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SEAMEO Basic Education Standards (SEA-BES): Common Core Regional
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SEAMEO Basic Education Standards(SEA-BES): Common Core Regional
Learning Standards (CCRLS) in
Mathematics and Science

Editors
Dominador Dizon Mangao
Nur Jahan Ahmad
Masami IsodaiCopyright © 2017 SEAMEO RECSAMSEAMEO Basic Education Standards (SEA-BES):
Common Core Regional Learning Standards (CCRLS) in
Mathematics and Science
For more information about this book contact:
The Director
SEAMEO RECSAM
Jalan Sultan Azlan Shah
11700 Gelugor
Penang, Malaysia

Tel: +604-6522700
Fax: +604-6522737
Email: director@recsam.edu.my
URL: http://www.recsam.edu.my

Publication by:
Publication Unit
SEAMEO RECSAM
Penang, Malaysia
All rights reserved, except for educational purposes with no commercial
interests. No part of this publication may be reproduced, transmitted in any
form or by any means, electronic or mechanical including photocopying,recorded or by any information storage or retrieval system, without priorpermission from the Director, SEAMEO RECSAM.
ISBN: 978-967-930-039-0ii

Foreword

FOREWORD
SEAMEO Secretariat takes pride in the publicationof the SEA-BES Common Core Regional LearningStandards (CCRLS) in Mathematics and Science
under the leadership of SEAMEO RECSAM andits collaborating partners. This publication is ananswer to the challenge of what 21st Century scienceand mathematics education should be and what
21st Century skills, knowledge, understanding, values
and attitudes should all learners possess particularlyin the development of scientific and technologicalskills and numeracy skills through education in mathematics and science.
The SEA-BES Common Core Regional Learning Standards (CCRLS) in
Mathematics and Science put forth the development and enhancement of
21st century skills comprising of character education, entrepreneurshipeducation, Information and Communications Technology, language andliteracy and scientific and technological literacy in all learners. Under the new
SEAMEO Education Agenda (2015-2035), SEA-BES CCRLS in Mathematics
and Science is re-aligned into Priority Area #7 “ Adopting a 21st Century
Curriculum.”
I fervently hope that Ministries of Education of SEAMEO would takecognizance of the purposes of the SEAMEO Basic Education Standards CCRLS
in Mathematics and Science as a tool to strengthen regional collaboration on
curriculum standards and learning assessment, curriculum and professional
development and a mechanism to enhance competitiveness in the eraof globalization, nurturing ASEAN values and spirit and in building aharmonious progressive, peaceful and sustainable ASEAN community.
My sincere appreciation and congratulations to SEAMEO RECSAM,
collaborating partner institutions for the expertise and financial support,
the consultants, the science and mathematics specialists from SEAMEO sister
centres, the Malaysian and Japanese educators, and master/experienced
teachers from Penang State for all the hard work and commitment.

Dr. GATOT HARI PRIOWIRJANTO
Director, SEAMEO Secretariat, Bangkok, Thailand
iii

Foreword

It is widely acknowledged that education potentiallyserves as a building block towards a nation’s progressand development. SEAMEO Member Countries are
particularly privileged, sharing a common platform
under the spirit of building one ‘ASEAN Community’.
This ASEAN platform potentially provides for the
harmonisation of each SEAMEO Member’s national
education policy frameworks. Consequently, thisraises the education level towards greater heights,
through the sharing of knowledge and integration ofregional educational ideals and standards.
On that thought, it is my honour to represent SEAMEO RECSAM,
which initiated the publication of the SEAMEO Basic Education Standards(SEA-BES): Common Core Regional Learning Standards (CCRLS) in
Mathematics and Science. This challenging idea of developing a common
basic education curriculum was rooted since the inception of the SEAMEO
Vision 2010 and reflected in the SEAMEO Strategic Plan 2011-2020.
SEAMEO RECSAM has tackled this challenge head-on and is proud to be
entrusted with this project which is further aligned with the current seven
Priority Areas of SEAMEO Education Agenda (2016-2020) particularly Priority#7 “Adopting a 21st Century Curriculum.” SEAMEO RECSAM believes theASEAN Community provides the opportunity for the development of an
educational policy framework for all SEAMEO Member Countries and isconfident this project would lead the way forward towards an enhanced
access in education opportunities and support in the development of quality
basic education particularly in science and mathematics.
In envisaging the challenges of the future, the agreed upon learning
standards emphasise and incorporate the 21st century skills that encompass
learning, literacy and life skills as well as competencies (OECD,1997).
Our societies are continuously changing and the path towards success isprogressively adapting according to the political, economic, technological,
and social stability demands. In this context, it is hoped that a well-designed
curriculum can maximise the development of knowledge and skills thatenable individuals to attain holistic well-being, sense of responsibility andself-reliance. Ultimately, successful individuals are able to live harmoniously
and further contribute to society.
The process of developing CCRLS was very demanding and challenging
yet a rewarding endeavour. As such, I would like to first convey my sincere
appreciations to SEAMEO Secretariat for entrusting this monumentaliv

Forewordtask to SEAMEO RECSAM and for their expertise and financial support.
Moreover, I extend a measure of gratitude to Prof. Masami Isoda (CRICED,
University of Tsukuba, Japan) for his tireless efforts in providing consultancy
in the Mathematics Learning Standards and to Dr. Mark Windale(Centre for Science Education, Sheffield Hallam University, United Kingdom)
for his contributions in providing expertise in the Science Learning Standards.
Furthermore, I thank Prof. Kerry J. Kennedy (Hong Kong Institute of
Education, Hong Kong) for providing valuable inputs that helped shape
the learning standards to its current form. These learning standards would
not have succeeded without the support and contributions of the scienceand mathematics curriculum experts from the 11 Ministries of Education,
professors, teacher educators and teachers from various institutions in
Malaysia and across SEAMEO Member Countries for whom I offer my sincere
thanks and appreciation. Acknowledgement is also extended to the Japanesemathematics and science professors who specially travelled from Japan to
SEAMEO RECSAM to partake in this project. Likewise, appreciation goesto collaborating partners for their expertise and financial support such as
UNICEF EAPRO, British Council Regional Office, British Council Thailand,
and the Institute for the Promotion of Teaching Science and Technology,
Thailand. Last but not least, I thank the committed and dedicated
SEAMEO RECSAM academic and support staff who have contributed directly
or indirectly in the development and finalisation of the CCRLS.
I hope the CCRLS in Mathematics and Science will be successful as a toolthat will initiate systematic discussion towards the future development of aregional integrated curriculum suitable for ASEAN integration with emphasison 21st century skills. Moreover, the CCRLS will serve as a platform thatencourage the establishment of best practices to overcome differences incurriculum. Ultimately, the CCRLS aimed to strengthen ASEAN collaboration
on developing quality curriculum standards and learning assessment which
will effectively tackle the changing global context and complexity of ASEAN.

Dr. HJ MOHD JOHAN BIN ZAKARIA, D.J.N.
Centre Director, SEAMEO RECSAM, Penang, MalaysiavForeword

It is my pleasure to present the document of SEAMEO
Basic Education Standards (SEA-BES): Common Core
Regional
Learning
Standards(CCRLS)
for
Mathematics and Science. This document is designed
to bridge further development activities foreducational reforms in SEAMEO Member Countries
under the 7 priority areas of the SEAMEO Education
Agenda. This three-year project under the purview of
SEAMEO RECSAM is also aligned with the movementof the ASEAN Community for “one vision, one
identity and one community”.
The process of developing SEABES-CCRLS is indeed very challenging
and yet a rewarding endeavour right from the initiation until the finalizationof the document. On behalf of the project management team, I would like toextend my gratitude and appreciation to all the contributors who had directly
or indirectly contributed their effort in realizing the document. Based on
the diverse backgrounds and a wide range of expertise gathered from thecontributors, the ideas, knowledge, resources, and effort consolidated enable
the possibility to develop a leading document for state-of-the-art educational
reforms in the region and also to be influential for reforms all over the world
under the OECD issues.
All the preparatory activities organized by SEAMEO RECSAM pertaining to
the development of the learning standards had provided ample opportunities
for all personnel involved to learn and work together, recognizing thediversities in SEAMEO to describe the curriculum standards for science andmathematics. Specialists from every SEAMEO Member Country were very
persevered and committed in the contribution and elaboration, integrating
the necessary competencies in mathematics and science for the completion ofthis document. In relation to the long-term Japanese friendships with ASEAN
countries and East Timor, University of Tsukuba, as an affiliate member of
SEAMEO contributed a vital role to set the opportunities in establishing andagreeing on the framework of CCRLS at the SEAMEO RECSAM-Universityof Tsukuba Joint Seminar1: Searching for Quality Mathematics Curriculum
Framework on the Era of Globalization in February 15-18, 2016. The event washeld as the back to back meeting of APEC-Tsukuba International Conferencewith contributions of curriculum specialists from SEAMEO Member Countries
as well as leading researchers in the world2.
1 The University of Tsukuba, Japan, is an affiliate member of SEAMEO.
2 The APEC Lesson Study Project proposed from Japan (Masami Isoda, University of Tsukuba) and Thailand(Maitree Inprasitha, Khon Kaen University). In the meeting, leading researchers such as the president ofInternational Society of Mathematics Education (IGPME) contributed.

vi

Foreword

In these engagements, I would like to extend the acknowledgment to
the Japanese counterparts and the supporting institutions, particularly inthe support of grants from CRICED of the University of Tsukuba and JSPS3.
I would also like to extend my appreciations to the curriculum specialists from
SEAMEO Member Countries who were working very hard and contributing
diligently under the flagship of each government, as well as the researchers
who had provided the academic commentaries to finalize the document:Colleen M. Eddy, Ivan R. Vysotski, Marsigit, Fumi Ginshima, Mikio Miyazaki,
Kimiho Chino, Kotaro Komatsu, Toshinobu Hatanaka, Yoshisuke Kumano,Takeshi Fujita, Kenji Matsubara, Ryugo Oshima, Yoshiyuki Gunji, Izumi Imai,
Gabriel Matney, Hee-Chan Lew, Maitree Inprashita, and Shizumi Shimizu.
Last but not least, on behalf of the project management team, I would
like to thank the dedicated and committed co-workers in SEAMEORECSAM who were involved in this project, namely; Pedro Montecillo Jr.,
Teh Kim Hong, Mohd Sazali bin. Hj. Khalid, Suhaidah Tahir, Nur Jahan Ahmad,
and Dominador Dizon Mangao. We had been working together, stretchingacross different phases for the last three years to finalize this document under
the guidance and support of the former director, Hj Mohd Johan Bin Zakaria.

MASAMI, ISODA Prof/PhD
Director, Center for Research on International Cooperationin Educational Development
University of Tsukuba, Japan

3 MEXT/JSPS KAKENHI Grant Number: 26245082, 16K13568

vii

PANEL OF REVIEW EDITORS
Prof. Masami Isoda, University of Tsukuba, Japan
Dr. Mark Windale, Sheffield Hallam University, United Kingdom
Assoc. Prof. Hatanaka Toshinobu, Toho University, Japan
Mr. Dominador Dizon Mangao, SEAMEO RECSAM
Dr. Nur Jahan Ahmad, SEAMEO RECSAM
Mr. Pedro L. Montecillo, Jr., SEAMEO RECSAM
Ms. Teh Kim Hong, SEAMEO RECSAM
Editorial Assistant
Ms. Ong Mei Yean

viii

TABLE OF CONTENTS
Foreword
Panel of Review Editors
PrefaceAcknowledgements
Vision of SEAMEO and Purpose of CCRLS
Purposes of CCRLS under the SEA-BES Project
Development Process of CCRLS
SEA-BES Project Framework in 2014
Methodology to Develop SEA-BES
Series of SEA-BES Workshops
Participation and Involvement of Experts, Educators andInstitutions

iii
viii
xiii
xvi
xviii
xx
xxi
xxi
xxi
xxiii

Common Core Regional Learning Standards in Mathematics

1

xxiv

Chapter 1: Framework for CCRLS in Mathematics
2
Nature of Mathematics
2
Aims of Mathematics in CCRLS
4Mathematical Values, Attitudes and Habits for Human Character 6
Mathematical Thinking and Processes
7
Content
8
Context to Link the Three Components
9
Description Format of SEA-BES CCRLS in Mathematics
11
Sample Format
13
Chapter 2: Key Stage 1
14Strand: Numbers and Operations
14
Strand: Quantity and Measurement
22
Strand: Shapes, Figures and Solids
25
Strand: Pattern and Data Representations
27
Strand: Mathematical Process - Humanity
29ixChapter 3: Key Stage 2
Strand: Extension of Numbers and Operations
Strand: Measurement and Relations
Strand: Plane Figures and Space Solids
Strand: Data Handling and Graphs
Strand: Mathematical Process - Humanity
Chapter 4: Key Stage 3
Strand: Numbers and Algebra
Strand: Relations and Functions
Strand: Space and Geometry
Strand: Statistics and Probability
Strand: Mathematical Process - Humanity
References

33
33
39
45
47
49
54
54
58
60
62
64
69

Common Core Regional Learning Standards in Science71

Chapter 5: Framework for CCRLS in Science
Nature of Science
Aims of Science in CCRLS
Components of the Framework
The Content Strands
Scientific Skills, Processes and Thinking
Values and Attitudes
Context to Link the Three Components
Chapter 6: Science Inquiry
Strand Description
Science Process Skills
Managing Laboratory Apparatus and Specimens
Observing Safety in the Laboratory
Ethics, Scientific Attitudes, and Noble Values
Scientific Investigations
The World of STEM

72
72
74
75
78
78
81
84
86
86
87
92
94
95
95
96

x

Chapter 7: Life and the Living World
Strand Description
Living Things and Non-Living Things
Personal Health and Healthy Lifestyle
Human Organ Systems
Animals
PlantsEcosystem and Environment
Biodiversity
Microorganisms
Cells
Biotechnology
Chapter 8: Material World
Strand Description
MatterComposition of Matter
Classification of Matter
Water as Matter
Acids, Bases and Salts
Chemical Reactions
Aqueous Solutions and Ions
Chapter 9: Energy and Change
Strand Description
Sound
Light
Waves
Electricity
Magnetism
Force and Motion
Pressure
Energy, Work, and Power
Heat
Nuclear Physics

xi

97
97
98
98
100
107
110
114
115
116
117
118
120
120
120
123
123
124
126
127
127
128
128
128
129
131
132
135
136
138
139
141
142

Chapter 10: Earth and Space
Strand Description
Soil
Water
Solid Earth
Atmosphere
Weather and Climate
Faults, Earthquakes, Volcanic Eruptions and Disaster Management
Earth, Solar System and the Universe
Space Technology
Chapter 11: Science, Engineering and Technology for Sustainable
Society
Strand Description
Environment and Conservation of Natural Resources
Ecosystem and Environmental Management
Human Health and Management
Scientific, Technological and Engineering BreakthroughReferences

xii

144
144
144
145
145
147
148
150
151
152
153
153
153
156
158
160
163

PREFACE
The Southeast Asian Ministers of Education Organisation (SEAMEO) wasestablished to promote cooperation in education, science and culture in theSoutheast Asian region. It is mandated to enhance regional understanding andcooperation and unity of purpose among SEAMEO Member Countries in orderto achieve a better quality of life. These mandates are carried out through theestablishment of networks and partnerships, the provision of an intellectualforum for policy makers and experts, promotion of sustainable humanresource development, enhancement of the capacities of teachers and school
managers, and collaboration with global and international organisations, andinstitutions.
The on-going setting up of the ASEAN Community brings challenges
and opportunities that call for dynamic and comprehensive approach among
governments in the region. As regional integration progresses, educational
institutions are feeling the pressure of working together to bring their systems
closer and develop a more comparable, complementary and harmonised
programmes and curricula especially in higher education.
To face the reality of the inevitable scenario of regional integration,
SEAMEO developed its Strategic Plan (2011-2020) identifying 12 priority
initiatives to be pursued in order to achieve the Golden SEAMEO Visionby 2020. The vision is characterised by programme dynamism, excellence,
greater prowess, deeper cooperation and enhanced international visibility
yet increasing its internal capacity building and striving to create regional
standard and social cultural responsibility. SEAMEO has 24 specialist centres
called the SEAMEO Centres which carry out these initiatives encompassing
capacity building and development, research and development, informationand knowledge exchange and management, community work and extension.
SEAMEO RECSAM with its mandate to promote science and mathematics
in the Southeast Asian region, led one of the 12 initiatives known as
SEAMEO Basic Education Standards (SEA-BES) and Student Networking,which later became two separate projects. The SEA-BES project came into life
in November 2014 through a regional consultative meeting back to back with
the Southeast Asia Primary Learning Metrics (SEA-PLM) project with funding
from UNICEF East Asia Pacific Regional Office (UNICEF EAPRO).
Under the new SEAMEO Education Agenda (2015-2035), SEA-BES projectis re-aligned into Priority Area #7 “Adopting a 21st Century Curriculum”
which states to pursue a radical reform through systematic analysis ofknowledge, skills, and values needed to effectively respond to changing

xiii

global contexts, particularly to the ever-increasing complexity of the Southeast
Asian economic, socio-cultural and political environment, developing teacher
imbued with ASEAN ideals in building ASEAN Community within 20 years.
The SEAMEO Basic Education Standards (SEA-BES) is a regional
curriculum project with the purpose of developing learning standards known
as the Common Core Regional Learning Standards (CCRLS) in Mathematics
and Common Core Regional Learning Standards (CCRLS) in Science.
The SEA-BES CCRLS serves the goal of improving the quality of educationin the SEAMEO Member Countries through comparison and identification ofgaps in terms of curriculum content (i.e. knowledge, skills, attitudes, habits)
as well as bases for assessing student learning outcomes. The SEA-BES projectenvisions to developing common shared and agreed standards for what every
learner should know, be able to do and value in mathematics and science.
The CCRLS can be used to improve the quality of SEAMEO Member Countries’
national curriculum creating equity in curricular provisions across countries
and high expectations for all students and learning outcomes that will enable
students to contribute productively to their individual countries and theirregion.
The development of the CCRLS was made possible with the participationand involvement of mathematics and science teachers and experts across theSoutheast Asian region and beyond through a series of workshops conductedin-house, local level and regional level as well as international level.
The CCRLS was built upon the strength of the existing standards of the
SEAMEO Member Countries and further enhanced by the standards ofhigh-performing countries on international student assessments as well as
carefully studying the research and literature available on what students needto know, be able to do and value to be successful in post-secondary school,
college, career and life.
The publication of SEA-BES Common Core Regional Learning Standards
in Mathematics and Science serves as reference to developing the national
science and mathematics curriculum of SEAMEO Member Countries in theirvarious efforts of educational reforms. This book publication is comprisedof two separate learning standards, namely; the SEA-BES Common Core
Regional Learning Standards in Mathematics and SEA-BES Common Core
Regional Learning Standards in Science. Both Learning Standards share thesame introductory chapter “Vision of SEAMEO and Purpose of CCRLS” butonly appears in CCRLS in Mathematics. Each Learning Standard maintains its
own set of references.

xiv

The SEA-BES CCRLS in Mathematics contains four chapters coveringvarious topics, namely; Framework of CCRLS for Mathematics - Nature of
Mathematics, Aims of Mathematics in CCRLS, Components of the Framework,
Context to Link the Three Components, Description of Format and Sample
Format; Strands in Key Stage 1 – Numbers and Operations, Quantity andMeasurement, Shapes, Figures and Solids, Pattern and Data Representations,and Mathematical Process - Humanity; Strands in Key Stage 2 – Extensionof Numbers and Operations, Measurement and Relations, Plane Figures
and Space Solids, Data Handling and Graphs, and Mathematical Process Humanity; and Strands in Key Stage 3 – Numbers and Algebra, Relations andFunctions, Space and Geometry, Statistics and Probability, and Mathematical
Process - Humanity. Mathematical Process-Humanity is embedded in every
Strands as well as encompasses mathematical activities aimed to bridge thecontent standards across the every Key Stage.
On the other hand, SEA-BES CCLRS in Science is consisted of sevenchapters, namely; Framework of CCRLS for Science, Science Inquiry Strand,Life and the Living World Strand, Material World Strand, Energy andChange Strand, Earth and Space Strand, and lastly, Science, Engineering andTechnology for Sustainable Society Strand. The strands on Science Inquiry,
and Science, Engineering and Technology for Sustainable Society may be
integrated into the main four content strands. The four content strands serveas the context whereby science content knowledge, scientific skills, processes
and thinking, and attitudes and values are developed in the learners across thethree Key Stages.
The Learning Standards are intended for use by curriculum makers,
educators, teachers, instructional leaders and researchers. Furthermore,
the Learning Standards serve as bases to explore high quality mathematics
and science teaching, motivate and challenge the development of relevant andmeaningful curriculum, pedagogy and learning assessment, and a mechanism
to enhance 21st Century skills in the era of globalisation, nurture ASEAN
values and spirit to build a harmonious progressive, peaceful and sustainable
ASEAN Community.
Editors
Dominador Dizon Mangao
Nur Jahan Ahmad, Ph.D.
Masami Isoda, Ph.D.

xv

ACKNOWLEDGEMENTS
This book was published under the leadership of SEAMEO RECSAM andthe guidance of SEAMEO Secretariat in Bangkok, Thailand. The editors
wish to acknowledge and express their gratitude to the following persons
and institutions for their roles and contributions in making this project andpublication a reality:

Dr. Witaya Jeradechakul and Dr. Gatot Hari Priowirjanto, past and present
SEAMEO Center Directors respectively, together with the SEAMES staff
for their leadership in crafting the Golden SEAMEO Vision 2020 with its
12 project initiatives reflected in the SEAMEO Strategic Plan 2011-2020.

Dr. Azian T.S. Abdullah and Dr. Hj. Mohd Johan bin Zakaria, D.J.N.,
past Centre Directors for their leadership, motivation and inspiration toaccept the challenge of leading this project and in the publication of this
book.



Dr. Jim Ackers, Education Advisor, UNICEF East Asia Pacific Regional
Office and his staff, Ms. Camille Woeldike for the financial support in
conducting the first Regional Consultative Meeting of SEA-BES and
SEA-PLM.



British Council Regional Office and British Council Thailand; Instituteof the Promotion of Teaching Science and Technology-MOE Thailand,
and SEAMEO Secretariat for the financial assistance in conducting the
2nd SEA-BES CCRLS Regional Consultative Meeting and Workshop as
well as locally organized series of workshops.



The 11 Ministers of Education of SEAMEO for the financial support.



Science and mathematics curriculum specialists from the 11 Ministriesof Education of SEAMEO for their hard work, time and expertise in thedevelopment and finalization of the CCRLS.



Prof. Masami Isoda, CRICED, University of Tsukuba, Japan and
Dr. Mark Windale, Sheffield Hallam University, United Kingdom,
consultants in mathematics and science respectively for their expertise,commitment, and dedication in the development of the CCRLS.



Science and mathematics specialists from SEAMEO centers (i.e. RECSAM,QITEP in Science, QITEP in Mathematics, SEAMOLEC) and national
science and mathematics centers (i.e. Institute for the Promotion ofTeaching Science and Technology and University of the PhilippinesNational Institute in Science and Mathematics Education Development)
for their technical expertise.

xvi



Mathematics professors and experts from APEC economy members
who were present during the APEC-Tsukuba International Conference
X and APEC-Tsukuba International Conference XI (Grant No. 26245082
and APEC HRD 03-2015A) such as Colleen M. Eddy, Ivan R. Vysotski,
Fumi Ginshima, Mikio Miyazaki, Kimiho Chino, Kotaro Komatsu,
Gabriel Matney, Hee-Chan Lew, Maitree Inprashita, and Shizumi Shimizu
for their technical expertise.

Science and mathematics professors and curriculum specialists fromJapan for their technical expertise and financial support under the projectof Japan Society for Promotion of Science (JSPS-Grant No.16K13563
and 26245082 including Toshinobu Hatanaka, Yoshisuke Kumano,Takeshi Fujita, Kenji Matsubara, Ryugo Oshima, Yoshiyuki Gunji, andIzumi Imai.



Science and mathematics educators from Malaysian educational
institutions (i.e. Universiti Sains Malaysia, Universiti Pendidikan Sultan
Idris, Institut Pendidikan Guru – Kampus Pulau Pinang, Kampus Tuanku
Bainun and Kampus Ipoh) for their time and expertise.

Elementary and secondary science and mathematics master andexperienced teachers from Penang State.



Review Editors.

R & D Division.

Training Programme Division.

Administration Division.



Staff from the Publication Unit, namely Wong Lai Cheng, Shaneem
Kamarudin, Muhammad Nadzrul Shafiq Zulkefli and RECSAM support
staff for working tirelessly to publish this book.

Editors
Dominador Dizon Mangao
Nur Jahan Ahmad, Ph.D.
Masami Isoda, Ph.D.

xvii

Vision of SEAMEO and Purpose of CCRLS
The goal of regional integration in the development of an ‘ASEAN Community’
provides the opportunity for the development of an educational policy
framework for all SEAMEO Member Countries in order to enhance accessto educational opportunities, to support the development of quality basic
education and to encourage regional mobility. Such a framework will support
all Governments as the main providers of basic education to meet the learningneeds of all students.
Indeed the SEAMEO Education Agenda #7 “Adopting a 21st Century
Curriculum” states to pursue a radical reform through systematic analysis
of knowledge, skills, and values needed to effectively respond to changing
global contexts, particularly to the ever-increasing complexity of the Southeast
Asian economic, socio-cultural, and political environment, developing teacher
imbued with ASEAN ideals in building ASEAN community within 20 years(2015-2035). SEAMEO established the Action Agenda from 2016 - 2020 underthe 7 priority areas. SEA-BES is one of the projects for action agenda under #7.
SEAMEO Council consisting of the Ministers of Education (2015) enhanced
the linking of the seven priority areas with the curriculum and moving
towards global citizenship. Inevitably, the region needs the common grounds
that allow the stakeholders to develop the fullest potential and capabilities
of its citizens. In SEAMEO Member Countries, mathematics and science aremajor component subjects to be learned. Mathematics can be known as part ofthe most basic literacy for learning other subjects as well as to think and reason
as an independent citizen. Science is known as part of the most necessary
literacies for technological and environmental concerns of the society as well
as scientific exploration of nature. This document is envisioned to serve as
tool for analysing curriculum for 21st century skills, collaboration of ASEAN
for changing global context, to produce best practices for reform, systematic
discussion for further integration, a platform for curriculum and professional
development, and assessment4.

