractions of thousandths to decimals and vice-versa.

3

Add and subtract decimal numbers up to three decimal places; multiply and divide decimal numbers with one-digit number, 10, 100 and 1000, and the answer up to three decimal places.

4 Solve daily routine problems involving decimal numbers up to three decimal places in addition, subtraction, multiplication and division.

5 Solve daily routine problems involving decimal numbers up to three decimal places using various strategies.

6

Solve daily non-routine problems involving decimal numbers up to three decimal places creatively and innovatively.


8. DECIMALS

33

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

8.5 Division of

decimal numbers.

8.6 Problem solving involving decimals.

(i) Divide decimal numbers by one-digit

number, and the quotient up to three decimal places.

(ii) Divide decimal numbers by 10, 100 and 1000, and the quotient up to three decimal places.


addition, subtraction, multiplication and division.


8. DECIMALS

34

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

9.1 Value of percentage.

(i) Convert decimals up to two decimal places to percentage and vice-versa.

.

1 State the decimals and percentage based on concrete materials and diagrams.

2 Convert percentage to decimals.

3 Convert decimals up to two decimal places to percentage.

4 Solve daily routine problems involving the conversion of decimal to percentage and vice-versa.

5 Solve daily routine problems involving the conversion of decimal to percentage and vice-versa using various strategies.

6 Solve daily non-routine problems involving conversion of decimal to percentage and vice-versa creatively and innovatively.


9. PERCENTAGE

35

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

10.1 Value of money up to RM100 000.

10.2 Addition of

money. 10.3 Subtraction of

money. 10.4 Addition and

subtraction of money.

10.5 Multiplication of

money. 10.6 Division of

money.

(i) State combinations of money with value up to RM100 000 based on daily situations.

(ii) Round off money to the nearest ringgit.

(i) Add up to three values of money

with the sum up to RM100 000. (i) Subtract up to two values of money

from one value of money up to RM100 000.

(i) Add and subtract values of money

up to RM100 000. (i) Multiply values of money by

numbers up to two-digit, 100 and 1000 up to RM100 000.

(i) Divide values of money by number

up to two-digit, 100 and 1000 up to RM100 000.

1

State a) currencies of ASEAN and major countries in the world, b) payment instrument, c) equivalent value of RM1 to currencies of other countries

2 State any combined value of money up to RM 100 000.

3

a) Do addition of money up to three values with the sum up to RM 100 000,

b) Do subtraction up to two values from one value of money up to RM 100 000, c) Do multiplication and division of money by numbers up to two digits, 100 and 1000, d) Do mixed operations involving addition and subtraction

up to RM100 000.

4 Solve daily routine problems involving addition, subtraction, multiplication and divison of money.

5 Solve daily routine problems involving addition, subtraction, multiplication and divison of money with various strategies.

6 Solve daily non-routine problems involving addition, subtraction, multiplication and divison of money creatively and innovatively.


10. MONEY UP TO RM100 000

36

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR


10.8 Foreign

currencies. 10.9 Payment

instrument.

(i) Solve daily problems including transaction of items and services involving addition, subtraction, multiplication, and division of money

(i) Recognise currencies of ASEAN and

major countries in the world. (ii) State the equivalent value of RM1 to

currencies of other countries. (i) Recognise various payment

instruments.


10. MONEY UP TO RM100 000

0

37

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

11.1 Relationship in time.

11.2 Addition of

time.

11.3 Subtraction of

time. 11.4 Multiplication of

time.

(i) State the relationship between units of time involving: (a) day and hour, (b) week and day, (c) year and month.

(i) Add up to three units of time

involving: (a) day and hour, (b) week and day, (c) year and month,

with and without conversion of units. (i) Subtract up to two units of time from

one unit of time involving: (a) day and hour, (b) week and day, (c) year and month,

with and without conversion of units. (i) Multiply units of time involving:

(a) day and hour, (b) week and day, (c) year and month,

by one digit with and without conversion of units.

1 State the relationship between units of time.

2 Add, subtract, multiply, and divide units of time without conversion of units.

3 Add, subtract, multiply, and divide units of time with conversion of units.

4 Solve daily routine problems involving time.

5 Solve daily routine problems involving units of time using various strategies.

6 Solve daily non-routine problems involving units of time creatively and innovatively.

MESUREMENT AND GEOMETRY

11. TIME

38

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

11.5 Division of time.

11.6 Problem

solving involving time.

(i) Divide units of time involving: (a) day and hour, (b) week and day, (c) year and month,

by one digit with and without conversion of units. (i) Solve daily problems involving

addition, subtraction, multiplication and division of time.

MESUREMENT AND GEOMETRY

11. TIME

39

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

12.1 Units of length. 12.2 Measurement

and estimate length.

12.3 Addition of

length. 12.4 Subtraction of

length.

(i) Recognise units of length: (a) milimetre (mm), (b) kilometre (km).

(ii) State the relationship between: (a) centimetre and milimetre, (b) kilometre and metre,

and vice-versa. (i) Measure objects in unit of millimetre. (ii) Estimate distance in unit of

kilometre. (i) Add up to three units of length

involving: (a) centimetre and millimetre, (b) kilometre and metre,

with and without conversion of units. (i) Subtract up to two units of length

from one unit of length involving: (a) centimetre and millimetre, (b) kilometre and metre,

with and without conversion of units.

1 State the relationship between the units of length.

2 a) Measure objects in unit of millimetre. b) Estimate distance in unit of kilometre.