4 Common Core Regional Learning Standards(CCRLS) is a document for the development of regional
curriculum standards which is not the curriculum itself. It is a key reference for further collaboration of thecurriculum development, assessments, and professional development on the demands of 21st century which isrelated with SEAMEO Priorites No.5 and 7. National Curriculum Standards in every SEAMEO Member
Countries which are established under every country are respected. The document will be fuctioning for
progressive syncronization of curriculum developers and teacher educators in SEAMEO Member Countries
directed for ASEAN Community and revised for these demands. For these demands, it is described for
curriculum developers and teachers educators.

xviii

The 21st century curriculum encompasses learning, literacy and life
skills. Competent learners should be able to use tools such as language andtechnology to convey ideas and thoughts, can act autonomously based onrational decisions and ability to interact well with others in the community.
In that context, learners will grow and develop with knowledge and skills thatenable them to find jobs, being responsible, self-reliant and contributing tosociety.
OECD clarified the 21st century skills by the terms of competency(OECD, 2005). It defined competency for successful life and well-functioning
society. Societies are continuously changing for seeking success and welfare
development. United Nations sets the sustainable development goals(UN, 2015) under the necessity of the development of every society as well assustainability of social welfare. On this context, Mathematics and Science arenecessary subjects in education for success in various fields as well as welfare
in our life based on mutual understanding. Mathematics and Science are thetools for overcoming the challenges of diversities in Southeast Asia throughdeveloping the competency for competitiveness and understanding others forcreating a harmonious society.
The purposes of the Common Core Regional Learning Standards forMathematics and Science are to develop basic human characters, creative
human capital, and well qualified citizens in Southeast Asia for a harmonious
society through mathematics and science education. The purposes can be
developed and achieved through three major components. Firstly, cultivating
basic human characters, values, attitudes and habits of mind are essentials
to be developed through mathematics and science. Values are bases forsetting objectives of undertakings and making decisions for future directions.
Attitudes are mind-sets for attempting to pursue endeavours. Habits of mind
develop soft skills which are necessary for living harmoniously in the society.
Secondly, for developing creative human capital, process skills need to be
developed. Thirdly, knowledge of mathematics and science are essential for
cultivating well qualified citizens.
Developing the competency under the three components, includes theselection of necessary content for teaching and context for exploration which
encompasses metacognition, critical reasoning and communication. Under theselected content and the context, the three components are well connected andthe competency developed through the reflection of the processes. Proficiency
in applying competency is also developed through content and context inappropriate situations. Those three components under the context will beclarified by the descriptions of the standard in later chapters.

xixBased on the preceding background, the purposes of the SEA-BES project
were conceptualised in 2015 stated as follows:

Purposes of CCRLS under the SEA-BES Project
The SEAMEO Basic Education Standards initiative would support SEAMEOMember Countries in the following respects:a)to use it as an analytical tool to support future development of regional
integrated curriculum necessary for ASEAN integration with emphasis on
21st century skills;b)to strengthen ASEAN collaboration on curriculum standards and learningassessment across different educational systems to effectively respond tothe changing global context and complexity of ASEAN ;c)

to promote in every member country the establishment of best practices toovercome differences in curriculum;d) to produce systematic discussion process for the establishment of theregional integrated curriculum and assessment;e)

to use as a platform for curriculum development and professional
development for all stakeholders developing teachers imbued with
ASEAN ideals in building ASEAN community; andf)to serve as a platform for assessment such as the Southeast Asia Primary
Learning Metrics (SEA-PLM).

On these purposes of the SEA-BES project, CCRLS defines the standards onmathematics and science based on the following principles:i.

The standards are the common ground to develop the fullest potential andcapabilities to acquire competency in the 21st century.

i.

The standards are presumed for competitiveness in this globalization era
and understanding others in creating the ASEAN harmonious society
under global citizenship.

ii.

The standards serve as tools for analysing curriculum for the purpose of
the project as stated in (a) to (f).

Those principles are elaborated for a well-functioning ASEAN societies
taking into account the cultural differences and development disparity.
The standards for mathematics and science will be discussed separately at thelater chapters.

xxDevelopment Process of CCRLS
SEA-BES Project Framework in 2014
SEA-BES Project was initiated in 2014 before the establishment of the 7 Priority
Areas and as response for the SEAMEO College Project for preparation of theASEAN Community. The original conceptual framework is shown in Figure 1.

1. Theposition
CCRLS under
under theproject
framework.
FigureFigure
1. Thepositionof ofthetheCCRLS
theSEA-BES
SEA-BES
project
framework.

Methodology
to Develop
Methodology
to Develop
CCRLSCCRLS

Figure 2 shows the original flow process of the development of the common

Figure2 shows theoriginalstandards
flow processof the developmentof the common core regionalcore regional
learning
in mathematics
and science.
learning standards in mathematics and science.

Figure2.2.Framework
Frameworkin developing
the CCRLS
in Mathematics
Science
Figurein developing
the CCRLS
in Mathematics
and Scienceandfor SEA-BES
for SEA-BES(Mangao,and Zakaria,
2015).
(Mangao,
Tahir, Tahir,and Zakaria,
2015).
The CCRLS was developed based from the strengths of the existing national education
standards of the SEAMEO Member Countries. The various activities in the development of
the CCRLS document for Mathematics and Science undertook the following processes:
 curriculum review and comparison of the national education curriculum of the seven
SEAMEO Member Countries in Mathematics and Science, namely; Brunei
xxi
Darussalam, Cambodia, Indonesia, Malaysia,
Philippines, Singapore and Thailand; identificationofsimilarities
anddifferences
in
terms
of
content/domain/topics/strand/year level by country; and tracking of content/domain/topics/strands across grade levels from the primary to
secondary level.
There are diversities among SEAMEO Member Countries. The year levels are not always thesame. Thus, the CCRLS in Mathematics and Science documents are categorised into threeThe CCRLS was developed based from the strengths of the existing
national education standards of the SEAMEO Member Countries. The various
activities in the development of the CCRLS document for Mathematics andScience undertook the following processes:•

curriculum review and comparison of the national education curriculumof the seven SEAMEO Member Countries in Mathematics and Science,
namely; Brunei Darussalam, Cambodia, Indonesia, Malaysia, Philippines,
Singapore and Thailand;•

identification of similarities and differences in terms of content/domain/
topics/strand/year level by country; and•tracking of content/domain/topics/strands across grade levels from theprimary to secondary level.

There are diversities among SEAMEO Member Countries. The year
levels are not always the same. Thus, the CCRLS in Mathematics andScience documents are categorised into three key stages: Key Stage 1 covers
Grades 1 to 3, Key Stage 2 covers Grades 4 to 6 and Key Stage 3 covers
Grades 7 to 9.
Other activities undertaken include the development of the appropriate
strands for every stage and the topics under the strand and the elaborationof every standard description under the participation of representatives from
Member Countries (including Myanmar, Vietnam, Lao PDR and Timor Leste)and other leading researchers from non-SEAMEO Member Countries such as
APEC Economies.
The consolidated SEAMEO Mathematics and Science Standards were
benchmarked with the standards of high qualified education countries/
economies such as Hong Kong, Japan, Australia, United Kingdom and theU.S.; reviewed documents such as Trends in International Mathematics andScience Study (TIMSS), Programme for International Student Assessment(PISA), and National Council of Teachers of Mathematics (NCTM) as well as
research studies and literature available related to curriculum development.
Standards found in every stage are useful for every country to engage
in their own activity on purposes (a) to (f) especially for considering theexperiment and challenges for every country’s reform.

xxii

Series of SEA-BES Workshops
A series of workshops which aimed to develop the Common Core Regional
Learning Standards (CCRS) in Mathematics and Science were conducted on
different dates, levels and venues as follows:
A. National Level

B.

•

2 April 2015 (In-house/Local Level, SEAMEO RECSAM, Malaysia)•

11 May 2015 (In-house/Local Level, SEAMEO RECSAM, Malaysia)•

21-22 May 2015 (In-house/Local Level, SEAMEO RECSAM, Malaysia)•

23 July 2015 (In-house/Local Level, SEAMEO RECSAM, Malaysia)•

27 August 2015 (In-house/Local Level, SEAMEO RECSAM, Malaysia)•

17 September 2015 (In-house/Local Level, SEAMEO RECSAM,
Malaysia)•

27-28 January 2016 (In-house/Local Level, SEAMEO RECSAM,
Malaysia)•

24-25 March 2016 (In-house/Local Level, SEAMEO RECSAM,
Malaysia)

Regional Level•

4-5 November 2014 (Regional Level, SEAMEO RECSAM, Malaysia)•

20-22 October 2015 (Regional Level, SEAMEO RECSAM, Malaysia)•

15-18 February 2016 (Regional Level, University of Tsukuba, Japan– Only for Mathematics Standards)•

9-12 February 2017 (Regional Level, University of Tsukuba, Japan– Only for Mathematics Standards)•

28-30 March 2017 (Regional Level, SEAMEO RECSAM, Malaysia)xxiii

Participation and Involvement of Experts, Educators and Institutions
Maximum participation and involvement of experts and teachers across theSoutheast Asian region and beyond were solicited in the development of the
CCRLS document. Their tasks include being a member of curriculum working
group giving inputs and providing specific, constructive feedback on the draft
Standards. The following groups were involved:•

Consultants (Professor Masami Isoda, Center of Research on International
Cooperation in Educational Development, University of Tsukuba, Japan;
Dr. Mark Windale, Centre for Science Education, Sheffield Hallam
University, United Kingdom; and Professor Kerry J. Kennedy, Hong Kong
Institute of Education, Hong Kong)•

Curriculum experts in science and mathematics from the 11 Ministries of
Education of SEAMEO Member Countries•

SEAMEO Secretariat•

Science and mathematics specialists from SEAMEO centres (i.e. RECSAM,QITEP in Science, QITEP in Mathematics, SEAMOLEC)•

Mathematics professors and experts from APEC economy members who
were present during APEC-Tsukuba International Conference X andAPEC-Tsukuba International Conference XI (Grant No.26245082 andAPEC HRD 03-2015A)•

Science and mathematics professors and curriculum specialists fromJapan under the project of Japan Society for Promotion of Science(JSPS-Grant No.16K13563 and 26245082)•

Science and mathematics professors and lecturers from Malaysian
educational institutions (i.e. Universiti Sains Malaysia (USM),
Universiti Pendidikan Sultan Idris (UPSI), Institut Pendidikan Guru (IPG)– Kampus Pulau Pinang, Kampus Tuanku Bainun and Kampus Ipoh) in
Malaysia•

Science and Mathematics National Centres (i.e. Institute for the Promotionof Teaching Science and Technology (IPST), University of the PhilippinesNational Institute for Science and Mathematics Education Development(UP-NISMED)•

Elementary and secondary science and mathematics master andexperienced teachers from Penang Statexxiv

Chapter 1

COMMON CORE REGIONAL LEARNING
STANDARDS IN MATHEMATICS

1Chapter 1

Chapter 1

Framework for CCRLS in Mathematics
The first chapter describes the direction of CCRLS for creating a harmonious
society of ASEAN in this competitive era through mutual understanding.
The CCRLS serves as a tool to develop basic human characters, creative
human capital, and well qualified citizens through mathematics and science.
The direction of CCRLS describes three major components. Firstly, for cultivating
basic human characters through mathematical values, attitudes and habits ofmind. Secondly, for developing creative human capital, process skills need
to be developed. Thirdly, knowledge of mathematics and science are forcultivating well qualified citizens. For clarifying how these three components
function within the mathematics framework, the nature of mathematics is
considered initially and the aims of CCRLS in mathematics are deduced from it.
Lastly, the format of describing the CCRLS in mathematics will be shown before
elaboration of every standard.

Nature of Mathematics
Mathematics has been recognized as a necessary literacy for citizenship and not
only living economically but also to establish a society with fruitful arguments
and creations for better living. It has been taught as a basic language for allacademic subjects using visual and logical-symbolic representations. In thisinformation society, mathematics has increased its role to establish 21st century
skills through reviewing mathematics as the science of patterns for future
prediction and designing with big data which produces innovation not only
for technology advancement but also for business model.
Mathematics is an essential subject to establish common reasoning forsustainable development of society through viable argument in understanding
each other and develop critical reasoning as the habits of mind. Mathematics
should be learned as basis for all subjects. For clarifying the framework in
CCRLS on mathematics and by knowing the role of mathematics education, thehumanistic and philosophical natures of mathematics are confirmed as follows;
Humanistic nature of mathematics is explained by the attitudes ofcompetitiveness and understanding of others by challenging mathematicianssuch as Blaise Pascal, Rene Descartes, Isaac Newton and Gottfried Wilhelm
Leibniz. For example, if you read the letter from Pascal to Pierre de Fermat
you recognize competitive attitude of Blaise Pascal to Fermat’s intelligence andseeking the way to be understood by his Excellency of his finding on Pascal’s

2Chapter 1

Triangles. If we read the Pascal’s pensee you recognize how Pascal denies
Descartes geometry using algebra from the aspect of ancient Greek geometry.
On the other hand, Descartes tried to overcome the difficulties of ancient
geometry by algebra. If you read the letter from Descartes to Elisabeth,
you recognize how Descartes appreciated and felt happy when theRoyal Highness Elisabeth used his ideas of algebra in geometry. Despite beinga princess, Elisabeth had been continuously learning mathematics in her life.
There were discussions on who developed calculus between Britain andContinental mathematician. On that context, Johann Bernoulli, a continental
mathematician, posed a question on the journal about the Brachistochrone
problem, locus of the point on circumference of the circle when it rotates on theline. No one replied and Bernoulli extended the deadline of the answer and asked
Newton to reply. Newton answered it within a day. Finally, six contributions of
the appropriate answer including Newton and other Continental mathematicians
were accepted. All those stories show that mathematics embraces the humanistic
nature of proficiency for competitiveness and understand others for sharing
ideas.
Philosophical nature of mathematics can be explained on ontological andepistemological perspectives. On the ontological perspective, mathematics
can be seen as a subject for universal understanding and common scientificlanguage. Plato and Aristotle are usually compared on this perspective.
Plato believes that the existence of the world of “idea” and mathematics
existed in the world of “idea” on Platonism. On this context, mathematicalcreation is usually explained by the word “discover” which means taking
out the cover from which it has already existed. At the moment of discovery,
reasonable, harmony and beautifulness of mathematical system is usually felt.
Aristotle tried to explain about reaching idea from the “material” to the “form”.
This explains that abstract mathematics can be understood with concrete materials
using terms such as “modelling”, “instruments”, “embodiment”, “metaphor”
and “change representation”. From both ontological and epistemologicalperspectives, mathematics can be understandable and acquirable by everyone
and if acquired, it serves as a common scientific language which is used toexpress in any subjects. Once representing the ideas using the shared common
language, the world can be possibly perceived in the same view autonomously.
On the epistemological perspective, mathematics can be developed throughprocesses which are necessary to acquire mathematical values and ways ofthinking. From this perspective, idealism and materialism are compared.
On the context of Hegel, a member of German idealism, Imre Lakatos explained
the development of mathematics through proof and refutation. On his context,3

Chapter 1

mathematics is not fixed but an expandable system that can be restructured
through a process of dialectic in constructing viable arguments. Plato also useddialectic for reaching ideas with the examples of mathematics. The origin of
dialectic is known as the origin of indirect proof. In education today, dialectic
is a part of critical thinking for creation. Parallel perspectives for mathematicaldevelopments are given by George Polya and Hans Freudenthal. For the
discovery of mathematics, Polya explained mathematical problem solving
processes with mathematical ideas and mathematical ways of thinking in
general. Freudenthal enhanced the activity to reorganize mathematics by theterm mathematization.
Genetic epistemologist Jean Piaget established his theory for operations
based on the various theories including Freudenthal’s discussion and explained
mathematical development of operations by the term reflective abstraction.
Reflection is also a necessary activity for mathematization by Freudenthal.
On materialism, under Vygotskyian perspective, intermediate tools such as
language become the basis for reasoning in the mind. Under his theory, the highquality mathematical thinking can be developed depending on the high quality
communication in mathematics classrooms. Dialectical-critical discussion should
be enhanced in the mathematics class. From both epistemological perspectives,
mathematics can be developed through the processes of communication,
problem solving and mathematization which include reorganization ofmathematics. Those processes are necessary to acquire mathematical values
and ways of thinking through reflection.

Aims of Mathematics in CCRLS
The aims of mathematics in CCRLS for developing basic human characters,
creative human capital, and well qualified citizens in Southeast Asia for aharmonious society through mathematics are as follows:•

Develop mathematical values, attitudes and habits of mind for humancharacter,•

Develop mathematical thinking and enable to produce appropriate
process,•

Acquire proficiency in mathematics content and apply mathematics inappropriate situations.

4Chapter 1

Framework for CCRLS in Mathematics as shown in Figure 3 is developed
under the three components and the discussion of humanistic and philosophicalFigure3: CCRLS
for Mathematics
and Aims of Mathematics
Learning
natureof Framework
mathematics.
The framework
also provides
the concrete ideas ofmathematics learning on the above aims.
Mathematical Values, Attitudes and Habits for Human Character
Mathematical Values:
Seeking ‐ Generality andexpandability
 Reasonableness andharmony Usefulness andefficiency
 Simpler and easier Beautifulness

Mathematical Attitude
Attempting to ‐
 See and think mathematically Pose questions and develop
explanations
 Generalize and extend
 Appreciate others’ ideas andchange representations formeaningful elaborations

Mathematical Habits of Mind
For living ‐ Reasonably and critically while
respecting and appreciating others
 Autonomously and socially Creatively, innovatively andharmoniously to develop citizenship Judiciously in using various tools
 With empowerment in predicting thefuture through lifelong learning

Mathematical Thinking and Processes
Mathematical Ideas:
Set, Unit, Comparison,
Operation, Algorithm,
Fundamental principles,
Permanence of form,
various representations andTranslations.

Mathematical Thinking: Generalisation and specialisation
 Extension and integration
 Inductive, analogical and deductive
reasoning Abstracting, concretising and embodiment Objectifying by representation andsymbolising Relational and functional thinking
 Thinking forward and backward

Mathematical Activities:
 Problem solving
 Exploration and inquiry
 Mathematical modeling Conjecturing, justifying andproving Conceptualisation andproceduralisation
 Representation and sharing

Contents
Key Stage 1
 Numbers & Operations
 Quantity & Measurement
 Shapes, Figures and Solids
 Pattern & Data
Representations

Key Stage 2
 Extension of Numbers andOperations
 Measurement & Relations
 Plane Figures & Space Solids
 Data Handling & Graphs

Key Stage 3
 Numbers & Algebra Relations & Functions
 Space & Geometry
 Statistics & Probability

Figure 3. CCRLS Framework for Mathematics.

5

Chapter 1

Mathematical Values, Attitude and Habitsfor Human Character
For cultivating basic human characters, values, attitudes and habits of mind areessentials to be developed through mathematics. Values are basis for setting
objectives and making decisions for future directions. Attitudes are mind-sets
for attempting to pursue undertakings. Habits of mind are necessary for soft
skills to live harmoniously in the society. Mathematical values, mathematical
attitudes and mathematical habits of mind are simultaneously developed andinculcated through the learning of the content knowledge.
Essential examples on values, attitudes and habits of mind are given in
Figure 3. On values, in mathematics, generalizable and expandable ideas areusually recognised as strong ideas. Explaining why such as proving is necessary
in mathematics, then it is usually seeking reasonableness. Harmony andbeautifulness are described not only in relation to mathematical arts, but also
in science of patterns and the system of mathematics. Usefulness and simplicity
are used in selection of mathematical ideas and procedures.
On mathematical attitudes, “seeing and thinking mathematically” means
attempting to use the mathematics learned for seeing and thinking the objects.
Posing questions and providing explanation such as the “why” and the “when”
are ordinary sequence for thinking mathematically. Changing representation toother ways such as modelling can overcome the running out of ideas in problem
solving. The mindset for trying to understand others is the basis to explain own
ideas that is understandable to the rest with appreciation. Producing the concept
with definition operationally is a manner of mathematics.
On habits of mind for citizens to live, mathematical attitudes and values arenecessary to reason out critically and reasonably. Appreciating and respecting
other ideas is also necessary. Mathematics is developed independently for those
who appreciate life creatively, innovatively and harmoniously. Seeking the easierand effective manner selection of appropriate tools is necessary. Mathematics
as a subject to challenge and experience competitiveness, appreciation withothers, develop the mindset for lifelong learning, personal development andsocial mobility.

6Chapter 1

Mathematical Thinking and Processes
For developing creative human capital, mathematical ideas, mathematicalthinking and mathematical activities are essential. Mathematical ideas areprocess skills involving mathematical concepts. Mathematical thinking ismathematical way of reasoning in general which does not depend on specificconcepts. Mathematical activities are various types of activities such asproblem solving. Mathematical processes which include these components arenecessary skills to use mathematics in our life, such as innovation in this society(e.g. Internet of Things (IOT)). In the context of education, competency referring
to mathematical processes is basis for STEM and STEAM5 education as well as
basis for social science and economy education.
Mathematical ideas serve as the basis of content knowledge related
to promoting and developing mathematical thinking. Some key ideas ofmathematics are used as special process. The fundamental ideas of set and unit
lead to a more hierarchical and simple structural relationship. The ability tocompare, operate, and perform algorithm of related functions enables efficient
ways of learning mathematics and solving problem in life with mathematics.
In the case of set, set as mathematical ideas is related with conditions andelements. It is related with activity in grouping and distinguishing with othergroups by conditions. Example, 3 red flowers and 4 white flowers become 7
flowers, if we change the condition of the set by not considering the colours.
“A and non A” is a simple manner to distinguish sets with logical reasoning.
For categorizing, we use intervals such as x > 0, x < 0, x = 0. This situation canbe seen in the hyperbolic graph where y=1/x.
In the case of unit, it is a mathematical idea that is related with the process
to produce and apply the unit with operations. On some cases, trying to findthe common denominator is the way to find the unit of two given quantity.
Tentative unit such as arbitrary units can be set and applied locally whereas
standard units are used globally. In the combination of different quantities it
produces new measurement quantity such as distance with respect to time
produce speed. Square unit such as square centimetres is a unit for area.
Mathematical thinking is well discussed by George Polya. Inductive,
analogical and didactical reasoning are major logical reasoning at school however,didactical reasoning is enhanced in relation to formal logic and inductive andanalogical reasoning are not well recognized. Polya enlightens the importanceof those reasoning in mathematics. On the process of mathematization by
5 STEM refers to Science, Technology, Engineering and Mathematics. STEAM refers to Science, Technology,
Engineering, Arts and Mathematics or Applied Mathematics.

7

Chapter 1

Hans Freudenthal, objectifying of the method is necessary. David Toll mentioned
it by the term thinkable concept on the process of conceptual development.
Polya mentioned thinking forward and backward in relation to ancient Greek
term analysis.
Mathematical activities are ways to represent mathematical process.
Problem solving process was analysed by Polya. He influenced encompassing
problem solving with various strategies. Technology enhances the activities
of conjecturing and visualizing for inquiries. Conceptualization is done basedon procedures such as the procedure 3+3+3+3=12, become the basis for 4x3.
The proceduralization of multiplication is done through developing themultiplication table, idea of distribution and memorizing.

Content
For cultivating well qualified citizens, content knowledge of mathematics isessential. Content of mathematics is usually divided by the set of mathematics.
However, for developing human characters and creative human capitals,
it should be developed through the mathematical processes. Values, attitudes
and habits of mind are driving force to engage in mathematical processes.
Thus, without involving human character formations with mathematicalprocess skills, content knowledge of mathematics cannot be realised.
The content is divided into three stages in CCRLS and every stage has four
strands. Between the stages, the names of the strands are directly connected.
However, on the standard level, content standards are well connected.
The names of strands for every key stage are as follows:
Key Stages 		Strands

Key Stage 1 		Numbers and Operations
Quantity and Measurement
Shapes, Figures and Solids
Pattern & Data Representations

Key Stage 2 		Extension of Numbers and Operations
Measurement and Relations
Plane Figures & Space Solids
Data Handling and Graphs

Key Stage 3 		Numbers and Algebra
Relations and Functions
Space and Geometry
Statistics and Probability

8Chapter 1

In every stage, four content strands are mutually related6. Between key
stages, all strands in different key stages are mutually related. The same content
strand names are not used to indicate development and reorganization beyond
each stage. For example, “Numbers and Operations” in Key stage 1, “Extensionof Numbers and Operation” in Key stage 2, and “Numbers and Algebra” inKey stage 3 are well connected. These names of the content strands show theextension and integration of content. For example, even and odd numbers
can be taught at any stages with the different definition. At Key stage 1 evennumbers can be introduced “counting by two” which does not include zero.
In Key stage 2 it can be re-defined by a number divisible by two. Finally,in Key stage 3 it can be re-defined multiple of two in integers which includes zero.
Although we use the same name as even number, they are conceptually different.
Key stage 1 definition is based on the counting, Key stage 2 is based on division
while Key stage 3 is based on algebraic notation7. For expressing such theoreticaldifferences, name of strands for content should be distinguished. In the caseof measurement, there is no strand name of measurement in Key stage 3.
Key stage 1 relates with quantity and setting the units. In Key stage 2, it extends
to non-additive quantity beyond dimension. In Key stage 3 the idea of unit
and measurement is embedded in every strand. For example, square root in
Number and Algebra strand is an irrational number which means unmeasurable.
Pythagorean Theorem in Space and Geometry strand is used for measuring
proportional function in Relations and Functions strand which is used forcounting the number of nails by weight, and in Statistics and Probability strand,
new measurement units are expressed such as quartile for boxplot.

Context to Link the Three Components
Three components in Figure 3 should be embedded in every key stage as
standards for the content of teaching. “Mathematical values, attitudes, habits
for human character” component and “Mathematical thinking and processes”
component cannot exist without “Content” component. The first twocomponents can be taught through teaching with the content. For teaching those
three components at the same time, context is introduced as shown in Figure 4.

6 Strands used to explain mutual relation of content (Jeremy Kilpatrick, Jane Swafford, Bradford Findell.
“Adding it up”, National Academies Press. 2001).The term domain is sometimes used for compartmentalization
through categorization of content.
7 In algebraic notation of numbers, addition and multiplication are major operations. Subtraction can be
represented by addition of negative numbers and division can be represented by reciprocal or multiplicative
inverse property.

9Chapter 1

Mathematical Values, Attitudes andHabits for Human Character

Mathematical Thinking
and Processes

Content

Figure4.4.Interlinking
with thethecontext.
context.
FigureInterlinkingofofthe
thethreethree components
components withOn the givenOncontext,
three
components
are wellOn thisreason,classroom
the givencontext,
three components
areconnected.
well connected.
On thisreason,classroom
activities
for developing
competencies
shoulddesigned
linkfollowing
activities fordeveloping
competencies
shouldbe designed
to be
link
them. toThe
them.
The following contexts are samples:
contexts are
samples: Explore
a problemwithcuriosity
situation
and attempting
to formulate• Explore
a problemwithcuriosity in a asituation
and attempting
to formulatemathematicalproblems
mathematicalproblems
 Applymathematics
learned,listenlisten
to other’sideas
andandappreciatethetheusefulness,
• the
Apply
the mathematics
learned,to other’s
ideas
appreciate
power andbeauty powerof mathematics
usefulness,and beauty of mathematics
 Enjoy
communications
on mathematicalideas insolvingproblems with• classroom
Enjoy classroom
communications
on mathematicalideas
in solving
patienceproblems
and develop
persistencewith patience and develop persistence Feel the excitement of “Eureka” with enthusiasm for the solutions and explanation of• Feel the excitement of “Eureka” with enthusiasm for the solutions andunknown problems
explanation of unknown problems
 Think about ways of explanation using understandable representations such as• Think
about diagrams
ways of explanation
using
understandable representations
language,
symbols,
and notationof mathematics
such as language, symbols, diagrams and notation of mathematics
 Discuss the differences in seeing situations before and after learning mathematics• Discuss
the differences
seeing situations
beforeand after learning Explain,
understandothers andin
concludemathematicalideas
mathematics
 Explore ideas through inductive and deductive reasoning when solving problems to• mathematical
Explain, understandothers and conclude mathematical ideas
fostercuriosity
 Explore ideas with examples and counter examples
 Feel confident in using mathematics to analyse and solve contextual problems both inschool and in real-life situations
 Promote knowledge, skills and attitudes
10 necessary to pursue further learning inmathematics
 Enhance communication skills with the language of mathematics
 Promote abstract, logical, critical and metacognitive thinking to assess their own andothers’ work
 Foster critical reasoning for appreciating other’s perspectives
 Promote critical appreciation on the use of information and communications

Chapter 1•

Explore ideas through inductive and deductive reasoning when solving
problems to foster mathematical curiosity•

Explore ideas with examples and counter examples•

Feel confident in using mathematics to analyse and solve contextual
problems both in school and in real-life situations•

Promote knowledge, skills and attitudes necessary to pursue further
learning in mathematics•

Enhance communication skills with the language of mathematics•

Promote abstract, logical, critical and metacognitive thinking to assess
their own and others’ work•

Foster critical reasoning for appreciating other’s perspectives•

Promote critical appreciation on the use of information and communications
technology in mathematics•

Appreciate the universality of mathematics and its multicultural andhistorical perspectives

Those contexts are chosen for illustrating the interwoven links of the twocomponents with contents. It looks methods of teaching however all threecomponents are the subject of teaching on the contexts.

Descriptions Format for SEA-BES CCRLS in Mathematics
Curriculum standards in every country are written under specific format for
all school subjects under the regulation and policy of the Ministry of Educationin every country and with direction of curriculum reform. The format itself
embedded the direction of national reform of movement itself.
The format of writing the CCRLS is produced under Figures 3 and 4, and thecontent standards and the process-humanity strands with the defined context
as follows:
Each key stage has four content strands and one mathematical processhumanity strand. The content strands describe the content standards.
The mathematical process-humanity strands describe the elements covered
under mathematical thinking and process component, and values, attitudes andhabits of human character component in Figure 3. The word “process” refers
to the mathematical thinking and processes discussed in Figure 3. The word
“humanity” refers to the elements in the components of mathematical values,
attitude and habits. The mathematical process-humanity standards of each key
stage imply the context for learning those two components. The descriptions of11

Chapter 1

every standard under the process-humanity strands are commonly discussed
across different content strands8 within the same key stage.
Mathematical process-humanity strand includes three processes(Mathematical Ideas, Thinking and Activities) and the three humanities(Mathematical Values, Attitudes and Habits of mind for Citizen to live).
The above contexts shown explain three processes for developing
mathematics such as: Argumentation for understanding others and develop
sophistication through critique; and Applying mathematics through modelling
and replacement. Extension and generalization are essential elements fordeveloping mathematics.
In argumentation, producing understandable explanations are usuallyrelated to understandable representation such as diagram and materials forshowing the simple structure. Example is used for demonstration of specificcase and counter example is used for checking generality. Process of modelling
usually includes problem formation, solving mathematically, and explaining themeaning. Within these three processes, three humanities such as recognizing
beautifulness of patterns are learned through the appreciation of mathematicalexperiences, appreciation of other’s ideas also includes understanding ideas
with sense such as recognize the usefulness of idea or otherwise.
Under those explanations, the writing format is defined with content
standards and process-humanity standards. It includes the choosing ofnecessary content for teaching and exploratory sequence which encompasses
metacognition, critical reasoning and communication, and reflection.
Under the selected content and the context, the three components in
Figure 3 are well connected. Proficiency of skills and procedures is also
developed through content and context in appropriate situations and necessary
exercise.

8 The delegates from SEAMEO Member Countries worked together at the SEAMEO RECSAM-University ofTsukuba Joint Seminar: Searching for Quality Mathematics Curriculum Framework on the Era of Globalization,
February 15-18, 2016 (The University of Tsukuba is an affiliated member of SEAMEO) for the establishmentof agreement on the format of curriculum. In the meeting, 21st century curriculum frame work and every
countries frame work were presented. The four content strands and one process-humanity strand for every
learning stage were agreed. The hierarchy under content strands is also deduced as follows: every content
strand, topic is described in a sentence beginning from a verb in a gerund form to embed context into content,
every topic standard is described in sentences with a verb and adjective to emphasize the activity and value.

12Under those explanations, the writing format is defined with content standards and processhumanity standards. It includes the choosing of necessary content for teaching andexploratory sequence which encompasses metacognition, critical reasoning andcommunication,and reflection. Under the selected content and the context, the three
Chapter
1
components in Figure 3 are well connected. Proficiency of skills and procedures is also
developed through content and context in appropriate situations and necessary exercise.

SampleFormatSample Format
SEA-BES CCRLS Mathematics is developed under the Framework in Figure 3
SEA-BES CCRLSstMathematics is developed under the Framework in Figure 3 and for theandfor theskills
21 andcentury
and choses
followingand
formatto distinguish21st century
chosesskills
the following
formatthe
to distinguish
relate thedescriptions
andrelate thedescriptionsof thisstandards
beyondthe stages.
Onideasthis forformat,of standards
beyondthe stages. On
format, every
standard
embeds thewhat
are expected
to be learned,
is related
other
and
it is necessary
every
standard
embedshow
theitideas
forwithwhat
arestandards
expected
towhy
be learned,
howforit
furtherlearning.
isrelatedwith other standards and why it is necessary for further learning.
Key Stage Number
General explanation for every stage.
Strand: Title of Strand under the Stage
The description of each strand gives clear images for the developmental level in three
Key Stages.
Topics:A set of Content standards is described under the topic. Every topic sentence begins fromthe gerund form of the verb that implies mathematical process-humanity. In the case of
Mathematical Process-Humanity Strand in every stage, every standard is described under
the strand without categorizing into the topics.
Standard:
Every standard is described with gerund form and verb to show process and adjective tocite value and attitude as follows:(Sample) Enjoying counting orally and manipulatively with number names,
without symbolic numeralsi.
ii.

Develop the fluency of the order of number names and use it based on
the situation
Set initial object for counting, direction of counting and recognize the endof objects with one to one correspondence32

13Chapter 2

Chapter 2

Key Stage 1
Key Stage 1 (KS1) serves as the foundation of knowledge covering the basic
facts and skills developed through simple hands-on activities, manipulation of
concrete objects, pictorial and symbolic representations. This stage focuses on
arousing interest, enjoyment and curiosity in the subject through explorationof pattern, characterization, identification and describing shapes, performing
the four fundamental operations, identify its algorithm, and understanding
basic mathematical concept and skills experienced in daily life. Calculationof quantities will also be established to carefully and wilfully understand theattribution of objects that are used to make direct and indirect comparison.

Strand: Numbers and Operations
Number is introduced with situations, concrete objects, pictorial and symbolic
representations and extended based on knowledge and skills learned. Ways ofcounting and distributions are extended to addition, subtraction, multiplicationand division. Base ten number system is the key for extending the numbers andoperations for standard algorithms in vertical form. Also, various proceduresof calculations and algorithms are focused. Models and diagrams are used forextension instead of concrete materials itself. Number sense will be developed
through the establishment of fluency of calculations with connection to situations
and models. Fractions and decimals are introduced with manipulative.
Topics:Introducing numbers up to 120
Introducing addition
Introducing subtraction
Utilizing addition and subtraction
Extending numbers with base ten system up to 1 000 000 gradually
Producing the vertical forms for addition and subtraction and acquiring
fluency of standard algorithms
Introducing multiplication and producing multiplication algorithm
Introducing division and extending it to remainder
Introducing fractions and extending to addition and subtraction of similar
fractionsIntroducing decimals and extending to addition and subtraction
14

Chapter 2

Introducing numbers up to 120
Enjoying counting orally and manipulatively with number names, without
symbolic numerals;i.

Develop the fluency of the order of number names and use it based on
situations9ii.

Set initial object for counting, direction of counting and recognize the endof objects with one to one correspondence

Understanding and using the cardinality and ordinality of number with objects
and numerals10 through activities of grouping, corresponding and ordering,and developing number sense11:i.

Group objects for counting with conditions such as cups, flowers,
and rabbits on situations and introduce the numeralsii.

Obtain fluency of counting concrete objects and understand counting oniii. Compare different sets by one to one correspondence and recognize larger,
smaller or equal with appreciation in drawing paths between objects
iv. Compose and decompose numbers for strengthening the number sense12
and cardinalityv.

Understand the difference of ordinal and cardinal numbers and use themappropriately in situations and challenge the mixed sequence

vi. Acquire number sense13 in ordering numerals with and without concrete
objects
Introducing base ten system with groupings of 10 and extend numbers up to12014.
i.

Extend numbers to more than 10 with base ten manipulative representing
numbers in ones and tens, and appreciate base ten numeration system

ii.

Extend the order sequence of numbers to more than 10 in relation to thesize of ones and tens and compare numbers using numeral in every placeiii. Introduce number lines to represent the order of numbers starting fromzero to see it from counting by ones, twos, fives, and tens, and use it ascomparison
9 The denomination such as 3 cups, 2 cups, one cup is described at the Quantity and Measurement strand.
10 Inclusive in reading and writing of numerals.
11 Unit for counting that is described in the Quantity and Measurement strand.
12 Relationship of composing and decomposing numbers becomes the preparation for addition and subtraction
for inverse operation.
13 Number pattern is discussed under Pattern and Data Representations.
14 For discussing the difference of hundred twenty is not twelve ten in English.

15

Chapter 2

iv. Enjoy various ways of distribution of objects with counting such as
playing cards, and explain it and enhance number sensev.

Draw diagram for representing the size of number with base ten blocks
such as square for a unit of hundred and rectangular bar for a unit of ten

Introducing Addition
Understanding the situations for addition up to 10 and obtaining fluency using
addition in situationsi.

Introduce situations (together, combine, and increase) for addition andexplain it with manipulative and orally to define addition for operationii.

Develop fluency of addition expressions using composition of numbers
for easier calculation using number sense for composition of numbersiii. Apply addition with fluency in life
Extending addition to more than 10 and obtaining fluency using addition insituationsi.

Extend addition with situations and think about how to answer using theidea of making 10 with decomposition and composition of numbersii.

Explain the idea of addition with place value using block diagramsiii. Develop fluency of addition expressions to more than 10 for easiercalculation
iv. Apply addition fluency in life

Introducing Subtraction
Understanding situations for subtraction up to 10 and obtaining fluency using
subtraction in situationsi.

Introduce situations (remaining, decrease, and difference) for subtractionand explain it with manipulative and orally to and define subtraction for
operation15

ii.

Develop fluency of subtraction expressions using decomposition of
numbers for easier calculationiii. Apply subtraction fluency in life

15 Distinguish minuend and subtrahend.

16Chapter 2

Extending subtraction to more than 10 and obtaining fluency using subtraction
in situationsi.

Extend subtraction with the situations and think about how to answer
using the idea of 10 with addition and subtraction of numbersii.

Explain the idea of subtraction in place value using block diagramiii. Develop fluency of subtraction expressions to more than 10 for easiercalculation
iv. Apply subtraction fluency in daily life

Utilizing Addition and Subtraction
Utilizing addition and subtraction in various situations and understanding
their relationshipsi.

Understand the difference of addition and subtraction with diagrams on
situations

ii.

Explain subtraction as an inverse of addition on situations with diagramsiii. Understand addition with three numbers, subtraction with three numbers
and combination of addition and subtraction on situations
iv. Apply addition and subtraction in various situations such as ordering
numbers

Extending Numbers with Base Ten System Up To 1 000 000 Gradually
Extending numbers using base ten system up to 1 000i.

Experience counting of 1 000 by using various units and appreciate thenecessity of the base ten system

ii.

Extend the order of numbers to more than 1 000 in relation to the size ofones, tens and hundreds

iii. Use number line partially to compare size of numbers through translationof the size of every digit and select appropriate scale
iv. Represent appropriate diagram to show the size of numbers without
counting such as three of hundreds mean 30 of tens and visualize therelative size of numbersv.

Represent larger or smaller numbers by symbol of inequality

17Chapter 2

Extending numbers using base ten system up to 10 000i.

Visualize the 10 000 by using thousand, hundred, ten and one as unitii.

Extend the order sequence of numbers to more than 10 000 in relation to
the size of ones, tens , hundreds and thousandsiii. Use number line with appropriate scale to show size of numbers and toshow relative size of numbers while focusing on the scale
Extending numbers using based ten system up to 1 000 00016
i.

Extend numbers up to 10 000 and learn the representation of the placevalue for grouping every 3-digit numeral system up to millionii.

Write large numbers using grouping of 3-digit numeral system17 such as
thousand as a unit and compare numbers in relation to itiii. Develop number sense such as larger and smaller based on comparison ofplace values through visualization of relative size of numbers

Producing the vertical forms for addition and subtraction18 and acquiring
fluency of standard algorithms
Thinking about the easier ways for addition and subtraction and producing
vertical form with algorithms
i.

Think about easier ways of addition or subtraction in situations and use
models with base ten blocks meaningfully for representing base ten systemii.

Produce and elaborate efficient ways and identify the standard algorithms19
in relation to base ten system with appreciationiii. Explain the algorithms of borrowing and carrying with regrouping ofbase ten models
iv. Acquire fluency in addition and subtraction algorithms

16 One million is too big for counting and is introduced only for learning of the three digit system.
17 3-digit numeral system such as 123 times thousand equals the same way of reading plus thousand.
In the case of Chinese, four- digit numeral system is used.
18 Understanding the relationship of addition and subtraction is discussed under Pattern andData Representations.
19 Various algorithms are possible and there is no one specific form because depending on the country, verticalform itself is not the same. Here, standard algorithm means the selected appropriate form.

18

Chapter 2

Acquiring fluency of standard algorithm for addition and subtraction andextend it up to 4 digit numbersi.

Extend the vertical form addition and subtraction through the extensionof numbers and appreciate the explanation using block modelii.

Develop fluency of every extension up to 3-digit numbers and simple casefor 4 digit numbers

Developing number sense20 for estimation21 and using calculator sensibly for
addition and subtractioni.

Develop number sense for mental arithmetic with estimation for additionor subtraction of numbers

ii.

Identify necessary situation to use calculators sensibly in real lifeiii. Appreciate the use of calculator in the case of large numbers for finding
total and balance

Introducing Multiplication and Producing Multiplication Algorithm
Introducing multiplication and mastering multiplication tablei.

Understand the meaning of multiplication22 in situations with models
using the idea of addition and distinguish from just addition to find theamount that is a number of the base amountii.

Produce multiplication table in the case of counting by 2 and 5 witharray diagrams, pictures or block models and extend it until 9 and 1 withappreciation of patterns23

iii. Develop sense for multiplication through mental calculation with fluency
iv. Use multiplication in daily life, differentiating the situations for
multiplication in various situations with understanding that any number
can be a unit for counting in multiplication
Producing multiplication in vertical form and obtaining fluencyi.

Think about easier ways of multiplication in the case of numbers greaterthan 10 using array diagrams and block models

ii.

Develop multiplication in vertical form using multiplication table, array,model, and base ten system with appreciation

20 Money system is discussed under Measurement and Relations.
21 Rounding numbers are treated in Key Stage 2 under Measurement and Relations.
22 Meaning of area is described in Measurement and Relations.
23 Multiplication row of 1 is not a repeated addition.

19

Chapter 2iii. Extend multiplication algorithm to 3- digits times 2-digits number
iv. Obtain fluency for standard algorithm for multiplicationv.

Use estimation with multiplication of tens or hundreds in life

vi. Compare the multiplication expressions which is larger, smaller or
equivalentvii. Appreciate the use of calculator sensibly in life in the case of large numbers

Introducing Division and Extending It to Remainder
Introducing division with two different situations and find the answer bymultiplicationi.

Understand division with quotative and partitive division for distribution
situationsii.

Think about how to find the answer of division situations by the
distributions using diagrams, repeated subtractions and multiplicationiii. Obtain fluency to identify answers of division through inverse operationof multiplication
iv. Appreciate the use of multiplication table for acquiring mental division
Extending division into the case of remainders and use division for distribution
in daily situationsi.

Extend division in situations with remainders and understand divisioneven it has the same as repeated subtraction with different remaindersii.

Obtain fluency for division and apply it in daily situations

iii. Understand division algorithm in simple case

Introducing Fractions and Extending to Addition and Subtraction of
Similar Fractions
Introducing simple fractions such as halves, quarters and so on based on thenumber of halves, quarters and so on using paper folding and drawing thediagrami.

Introduce simple fractions using manipulative such as paper folding anddrawing diagram on the context of part whole relationshipii.

Use “a half of” and “a quarter of” in the daily context such as half a slice of
bread

20

Chapter 2iii. Count a quarter for representing one quarter, two quarters, three quarters,
and so on
iv. Compare simple fractions in the case where the whole is the same andexplain
Extending fractions using tape diagram and number line to one, and think about
how to add or subtract with similar fractions for producing simple algorithmi.

Extend fractions to more than one unit quantity for representing theremaining parts such as measuring the length of tape, recognizing theremaining parts as a unit measure of length, and understand proper andimproper fractionsii.

Appreciate fractions with quantities in two ways; firstly, whole is a unit ofquantity and secondly, based on the number of unit fractioniii. Compare fractions in the case where the whole is the same and explain itwith tape diagram or number line, and develop number sense of fractions
such as 1/10 with quantities and so on
iv. Think about how to add or subtract similar fractions with tape diagram or
number line and produce simple algorithm with fluency

Introducing decimals and extending to addition and subtraction
Introducing decimals to tenths, and extend addition and subtraction into
decimalsi.

Introduce simple decimals to tenths by remaining part such as tapediagram with appreciationii.

Compare size of decimal numbers on the number line with the idea ofplace valueiii. Extend addition and subtraction of decimals with utilizing the place value
system in vertical form until up to tenths
iv. Think about appropriate place value for applying addition and subtraction
in life21

Chapter 2

Strand: Quantity and Measurement
Attributes of objects are used to make direct and in-direct comparison.
For comparison, the non-standard and standard units are used.
Counting activities denominate units of quantities such as cups for volumes,
arm-length and hand-spans for length. Standard units such as meter, centimeter,
kilogram and liter are introduced. Time and durations which are not base tensystem are introduced. Money is not a complete model for base 10 system.
The concept of conservation of quantities will be established through thecalculation of the quantities. The sense for quantity is developed through theappropriate selection of measurement tools.
Topics:Comparing sizes directly and indirectly using appropriate attributes andnon-standard units
Introducing quantity of length and expanding it to distanceIntroducing quantity of mass for its measurement and operation
Introducing quantity of liquid capacity for its measurement and operation
Introducing time and duration and its operation
Introducing money as quantity

Comparing Size Directly and Indirectly Using Appropriate Attributes
and Non-Standard Units
Comparing and describing quantity using appropriate expressioni.

Compare two objects directly by attributes instead of stating in length andamount of water such as longer or shorter and less or moreii.

Compare two objects indirectly using non-standard units to appreciate
the unification of unitsiii. Use appropriate denomination24 of quantity (such as number of cups) for
counting and appreciate the usage of units for quantity for suitable context

24 Denomination is necessary for learning the group of counting. It is also described in the strands of Patternand Data Representations and Numbers and Operations both of Key Stage 1.

22

Chapter 2

Introducing quantity of length and expanding it to distanceIntroducing centimeter for length and extend to millimeter and meteri.

Compare length of different objects and introduce centimeter withcalibrated tape25 of one centimeterii.

Demonstrate equivalent length with addition and subtraction such as
part-part wholeiii. Extend centimeter to millimeter to represent remaining parts with ideas ofequally dividing and idea of making tens
iv. Extend centimeter to meter to measure using meter stickv.

Estimate length of objects and select appropriate tools or measuring unit
for measurement with fluency

vi. Convert mixed and common units of length for comparison26
vii. Convert mixed and common units of length when adding or subtractingin acquiring the sense for quantity
Introducing distance for the extension of lengthi.

Introduce kilometer to measure distance travel using various tools andappreciate the experiences of measuring skills

ii.

Distinguish distance travel and the distance of two places on the map

iii. Compare mixed units of length with appropriate scale on number line

Introducing Quantity of Mass for Its Measurement and Operation
Introducing gram for mass and extend to kilogram and tonsi.

Compare mass of different objects directly using balance and introduce
gram

ii.

Demonstrate equivalent mass with addition and subtraction such as
part-part wholeiii. Extend gram to kilogram, measure with weighing scale
iv. Extend kilogram to metric ton through relative measure (such as
25 children, each weigh 40 kilogram)
25 The plane tape can be used for direct comparison and indirect comparison by marking. If the tape is scaled
by non-standard unit we can use it for measurement. If the tape is scaled by one centimeter we can define thelength of centimeter.
26 Which one is longer 2 m, 3 cm or 203 mm?

23

Chapter 2v.

Estimate mass of objects and select appropriate tools or measuring unit formeasurement with fluency

vi. Convert mixed and common units of mass for comparisonvii. Convert mixed and common units of mass for addition and subtraction in
acquiring the sense for quantity

Introducing Quantity of Liquid27 Capacity for Its Measurement andOperation
Introducing liter for capacity of liquid and extend to milliliteri.

Compare amount of water in different containers and introduce liter withmeasuring cups of 1 literii.

Demonstrate equivalent capacity with addition and subtraction such as
part-part wholeiii. Extend liter by deciliter/100 millilitre cup for representing remaining parts
with ideas of equally dividing and making 10, and extend until milliliter
iv. Estimate capacity of containers and select appropriate measuring unitv.

Convert mixed and common units of capacity for comparison

vi. Convert mixed and common units of capacity for addition and subtractionin acquiring the sense for quantity

Introducing Time and Duration, and Its Operation
Introducing analog time and extend it to durationi.

Tell and write analog time of the day corresponding with different
activities in daily life such as morning, noon, afternoon, day and nightii.

Show time by using clock face with hour hand and minute handiii. Understand the relative movement of clock hands
Extending clock time to duration of one day28
i.

Introduce duration in hours and minutes based on beginning time andend time of activities

27 The density which explains the relationship between mass and liquid capacity is usually learned in Scienceat later stage. In the case of CCRLS Science it starts in Key Stage 2 such as 1 cubic centimeter of water isequivalent to 1 gram.
28 Calendar is possible in the Key Stage 1 under Pattern and Data Representations.

24

Chapter 2ii.

Express time and duration on time line, and understand duration as
difference of two distinguished timesiii. Addition and subtraction of duration and time
iv. Extend time and duration to secondsv.