3 Add, subtract, multiply and divide involving units of length.

4 Solve daily routine problems involving units of length.

5 Solve daily routine problems involving units of length using various strategies.

6 Solve daily non-routine problems involving units of length creatively and innovatively.

MEASUREMENT AND GEOMETRY

12. LENGTH

40

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

12.5 Multiplication of length.

12.6 Division of

length. 12.7 Problem

solving involving length.

(i) Multiply units of length involving: (a) centimetre and millimetre, (b) kilometre and metre,

by one digit number with and without conversion of units.

(i) Divide units of length involving:

(a) centimetre and millimetre, (b) kilometre and metre,

by one digit number with and without conversion of units.


addition, subtraction, multiplication and division of length.


12. LENGTH

41

Year 4

CONTENT STANDARD LEARNING STANDARD PERFORMANCE STANDARD

LEVEL DESCRIPTOR

13.1 Mixed operations involving mass.

13.2 Problem

solving involving mass.

(i) Add and subtract mass involving kilogram and gram, with and without conversion of units.

(ii) Multiply and divide mass involving kilogram and gram, with and without conversion of units.


mixed operations of mass.

1 Add, subtract, multiply and divide involving units of mass.

2 Able to do mixed operations involving addition and subtraction, multiplication and division involving kilogram and gram without conversion of units.

3 Able to do mixed operations involving addition and subtraction, multiplication and division involving kilogram and gram with conversion of units.

4 Solve daily routine problems involving mixed operations of mass.

5 Solve daily routine problems involving mixed operations of mass using various strategies.

6 Solve daily non-routine problems involving mixed operations of mass creatively and innovatively.


13. MASS

42

Year 4

CONTENT STANDARD LEARNING STANDARD PERFORMANCE STANDARD

LEVEL DESCRIPTOR

14.1 Mixed operations involving volume of liquid.

14.2 Problem solving involving volume of liquid.

(i) Add and subtract volume of liquid involving litre and millilitre, with and without conversion of units.

(ii) Multiply and divide volume of liquid involving litre and millilitre, with and without conversion of units.

(i) Solve daily problems involving mixed operations related to volume of liquid.

1 Add, subtract, multiply and divide involving volume of liquid.

2 Do mixed operations involving addition and subtraction, multiplication and division involving litre and millilitre without conversion of units.

3 Do mixed operations involving addition and subtraction, multiplication and division involving litre and millilitre with conversion of units.

4 Solve daily routine problems using mixed operations involving volume of liquid.

5 Solve daily routine problems using mixed operations involving volume of liquid with various strategies.

6 Solve daily non-routine problems using mixed operations involving volume of liquid creatively and innovatively.


14. VOLUME OF LIQUID

43

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

15.1 Angles. 15.2 Parallel and

perpendicular lines.

15.3 Perimeter and

area. 15.4 Volume.

(i) Recognise and name right angles, acute angles and obtuse angles for rectangle, square and triangle.

(i) Recognize and name:

(a) parallel lines, (b) perpendicular lines, on two-dimensional basic shapes.

(i) Determine perimeter of rectangle,

square, triangle and polygon. (ii) Determine area of rectangle, square,

and triangle using square grid and formula.

(i) Determine volume of cube and

cuboid using unit of one cubic

centimeter ( ) cubes and formula.

1 State the types of angle and line on two-dimensional basic shapes.

2 State the meaning of perimeter, area and volume with formula.

3 Calculate perimeter, area and volume.

4 Solve daily routine problems involving angles, lines, perimeter, area, and volume.

5 Solve daily routine problems involving angles, lines, perimeter, area, and volume using various strategies.

6 Solve daily non-routine problems involving angles, lines, perimeter, area, and volume creatively and innovatively.


15. SPACE

44

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

16.1 Coordinates in the first quadrant.

(i) State vocabulary to explain the meaning of horizontal axis and vertical axis.

(ii) Name the objects based on the position on the horizontal axis and vertical axis on grid paper.

(iii) Determine and state the position of objects on the horizontal axis and vertical axis on grid paper.

1 State vocabulary related to horizontal axis and vertical axis.

2 State object based on the position on the horizontal axis and vertical axis.

3 Determine the position of objects on the horizontal axis and vertical axis.

4 Solve daily routine problems involving coordinates.

5 Solve daily routine problems involving coordinates using various strategies.

6 Solve daily non-routine problems involving coordinates creatively and innovatively.

RELATIONSHIP AND ALGEBRA

16. COORDINATES

45

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

17.1 Proportion.

(i) Determine a value using unitary method in daily life.

1 State the meaning of unitary.

2 Compare the value for one unit.

3 Find the value using unitary method.

4 Solve daily routine problems involving unitary method.

5 Solve daily routine problems involving unitary method using various strategies.

6 Solve daily non-routine problems involving unitary method creatively and innovatively.

RELATIONSHIP AND ALGEBRA

17. RATIO AND PROPORTION

46

Year 4

CONTENT STANDARD


LEVEL DESCRIPTOR

18.1 Data.

(i) Read and get information from: (a) pictograph, (b) bar chart, (c) pie chart.

(ii) Compare information from: (a) pictograph, (b) bar chart, (c) pie chart.

1 Name types of graph: pictograph, bar chart, and pie chart.

2 State information from pictograph, bar chart and pie chart.

3 Compare the information from pictograph, bar chart or pie chart.

4 Solve daily routine problems involving data representation.

5 Solve daily routine problems involving data representation using various strategies.

6 Solve daily non-routine problems involving data representation creatively and innovatively.

STATISTICS AND PROBABILITY

18. DATA HANDLING

Terbitan:

KEMENTERIAN PENDIDIKAN MALAYSIA

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