Convert mixed and common units of duration for comparison

vi. Estimate duration of time and select appropriate measuring unit formeasurement with fluency and appreciate the significance of time andduration in life
vii. Appreciate the difference in time depending on the area (time zone) andthe seasons

Introducing Money as Quantity
Introducing money as quantity and use it as the model of base ten system29i.

Introduce unit of money using notes and coins and determine the correct
amount of moneyii.

Use counting by fives and so on for base ten system

iii. Appreciate the fluency for calculation of money with all the four operations
iv. Appreciate number sense for conversion and transaction of money in life

Strand: Shapes, Figures and Solids
Basic skills of exploring, identifying, characterizing and describing shapes,
figures and solids are learned based on their features. Activities such as paper
folding enable exploration of various features of shapes. Identification ofsimilarities and differences about shapes and solids enable classification to bedone for defining figures. Using appropriate materials and tools, relationship indrawing, building and comparing the 2D shapes and 3D objects are considered.
Through these activities, the skills for using the knowledge of figures and solids
will be developed. The compass is introduced to draw circles and scale withthe same length.
Topics:Exploring shapes of objects
Characterizing the shapes for figures and solids
Explaining positions and directions
29 Coins and notes are depending on the country. Some country use currency unit of twenty and twenty-fivewhich are in coins or notes. These forms are not appropriate for the model of base 10 system.

25

Chapter 2

Exploring Shapes of Objects
Exploring shapes of objects for finding their attributesi.

Roll, fold, stack, arrange, trace, cut, draw, and trail objects ( blocks such asboxes, cans and so on) for knowing their attributesii.

Use attributes of blocks for drawing the picture by tracing the shape on
the paper and explain how to draw it with the shapeiii. Create patterns of shapes (trees, rockets and so on) by using the attributes
and recognize the characteristics of shapes30
iv. Appreciate the functions of shapes of objects in life

Characterizing the Shapes for Figures and Solids
Describing figures with characters of shapesi.

Use characters of shapes for understanding figures (quadrilaterals, square,
rectangle and triangle, right angle, same length)ii.

Introduce line and right angle with relations to activities such as paper
folding and use it for describing figures with simple properties such as
triangle has 3 linesiii. Appreciate the names of figures in daily life by using mother-tongue suchas “segi tiga” and “segi empat” in Malay and “tatsulok” in Tagalog
iv. Classify triangles by specific properties, such as sides, angles and vertex(right triangle, equilateral, isosceles)
Describing solids with characters of shapesi.

Use the characters of shapes, understanding solids such as boxes can be
developed by six rectangular parts with simple properties

ii.

Develop boxes with the properties

iii. Appreciate the solids around daily life through considering the functionof the solids
Drawing circle and recognizing sphere based on circle
i.

Think about how to draw a circle and find the center and radiusii.

Draw a circle with an instrument such as compass

iii. Enjoy drawing pictures using the function of circles such as Spirograph
30 Pattern of shapes is discussed in Key Stage 1 under Pattern and Data Representations.

26

Chapter 2

iv. Find the largest circle through cutting the sphere and recognize the sphereby the center and radiusv.

Appreciate function of circles and spheres in daily life such as thedifference between soccer ball and rugby ball

Explaining Positions and Directions
Exploring how to explain the position and directioni.

Identify simple positions and directions of an object accurately using
various ways such as in my perspective, in your perspective in theclassroom, and the left, right, front, back, west, east, north, south and withmeasurementii.

Draw the map around the classroom with consideration of the locationiii. Design a game to appreciate the changing of positions and directions in aclassroom

Strand: Pattern and Data Representations
Various types of patterns are treated such as the number sequences andrepetitions of shapes. Size of pictures can be represented by the number
sequences. Tessellation of shapes and paper folding can be represented by therepetition of shapes. Exploration of patterns and features are also considered
to represent the data structure in our life with pictographs and bar graphs.
Patterns and features produce meaning of data and represent mathematicalinformation. Patterns are represented by diagrams and mathematical sentences
which are also used for communication in identifying and classifying situations
to produce meaningful interpretations.
Topics:Using patterns under the number sequence
Producing harmony of shapes using patterns
Collecting data and representing the structure

Using Patterns under the Number Sequence31
Arranging objects for beautiful pattern under the number sequencei.

Know the beautifulness of patterns in cases of arranging the objects
depending on number sequenceii.

Arrange objects according to number sequence to find simple patterns

31 Number sequence will be discussed in Key Stage 1 under Numbers and Operations.

27

Chapter 2iii. Arrange expressions such as addition and subtraction to find simple
patterns
iv. Express the representation of patterns using placeholders (empty box)v.

Enjoy the arrangement depending on number sequence in daily life

vi. Find patterns on the number table such as in calendars32

Producing harmony of shapes using patterns33
Arranging tiles of different or similar shapes in creating harmonyi.

Know the beautifulness of patterns in cases of arranging the objects
depending on shapes, colours and sizesii.

Arrange objects according to shapes, colours and sizes to show patternsiii. Arrange boxes according to shapes, colours and sizes to create structure
iv. Arrange circles and spheres for designingv.

Enjoy the creation depending on different shapes, colours and sizes indaily life

Collecting data and representing the structure
Counting data through categorization for getting informationi.

Explore the purpose of why data is being collectedii.

Group the data in creating similar attributes on the denomination34 ofcategories and count them (check mark and count)iii. Think about what information is obtained from the tables with categories
and how to use it
Organizing the data collected and represent using pictogram for easy
visualizationi.

Produce the table and pictograms from collected data under eachcategories

ii.

Interpret tables and pictograms as a simple conclusion about the data
being presented

iii. Appreciate pictograms through collecting data and adding data in daily
activities in life
32 Time and duration are discussed in key stage 1 under Quantity and Measurement.
33 Harmony of shapes will be discussed in Key Stage 1 under Shapes, Figures and Solids.
34 Denomination will be learned in Key stage 1 under Quantity and Measurement.

28

Chapter 2

Representing a data structure by using bar graph to predict the future ofcommunitiesi.

Understand how to draw bar graph from table using data categories andsort the graph for showing its structureii.

Appreciate ways of presenting data such as using tables, pictograms andbar graphs with sorting for predicting future communitiesiii. Appreciate the use of data for making decision

Strand: Mathematical Process - Humanity
Enjoyable mathematical activities are designed to bridge the standards in
different strands. Exploration of various number sequence, skip counting,addition and subtraction operations help to develop number sense that isessential to support explanation of contextual scenarios and mathematical ideas.
Mathematical ways of posing questions in daily life are also necessary learnedat this stage. Ability to select simple, general and reasonable ideas enables
effective future learning. Application of number sense provides facility for
preparing sustainable life. The use of ICT tools and other technological tools
provide convenience in daily life. At initial stage, concrete model manipulationis enjoyable, however drawing diagram is most necessary for explaining
complicated situations by using simple representation.
Standards
Enjoying problem solving through various questioning for four operations insituations
Enjoying measuring through setting and using the units on various situations
Using blocks as models and its diagram for performing operations in base ten
Enjoying tiling with various shapes and colours
Explaining ideas using various and appropriate representations
Selecting simple, general and reasonable ideas which can apply for futurelearning
Applying number sense acquired in Key Stage 1 for preparing sustainable life
Utilizing ICT tools such as calculators as well as other tools such as note bookand other instrument such as clocks
Promoting creative and global citizenship for sustainable development ofneighbourhood using mathematics

29

Chapter 2

Enjoying problem solving through various questioning for four operations insituation35
i.

In addition, pose questions for altogether and increase in situationsii.

In subtraction, pose questions for remain and difference in situations

iii. In multiplication, pose questions for number of groups in situations
iv. In division, pose questions for partition and quotation in situationsv.

Enjoy questioning by using combination of operations in various situations

vi. In operations, pose questions to find the easier ways of calculationvii. Use posing questions for four operations on measurements in daily life
Enjoying measuring through setting and using the units on various situations36
i.

Compare directly and indirectlyii.

Set tentative units from difference for measuringiii. Give appropriate names (denominations) for counting units
iv. Use measurement for communication in daily lifev.

Use tables and diagrams for showing the data of measures

Using blocks as models and its diagram for performing operations in base ten37i.

Show increasing and decreasing patterns using blocks

ii.

Show based ten system using blocks, unit cube is 1, bar stick is 10 and flat
block represents 100

iii. Explain addition and subtraction algorithm in vertical form using base ten
block modeliv. Explain multiplication table with number of group blocksv.

Explain division using equal distribution of blocks and repeatedsubtraction of blocks

vi. Use the number of blocks as for measurement in daily life
Enjoying tiling with various shapes and colours38
i.

Appreciate to produce beautiful designs with various shapes and find thepattern to explain it

35 It is related with Numbers and Operations and Quantity and Measurement both in Key Stage 1.
36 It is related with Quantity and Measurement and Pattern and Data Representations both in Key Stage 1.
37 It is related with Pattern and Data Representations and Numbers and Operations both in Key Stage 1.
38 It is related with Shapes, Figures and Solids and Pattern and Data Representations both in Key Stage 1.

30

Chapter 2

ii.

Reflect, rotate and translate to produce patternsiii. Cut and paste various shapes and colours to form the box and ball such as
develop the globe from map
Explaining ideas using various and appropriate representations39
i.

Explain four operations using pictures, diagrams, blocks and expressions
for developing ideas

ii.

Explain measurement using measuring tools, tape diagrams, containerand paper folding for sharing ideas

iii. Make decision on how to explain the figures and the solids by using
manipulative objects or diagrams or only verbal explanation
iv. Explain patterns using diagrams, numbers, tables and expressions withblank boxv.

Ask questions using terms such as why, how, what, if and if not, and reply
using examples and ‘for example’ in discussion

vi. Change the representation and translate it appropriately in daily life
Selecting simple, general and reasonable ideas which can apply for futurelearning40
i.

Discuss the argument for the easier ways for addition and subtraction
algorithm in vertical formii.

Extend the algorithm to large numbers for convenience and fluency

iii. Use the pattern of increase in multiplication table for convenience
iv. Use multiplication tables for finding the answers of division
Applying number sense41 acquired in Key Stage 1 for preparing sustainable
life42i.

Use mathematics for the minimum and sequential use of resources insituations

ii.

Estimate for efficient use of resources in situations

iii. Maximize the use of resources through appropriate arrangement in space
iv. Understand equally likely of resources in situations
39 It is related to all strands in Key Stage 1.
40 It is related to Numbers and Operations and Pattern and Data Representations both in Key Stage 1.
41 It is related to  Numbers and Operations, Pattern and Data Representations and Quantity and  Measurement
all in included in Key Stage 1.
42 Sustainable development goals were crafted at the 70th Session of the United Nations General Assembly
and indicated them as universal value in education.

31

Chapter 2

Utilizing ICT tools such as calculators as well as other tools such as notebook
and other instrument such as clocks43i.

Use calculators for poly addition in situationsii.

Use mental calculations for estimations

iii. Use balance scale to produce equality and inequality
iv. Use cups, tapes, stop watch, and weighing scale for measuring distances
and weightsv.

Use calculators to explain the process of calculation by solving
backward and understand the relationship of addition and subtraction,and multiplication and division

vi. Enjoy using of notebooks to exchange learning of each other such as
mathematics journal writingvii. Enjoy presentations with board writingviii. Use various tools for conjecturing and justifying
Promoting creative and global citizenship for sustainable development ofneighbourhood using mathematicsi.

Utilize the notebooks and journal books to record and find good ideas andshare with othersii.

Prepare and present ideas using posters to promote good practices inneighbourhoodiii. Listen to other’s ideas and asking questions for better creation
iv. Utilize information, properties and models as basis for reasoningv.

Utilize practical arts and outdoor studies to investigate local issues for
improving welfare of life

43 STEM education is enhanced. Mathematics is the major and base subject for STEM Education in
Key Stage 1 hence, technological contents are included in Mathematics.

32

Chapter 3

Chapter 3

Key Stage 2
Key Stage 2 (KS2) can be learned based on the Key Stage 1. This stage provides
the extension of numbers, measurement and relations, plane figures andsolid figures and data handling and graphs. This stage enables to extend four
operations to daily use of numbers such as decimal and fraction and allows theuse of mathematical terminologies, performing investigations and establish
the ground for analyzing, evaluating and creating their life. Appreciating thebeauty of the structure of mathematics will enable them to enjoy and sustain
their learning which provides basis for Key Stage 3.

Strand: Extension of Numbers and Operations
Numbers are extended to multi-digits, fractions and decimals. Multiplicationand division algorithms are completed with fluency. Fraction becomes numbers
through the redefinition as a quotient instead of part - whole relationship.
Multiplication and division of decimals and fractions are also explored to
produce the procedures for calculation. Various representations are used toelaborate and produce meaning for the calculation. Number sense such as
approximating numbers, relative size of numbers and values are enhanced forpractical reasoning in the appropriate context of life.
Topics:Extending numbers with base ten up to billion and also to thousandths withthree digit numeral system gradually
Making decision of operations on situations with several steps and integratethem in one expression and think about the order of calculations and produce
the rule (PEMDAS)
Producing the standard algorithm for vertical form division with whole numbers
Extending the vertical form addition and subtraction with decimals tohundredths
Extending the vertical form multiplication and division with decimals and findthe appropriate place value such as product, quotient and remainder
Using multiples and divisors for convenience
Introducing improper and mixed fractions and extending to addition andsubtraction of fractions to dissimilar fractions

33

Chapter 3

Extending fractions as numbers and integrate
Extending multiplication and division to fractions

Extending Numbers with Base Ten Up to Billion and Also to Thousandths
with Three Digit Numeral System Gradually
Extending numbers using base ten system up to billion44 with three digit
numeral system45i.

Adopt the three digit numeral system, extend numbers up to billion with
the idea of relative size of numbersii.

Compare numbers such as larger, smaller with base46 ten system of placevalues through visualization of relative size of numbers using cubes, plane,
bar and unit

Extending decimal numbers to hundredths, and to thousandths47
i.

Use the idea of quantity and fractions, extend decimal numbers from tenths
to hundredthsii.

Compare decimal numbers such as larger, smaller with base ten systemof place valueiii. Adopt the ways of extension up to thousandths and so on, and compare
the relative sizes

Making Decision of Operations on Situations with Several Stepsand Integrate them in One Expression and Think about the Order ofCalculations and Produce the Rule (PEMDAS)
Finding the easier ways of calculations using the idea of various rules ofcalculations48 such as the associative, commutative and distributive rulei.

Find the easier ways of addition and subtraction and use it, if necessary, suchas answer is the same if add same number to the subtrahend and minuend

ii.

Find the easier ways of multiplication and division and use them inconvenient ways such as 10 times of multiplicand produce the product10 times

44 Billion is too large for counting and it is introduced in the three digit system under relative size of number.
45 In British system, it is referred as short scale.
46 Metric system names of units are discussed under Measurement and Relations.
47 Under the three digit system, if we teach until thousandths we can extend by three digits.
48 Use of constant sum, difference, product and quotient is described in Measurement and Relations.
(e.g. 25 -21 = 4,  26 – 22 = 4, 27 – 23 = 4)34

Chapter 3iii. Use associative, commutative and distributive rules of addition andmultiplication for easier ways of calculation, however commutative
property does not work in subtraction and division
iv. Appreciate the use of simplifying rules of calculations
Thinking about the order of calculations in situations and produce rules andorder of operationsi.

Integrate several steps of calculation into one mathematical sentenceii.

Produce the rule of PEMDAS and apply it to the several steps situationiii. Think about the easier order of calculation and acquiring fluency of
PEMDAS and rules with appreciation

Producing the Standard Algorithm for Vertical Form Division with Whole
Numbers
Knowing the properties of division and use it for easier way of calculationi.

Find the easier ways of division and use it, if necessary, such as answer
is the same if multiplying the same number to the dividend and divisorii.

For confirmation of answer of division, use the relationship among divisor,quotient and remainder and appreciate the relationshipKnowing the algorithm of division in vertical form and acquiring fluencyi.

Know the division algorithm with tentative quotient and confirm thealgorithm by the relationship among divisor, quotient and remainderii.

Interpret meaning of quotient and remainder in situations

iii. Acquire fluency for division algorithm in the case of up to 3-digit whole
number divided by 2-digit
iv. Think about the situations with or without remainder in relation tosituations for quotative and partitive division

Extending the Vertical Form Addition and Subtraction with Decimals
to Hundredths
Extending the vertical form addition and subtraction in decimals to hundredthsi.

Extend the vertical form addition and subtraction to hundredths49 placeand explain it with models

ii.

Appreciate the use of addition and subtraction of decimals in life

49 Discussion of decimals to hundredths is related to the use of money. It is a minimum requirement.
If teaching to hundredths, further extension of place value can be understood.

35

Chapter 3

Extending the Vertical Form Multiplication and Division with Decimals
and Find the Appropriate Place Value such as Product, Quotient andRemainder
Extending the multiplication from the whole number to decimal numbersi.

Extend the meaning of multiplication with the idea of measurement by
the number of unit length for multiplication of decimal numbers anduse diagrams such as number lines to explain them with appreciation insituationsii.

Extend the vertical forms multiplication of decimals up to 3 digits by 2
digits with consideration of the decimal places step by stepiii. Obtain fluency using multiplication of decimals with sensible use of
calculators in life
iv. Develop number sense in multiplication of decimals50 such as comparing
sizes of products before multiplying
Extending the division from the whole number to decimal numbersi.

Understand how to represent division situations using diagrams such as
number lines, and extend the diagram of decimal numbers for explaining
division by decimal numbers

ii.

Extend the division algorithm in vertical form of decimal numbers andinterpret the meaning of decimal places of quotient and remainder withsituations

iii. Acquire fluency in division algorithm of decimals up to 3 digits by 2 digits
with consideration of decimal places step by stepiv. Obtain fluency using division of decimals with sensible use of calculators
in lifev.

Develop number sense of division in decimals such as comparing sizes ofquotient before multiplying

vi. Distinguish the situations with decimal numbers of multiplication anddivision

50 Applying the idea of multiplication into ratio, percent and proportion is discussed in Measurement andRelations.

36

Chapter 3

Using Multiples and Divisors for Convenience
Using multiples and divisors for convenience with appreciation to enrich
number sensei.

Understand set of numbers by using multiple and divisor

ii.

Find common multiple and appreciate the use in situations, and enrich
number sense with figural representations such as arrangement of rectangles
to produce a squareiii. Find common divisor and appreciate its use in situations, and enrich
number sense with figural representations such as dividing a rectangle
into pieces of square
iv. Understand numbers as composite of multiplication of numbers as factors51
v.

Appreciate ideas of prime, even and odd numbers in situations using
multiples and divisors

vi. Acquire the sense of number to see its multiple for convenience

Introducing Improper and Mixed Fractions and Extending to Addition
and Subtraction of Fractions to Dissimilar Fractions
Extending fractions to improper, mixed and equivalent fractionsi.

Extend fractions to improper and mixed fractions using number line ofmore than one by measuring with unit fraction52

ii.

Find ways of determine equivalent fractions with number lines and with
the idea of multiple of numerator and denominatoriii. Compare fractions using number line and the idea of multiple
Extending addition and subtraction of similar fractions to improper and mixed
fractions, and dissimilar fractionsi.

Extend addition and subtraction of similar fractions to proper and mixed
fractions with explanations using models and diagramsii.

Extend addition and subtraction into dissimilar fractions with explanations
using diagrams and common divisorsiii. Acquire fluency of addition and subtraction of fractions with appreciationof idea to produce the same denominators
51 This idea is related to the strand on Measurement and Relations in Key Stage 2 under the area of rectangle.
52 Extension of fraction more than one is done by using the fraction with quantity for situation such as  

37

Chapter 3

Extending Fractions as Numbers and Integrate53
Seeing fractions54 as decimals and seeing decimals as fractionsi.

See fractions as decimals using division and define quotient from the caseof indivisibleii.

See decimals as fractions such as hundredths is per hundrediii. Compare decimals and fractions and ordering them on the number line

Extending Multiplication and Division to Fractions
Extending multiplication to fractioni.

Extend the multiplication to fraction with situations using diagrams
such as number lines, step by step, and find the simple algorithm for themultiplication of fractionsii.

Acquire fluency with multiplication of fractions

iii. Develop number sense55 of multiplication of fractions such as comparing
sizes of products before multiplying
Extending division to fractioni.

Extend the division to fraction with situations using diagrams such as
number lines, step by stepii.

Acquire fluency with division of fractions

iii. Develop number sense of division of fractions such as comparing sizes ofquotients before dividing

53 Selecting the appropriate denomination of quantities and units for fraction in the context ( is two ofand the whole is 1m, howeveris; the structure is the same as tens is ten of units and discussed
under Measurement and Relations.
54 Fraction as ratio is introduced in Measurement and Relations.
55 Applying the idea of the multiplication of fraction into ratio, proportion, percentage and base is discussed
in Measurement and Relations.

38

Chapter 3

Strand: Measurement and Relations
Additive quantity such as angles, areas and volume and relational quantities
such as population density, and speed are introduced. Additive quantity can be
introduced by establishment of the standard unit which is the same way as the
Quantity and Measurement of Key Stage 1. Relations of quantities in situations
are discussed with patterns such as sum is constant, difference is constant,product is constant and quotient is constant using tables and represented bymathematical sentences and letters. Proportion and ratio are introduced withrepresentations of diagrams, graphs and tables for multiplication, and connectedwith decimals and fractions. Percent is introduced with diagrams in relation toratio and proportion. Relational quantity is produced by different quantities
with understanding of ratio. Area of a circle is discussed through a proportional
relationship between radius and the circumference. Ideas of ratio and proportionare fluently applied for real world problem solving.
Topics:Introducing angle and measuring it
Exploring and utilizing constant relation
Extending measurement of area in relation to perimeter
Extending measurement of volume in relation to surface
Approximating with quantities
Extending proportional reasoning to ratio and proportion
Producing new quantities per unit
Investigating the area of a circle
Exchanging local currency with currency in ASEAN community
Extending the relation of time and use of calendar in life
Converting quantities in various system of units
Showing relationship using Venn diagram

39

Chapter 3

Introducing Angle and Measuring It56
Introducing angle by rotation, enabling measuring and acquire fluency using
the protractori.

Compare extent of rotation and introduce degree as a unit for measuring
angle

ii.

Recognize right angle is 90 degrees, and adjacent angle of two right angles
is 180 degrees, and 4 right angles is 360 degrees

iii. Acquire fluency in measuring angles using the protractor
iv. Draw equivalent angles with addition and subtraction using multiples of
90 degreesv.

Appreciate measurement of angles in geometrical shapes and situations
in life57

Exploring and Utilizing Constant Relation
Exploring equal constant relation with utilization of letters to represent
placeholders58
i.

Explore two possible unknown numbers such that their sum (or difference/
product/quotient) is constant 59, for example □+∆=12 (□ and ∆ areplaceholders)ii.

Use letters instead of placeholder60 (empty box) to derive equivalent relationiii. Understand the laws for operations (e.g. associative, commutative anddistributive, etc.) to explain the simpler way of calculation
iv. Appreciate the use of diagrams such as number lines and area to represent
relation when finding solutions

Extending Measurement of Area in Relation to Perimeter
Introducing area and produce formula for the area of rectanglei.

Compare extent of area and introduce its unit, and distinguish it fromperimeterii.

Introduce one square centimeter as unit for area and its operation using
addition and subtraction

56 Right angles are learned at Key Stage 1 in Shapes, Figures and Solids for explaining the properties of figures.
57 Conservation of angles will be re-learnt in triangle under Key Stage 2 Plane Figures and Space Solids.
58 The idea for the use of Numbers and Operations (Key Stage 2) in finding the easier ways of calculations
with the idea of  rules of calculations.
59 Constants of multiplication and division correspond to proportionality in multiplication table at
Key Stage 1 under Numbers and Operations. Constants of addition and subtraction are treated in
Key Stage 1 under Pattern and Data Representations.
60 Place folders are introduced in Key Stage 1.

40

Chapter 3iii. Investigate area of rectangles and squares and produce the formula of area61
iv. Extend square centimeter to square meter and to square kilometer formeasure of large areasv.

Convert units and use appropriate units of area with fluency

vi. Draw the equivalent size of rectangular area based on a given area withthe composite numbers62
vii. Appreciate the use of areas in daily life such as comparing of land sizes
Extending area of rectangle to other figures to derive formulai.

Explore and derive formula for the area of parallelogram by changing its
shape to rectangle without changing its areaii.

Explore and derive formula for the area of triangle by bisecting a rectangle
into two triangles without changing its areaiii. Appreciate the idea of changing or dividing shapes of rectangle,
parallelogram, or/and triangle for deriving the area of other figures
iv. Use the formulas to calculate areas in daily life

Extending Measurement of Volume in Relation to Surface
Introducing volume from area and derive formula for cuboidi.

Compare extent of volume and introduce its unit, and distinguish it fromsurfaceii.

Introduce one cubic centimeter as unit for volume and its addition andsubtractioniii. Investigate volume of cuboid and cube and produce the formulas
iv. Extend cubic centimeter to cubic meter to measure large volumev.

Convert units and use appropriate units of volume with fluency

vi. Appreciate the use of volume in life such as comparison of capacity ofcontainers
Extending volume of cuboid to other solid figures to derive formulai.

Extend the formula for the volume of cuboid as base area x height for
exploring solid figures such as prism and cylinder

61 Multiplications are studied in Key Stage 1 Number and Operations.
62 The idea of composite numbers such as 2 times 10 equals 5 times 4 is related to the factors in extending
the numbers and operations at Key Stage 2.

41

Chapter 3ii.

Extend the formula for the volume of prism and cylinder to explore andderive the volume formula of pyramid and coneiii. Use the formulas to calculate volume in daily life

Approximating with Quantities
Approximating numbers with quantities depending on necessity of contextsi.

Understand the ways of rounding such as round off, round up and round
down

ii.

Use rounding as approximation for making decision on the quantity withrelated context

iii. Critique over approximation beyond the context with a sense of quantity
such as based on relative size of unit

Extending Proportional Reasoning to Ratio63 and Proportion
Extending proportional reasoning to ratio and percenti.

Understand ratio as relationship between two same quantities or between
two different quantities (the later idea is rate)64

ii.

Express the value of ratio by quotient such as rate of two different quantities65

iii. Understand percent as the value of ratio with same quantity66
iv. Understand proportion with ratiov.

Apply the rule of three67 in using ratio

Extending proportional reasoning to proportioni.

Extend proportional reasoning on multiplication tables as equal ratio andunderstand proportionsii.

Understand proportion by multiple and constant quotient, not changing
the value of ratio68

63 Band graph and pie chart for representing ratio are discussed under Key Stage 2 on the strand
Data Handling and Graphs.
64 Ratio of different quantity is rate. Ratio of the same quantity is a narrow meaning of ratio.
65 The value of fraction as ratio is not necessary a part of whole in situations. Fraction as ratio is usually usedon the context of multiplication in situation, where denominator is the base or unit for comparison.
66 Percent is used in Data Handling and Graphs.
67 Rule of three is the method on the table to find one unknown term from the three known terms using
proportional reasoning such as;ac?
d
68 Enlargement is discussed in Key stage 2 under Plane Figures and Space Solids. The graph is treated at
Key Stage 2 under Data Handling and Graphs strand.

42

Chapter 3iii. Demonstrate simple inverse proportion by constant product69
iv. Express proportion in mathematical sentence by letters and graph70
v.

Use properties of proportionality to predict and explain phenomenon indaily life

Producing New Quantities by Per Unit
Producing new quantities by per unit with the idea of average such as population
density and speedi.

Introduce average as units for distribution and comparison of different
sets of valuesii.

Introduce population density with the idea of average and appreciate it
for comparison

iii. Introduce speed with the idea of average and appreciate it for comparison
iv. Appreciate using diagrams such as number lines and tables to decide theoperations on the situations of measurement per unit quantityv.

Compare on the context of different quantities with the idea of averageas rate71

vi. Apply the idea of measurement per unit quantity in different context72

Investigating the Area of Circle
Areas of a circle are discussed through relationship between radius and thecircumferencei.

Investigate relationship between the diameter of circle and its circumference
using the idea of proportionii.

Investigate area of a circle by transforming into triangle or parallelogramand find the formula of circle

iii. Estimate the area of inscribed and outscribed shapes based on known
formula of area73
iv. Enjoy to estimate the area of irregular shapes with fluency in life
69 Proportion and Inverse proportion are necessary in Key Stage 3 in Science.
70 This will be discussed in detail in Key Stage 2 under Data Handling and Graphs.
71 On Numbers and Operations in Key Stage 2, rate is the value of division as quotient.
72 Using measurement per unit quantity with fluency to make logical judgment in daily life, refer to
Key Stage 2 Data Handling and Graphs.
73 Relationships on polygons and circles are discussed in Key Stage 2 under Plane Figures and Solids.

43

Chapter 3

Exchanging Local Currency with Currency in ASEAN Community
Exchanging local currency in ASEAN community with the idea of ratei.

Extend the use of ratio for currency exchange (rate of exchange)ii.

Apply the four operations for money in appropriate notation in lifeiii. Appreciate value of money

Extending the Relation of Time and Use of Calendar in Life
Extending the relation of time and use of calendar in lifei.

Convert time in 12-hour system with abbreviation a.m. and p.m. to 24-hoursystem and vice versa

ii.

Investigate the numbers in calendar to relate days, weeks, months and year
using the idea of number patternsiii. Appreciate the significance of various calendars in life

Converting Quantities in Various System of Units
Converting measurement quantities on international and non-international
system with idea of base 10i.

Convert measurement system of meter and kilogram with prefixes deci-,
centi-, and milli-, and with deca-, hecto-, and kilo-ii.

Convert measurement system of liter with cubic centimeteriii. Convert measurement system of area using acre (a) and hectare (ha) withsquare meteriv. Convert measurement of local quantities with standard quantitiesv.

Understand the unit system with power, such as meter, square meter andcubic meterShowing Relationship Using Venn Diagram
Using Venn diagram to show relationships of numbers and figuresi.

Show relationship of square, rectangles, rhombus, parallelogram, trapezoid
and quadrilateral by using Venn diagramii.

Show relationship of numbers

44

Chapter 3

Strand: Plane Figures and Space Solids
Through tessellation, figures can be extended through plane figures.
Parallelogram and perpendicular lines are tools to explain properties oftriangles and the quadrilaterals as plane figures. For identifying and recognizing
symmetry and congruence parallelogram and perpendicular lines are alsoneeded. Plane figures are used to produce solid in space and vice versa. Opening
faces of solids would produce plane figures which are referred as nets. Activities
related to building solids from plane figures are emphasized and encouraged
to facilitate finding the area of a circle through numerous sectors of the circle
to construct a rectangle. Circles are used for explaining the nets of cylinders.
Topics:Exploring figures with their components in the plane
Exploring solids with their components in relation to the plane
Exploring figures with congruence, symmetry and enlargement

Exploring Figures with Their Components in the Plane
Exploring figures with their components in the plane and use propertiesi.

Examine parallel lines and perpendicular lines by drawing with instrumentsii.

Examine quadrilaterals using parallel and perpendicular lines, and identify
parallelogram , rhombus, trapezium by discussioniii. Find properties of figure through tessellations such as triangle where thesum of the angles is 180 degree, straight angle
iv. Extend figures to polygons, and expand it to circles with knowing andusing its properties

Exploring Solids with Their Components in Relation to the Plane
Exploring rectangular prisms and cubes with their componentsi.

Identify relationship among faces, edges and vertices for drawing sketchii.

Explore the nets of rectangular prism and find the corresponding position
between components

iii. Explore perpendicularity and parallelism between faces of rectangularprism
iv. Explain positions in rectangular prisms with the idea of 3 dimensions

45

Chapter 3

Extending rectangular prism to other solids such as prisms and cylindersi.

Extend the number of relationships among faces, edges and vertices fordrawing sketchii.

Explore nets of prisms and cylinders, and find the corresponding position
between components

iii. Distinguish prism and cylinder by the relationship of their faces

Exploring Figures with Congruence, Symmetry and Enlargement
Exploring the properties of congruencei.

Explore properties of figures which overlap and identify conditions ofcongruency with corresponding points and sides

ii.

Draw congruent figures using minimum conditions and confirm bymeasuring angles and sides

iii. Appreciate the power of congruent figures by tessellation
Exploring the properties of symmetryi.

Explore the properties of figures which reflect and identify conditions ofsymmetry with line and its correspondenceii.

Draw symmetrical figures using conditions in appropriate locationiii. Appreciate the power of symmetry in designs
Exploring the properties of enlargement74
i.

Explore properties of figures in finding the center of enlargement in simple
case such as rectangleii.

Draw enlargement of rectangle using ratio (multiplication of the value ofratio75)

iii. Appreciate the power of enlargement in interpretation of map

74 General case for enlargement will be discussed in Key Stage 3, Space and Geometry.
75 Ratio and rate are discussed in Key Stage 2 under Measurement and Relations.

46

Chapter 3

Strand: Data Handling and Graphs
The process of simple data handling is introduced through data representationsuch as using table, bar graph, line graph, bar chart and pie chart. Graphs are
utilized depending on the qualitative and quantitative data used such as bar
graph is for distinguishing and counting in every category. The discussion of
producing the line graph includes taking data at specific intervals, suitable scale
used and slope. Histogram is necessary for interpreting the data representationof social study and science, and is also used as a special type of bar graph.
Average is introduced based on the idea of ratio for making the dispersionof bar chart even, and used for summarizing and comparing data on a table.
Problem-Plan–Data Analysis–Conclusion (PPDAC) cycles are experienced
through the process of data handling by using those data representation skills.
Those skills are necessary for learning of sustainable development.
TopicsArranging tables for data representations
Drawing and reading graphs for analyzing data
Using graphs in PPDAC cycle appropriately
Applying Data Handling for Sustainable Development

Arranging Tables for Data Representationsi.

Explore how to collect multi category data based on a situationii.

Explore how to arrange and read multi category data on appropriate tablesiii. Appreciate in using multi category tables in situation

Drawing and Reading Graphs for Analyzing Data
Drawing and reading line graphs for knowing the visualized pattern as basics
on central tendencyi.

Introduce line graphs based on appropriate situations such as rainfall,temperature and othersii.

Distinguish line graph from bar graph for observation such as increase,decrease, and no-changeiii. Introduce the graph of proportion using the idea of line graph and readthe gradient by constant ratio76
iv. Appreciate the line graph in various situations
76 Proportions are learnt in the Key Stage 2 under Measurement and Relations.

47

Chapter 3

Drawing and reading band graph and pie chart for representing ratio in a whole77
i.

Explore how to scale the bar or circle for representing ratio or percent

ii.

Use the band graph and pie chart for comparison of different groupsiii. Appreciate the band graph and pie chart in situation
Reading histogram78 for analyzing frequency distributioni.

Draw a simple histogram79 from frequency table on situations

ii.

Read various histograms for analyzing data distribution

iii. Use mean80 to compare different groups in the same situation withhistograms

Using Graphs in PPDAC81 Cycle Appropriately
Identifying appropriate graphs for data handling in PPDAC cyclei.

Critique a situation and discuss the expectation before taking data for
proper clarification of the objectiveii.

Plan the survey for the expectationiii. Take the data based on the objective of the situation
iv. Use appropriate graphical representation which is most suitable for theobjectivev.

Appreciate the use of graphs before making the conclusion

Applying Data Handling for Sustainable Living
Applying data handling for sustainable development82 and appreciate the powerof data handling for predicting the future.
i.

Read data related to sustainable development such as emergency
preparedness and resiliency , food and energy security, world weather
warming, inclusion and human connectivity in society, and lifelong
learning in the changing society such as TVET (Technical and Vocational
and Training) and adopting positive views for changing the society

77 Ratio is learnt under Key Stage 2 Measurement and Relations.
78 How to draw histogram is discussed in Key Stage 3 under Statistics and Probability. Reading histogramis necessary in Social Studies and Science.
79 Using ICT for drawing graph will be mentioned in mathematical activities.
80 Mean is introduced as average in Key Stage 2 under Measurement and Relations.
81 PPDAC itself will be described in the mathematical activities later.
82 This standard is related to SDG as inter subject content between Social Studies and Science.

48

Chapter 3ii.

Understand the idea of probability as ratio and percentage in reading thedata for situations related to sustainable development such as weather
report and risk analysisiii. Experience a project of reasonable size in data handling purposes forsustainable development and appreciate the power of data handling

Strand: Mathematical Processes – Humanity
As a follow up of Key Stage 1, activities are designed to enable an appreciationof knowledge and skills learned and the ways of learning such as applying
knowledge of number sense to solve daily problems. Mathematical processes
such as communication, reasoning are used to provide explanation formathematical problems and modelling. The ability to connect and reason
mathematical ideas would trigger an excitement among learners. Discussionsof misconceptions are usually enjoyable and challenging. Mathematics learning
usually begins from situations at Key Stage 1. In Key Stage 2, the development ofmathematics is possible through the discussions for the extension of the forms.
Appreciation of ideas and representations learned become part of the enjoyable
activities. Through the consistent use of representations such as diagrams,
application of learning becomes meaningful.
Standards
Enjoying problem solving through various questioning and conjecturing forextension of operations into decimals and fractions with proportionality andnew quantities such as area and volume
Enjoying measuring through settings and using the area and volume in situations
Using ratio and rate in situations
Using number lines, tables, and area diagrams for representing operations andrelations in situations
Establishing the idea of proportion to integrate various relations with consistencyof representations
Enjoying tiling with various figures and blocks
Producing valuable explanation based on established knowledge, shareable
representations and examples
Performing activities of grouping and enjoy representing with Venn diagram
Experiencing PPDAC (Problem-Plan-Data Analysis-Conclusion) cycle andmodelling cycle in simple projects in life
Preparing sustainable life with number sense and mathematical representations
49

Chapter 3

Utilizing ICT tools as well as notebooks and other technological tools
Promoting creative and global citizenship for sustainable development ofcommunity using mathematics
Enjoying problem solving through various questioning and conjecturing forextension of operations into decimals and fractions with proportionality andnew quantities such as area and volume83i.

Pose questions to develop division algorithm in vertical form using
multiplication and subtractionii.

Pose questions to develop multiplication and division of decimal numbers
using the idea of proportionality with tables and number linesiii. Pose questions to develop multiplication and division of fractions using
the idea of proportionality with tables, area diagrams and number lines
iv. Pose questions to extend multiplication and division algorithm in verticalform to decimal numbers and discuss about decimal pointsv.

Pose questions to use decimals and fractions in situations

vi. Pose questions to use area and volume in life
vii. Pose questions to use ratio and rate in life
viii. Pose conjectures based on ideas learned such as when multiplying, theanswer becomes larger
Enjoying measuring through settings and using the area and volume in situationsi.

Compare directly and indirectly areas and volumesii.

Set tentative units from difference for measuring area and volume84

iii. Give the formula for the area and volume for counting units
iv. Use measurement for communication in daily life
Using ratio and rate in situations85i.

Understand division as partitive (between different quantities) andquotative (between same quantity) in situationsii.

Develop the idea of ratio and rate utilizing the idea of average and per unit
with tables and number linesiii. Communicate using the idea of population density and velocity in life
83 This is connected to the three strands, Extension of Numbers and Operations, Measurement and Relations,and Plane Figures and Space Solids.
84 Euclidean algorithm is a method of finding the largest common divisor of two numbers.
85 Ratio and proportion bridge multiplication and division in situation of two quantities with reference toExtension of Numbers and Operations and Measurement and Relations.

50

Chapter 3

Using number lines, tables, and area diagrams for representing operations andrelations in situations86i.

Represent proportionality on number lines with the idea of multiplicationtablesii.

Use number lines, tables, and area diagrams for explaining operations andrelations of proportionality in situations

Establishing the idea of proportion to integrate various relations with consistencyof representations87
i.

Use the idea of proportion as the relation of various quantities in lifeii.

Identify through the idea of proportion using tables, letters, and graphsiii. Adopt the idea of proportion to angles, arcs and area of circles
iv. Adopt the idea of proportion to area and volumev.

Adopt the idea of proportion to enlargement

vi. Use ratio for data handling such as percent and understand the difficulties
to extend it to proportion
Enjoying tiling with various figures and blocks88i.

Appreciate to produce parallel lines with tessellation of figuresii.

Explain the properties of figures in tessellations by reflections, rotations
and translations

iii. Develop nets from solids and explain the properties of solids by each of
the component figures
iv. Use the idea of tiling for calculating the area and volume
Producing valuable explanations based on established knowledge, shareable
representations and examplesi.

Establish the habit of explanation by referring to prior learning and ask
questions using terms such as why, how, what, if and if not, and reply
using examples and ‘for example’ in discussionii.

Assessing the appropriateness of explanations using representations suchas generality, simplicity and clarityiii. Use other’s ideas to produce better understanding
iv. Use inductive reasoning for extending formulas
86 This is a bridge to the Extension of Numbers and Operations and Measurement and Relations.
87 Bridge to the three strands, Measurement and Relations, Plane Figures and Space Solids andData Handling and Graphs.
88 Connected to the two strands, Measurement and Relations, and Plane Figures and Space Solids.

51

Chapter 3

Performing activities of grouping and enjoy representing with Venn diagrami.

Use the idea of Venn diagram for social studyii.

Understand classifications based on characteristics and represent by using
Venn diagrams

Experiencing PPDAC (Problem-Plan-Data Analysis-Conclusion) cycle andmodelling cycle in simple projects in lifei.

Understand the problem of context

ii.

Plan appropriate strategies to solve the problem

iii. Gather data and analyse using appropriate methods and tools
iv. Draw conclusion with justification based on data analysis
Preparing sustainable life with number sense and mathematical representations89i.

Use minimum and sequential use of resources in situationsii.

Use data with number sense such as order of quantity and percentage forthe discussion of matters related to sustainable developmentiii. Estimate the efficient use of resources in situations
iv. Maximize the use of resources through appropriate arrangement in a spacesuch as a roomv.

Understand “equally likely” of resources in situations

Utilizing ICT tools as well as notebooks and other technological toolsi.

Use internet data for the discussion of matters related to sustainable
developmentii.

Distinguish appropriate or inappropriate qualitative and quantitative datafor using ICTiii. Use calculators for organizing data such as average
iv. Use calculators for operations in necessary contextv.

Use projectors for sharing ideas as well as board writingvi. Enjoy using of notebooks to exchange learning experiences between eachother such as in mathematics journal writingvii. Use protractors, triangular compasses, straight edges, clinometers fordrawing and measuring
89 It is related to Numbers and Operations, Pattern and Data Representations and Quantity and Measurement
all under Key Stage 1.

52

Chapter 3viii. Use the idea of proportionality to use mechanism such as rotate once andmove twice (wheels, gears)
ix. Use various tools for conjecturing and justifying
Promoting creative and global citizenship for sustainable development ofcommunity using mathematicsi.

Utilize notebooks, journal books and appropriate ICT tools to record andfind good ideas and share with othersii.

Prepare and present ideas using posters and projectors to promote goodpractices in the communityiii. Listen to other’s ideas and ask questions for better designs
iv. Utilize information, properties, models and visible representations as thebasis for reasoningv.

Utilize practical arts, home economics and outdoor studies to investigate
local issues for improving welfare of life

53

Chapter 4

Chapter 4

Key Stage 3
Key Stage 3 (KS3) can be learned based on the Key Stage 2. This stage learns
number and algebra90, relations and function, space and geometry and statistics
and probability. Symbolic representations allow dealing abstract ideas andconcepts that enhance critical thinking, creative thinking through the applicationof knowledge. Understanding and using of concepts and principles in thisstage through participating discussions, dialogue, and arguments enable themto participate in contemporary societal, economic, technological, political,
environmental and mathematical issues. This stage is the basis for the creationof better future with predictions. It bridges further mathematics learning invarious job demands.

Strand: Numbers and Algebra
Numbers are extended to positive and negative numbers, and square roots.
Algebraic expressions are already introduced by the mathematical sentences andsymbols at KS2. At Key Stage 3, algebra is operated by expressions and equations
until second degree. On the extension from numbers to symbolic algebra,
various possible ways of calculations are explored until its appropriateness isestablished. Like and unlike terms are introduced in an algebraic sentence andin simplifying expressions. Properties of equations are introduced for finding
simple equivalent and solving equations with fluency. Substitution, addition andsubtraction of equations enable further operations of simultaneous equations.
Expansion and factorization enable further operations of the polynomials.
Finally, quadratic equations can be solved using various operations.
Topics:Extending numbers to positive and negative numbers
Utilizing letters for algebraic expression and equations
Algebraic expressions, monomial and polynomials and simultaneous equation
Expansion and factorization of polynomial
Extending the numbers with square roots
Solving quadratic equations
90 In algebraic notation of numbers, addition and multiplication are major operations. Subtraction can be
represented by addition of negative numbers and division can be represented by reciprocal or multiplicative
inverse property.

54

Chapter 4

Extending Numbers to Positive and Negative Numbers
Extending numbers to positive and negative numbers and integrate four
operations into addition and multiplicationi.

Understand the necessity and significance of extending numbers topositive and negative numbers in relation to directed numbers withquantity91

ii.

Compare numbers which is larger or smaller on the extended number line
and use absolute value for distance from zeroiii. Extend operations to positive and negative numbers and explain thereasoniv. Get efficiency on calculation in relation to algebraic sum

Utilizing Letters for Algebraic Expression and Equations
Extending the utilization of letters for general representation of situations andsearch the ways of simplifying of algebraic expressioni.

Appreciate the utilization of letter for general representation of situations
to see the expression as process and valueii.

Find the ways to simplify expressions using distribution law and figuralexplanations, establish the calculation with like and unlike letteriii. Acquire fluency of simplifying expression and appreciate it for
representing the pattern of situation
Thinking about set of numbers in algebraic expression with letters as variables
and represent them with equality and inequalityi.

Recognize numbers as positive and negative numbers, and explain
integers as a part of numbers

ii.

Represent a set of numbers using variables with equality and inequalityiii. Translate given sets of numbers on the number lines using interval andinequality notations
iv. Appreciate redefining of even and odd numbers using letters to represent
different sets of variables

91 The study of negative numbers such as temperature is necessary in Science, Home Economics andSocial Studies. For that reason, negative numbers are introduced in other subjects in Key Stage 2.

55

Chapter 4

Thinking about how to solve simple linear equationi.

Review the answers of equations from the set of numbers and thinking
backward

ii.

Know the properties of equations which keep the set of answers ofequation

iii. Appreciate the efficient use of the properties of equations to solve linear
equation
iv. Use equations based on life situations to develop fluency, to solve
equation, and interpret the solution

Algebraic Expressions, Monomial and Polynomials and Simultaneous
Equation
Thinking about the calculations of monomial and polynomials, simple case92
i.

Introduce term, monomial and polynomialsii.

Introduce a number raise to a power of two as square, and a number raise
to a power of 3 as cubeiii. Get fluency for the calculation of polynomials such as combining like
terms and the use of the four operations in simple cases
Thinking about how to solve simultaneous equation in the case of linear
equationsi.

Understand the meaning of solution of linear equations and simultaneous
linear equation as a pair of numbersii.

Know the substitution and elimination methods of solving simultaneous
linear equations93

iii. Get fluency for selecting the methods from the form of the simultaneous
linear equations
iv. Appreciate simultaneous linear equation on the situation

92 Simple case may vary from and depending on the countries based on the mapping of curriculum.
93 Understanding two ways of solving simultaneous equations maintains the set of answer to both equations
in higher level of Mathematics.   

56

Chapter 4

Expansion and Factorization of Polynomial
Acquisition to see the polynomial in second degree with expansion andfactorization and use iti.

Use the distributive law to explain the formulae for expansion and explainthem on diagramsii.

Get proficiency for selecting and using the appropriate formulaiii. Use the expansion formula to factorize the second degree expression andrecognize both formula with inverse operation
iv. Solve simple second degree equation using the factorization and apply onlife situations

Extending the Numbers with Square Roots
Extending the numbers with square roots and calculate the square roots
algebraicallyi.

Define the square root and discuss the existing length and identify thenearest value by sandwich theoremii.

Understand some of square roots cannot be represented by the fractions94

iii. Compare square root using the number line and understand that orderdoes not change but distanceiv. Think about multiplication and addition of square root and understand thealgebraic way of calculation similar to polynomialv.

Appreciate square roots in applying to situations in life95

Solving Quadratic Equations
Solving simple second degree equation using the factorization and apply on
the situationi.

Find the answers of simple second degree quadratic equations by
substitution and explore by completing the square, quadratic formula,and factorization96

ii.

Get fluency to select the appropriate ways for solving quadratic equations

iii. Apply quadratic equations in life situations
94 Not necessary students are to explain however without explanation we cannot introduce rational andirrational numbers.
95 Pythagorean Theorem is discussed in Space and Geometry strand.
96 The graph of quadratic equation will be treated in the Relations and Functions strand.

57

Chapter 4

Strand: Relations and Functions
Relationships are represented by equations and system of equations. Functional
relations are treated amongst situation, table, and equation of function are
introduced based on patterns and relations with algebraic representation on
Key Stage 2 and Key Stage 3. Solution of simple equation is done by equivalence
deduction based on algebra learnt earlier. Two variables in simultaneous
equations as simple system of equations are solved by substitution andadditive-subtractive methods. Three representations, table, equation and graph,
are used as methods to analyze the properties of every function. Proportionand inverse proportions are redefined with those representations mentioned.
Proportional function is extended to line functions. The comparisons of inverse
proportion and line functions are made clear by the property of linearity with‘constant ratio of change’. The concept of proportion is extended to function of
y = ax2. Ways of translations between table and equation, equation and graph,graph and table are specific skills for every function with fluency.
Topics:Extending proportion and inverse proportion to functions with variables
Exploring linear function in relation to proportions
Exploring simple quadratic function
Generalizing functions

Extending Proportion and Inverse Proportion to Functions with Variables
Extending proportion and inverse proportion to functions with variables on
positive and negative numbersi.

Extend proportions to positive and negative numbers, using tables andequations on situationsii.

Plot set of points as graph for proportions defined in ordered pairs(x, y) in the coordinate plane using appropriate scales precisely97

iii. Introduce inverse proportion using tables, equations and graphs
iv. Introduce function as correspondences of two variables in situationsv.

Explore the property of proportional function with comparison of inverse
proportional function

vi. Appreciate proportion and inverse proportion functions in life
97 Utilizing ICT is recommended in mathematical activities.

58

Chapter 4

Exploring Linear Function in Relation to Proportions
Exploring linear function in relation to proportion and inverse proportionsi.

Identify the linear equation on the situations with tables and compare itwith proportional function

ii.

Explore properties of linear function by tables, equations and graphs andcomparing it with direct and indirect proportional functioniii. Acquire fluency to translate the rate of change represented in a table,
coefficient in an expression and slope in graph98
iv. Acquire fluency to translate y values of x = 0 in a table, constant in an
expression, and y intercept in graphv.

Apply the graph of linear function to solve simultaneous equations

vi. Apply the linear function for data representation on situations todetermine best fit line

Exploring Simple Quadratic Function
Exploring quadratic function y = ax2 in relation to linear functioni.

Identify the quadratic function on the situations with tables and compare
it with linear function

ii.

Explore properties of quadratic function by tables, equations and graphs
and comparing it with linear functioniii. Apply the quadratic function on situations in daily life and appreciate it
Generalizing Functions
Generalizing functions with various representations99 on situationsi.

Distinguish domain, range and intervals and is appropriately use for
explaining functionii.

Use various situation for generalizing ideas of functions such as
moving point A and moving point B with timeiii.

Compose a graph as a function of two or more graphs with different
domains in a situation

iv.

Introduce situations of step-functions100 with graph for generalization
the idea of function which cannot be represented by equation

98 Family of linear functions recommends the use of ICT tool in mathematical activities.
99 Utilizing functions as model in daily life which is necessary for STEM education.
100 Intervals are taught in Key Stage 3 Numbers and Algebra.

59Chapter 4

Strand: Space and Geometry
Space and Geometry provide the ways of reasoning for exploring properties ingeometry and produce the ways of argument to explain justifications of visualreasoning. The calculations of angles are not just simple calculation but also theways of using the geometric propositions to justify answers through explaining
why it is correct based on basic properties. By explaining the relationship offigures using transformation, the properties of congruency and describing
similarity are identified and described. Finding the value of angles and buildingarguments for proving are means for developing the habit of reasoning in theproperties of plane figures. The conditions of congruence and similarities,
properties of circles, are also used to explain and prove appropriatenessof geometric conjectures in relation to triangles, quadrilaterals, and circles.
Dynamic geometric software as well as simple compass and ruler are used forconjecturing. It shows general ideas from consistency in variations. Counterexample is also found as special case from variations.
TopicsExploring angles, construction and designs in geometry
Exploring the space with its components
Exploring the ways of argument for proving and its application in geometry

Exploring Angles, Construction and Designs in Geometry
Exploring angles to explain simple properties on the plane geometry and do
the simple geometrical Construction101i.

Explain how to determine the value of angles using the geometricalproperties of parallel lines, intersecting lines , and properties of figuresii.

Use ruler and compass to construct a simple figure such as perpendicularlines and bisectors

iii. Appreciate the process of reasoning that utilizes the properties of angles
and their congruency in simple geometrical constructions)101 Simple geometric construction is discussed by the ruler and compass with reasoning. Dynamic Geometricsoftware usually draws entire circles. For knowing invariant, dynamic geometric software is useful.

60Chapter 4

Exploring the relationship of figures using congruency and enlargement for
designsi.

Explore the congruence of figures through reflection, rotation andtranslation and explain the congruency using line of symmetry, point ofsymmetry and parallel linesii.

Explore similarity of figures with enlargement using points, ratio, andcorrespondencesiii. Enjoy using transformations in creating designs

Exploring the Space with its Components
Exploring space by using the properties of planes, lines and their combinations
to form solidsi.

Explore the properties produced by planes, lines and their combinations,such as parallel lines produced by intersection of parallel planes withanother planeii.

Produce solids by combining planes such as nets and motion such as
rotation, reflection and translationiii. Recognize the space of an object based on its properties and projection inlife

Exploring the Ways of Argument for Proving and Its Application inGeometry102
Exploring properties of congruency and similarity on plane geometryi.

Explore ways of arguments using the congruence of two triangles andappreciate the logic of argument in simple proving

ii.

Explore ways of arguments using the similarity of two triangles based onratio and angles and appreciate the logic of arguments in simple provingiii. Explore the proof of the properties of circles such as inscribed angles,
intercepted arcs
iv. Appreciate the order of proving properties

102 Dynamic Geometric software is useful to find the invariant properties which is discussed in Mathematical
Process and Humanity strand in Key Stage 3.

61

Chapter 4

Exploring Pythagoras’ theorem in solving problems in plane geometry andspacesi.

Explore the proving of Pythagoras’ theorem using diagram and use it insolving problems involving plane figuresii.

Apply Pythagoras’ theorem on the prism by viewing the figures throughfacesiii. Explore the situations for simple trigonometry using special angles inrelation to the Pythagorean theorem
iv. Appreciate the use Pythagoras’ theorem in life103

Strand: Statistics and Probability
Data handling are extended to explore the dispersion of histogram with mean,
median, mode and range. Exploratory Data Analysis (EDA) attempting torepresent and visualize the structure from the given data using Information
and Communications Technology (ICT) is enhanced. Histogram shows different
dispersion if we change the class. Probability is introduced as ratio with the lawof large numbers. Sample space with assumption of equal probability becomesthe point of discussion. Logical analysis to understand whole possible casessuch as a tree diagram is introduced for knowing the ways to represent logicalreasoning. Histogram can be seen relatively and produce frequency distribution
polygon. Difference between sample and population is discussed. Boxplots
with quartile is an extension of median and range is used for comparisons of
distributions. Using skills of statistics and probability make problem solving
in situations possible. Analyzing and identifying the trends in situations formaking decisions are necessary such as issues for sustainable living.
Topics:Exploring distribution with the understanding of variability
Exploring probability with law of large numbers and sample space
Exploring statistics with sampling

Exploring Distribution with the Understanding of Variability
Exploring distribution with histograms, central tendency to represent
variabilityi.

Investigate histogram to show distribution appropriately using class andrange

103 Pythagoras’ theorem is used for re-understanding the topic on square root  under Key Stage 3 Numbers
and Algebra.

62Chapter 4ii.

Identify alternative ways to show distribution such as dot plots, box-plot
and frequency distribution polygoniii. Investigate central tendencies such as mean, median, mode104, quartileand their relationship on the distribution
iv. Investigate dispersion such as class, interval, range and bimodalv.

Appreciate the analysis of variability through the finding of the hidden
structure of distribution on situation using the measure of central tendency
and dispersion

Exploring Probability with Law of Large Numbers and Sample Space
Exploring probability with descriptive statistics, law of large numbers andsample spacei.

Experiment with the help of coins and dice to explore the distribution ofratio and understand the law of large numbersii.

Use the idea of equally likely for inference to get the value of probability105

iii. Analyze the situation with tables to represent the sample space and using
it for predicting with probability
iv. Use various representations such as table, tree diagram , polygon diagramand frequency distribution polygon for finding probabilityv.

Analyze the discussion of matters related to sustainable development withprobability and inference from the data to forecast the future

Exploring Statistics with Sampling
Exploring sampling with the understanding of randomnessi.

Discuss the hidden hypothesis behind sample and population ratioii.

Use randomness to explain samplingiii. Analyze the data exploratory such as dividing the original into two forknowing better data representations and discuss appropriateness such as
regrouping
iv. Appreciate data sampling in a situation with sustainable development

104 Mean, median and quartile are fixed depending on the data. However, mode changes depending on the class.
105 The probability here is called equiprobability when all possible cases are “equally likely”. On the upper
grade level, probability will be redefined based on distributions.

63

Chapter 4

Strand: Mathematical Processes – Humanity
Enhance the critical argument in mathematics on communication with others
beyond Key Stage 2. Propose challenging activities to promote metacognitive
thinking at different level of arguments to make sense of mathematics.
Translating real life activities into mathematical models and solving problems
using appropriate strategies are emphasized in functional situations. The processof doing mathematical activities involves patience that develops perseverance inlearners and takes responsibility of one’s own learning. At this stage, the habitual
practice of self-learning will eventually develop confidence, thus, opportunity
for challenges to extend mathematics and the ability to plan sequence of futurelearning are also enhanced.
Standards
Enjoying problem solving through various questioning for extension ofoperations into algebra, space and geometry, relationship and functions, andstatistics and probability
Enjoying measuring space using calculations with various formulas
Producing proof in geometry and algebra
Utilizing tables, graphs and expressions in situations
Using diagrams for exploring possible and various cases logically
Exploring the graph of functions by rotation, by symmetry and by translationof proportional function
Understanding the ways for extension of numbers
Designing models for sustainability using mathematics
Utilizing ICT tools as well as other technological tools
Promoting creative and global citizenship for sustainable development of society
using mathematics
Enjoying problem solving through various questioning and conjecturing forextension of operations into algebra, space and geometry, relationship andfunctions, and statistics and probability106i.

Pose questions to extend numbers and operations into positive and negative
numbers, algebraic operations, and further extension into polynomial
operations, and numbers with square rootsii.

Pose questions to solve linear equations, simultaneous equations and simple
quadratic equations

106 Connected to the three strands, namely Numbers and Algebra, Relations and Functions, and Space andGeometry.

64

Chapter 4iii. Pose assumptions in geometry as objects of argument and proof
iv. Pose questions to transform three dimensional objects into two dimensional
shapes and vice versav.

Pose questions in relations and functions for knowing properties of different
types of function

vi. Pose questions to exploratory data handling for knowing structure of
distribution
vii. Pose questions that apply PPDAC in relation to statistical problem solving
viii. Pose questions in relation to “equally likely” events
ix. Pose assumptions to discuss hypothesis based on sample and populationx.

Pose conjecturing such as if x increases and y decreases then it is inverse
proportion

Enjoying measuring space using calculations with various formulas107i.

Extend the number line to positive and negative numbers and compare thesize of numbers with the idea of absolute valueii.

Derive the square root using unit squared paper through the idea of areaiii. Explain the expansion of polynomials using area diagrams
iv. Use the projection of space figures to plane figures using the Pythagorean
theoremv.

Apply similarity and simple trigonometry for measurement

vi. Use the common factors to explain factorization of area of rectangle basedon area of square
Producing proof in geometry and algebrai.

Have an assumption through exploration and produce propositionsii.

Justify the proposition using examples and counter examples forunderstandingiii. Rewrite propositions from sentence to mathematical expressions by using
letters and diagrams
iv. Search the ways of proving by thinking backward from the conclusion andthinking forward from the given
107 Connected to the three strands, namely Numbers and Algebra, Relations and Functions, andSpace and Geometry.

65

Chapter 4v.

Show the proof and critique for shareable and reasonablenessvi. Deduce another propositions in the process of proving and after proving
using what if and what if notvii. Adapt ways of proving to other similar propositions of proof
viii. Explain the written proof in geometry and algebra by the known
ix. Revise others’ explanation meaningfully
Utilizing tables, graphs and expressions in situations108i.

Explore the properties of functions by using tables, graphs and expressions
and establish fluency of connections among them for interpreting functions
in context

ii.

Analyze distribution of raw data by using tables, graphs and expressions
in daily life

Using diagrams for exploring possible and various cases logically109
i.

Use number line with inequality to identify range and setii.

Use circle to identify relationship between circumference and central angle(acute, obtuse and right)

iii. Use rectangle and rotating a point on the side rectangle to draw the graphof the area
iv. Use tree diagram for thinking about all possible cases sequentially
Exploring the graph of functions by rotation, by symmetry and by translationof proportional function110i.

Use the slope of graph for the proportional function to rotate the graph or
to determine the point of intersection

ii.

Explore to know the nature of two simultaneous equations by usingtranslationiii. Use the y-axis, x-axis and y=x as the line of symmetry to explore proportional
function
iv. Explain the graph of linear function by translation of proportional function

108 Connected to the strand on Relations and Functions.
109 Connected to the two strands on Relations and Functions, and Space and Geometry.
110 Connected to the two strands on Numbers and Algebra, and Relations and Functions.

66

Chapter 4

Understanding ways for extension of numbers111
i.

Extend the numbers based on the necessity of solving equations such as
x + 5 = 3 and x2 = 2, and show examples for demonstrating the existencesuch as on the number lines, and understand it as set

ii.

Compare the size of number and identify how to explain the order of
numbers and its equivalenceiii. Extend the operations for keeping the form112 beyond the limitations of
meaning113
Designing models for sustainability using mathematics114
i.

Discuss and utilize probabilities in life such as weather forecasting forplanningii.

Design cost saving lifestyle models through comparison of data such ascost of electricity, water consumption, and surveyiii. Plan emergency evacuation such as heavy raining and landslide where
the calculations on the amount of water in barrel per minute exceeds the
maximum standards
iv. Forecast the future with mathematics
Utilizing ICT tools as well as other technological toolsi.

Use dynamic geometry software for assumption, specialization andgeneralizationii.

Use graphing tool for comparison of the graph and knowing propertiesof functioniii. Use data to analyze statistics with software
iv. Use internet data for the discussion of sustainable developmentv.

Use calculators for operations at necessary context

vi. Use projector for sharing ideas such as project survey, reporting andpresentation
111 Connected to the strand on Numbers and Algebra.
112 There are three meanings of form: (1) Permanence of form means “keep the pattern of operation” such as(-3)x(+2)=-6, (-3)x(+1)=-3, (-3)x0=0, and (-3)x(-1)=+3, and (-3)x(-2)=+6. Here, the product of the patternincreases by 3; (2) The form means “Principle of the permanence of equivalence of form” which means to keep
the law of commutativity, associativity and distributivity; and (3) The form means the axiom of field in Algebra.
Normally, in education, we only treat (1) and( 2).
113 For the extension of the number to positive and negative numbers, beyond the limitations of meaning suchas subtract smaller number from larger number. For the extension of numbers to irrational number, beyond
the limitation of meaning such as rational number is quotient (value of division).
114 Connected to the three strands, Numbers and Algebra, Relations and Functions, and Space and Geometry.

67

Chapter 4vii. Use the idea of function to control mechanismviii. Use ICT tools for conjecturing and justifying to produce the object of proving
Promoting creative and global citizenship for sustainable development ofsociety using mathematicsi.

Utilize notebooks, journal books and appropriate ICT tools to wisely
record and produce good ideas for share with othersii.

Prepare and present ideas using posters, projectors, pamphlets and social
media to promote good practices in societyiii. Promote the beautifulness, reasonableness and simplicity of mathematics
through contextual situations in the society
iv. Listen to other’s ideas and ask questions for better designs, craftsmanshipand innovationsv.

Utilize information, properties, models and visible representations as
basis for making intelligent decisions

vi. Utilize practical arts, home economics, financial mathematics and outdoor
studies to investigate local issues for improving welfare of life

68

Chapter 4

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70

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COMMON CORE REGIONAL LEARNING
STANDARDS IN SCIENCE

71

Chapter 5

Chapter 5

Framework for CCRLS in Science
Nature of Science
There is no consensus and disagreement exists among philosophers of science,
historians of science, scientists, and science educators on the specific definition
for nature of science. Somehow this can be attributed to the multifaceted natureof science and complexity of scientific endeavour. However, briefly, nature ofscience refers to the epistemology of science, science as a way of knowing, or
the values and beliefs inherent to the development of scientific knowledge.
Review of literature presents characteristics of scientific knowledge, namely;
scientific knowledge is tentative and subject to change; scientific knowledge
is empirically based and in part derived from observations of the natural
world; scientific knowledge is subjective (theory-laden); scientific knowledge
necessarily involves human interference, imagination and creativity (involves
the invention of explanations; and scientific knowledge is socially and culturally
embedded (Lederman, 2013).
According to some authors the most salient feature of scientific knowledge
is its systematicity. The systematic character of scientific knowledge can be
examined with respect to five features of science, namely; how science describes,
how science explains, how science establishes knowledge claims, how science
expands knowledge and how science represents knowledge. These features ofscientific knowledge are systematic. Scientific descriptions represent the first
aspect of the systematicity of scientific knowledge. In the laboratory sciences,scientists aim for general descriptions that is, descriptions that provide
generalizations about a certain domain of phenomena or the regularities
holding in this domain. Science classifies phenomena in a systematic fashion.
Generalized descriptions can be used to predict, control, or explain phenomenaof the same kind. Scientists want to dig deeper than a mere knowledge of theseregularities that can be observed and described. Scientists want to understandthe regularities of the world.
Science typically creates theories. The systematic aspect of theories is very
important, specifically their power to provide causal explanations which
unify entire domains of phenomena. With the use of theories, the predictive
power of science increases tremendously. Science purports to provide a formof knowledge that is particularly reliable and trustworthy. However, scientificknowledge is tentative and opens to different viewpoints, perspectives andinterpretations. Error may arise as a result of mistakes, false assumptions,72

Chapter 5

entrenched traditions, belief in authorities, superstition, wishful thinking,prejudice, bias and even fraud. But science is extremely careful and successful
in detecting and eliminating all sorts of error. Experiments allow scientists totest claims about the existence and properties of postulated theoretical entities
much more rigorously compared with observations alone. Scientific knowledge
is produced when community of scientists agree on empirical evidences.
Knowledge that has been experimentally tested can immediately be usedpractically. This is because applying knowledge technologically is basically thesame series of physical actions as experimenting, but with different intentions.
Systematically discovering the strengths and weaknesses of particularknowledge claims is one of the hallmarks of science. Some researchers rather
emphasized the effects of human elements, such as creativity or subjectivity.
Science has managed to improve and expand its knowledge to unprecedented
degree through the availability of appropriate material resources. The essenceof the astonishing ability of science to expand our knowledge is the fact thatthe stock of already existing knowledge is systematically used in order tocreate new knowledge. During the last few decades, close scrutiny of science
has led to a move away from the idea of the scientific method. The proceduresof science appear much more individually cased-based. Productive scientificwork is largely fuelled by existing scientific results which it takes as models thenextends. Science is much more artful and playful than a strictly rule-governed
procedure. Science exploits technology. Technology is largely science based in
the sense that many scientific results enter technological innovations. Scienceis used to create new technologies and new technologies are used to improveand extend scientific knowledge. Knowledge generation may also contain anelement of chance. Science is even systematic in exploiting chance for generating
new insights. The results of science can and must be presented in an orderly,systematic fashion. In the empirical sciences, important distinctions have to
be made with respect to the representations of knowledge: the general has
to be distinguished from the particular, the well-established from the merely
hypothetical, the descriptive from the theoretical, the logically dependent fromthe logically independent, etc.
On the other hand there are drawbacks to the systematicity of science.
The two issues stemming from the systematicity of science are specializationand fragmentation, and over-extension of science. Specialization is an effectof systematically pursuing questions that present themselves in the courseof research. Specialization is the price one has to pay for systematic, in-depth
knowledge. There are also counter-tendencies in science that tend to overcome
specialization. These tendencies are due to systematic attempts to unify science73

Chapter 5with the use of overarching theories, and by internally driven interdisciplinary
research. But the fact remains that scientific knowledge is quite fragmented due
to specialization, at least in practice. There are various negative consequences ofthis kind of specialization and fragmentation. There is a communication problem
between science and the public, between science and science policy, and withinscience between different disciplines, even between sub-disciplines in the same
field. This resulted to difficulty for the public to understand what is going onin science; policy-makers have difficulties setting priorities; interdisciplinary
research poses special challenges; and so on. The second issue surrounding
the systematic and comprehensive character of science is the over-extensionof science- the belief that science really addresses everything. But science has
limitations. There are essential problems which do not call for scientific solutions.
It would be unrealistic to expect that the solutions to all our problems will be
provided by science by itself. Instead, human beings will have to make decisions
concerning priorities, concerning values, concerning conflicting priorities andvalues- and this both at local and global levels. In brief, these decisions are
essentially political, not scientific. Science, including social sciences can only
help especially in predicting the probable consequences of decisions and actions.

Aims of Science in CCRLS
Scientific and technological literacy plays a very vital role in ensuring an
economically and environmentally sound development of countries. Thus theneed to promote a world community of scientifically and technologically literate
citizens through science education is imperative. Scientific and technologicalliteracy for all is operationalised based on four educational pillars, namely;(1) personal development through acquisition of scientific knowledge,(2) personal mental development through use of scientific skills/processes;(3) development of individual attributes, attitudes and perceptions and(4) development of values and skills as a responsible member of society.
Science education for SEA-BES CCRLS aims to:•develop scientific literacy whereby scientific knowledge acquired throughthe processes of science with technology as an enabler is applied in daily
lives and used to acquire new knowledge;•

instill the ability to carry out scientific inquiry to understand the world
around us;•

demonstrate the understanding of the nature of science in the process ofcarrying out scientific investigation;•

develop scientific skills through hands-on and minds-on experiences;

74

Chapter 5•

develop understanding of the interrelationship of science with society,environment, technology, engineering and mathematics;•

demonstrate ethical behaviour, scientific attitudes and values when
undertaking scientific thinking and processes; and•demonstrate the ability to use the acquired scientific thinking and processes
in making informed decision, and debating scientific and social-culturalissues.

Components of the Framework
The development of an understanding of science is important for students intoday’s world if they are to become citizens who can make informed decisions
about themselves and the world in which they live. Students are faced witha myriad of information, and sifting fact from fiction and understanding thescientific basis of important social, economic, and environmental issues ispossible only if they have the tools to accomplish this. Students’ understandingof science should build throughout their schooling so that when they become
adults they are able to act from a sound basis decisions when faced with diverse
issues such as treatment of diseases, climate change, and the applications oftechnology. Across the world, there is an increased demand for those qualified
to pursue the careers in science, technology, and engineering that drive theinnovation and invention necessary for economic growth and improving thequality of life. To meet this demand, the SEA-BES Common Core Regional
Learning Standards in Science Framework is developed under the analysis ofnational curriculum in SEAMEO Member Countries.
The framework for CCRLS in Science as shown in Figure 3 is developed
under the three components and the discussion of humanistic and philosophicalnature of science. The framework also provides the concrete ideas of sciencelearning on the above aims.

75

Chapter 5

VALUES AND ATTITUDESSCIENTIFIC SKILLS, PROCESSES &THINKINGCONTENT

Figure 3. Components of the CCRLS Science framework.
Figure 3. Components of the CCRLS Science framework.
The CCRLS framework for Science consists of three interwoven componentsof content,scientificskills, processes
thinking
and valuescomponents
and attitudes.
The CCRLS
framework
for Science
consistsandof threeinterwovenof content,
The framework is the overall structure for organizing learning and teachingscientific skills, processes and thinking and values and attitudes. The framework is thefor the science subjects. Table 1 shows the specific elements covered in eachoverall structure for organizing learning and teaching for the science subjects. Table 1 shows
component of the framework.
the specific elements covered in each component of the framework.

76

Chapter 5

Table 1
Components of CCRLS Science Framework
Content
•
•
•
•
•
•

Scientific Inquiry
Life and the Living
World
Material World
Energy and Change
Earth and Space
Science, Engineering,and Technology for
Sustainable Society

Scientific Skills, Processes
and Thinking

Values and Attitudes

Science Skills and Process •
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•

Questioning
Observing
Classifying
Measuring
Hypothesizing
Predicting
Inferring
Explaining
Communicating
Evaluating
Identifying andcontrolling variables
Formulating andtesting hypothesis
Defining
operationallyInterpreting data
Planning
and carrying
investigations

Thinking
•
•
•
•
•
•
•
•
•

critical and creative
thinking
reasoningproblem solving
decision making
applying and creating
generating solutions
safe use of equipment
ICT skills
Collaboration skills

77

•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•

Caring for the living
and non-living
environment
Social awarenessSustainability
Responsibility
Truth
Interdependence
Integrity
Perseverance
Self-discipline
Self-esteem
Empathy
Appreciation
Trust
Critical reflection
Inventiveness
Tolerance
Uncertainty
Belief and interest
Curiosity
HonestyObjectivity
Open-mindedness
Respect for evidenceChapter 5

The Content Strands
The major learning contents in science are arranged into six strands yet thestrands should not be viewed as compartmentalized blocks of knowledge.
In order that students can have a coherent understanding of the world aroundthem, the diversity and multiplicity of scientific facts and concepts should belearned as interrelated “bigger ideas” in a conceptual scheme. The six content
strands are as follows:•

Science Inquiry•

Life and the Living World•

Material World•

Energy and Change•

Earth and Space•

Science, Engineering and Technology for Sustainable Society

Science Inquiry, and Science, Engineering and Technology for Sustainable
Society may be integrated to the four content strands. The four content strands
serve as the context from which science content knowledge, and scientific skills,
processes and thinking as well as values and attitudes are developed in thelearners across the three Key Stages.

Scientific Skills, Processes and Thinking
Scientific inquiry involves science process and thinking skills as well as generalinquiry processes such as problem-solving, logical reasoning, decision-making
and reflection. Science process skills are those employed by scientists tomake sense of the natural world. Science process skills include questioning,
hypothesizing, defining problems, generating solutions, predicting, observing,safe use of equipment, comparing, classifying, measuring, recording, inferring,
analyzing, verifying, explaining, reasoning, communicating, applying andcreating, evaluating and integrated science process skills of planning andcarrying-out investigations.
Other generic skills which are fundamental in helping students to learn
to acquire knowledge, to construct knowledge and to apply knowledge tosolve new problems include decision-making skills, collaboration skills,
communication skills, creative thinking skills, critical thinking skills, Information
and Communications Technology, leadership skills and connectivity.
Teachers are encouraged to provide opportunities for students to use
concepts and integrate skills and processes to inquire things and phenomena
around them.
78

Chapter 5

Skillsa)Engaging with an event, phenomena or problem through:Formulating hypothesis: This is the skill of general explanation for a related
set of observations or events. It is an extension of inferring.
Generating possibilities: This is the skill of exploring all the alternatives,
possibilities and choices beyond the obvious or preferred one.
Predicting: This is the skill of assessing the likelihood of an outcome basedon prior knowledge of how things usually turn out.

b)Collecting and presenting evidence through:Observing: This is the skill of using our senses to gather information about
objects or events. This also includes the use of instruments to extend therange of our senses.
Using apparatus and equipment: This is the skill of knowing the functions
and limitations of various apparatus, and developing the ability to selectand handle them appropriately for various tasks.

c)

Reasoning, making meaning of information and evidence through:Comparing: This is the skill of identifying the similarities and differences
between two or more objects, concepts or processes.
Classifying: This is the skill of grouping objects or events based on common
characteristics.
Inferring: This is the skill of interpreting or explaining observations or
pieces of data or information.
Analysing: This is the skill of identifying the parts of objects, informationor processes, and the patterns and relationships between these parts.
Evaluating: This is the skill of assessing the reasonableness, accuracy andquality of information, processes or ideas. This is also the skill of assessing
the quality and feasibility of objects.
Communicating: This is the skill of transmitting and receiving information
presented in various forms – written, verbal, pictorial, tabular or graphical.

79

Chapter 5

Processes
Processes are complex operations which call upon the use of several skills.
At the primary level, the processes expected of students are:Creative problem solving: This is a process of analysing a problem and choosing an
innovative and relevant solution in order to remedy or alter a problem situation.
Decision - making: This is a process of establishing and applying criteria to selectfrom among seemingly equal alternatives. The process of establishing criteria
involves consideration of the consequences and values.
Investigation: This involves formulating questions or hypotheses, devising fairmethods and carrying out those methods to find out answers to the questions
or to verify the hypotheses.
It must be pointed out that there is also no one definite sequence of priority
among the skills and processes listed above. For example, observation may
lead to hypothesising but at other times a hypothesis can lead to observation.
In science teaching and learning, effort should initially be directed atteaching explicitly each of the skills through the use of appropriate activities.
Later, effort should be directed to helping students integrate some or all of
the skills in scientific inquiry. The skills and processes can be introduced fromprimary level in an age-appropriate manner. Once introduced, these skills andprocesses should continue to be developed at the higher levels. The skills set
identified and the essential features of inquiry are shown in the table below.
Skills andProcesses

SkillsEngaging with an event,phenomenon or problem
through:•••

Collecting andpresenting
evidence through:Formulating hypothesis
Generating possibilities
Predicting••

Observing
Using
apparatus andequipment

Reasoning; making
meaning of
information andevidence through:
•
•
•
•
•

Comparing
Classifying
Inferring
Analysing
Evaluating

Communicating
Processes

Creative problem-solving, investigation and decision-making

Essential Question
featuresof inquiry

Evidence
Communication

80

ExplainConnectChapter 5

Thinking
Thinking is a mental process that requires an individual to integrate knowledge,
skills and attitude in an effort to understand the environment. Thinking skills canbe categorized into critical thinking skills and creative thinking skills. A person
who thinks critically always evaluates an idea in a systematic manner before
accepting it. A person who thinks creatively has a high level of imagination, able
to generate original and innovative ideas, and able to modify ideas and products.
Critical thinking skills include attributing, comparing and contrasting, grouping
and classifying, sequencing, prioritising, analyzing, detecting bias, evaluating
and making conclusions. Creative thinking skills include generating ideas,
relating, making inferences, predicting, making generalisations, visualizing,
synthesizing, making hypothesis, making analogies and inventing. Reasoning
is a skill used in making logical, just and rational judgements. Decision making
involves selection of the best solution from various alternatives based on specificcriteria to achieve a specific aim. Problem solving involves finding solutions tochallenging or unfamiliar situations or unanticipated difficulties in a systematicmanner.

Values and Attitudes
Values and attitudes should be permeated in the learning and teaching of scienceto foster the scientific ways of thinking and working.
The following is an outline of the values and attitudes advocated in theschool curriculum.
Personal Values
Core values

SocialSustaining values

Core values

Sustaining values•

sanctity of life•

Self-esteem•

Equality•

Plurality

•

truth

•

Self-reflection•

Kindness•

Due process of law•

aesthetics•

Self-discipline•

Benevolence•

Democracy•honesty•

Self-cultivation

•

Love

•

Freedom and liberty

•

human

•

Principled morality•

Freedom•

Common will

dignity•

self-determination•

Common good•

Patriotism•

rationality•

openness•

Mutuality•

Tolerance•

creativity•

independence•

Justice•

Equal opportunities•

courage•enterprise

•

Trust

•

Culture and•liberty•

integrity•

Interdependence•

affectivity•

simplicity•

Sustainability•

Heritage•

individuality•

sensitivity•

Betterment of•

Human rights and•modesty•perseverance

civilization

human kind81

responsibilities•

Rationality•

Sense of belonging•

Solidarity

Chapter 5

Attitudes

•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•

Optimistic
Participatory
CriticalCreative
Appreciative
Empathetic
Caring and concern
Positive
Confident
Cooperative
Responsible
Adaptable to changes
Open-minded
Diligent
With a desire to learn
With respect for self, life, quality and excellence, evidence, fair play, ruleof law, different ways of life, beliefs and opinions, the environment

Development of values and attitudes in science education are illustrated in
the following:•

Learners maintain curiosity and continued interest in science.

•

Learners are aware of the importance of the safety of oneself and others in
the laboratory and be committed to safe practices in daily life.

•

Learners develop personal integrity through observation and honest
recording of experimental data and analysing experimental evidence.

•

Learners show an awareness that the body of scientific knowledge is notstatic; and that experimental and investigatory work are important for its
advancement.

•

Learners develop an awareness of scientific advancement and its social,economic, environmental and technological implications.

•Learners are willing to communicate and comment on issues related toscience, value the suggestions and respect the decisions of others.

82

Chapter 5•

Learners develop a positive attitude in enhancing personal and community
health.

•Learners appreciate the wonders of Nature and show respect and care for
all forms of life.

•

Learners appreciate the imminent need for conservation and act
responsibly in conserving the environment.

•

Learners demonstrate a continued interest and enjoyment in the pursuitof scientific knowledge.

•

Learners are critical towards evidence, hypotheses and experiments.

•

Learners show an awareness of the evolutionary nature of scientificknowledge, and that experimental and investigative works are importantfor its advancement.

•

Learners develop open-mindedness, be able to show tolerance and respect
towards different opinions, viewpoints, and people with different beliefs
and value systems.

•

Learners reflect on ways that scientific and technological developments
influence the society.

•

Learners are committed and show continued effort to support activities
contributing to the personal and community health, protection of theenvironment, conservation of natural heritage, both locally and globally.

•

Learners develop positive attitudes and values towards sex on mattersrelated to the role of sexuality, parenthood, marriage, etc.

•

Learners show concern for the local, national and global scientific issues
and ethics arising from the conflicting use of places, environment, animal
testing, use of materials and related consequences and others.

•

Learners make informed and responsible decisions on matters related totheir health based on scientific knowledge, evidence and objectivity.

•

Learners are able to tolerate ambiguity, different opinions and people
with different value systems.

•

Learners are willing to contribute to the betterment of mankind in
local, national and global perspectives based on the acquired scientificknowledge.

83Chapter 5Context to Link the Three Components

The three components
shown inshown
Figurein3 Figure
previously
should beembeddedin everyinkey stage
The three components
3 previously
shouldbe embedded
as standards
forkeythestagecontentof teaching.
“Values,
attitudes”,
componentand “Scientificevery
as standards
for thecontent andof teaching.
“Values,
and attitudes”,
componentand “Scientificskills, processes
and thinking”
componentcomponent.
cannotskills, processes
and thinking”
component
cannot exist
without “Content”
The
exist withoutcan“Content”
component.
first two
components
can Forbe taught
first two components
be taught
through The
teachingwiththe content.
teaching thosethrough teaching
withtime,
the content.
teaching those
three components
three components
at the samecontextFor
is introduced
as shown
in Figure 4.at thesame time, context is introduced as shown in Figure 4.
Values and Attitudes

Scientific Skills,
Processes and Thinking

Content

Figure4: 4:Interlinking
withthethecontext.
context.
FigureInterlinkingofofthe
thethreethree components
components withthe givencontext,
three components
areconnected.
well connected.
reason,classroom
In the given Incontext,
three
components
are wellOn On
thisthisreason,classroom activities for developing competencies should be designed to link
activities for developing competencies should be designed to link them. The following
them. The following contexts are samples:
contexts are samples:• Explore
a problemwith curiosity
a situation
attemptingtotoformulate
formulate scientific Explore
a problemwith curiosity
in a insituation
andandattempting
scientificideas,
theoriesandprinciples
ideas, theories and principles
• the
Apply
the sciencelearned,to other’s
appreciate
 Applysciencelearned,listenlisten
to other’sideasideas
and andappreciatethetheusefulness,
usefulness,and beauty of science
power andbeauty powerof science Enjoy
communications
on onscienceinsolvingsolvingproblems with• classroom
Enjoy classroom
communications
sciencebig
bigideas
ideas inproblems
patiencewith
andpatiencedevelopand
persistencedevelop persistence Feel• theFeel
excitementof “Eureka”
with enthusiasm
for thefor
solutionsand explanationofthe excitementof “Eureka”
with enthusiasm
the solutions
andunknown
problems
explanation of unknown problems
 Think about ways of explanation using understandable representations such as
language, symbols, diagrams, charts, graphs and notation of science Discuss the differences in seeing situations
84 before and after learning science Explain, understand others and conclude scientific ideas
 Explore ideas through inductive and deductive reasoning when solving problems tofoster scientific inquiry
 Feel confident in using science to analyse and solve contextual problems both inschool and in real-life situations
 Promote knowledge, skills and attitudes necessary to pursue further learning inChapter 5•

Think about ways of explanation using understandable representations
such as language, symbols, diagrams, charts, graphs and notation ofscience•

Discuss the differences in seeing situations before and after learningscience•

Explain, understand others and conclude scientific ideas•

Explore ideas through inductive and deductive reasoning when solving
problems to foster scientific inquiry•

Feel confident in using science to analyse and solve contextual problems
both in school and in real-life situations•

Promote knowledge, skills and attitudes necessary to pursue further
learning in science•

Enhance communication skills with the language of science•

Promote abstract, logical, critical and metacognitive thinking to assess
their own and other’s work•

Foster critical reasoning for appreciating other’s perspectives•

Promote critical appreciation on the use of information and communication
technology in science•

Appreciate the universality of science and its multicultural and historicalperspectives

85

Chapter 6

Chapter 6

Science Inquiry
Strand Description
This strand aims ultimately for students to plan, carry out and evaluate own
scientific investigation. This will be achieved through the development ofstudents’ process skills and the application of knowledge and understandingin structured, guided and open-ended inquiries. Habits of mind are embraced
to development and application of scientific process skills, scientific ethics,
attitudes and noble values in carrying out scientific investigations.
This strand involves the development of science process skills, manipulativeskills, attitudes and values. It also involves the development of understandingof the importance of scientific inquiry as central to nature of science.
It involves science inquiry, science process and thinking skills as well as generalinquiry process such as creative thinking, problem solving, logical reasoning,decision-making and reflection. It also includes managing laboratory apparatus
and specimens; safety in the laboratory; scientific ethics, attitudes and noble
values; scientific investigations and the world of STEM.
In carrying out scientific investigations, students are expected to engage
collaboratively with peers to develop interest and inculcate positive values about
scientific learning. Experiments and investigations encourage development ofknowledge and understanding in students at higher cognitive levels as they
progress through the key stages. Students are able to solve everyday problems
through the application of the knowledge and understanding they developed
from their scientific investigations. From hands-on experiences students willdevelop explanations, ideas, scientific models and theories and present themthrough the use of ICT and other forms of representation. The process of doing
scientific investigations will develop students into learners with perseverance
who take responsibility for their own learning. The habitual practice ofself-learning will develop them as confident and good decision makers.
This strand is not a stand-along component but should be integrated
with other five (5) strands. It provides for the development of skills throughhands-on and minds-on activities that are the heart of doing science.

86Chapter 6

Topic: Science Process Skills
Sub-topic: Observing
Key Stage 1•

Make simple observations of the things around using one or more senses•

Use simple science apparatus to support observation•

Observe to answer simple questions

Key Stage 2•

Make systematic and careful observations using science apparatus•

Use microscope as a tool to support observation of tiny specimens•

Make qualitative and quantitative observations•

Observe to answer simple and complex questions

Key Stage 3•

Use microscope as a tool to support observation of selected microorganisms
and cells•

Use telescope and binoculars as tools to support observation•

Observe to answer complex and higher order thinking questions•

Make accurate and relevant qualitative and quantitative observations to
identify patterns or sequence of events or phenomena

Sub-topic: Questioning
Key Stage 1•

Ask simple questions that can lead to an experiment or an investigation

Key Stage 2•

Ask specific questions that can lead to the design of an experiment,
investigation, problem solving (which could lead to the development of asimple solution)

Key Stage 3•

Ask questions based on real life experiences, problems and issues that canlead to scientific investigations and problem solving (which could lead tothe development of a simple solution)

87

Chapter 6

Sub-topic: Classifying
Key Stage 1•

Group objects by observing their similarities and differences based on
certain characteristics using one or more senses•

Give a name to a group of objects or specimens possessing similar
characteristics•

Identify a characteristic as a basis to group the objects/specimens

Key Stage 2•

Classify objects using multistage classification

Key Stage 3•

Classify living things, matter and elements using multistage classification

Sub-topic: Identifying, Manipulating and Controlling Variables
Key Stage 1•

Identify the things that could be changed (variables) in an investigation•

Conduct simple fair test scientific investigation with teacher’s support(A simple fair test investigation is when you change one variable(independent variable) measure the effect of that change (dependent
variable) and keep all the other variables the same (constant variable)

Key Stage 2•

Understand the basic concept of a fair test•

Conduct a fair test that includes planning for repeat readings/observations

Key Stage 3•

Plan and conduct a whole/an open-ended fair test inquiry

Sub-topic: Hypothesising
Key Stage 1•

Make simple hypotheses with teacher’s support

Key Stage 2•

Identify a variable that may affect the outcome of an investigation and makea hypothesis that states the effect of changing the variable or the outcome

88Chapter 6

Key Stage 3•

Establish a relationship between the independent variable and dependent
variable to form a hypothesis that can be tested

Sub-topic: Measuring and Using Numbers
Key Stage 1•

Make measurements using non-standard units•

Make measurements using standard units for quantities such as length,
mass or time

Key Stage 2•

Make precise and accurate measurements using standard units for quantities
such as length, mass, volume, time and temperature•

Make measurements with increasing precision and accuracy and take repeat
readings when appropriate•

Use the S.I. units and their corresponding symbols•

Use symbols and values of prefixes for unit of length, volume, time,
temperature, mass and power: milli-, centi-, kilo-, deca-, square meter,
cubic meter

Key Stage 3•

Choose the measuring tools and instruments appropriate for the specificscientific investigations to ensure precision and accuracy•

Determine the area and volume of irregularly shaped objects using thewater displacement method

Sub-topic: Recording, Analysing and Interpreting Data
Key Stage 1•

Gather and record simple data from observation•

Record data from simple investigation•

Record findings using simple language•

Apply basic numeracy to calculate results•

Use drawing and labels to present results and use prepared simple tables
and charts with support

89

Chapter 6

Key Stage 2•

Use drawings, symbols, labeled diagrams, keys, and tables in recording data•

Process and analyse data to form simple conclusion•

Create own tables for investigations involving one independent variable•

Draw a bar chart with support•

Read values from the graph•

Make a general statement about simple patterns from the graph•Describe the relationship identified, linking both the independent anddependent variables

Key Stage 3•

Interpret observations and data, including identifying patterns and using
observations, measurement and data to draw conclusions•

Apply mathematical concepts and calculate results•

Create tables, charts and graphs appropriate for the investigation carried out•

Create appropriate tables, charts and graphs for the investigation carriedout using ICT•

Identify relationships by applying mathematical calculation•

Extrapolate and interpolate data from graph

Sub-topic: Communicating
Key Stage 1•

Make simple reports from observations through oral and/or written forms)•

Make simple reports on findings through oral and written, drawings,
display and other means of presentations

Key Stage 2•

Report and present observations, data and findings using appropriate
methods, including use of ICT with some guidance

Key Stage 3•

Report and present observations, data and findings using appropriate
methods, including use of ICT

90

Chapter 6

Sub-topic: Evaluating
Key Stage 1•

Use evidence to answer questions or to support findings•

Recognise any of the difficulties encountered with support

Key Stage 2•

Suggest how the difficulties accounted might be avoided•

Suggest how the investigation might be improved and raise further
questions•

Identify differences, similarities or changes related to simple scientific ideas
and processes•

Recognise some of the limitations of the findings•

Identify evidence that can been used to support or refute ideas or arguments

Key Stage 3•

Evaluate the precision, accuracy and reliability of methods and suggest
possible improvements•

Identify any anomalous result and explain how those have occurred•

Evaluate data, showing awareness of potential sources of random andsystematic error

Sub-topic: Predicting
Key Stage 1•

Use results to make predictions for further investigations with support

Key Stage 2•

Use results to make predictions to set up further investigations

Key Stage 3•

Make predictions using scientific knowledge and understanding•

Analyse data obtained to predict the future phenomenon

91

Chapter 6

Sub-topic: Explaining Results and Developing Solutions
Key Stage 1•

Develop simple ideas and explanations from the investigations carried out
with support•

Develop solutions to problems based on evidence and data collected withsupportKey Stage 2•

Develop ideas and explanations based on evidence and data collected frominvestigations•

Develop solutions to problems based on evidence collected frominvestigations•

Develop simple argument based on data and evidence collected•

Develop and design simple solutions to problems based on evidence anddata collected from investigations

Key Stage 3•

Develop explanations based on scientific knowledge and understanding•

Develop idea, explanations, theories and models based on data and evidencecollected•

Develop an argument based on data and evidence collected•

Develop and design complex solutions to problems based on evidence anddata collected from investigations

Topic: Managing Laboratory Apparatus and Specimens
Sub-topic: Use and Handle Apparatus and Substances Correctly
Key Stage 1•

Handle apparatus correctly•

Handle a range of apparatus including thermometers, magnifying glass,ruler, etc. and simple substances

Key Stage 2•

Use a range of scientific apparatus/equipment with increasing accuracy
and precision•

Use a range of apparatus/equipment appropriately

92

Chapter 6

Key Stage 3•

Use appropriately and safely all laboratory apparatus/equipment

Sub-topic: Handle Specimens Correctly, Carefully and Safely
Key Stage 1•

Handle simple specimens correctly, carefully and safely with teacher’s
supervision

Key Stage 2•

Handle simple specimens correctly, carefully and safely

Key Stage 3•

Handle specimens correctly, carefully and safely

Sub-topic: Clean Apparatus Using the Correct Method
Key Stage 1•

Clean simple apparatus carefully using the correct method with teacher
supervision

Key Stage 2•

Clean simple apparatus carefully using the correct method

Key Stage 3•

Clean apparatus carefully using the correct method

Sub-topic: Store Apparatus and Substances Correctly and Safely
Key Stage 1•

Store simple apparatus and substances correctly and safely with teacher’s
supervision

Key Stage 2•Store simple apparatus and substances correctly and safely

Key Stage 3•

Store apparatus and substances correctly and safely

93

Chapter 6

Sub-topic: Basic Microscopy
Key Stage 3•

Identify the basic parts of a microscope and state the function of each part•Prepare fresh biological specimen for observation under the microscopeusing iodine or methylene blue as stains, (i.e. cheek cell or liver cell andonion cell)•

Draw diagrams of mounted slides observed under the microscope

Topic: Observing Safety in the Laboratory
Sub-topic: Laboratory Safety
Key Stage 1•

Identify potential hazards in the laboratory and suggest necessary
precautions

Key Stage 2•

Identify potential hazards in the laboratory and suggest necessary
precautions•

Make decisions on the right things to do in the laboratory in case of accident
or emergency (e.g. fire or acid spills)

Key Stage 3•

Identify potential hazards in the laboratory and suggest necessary
precautions•

Make decisions on the right things to do in the laboratory in case of accident
or emergency (e.g. fire or acid spills)•

Demonstrate the use of fire extinguishers•

Carry out a risk assessment for the scientific investigation

94

Chapter 6

Topic: Ethics, Scientific Attitudes and Noble Values
Sub-topic: Realising the Need to Practise Scientific Attitudes and Noble
ValuesKey Stage 1•

Internalise scientific attitudes and noble values practiced by scientists suchas curiosity, open-mindedness, perseverance

Key Stage 2•

Internalise scientific attitudes and noble values practiced by scientists
such as curiosity, open-mindedness, perseverance, creativity, objectivity,
integrity and responsibility•

Practise scientific attitudes and noble values when planning and carryingout a scientific investigation

Key Stage 3•

Be aware that scientific methods develop with the development of newtechnologies and equipment•

Be aware that theories develop and change as earlier explanations are
modified as a result of new data or further research collected from that
research•

Be aware of the importance of publishing results and peer review•

Pay attention to objectivity and concern for precision, accuracy, reliability,
repeatability and reproducibility•

Practise scientific attitudes and noble values when carrying out a scientificinvestigation

Topic: Scientific Investigations
Sub-topic: Planning and Conducting Investigations
Key Stage 1•

Plan and carry out simple investigations involving the application of fairtest concept with support

Key Stage 2•

Plan and carry out investigations involving the application of fair test
concept95

Chapter 6

Key Stage 3•

Plan and carry out the most appropriate types of scientific investigations tofind answer to scientific question or test a prediction, including identifying
independent, dependent and control variables, where appropriate•

Use appropriate techniques, apparatus and materials during fieldwork andlaboratory work, paying attention to health and safety

Topic: The World of STEM
Sub-topic: How STEM Works
Key Stage 1•

List what they see around them that is related to STEM•

Explain the importance of STEM in everyday life

Key Stage 2•

Aware that men and women from different social, cultural and ethnic
background work as scientists and engineers•

Name some careers in science such as science teachers, doctors, engineers,
environmental scientists, biologists, etc.

•

Realise the possibilities and limitations of scientific knowledge•

Aware of the applications of science in everyday life

Key Stage 3•

Identify scientists and engineers rely on human qualities such as persistence,
precision, reasoning, logic, imagination and creativity•

Aware that scientists and engineers are guided by habits of mind such as
intellectual honesty, tolerance of ambiguity, skepticism, and openness to
new ideas•

Aware of advances in technology and engineering influence the progressof science, and science influences advances in technology•

Aware of the applications and implications of STEM in everyday life•

Aware of the nature/processes of science and engineering design process•

Aware of arguments develop from evidence and interpretation of evidence96Chapter 7

Chapter 7

Life and the Living World
Strand Description
This strand aims to develop understanding of scientific concepts and principles
related to the content of life and the living world. It revolves around five themes
dealing on structure and function, diversity of living things, continuity of life,
interaction of living things and the environment and applied biology. It includes
topics on living things and non-living things; personal health and healthy
lifestyle; human body and organ systems; animals; plants; ecosystem and theenvironment; biodiversity; microorganisms; cells and organisation; inheritance,
chromosomes, DNA and genes, and biotechnology.
This strand covers the knowledge, skills and values about the living world,
emphasizing life processes and the interaction between life and its surroundings.
Humans, animals and plants are closely interrelated, so it is important to sustaina stable and dynamic interaction between them. The well-being of mankind isof utmost importance and everyone should acquire substantial knowledge andunderstanding about the human body and how to manage their health wisely.
In carrying out scientific activities, students are expected to engage
collaboratively with other peers to develop interest and inculcate positive values
about scientific learning. The use of challenging activities should encourage thedevelopment of higher order thinking and deep understanding of the science
introduced. Students should be encouraged to solve real-world problems.
Students should develop own ideas from hands-on experience including theuse of scientific models. This can be achieved through the use of appropriate
ICT and other representations. The use of scientific activities should encourage
students to take responsibility for their learning and develop confidence andinformed decision.
The students are expected to explore the things around them using scientificthinking and process skills. These skills will enhance the development of criticaland creative thinking. This will lead to an accurate and appropriate reasoning
and decision making in life. Students can apply critical reflection and inculcatesense of caring for living things and the environment by providing a platform
for the students to develop open mindedness, curiosity, responsibility and social
awareness with regard personal well-being, community and local environment.

97

Chapter 7

Topic: Living Things and Non-Living Things
Sub-topic: Characteristics of Living Things and Non-Living Things
Key Stage 1•

Identify the examples of living and non-living things•

State the differences between living and non-living things•

Identify the basic needs of living things – air, water, food•State life processes of living things (breathe, eat, grow, move, reproduce,and react to light, touch, and temperature)

Key Stage 2•

Understand the life processes of living things

Key Stage 3•

Apply the understanding of the life processes of living things

Topic: Personal Health and Healthy LifestyleSub-topic: Hygiene and Safety at HomeKey Stage 1•

Describe how to clean the different parts of the body•

Explain why we need to keep the body clean•

State how to use the toilet correctly•

Explain the importance of using the toilet correctly•

Explain how each part of the body can be cleaned and cared for•

Be aware of responsibilities for ones’ own health•Name common accidents at home•

Identify how the risk of accidents can be reduced at home

Key Stage 2•

Name some contagious diseases in everyday life•

Explain various ways how the named diseases are spread•

Suggest ways on how to prevent the spread of contagious diseases

Key Stage 3•

Explain how contagious diseases are treated and the effects of the treatment•

Practise methods and measures in the prevention of contagious diseases
98Chapter 7

Sub-topic: Food and Its Importance
Key Stage 1•

Identify healthy and unhealthy food and give examples•

Give reasons why some foods are healthy and some are unhealthy for the
body•State why is it important to eat a variety of foods•

Demonstrate good food eating habits•

Explain how to handle, keep and eat food safely•

Explain the causes of diarrhea and ways to prevent it

Key Stage 2•

Differentiate the types/classes of food•

Explain the dietary importance of protein, carbohydrates, fats, vitamins,
minerals, salts, water and fibre to the body•

Explain the importance of eating a balanced diet•

Plan or prepare a healthy dish or menu•

Plan how to manage the amount of food required to avoid food wastage

Key Stage 3•

Evaluate the calorific value of food•

Explain the factors that affect the total calories required by an individual•

Explain the effects of unbalanced diet with reference to malnutrition,
obesity, diabetes, underweight and coronary related conditions•

Evaluate and practise the habits of healthy eating

Sub-topic: Drugs
Key Stage 2•

Differentiate between medicinal drugs and harmful drugs•

Explain that antibiotics should be taken as prescribed by doctors•

Explain the harmful effects of alcohol, cigarettes and illicit drugs on themind and body•

Explain the harmful effects of passive smoking and addiction99

Chapter 7

Key Stage 3•

Explain the consequences of drug trafficking•

Present argument on the reasons why alcohol is harmful to health•

Explain how alcohol and illicit drugs can lead to addiction

Topic: Human Organ Systems
Sub-topic: Humans Have Basic Needs to LiveKey Stage 1•

State the basic needs of human beings in order to live

Sub-topic: Parts and Function of the Human Body
Key Stage 1•

Name the main external parts of the human body•

Draw and label the main external parts of the human body•State the function of the external parts of the human body•

Describe the external human body parts through observation or use of ICT•

Appreciate the external human body parts•

Respect and accept one’s and other’s external physical condition

Key Stage 2•

Name and state the function of the systems of the human body•

Describe the internal human organs and their functions through observation
or ICT•

Respect and accept one’s and other’s physical condition

Key Stage 3•

Explain that all body systems work together to enable functioning of the
body as a whole

Sub-topic: Human Sense Organs
Key Stage 1•

Recognise information provided by the five sense organs•

State and label the parts of ears, eyes, tongue, nose and skin•Give examples of how the five sense organs are used in everyday life
activities
100Chapter 7

Key Stage 2•

Explain the functions of sensory organs

Key Stage 3•

Describe the structure of sensory organs in humans•

Explain the function of each part of the sensory organ•

Explain the limitation of sight and how to correct it

Sub-topic: Human Nervous System
Key Stage 2•

Describe how humans respond to stimulus, through activities•

Give reasons why humans respond to stimuli•

Make inferences on the importance of human beings responding to various
stimuli

Key Stage 3•

Identify the main parts of the human nervous system•

Describe the gross function of the nervous system•

Explain how the parts of the nervous system work

Sub-topic: Human Respiratory System
Key Stage 2•

Illustrate the path of air during inhalation and exhalation•

Describe the movement of the chest cavity during inhalation and exhalation•

Explain how the human breathing system works•

Compare the differences between inhaled and exhaled air•

State that oxygen inhaled is needed to produce energy from food•State that breathing rates depend on the types of human activities

Key Stage 3•

Identify the organs in the respiratory system of human beings•

Describe the main function of the respiratory system•

Describe the human breathing mechanism•

Explain the transport of oxygen in the human body•

Explain gaseous exchange in the human body101Chapter 7

Sub-topic: Human Digestion System
Key Stage 1•

Identify the organs in the human digestive system

Key Stage 2•

Describe briefly the importance of food digestion•

Identify the products of human digestion•

Draw and label main parts of the digestive system•

Describe the functions of organs in the human digestive system•

Describe some diseases that affect the digestive system and ways to prevent
them•

Identify the different types of teeth and their functions•

Draw and label the parts of the teeth•

Describe the role of teeth in mastication•

Practise good health habits to protect the teeth

Key Stage 3•

Explain what is meant by digestion•

Describe the digestive system in humans and explain how it works•

Identify the main parts of the digestive system and the processes that take
place

•

Describe the main function(s) of mouth, stomach, small intestine and large
intestine•

Describe the role of digestive enzymes present in the mouth, stomach andsmall intestine (limit to the three classes of enzymes i.e. carbohydrase,
protease and lipase)•

Investigate digestive enzymes•

Explain the process of digestion•

Explain the process of absorption of digested food•Describe the process of defecation and the reabsorption of water•

Explain causes, treatment and effects of treatment on ailments affecting
the digestive system

102

Chapter 7

Sub-topic: Human Excretion System
Key Stage 2•

State the meaning of excretion•

Identify the excretory organs and the products of human excretion•

Explain the processes of excretion

Key Stage 3•

Describe the function of each part of the human excretory system•

State the waste products excreted through the excretory organs•

Explain the importance of the human excretory system•

Explain the health problems related to a diseased kidney•

Explain causes, treatment and effects of treatment on kidney disease

Sub-topic: Human Circulatory System
Key Stage 2•

Identify the main parts of the circulatory system•

State the gross function of the circulatory system•

Identify and explain the function of the main parts of the circulatory system•

Explain the role of the circulatory system

Key Stage 3•

Describe the structure and function of the circulatory system•

Identify the main parts of the heart and their functions•

Identify the components of the blood (i.e. white blood cells, red blood cells,
platelets)•

Describe the functions of blood vessels (i.e. arteries, veins and capillaries)•

Describe the relationship of the heartbeat, pulse and blood pressure•

Compare coronary pulmonary circulation and systemic circulation•

Identify the four different blood groups•

Explain the importance of checking for blood compatibility to avoid
agglutination of blood•

Explain how heart rate changes and is controlled•

Explain the integration of the digestive system, respiratory system andcirculatory system in carrying out life processes
103Chapter 7

Sub-topic: Human Movement System
Key Stage 2•

State that movement is carried out by the bones and muscles•

Identify the main parts of the human skeletal system•

Describe the purpose of the human skeleton and muscles•

Draw and label the main parts of the human skeleton and the major muscles

Key Stage 3•

Explain breaks, strains and dislocations and suggest ways of preventing
and treating them•Construct a model and explain how the bones and muscles bend or
straighten the arm

Sub-topic: Human Growth
Key Stage 1•

Keep a personal chart to show growth•

Construct simple timeline to show main events in own life

Key Stage 2•

Explain the factors essential for growth•

Explain human growth from birth to adulthood

Key Stage 3•

Interview an elderly persons about their growth and development, and themain physical changes they have experienced

Sub-topic: Human Reproduction System, Puberty, Pregnancy, Pre-Natal
Care and Birth Control
Key Stage 2•

Describe the main function of the major reproductive organs in male andfemale•Draw and label main parts of the reproductive organs of a male and female•

List common diseases that affect the human reproductive system

104

Chapter 7

Key Stage 3•

Describe the structures and functions of the various parts of the male andfemale reproductive system•

Describe the physical, physiological and emotional changes that occur
during puberty and early adolescence•State what is meant by menstruation•

Describe menstrual cycle briefly (without details of hormones)•

Explain the hygiene aspects that should be taken care of during menstruation•

Explain what is meant by fertilization•

Describe briefly pregnancy and development of zygote•

Show an awareness of some forms of facilitated reproduction in humans(i.e. in-vitro fertilization, and artificial insemination)•

Describe the methods of birth control•

Differentiate temporary and permanent method of birth control•

Discuss the effects of maternal lifestyle on the fetus through the placenta•

Describe the physical and emotional development of pregnant woman•

State the purpose of pre-natal care•

Explain the process of conception and reproduction in human•

Identify and explain some common forms of contraception•

Explain how sexually transmitted diseases (STDs) are transmitted, treatedand prevented

Sub-topic: Human Immune System
Key Stage 3•

Explain the role of antibodies in human immune system•

Explain the effects of HIV and effect of weakened immune system•

Explain vaccination and other ways to strengthen immunity

105Chapter 7

Sub-topic: Human Inheritance, Cell Division and Mutation
Key Stage 2•

State that children inherit their parents’ characteristics•

Explain through examples physical characteristics of children that can be
inherited from their parents

Key Stage 3•

State the types of cell division•

Explain the stages of mitosis and meiosis•

Explain the importance of mitosis in the growth, development and repairof somatic cells•

Explain the importance of variations in plant and animal breeding•

Relate DNA to chromosomes and genes•

Explain the principles and mechanisms of inheritance•

Explain the sex determination of offspring from gametes•

Explain the formation of twins in human beings•

State what mutation is•

Explain how mutation can occur in humans and its importance•Describe the implications of mutation to real life cases•

Discuss variation among living things

Sub-topic: Human Coordination System
Key Stage 3•

State the systems that are involved in maintaining body coordination•

Describe the importance of body coordination in humans•

Explain how body coordination works

Sub-topic: Homeostasis in Humans and Animals
Key Stage 3•

Observe and explain behaviour of humans and animals in response tointernal and external stimuli•

Investigate the effects of homeostasis

106Chapter 7•

Explain maintenance of cellular homeostasis•

Explain the importance of homeostasis in body temperature of humans
and other animals

Topic: Animals
Sub-topic: Body Parts of Animals
Key Stage 1•

Identify the main parts of the body of animals•

Compare the body parts of different animals•

Generalise that some animals have the same characteristics while others
have different characteristics as to body parts•

Classify similarities and differences within groups of animals as to bodyparts

Key Stage 2•

Explain that the characteristics of body parts of animals are used as bases
in classification•

Explain that the characteristics of body parts of animals are suited to where
they live

Sub-topic: Basic Needs of Animals
Key Stage 1•

State the basic needs of animals•

Describe the food sources for animals•

Identify shelter for animals

Key Stage 2•

Identify various ways animals take care of their eggs•

Identify various ways animals take care of their young•

Understand the importance of survival of animals

107Chapter 7

Sub-topic: Importance of Animals
Key Stage 1•

State the importance/benefits of animals to humans, plants and otheranimals•

Give examples of animals that are raised for production and for labour

Sub-topic: Growth Processes or Life Cycle of Animals
Key Stage 2•

Identify the ways animals reproduce (i.e. giving birth and laying eggs)•

Identify babies of animals that resemble their parent and those which are
different•

Record changes/development in growth of animals such as butterfly or
frog through observation•

List two external factors necessary for the completion of the life cycle ofthe named animal•

Make simple comparisons of life cycles of insects, fish, amphibians, reptiles,
birds and mammals

Sub-topic: Breathing Structure of Animals
Key Stage 2•

Identify the breathing organs of animals through observation•

Understand that some animals have more than one breathing structure

Sub-topic: Animal Movements
Key Stage 1•

Describe the different kinds of animal movements•

Understand the importance of animal movements

Sub-topic: Animal Characteristics, Classification and Adaptations
Key Stage 1•

Identify the characteristics of the animals (Example: body parts, type offood eaten, skin covering, reproduction, locomotion, habitat, etc.)108Chapter 7

Key Stage 2•

Classify animals based on certain characteristics•

Describe distinguishing characteristics of vertebrates and invertebrates

Key Stage 3•

Describe adaptations or special characteristics in animals which protects
them from danger against enemies•

Describe adaptations or characteristics in animals which protects them fromextreme weather conditions

Sub-topic: Animal Teeth and Feeding
Key Stage 2•

State the eating habits/behaviour of animals: herbivores, carnivores,
omnivores•

Relate the structure of teeth of herbivores, carnivores, omnivores to thefood taken•

Predict what will happen if the animals only consume one type of food/
one eating habit

Sub-topic: Interaction between Animals
Key Stage 2•

State the purpose of interaction between animals•

Explain with examples that animals live together or solitary by observationor through various media•

Describe the advantages and disadvantages of animals living in groups
and solitary•

Explain the type of interaction between animals with examples,e.g. predator-prey relationship•

Describe competitive factors both intra-species and interspecies of animals
by observation or through various media

109

Chapter 7

Sub-topic: Endangered Animals and Conservation
Key Stage 2•

Identify endangered animals by giving examples•

Explain why animals become endangered in their natural habitat•

Identify how animals survive or become extinct due to changes in theenvironment•

Give examples of extinct animals•

Explain why certain animals are facing the threat of extinction•

Explain the impact of polluted water on animals

Key Stage 3•

Explain what conservation and preservation are•

Explain the steps taken to preserve and conserve animals•

Justify the importance of conservation and preservation of animals•

Support activities organised by various parties to preserve and conserve
animals

Topic: Plants
Sub-topic: Parts of the Plants
Key Stage 1•

Identify the major parts of the plant: roots, stem/trunk, leaves and flowers•

Describe the function of the major parts of the plant•

Classify plant parts based on observed characteristics

Key Stage 2•

Describe the functions of different parts of flowering plants•

Explain that plant parts are used as bases in classification•

Explain that plants have certain characteristics to survive in different
habitats•

Explore the importance of flowers in the life cycle of flowering plants,
including pollination, seed formation and seed dispersal•

Investigate the ways in which water is transported within plants

110Chapter 7

Sub-topic: Basic Needs of Plants
Key Stage 1•

Identify the basic needs of plants to grow such as water, air and sunlight•

Understand the needs of plants to survive•

Care for plants by providing them with basic needs to grow healthily

Key Stage 2•

Investigate the importance of water, air and light to plants through simple
research

Key Stage 3•

Investigate the requirements of plants for growth (air, light, water, nutrientsfrom soil, and environment to grow) and how they vary from plant to plant

Sub-topic: The Process of Photosynthesis and Cellular Respiration in Plants
Key Stage 2•

Investigate the requirements for photosynthesis•

Communicate findings on the requirements for photosynthesis

Key Stage 3•

Identify the reactants and the products of photosynthesis•

Investigate the factors that are essential for plant photosynthesis, andexplain that light, chlorophyll, carbon dioxide and water are essential forphotosynthesis•

Explain the importance of plant photosynthesis for living things and theenvironment•

Describe the energy process during the reactions in photosynthesis•

Differentiate the basic features of photosynthesis and respiration•

Identify the structures and functions of mitochondria as the main organelle
involved in cellular respiration

Sub-topic: Transportation in Plants
Key Stage 3•

Observe and explain the structures related to water and food transportation
systems in plants, including xylem an phloem•

Explain the importance of the transport system in plants
111

Chapter 7

Sub-topic: Excretion in Plants
Key Stage 3•

State the organs involved in excretion of plants•

List the waste products produced in plants and explain how they are
excreted

Sub-topic: Plant Growth and Reproduction
Key Stage 1•

Record changes of growth in plants with respect to height, number of leaves
or roots through investigation•

Observe and describe how seeds and bulbs grow into mature plants

Key Stage 2•

Describe the structures and functions of the parts of the flowers in flowering
plants•Explain asexual reproduction processes in plants including usage of various
plant parts for propagation•

Conduct experiment to show that new plants may be grown from plantparts using techniques such as grafting, budding, marcotting, etc.

Key Stage 3•

Explain the role of insects and wind in pollination•

Describe the process of fertilization•

Investigate the formation of fruits and seeds and dispersal, including
quantitative investigation of some dispersal mechanisms•

Investigate how plants protect themselves•

Investigate how pests and diseases affect common crops•

Investigate different methods of pest control

Sub-topic: Plant Characteristics, Classification and Adaptations
Key Stage 1•

Identify the different characteristics of plants

Key Stage 2•

Classify plants based on characteristics or criteria•

Describe the characteristics of flowering and non-flowering plants
112

Chapter 7

Key Stage 3•

Recognize that plants have adaptations for protection and survival

Sub-topic: Plant Responses and Homeostasis
Key Stage 2•

Investigate how plants respond to water, light and touch to grow and stayhealthy•

Describe the stimuli and responses in plants

Key Stage 3•

Investigate mechanisms for maintenance of water homeostasis in plants•

Explain mechanisms for maintenance of water homeostasis in plants

Sub-topic: Endangered Plants and Conservation
Key Stage 2•

Explain why plants become endangered in their natural habitat by giving
examples•Identify how plants survive or become extinct due to changes in theenvironment•

Give examples of extinct plants•

Explain why certain plants are facing the threat of extinction•

Describe the changes in physical factors in tropical rainforest, coral reef,
and mangrove swamps that lead to plants becoming endangered

Key Stage 3•

Explain what conservation and preservation are•

Explain the steps taken to preserve and conserve plants•

Justify the importance of conservation and preservation of plants•

Support activities organised by various parties to preserve and conserve
plants113

Chapter 7

Topic: Ecosystem and Environment
Sub-topic: Food Chain and Food Web
Key Stage 2•

Demonstrate understanding that plants use materials from the environment
to make their own food•Describe the meaning of a food chain•

Construct food chains in various habitats•

Understand the importance of food webs in ensuring survival of the species•

Identify the factors that could affect the food chain and therefore the survivalof organisms•

Trace the energy pathway from the Sun through a food chain•

Explain the roles of various organisms (i.e. producers, consumers, predators,prey) in a food chain and food web•

Explain that interlinked food chains are called a food web•

Construct food webs in various habitats•

State that different habitats support different communities•

Explain the impact of human activities on the environment

Key Stage 3•

Differentiate between the terms organism, population and community•

Predict the impact of population change on the food web•

Analyse and explain the energy transfer relationships of living things infood chains and food webs•

Illustrate energy transfer and ecological relationships of living things infood chains and food webs•

Discuss the effects of unfavourable environmental changes and conditions
on organisms

Sub-topic: Relationships in an Ecosystem
Key Stage 2•

Explore various ecosystems in the local area•

Explain relationships within the ecosystems (i.e. symbiosis, predation,
mutualism, commensalism, etc.)114

Chapter 7

Sub-topic: Water Cycle, Nitrogen Cycle and Carbon Cycle
Key Stage 2•

Explain water cycle and the importance of this cycle to the ecosystem

Key Stage 3•

Explain nitrogen and carbon cycles and the importance of these two cycles
to the ecosystem

Sub-topic: Factors Affecting Population Size
Key Stage 3•

Explain the factors affecting changes of population size in an ecosystem,
including birth rate, death rate, migration, disease, predators, food resourcesand drought

Sub-topic: Evolution
Key Stage 3•

Explain evolution, theory of natural selection, and scientific evidence fornatural selection

Sub-topic: Maintaining Equilibrium in the Environment
Key Stage 3•

Analyse problems concerning the environment and natural resources in
the local area and propose solutions•

Explain guidelines for maintaining the equilibrium of an ecosystem

Topic: Biodiversity
Sub-topic: Classification of Plants and Animals
Key Stage 3•

Recognise that there is a variety of plants and animals which can be grouped
according to their observable external characteristics•

Classify plants according to common observable characteristics namely,
plants without seeds and seed plants•

Classify animals according to common observable characteristics namely,
vertebrates and invertebrates•

Understand the existence of microorganisms such as fungi, bacteria andviruses which are not classified as either plants or animals
115

Chapter 7

Sub-topic: Species Diversity
Key Stage 3•

Examine the diversity of species•

Explain the advantages of high and low biodiversity•

Explore and explain biodiversity in the local area that enable living things
to co-exist in equilibrium•

Explain effects of biodiversity on humans, animals, plants and theenvironment

Sub-topic: Dichotomous Key and Hierarchical Taxonomic System of Species
Key Stage 3•

Construct a simple dichotomous key and use it to identify organisms•

Understand that species are further classified into a hierarchical taxonomic
system•Illustrate the hierarchical taxonomic system of species

Topic: Microorganisms
Sub-topic: Role of Microorganisms in Nature
Key Stage 1•

State that microorganisms exist that may cause illness in humans

Key Stage 2•

Identify the types of microorganisms by observation through various media•

Investigate life processes of microorganisms•

Generalise that microorganisms are living things and invisible to the naked
eyes•

Investigate the factors that affect the growth of microorganisms throughexperiment•

Explain the usefulness and harmful effects of microorganisms

Key Stage 3•

Understand the existence of microorganisms such as fungi, bacteria andviruses which are not classified as either plants or animals•

Explain the benefits and harmful effects caused by various types of
microorganisms
116

Chapter 7•

Explain methods of preventing infection due to microorganisms•

Examine the different treatment of diseases caused by microorganisms•

Examine the effects of microorganisms in the balance of nature

Sub-topic: Infectious Diseases Caused by Microorganisms
Key Stage 2•

Understand that some microorganisms can cause infectious diseases andillnesses•

Explain how common infectious diseases are spread through different
modes of transmission•

Explain ways to prevent the spread of diseases•

Explain the importance of practising healthy habits•

Explain the meaning of the terms immunization and vaccination•

Name some common vaccines and identify the illnesses they cure

Key Stage 3•

Explain how the human immune system responds to infectious diseases

Topic: Cells
Sub-topic: Cell Structure and Function
Key Stage 3•

State that all living things are made of cells, which are the basic unit of life•

Explain the functions of the basic structures of the cell•

Use light microscope to observe, and record cell structures•

Recognise that genes are found within the nucleus of a cell that control thetraits of humans and are passed from parents to children•

Explain that the body functions efficiently by having different types ofcells performing specific functions (bone cells, red blood cells, muscle cells,
sperm cells, egg cells)

117

Chapter 7

Sub-topic: Animal Cells and Plant Cells
Key Stage 3•

Label structures of typical plant cells and animal cells•

Describe similarities and differences between plant and animal cells•

Explain the functions of main structures of plant and animal cells

Sub-topic: Characteristics of Unicellular and Multicellular Organisms
Key Stage 3•

Observe and describe the shapes and characteristics of unicellular andmulticellular organisms•

Describe the structural adaptations of some unicellular organisms

Sub-topic: Cell Organisation
Key Stage 3•

Explain the hierarchical organisation of multicellular organisms•

Appreciate the wonders of our bodies where many different types of cells
work together effectively

Sub-topic: Diffusion and Osmosis in Cells
Key Stage 3•

Explain the terms osmosis, diffusion and cell membrane•

Investigate and explain the processes by which substances move throughcells by diffusion and osmosis

Topic: Biotechnology
Sub-topic: Application of Biotechnology Involving Microorganisms
Key Stage 3•

Explain the uses of microorganisms in developing useful products•

Cite some examples of genetic manipulation of microorganisms to produce
useful products

118

Chapter 7

Sub-topic: Application of Biotechnology in Human Beings
Key Stage 3•

Cite some applications of DNA technology in the human body and organsystems

Sub-topic: Application of Biotechnology in Animal and Plant Reproduction
Key Stage 3•

Explain the principles and effects of biotechnology applications in animal
breeding, livestock improvement and increased productivity, and apply
the knowledge•

Explain the principles and effects of biotechnology applications inpropagation, variety improvement and increased productivity of crops,
and apply the knowledge•

Cite some examples of DNA technology in animals and plants to improve
productivity and produce useful products

119Chapter 8

Chapter 8Material World
Strand Description
This strand aims to develop understanding of scientific concepts and principles
related to material world. The content of this strand reflects on fundamental
knowledge of matter as a Big Idea including states of matter, composition ofmatter, classification of matter, water as matter, solutions and suspensions,mixtures, acids and alkalis, chemical reactions, aqueous solutions and ions.
Matter is anything that has mass and occupies space. Matter comprises atom,
molecules and ions. The basic component of matter is further classified intoelements, compounds and mixtures. Different types of materials that we use in
our daily lives are made from matter of different composition. These materials
have different properties. It is important to relate knowledge of the propertiesof materials to their everyday use.
In carrying out scientific activities, students are expected to engage
collaboratively with other peers to develop interest and inculcate positive values
about scientific learning. The use of challenging activities should encourage thedevelopment of higher order thinking and deep understanding of the science
introduced. Students should be encouraged to solve real-world problems.
Students should develop own ideas from hands-on experience including theuse of scientific models. This can be achieved through the use of appropriate
ICT and other representations. The use of scientific activities should encourage
students to take responsibility for their learning and develop confidence andinformed decision.

Topic: Matter
Sub-topic: States and Properties of Matter
Key Stage 1•

Observe and identify apparent characteristics or properties of materials
used in daily life•

Identify materials and compare their properties such as in toys and othercommon objects•

Classify types and properties of materials that are components of toys andcommon objects

120Chapter 8

Key Stage 2•

State that an object which has mass and occupies space is matter•

Classify objects/materials collected from daily life into solid, liquid andgas based on their physical properties•

Conduct investigations using different types of materials•

Explain the utilisation of each kind of material•

Create a product using natural materials based on knowledge of theproperties of materials

Key Stage 3•

Compare and relate the properties of the three states of matter(solid, liquid and gas) in terms of arrangement, movement and energy
content of the particles

Sub-topic: Particle Theory of Matter
Key Stage 3•

State that matter consists of three types of particles: atoms, molecules andions•

Describe that matter is made up of tiny and discrete particles which are in
constant and random motion•

Explain diffusion in solids, liquids and gases in terms of movement ofparticles

Sub-topic: Solids Float or Sink in Liquids
Key Stage 1•

Observe different kinds of solids that float and sink in liquids•

Identify objects that float and sink through investigation and record theresults

Key Stage 2•

Explain the properties of materials that have the ability to float or sink•

Demonstrate methods of grouping different materials based on their ability
to absorb water; their ability to float or sink; and whether they are decaying
or non-decaying•

Modify objects that had sunk to float and objects that had floated to sink•

Describe density
121Chapter 8

Sub-topic: Changes in State of Matter
Key Stage 2•

Demonstrate that matter can be changed from one state to another

Key Stage 3•

Carry out investigations to observe the changes in the state of matter•

Observe similarities and differences in physical change including density
differences between solids, liquids and gases through experimentation•

Explain that temperature remains constant during freezing, melting, andboiling•

Explain the interconversion of the state of matter in terms of melting,freezing boiling, evaporation, condensation and sublimation•

Describe the Law of Conservation of Mass•

Carry out investigations on physical and chemical changes of matter•

Explain the difference between physical changes and chemical changes•

Give examples of useful chemical reactions and use word equations torepresent the reactions

Sub-topic: Effects of Forces, Heating and Cooling on Materials
Key Stage 2•

Conduct experiments and explain the effects of changes of materials whensubjected to forces or heating and cooling•

Conduct experiments to demonstrate the effects of water and force on
different materials•

Identify reversible changes in matter•

Conduct an activity to observe the irreversible changes in matter (burningand rusting)

Key Stage 3•

Explain the interconversion of the state of matter in terms of bonding andforces122

Chapter 8

Sub-topic: Harmful and Beneficial Effects of Changes in Materials
Key Stage 3•

Discuss potentially beneficial and harmful consequences of changes ofmaterials•

Explain the changes of substances that affect living things and theenvironment•

Describe the Big Ideas based on the knowledge of materials

Topic: Composition of Matter
Sub-topic: Elements, Compounds and Mixtures
Key Stage 3•

Describe the properties of elements, compounds and mixtures

Topic: Classification of Matter
Sub-topic: Overview of the Periodic Table of Elements
Key Stage 3•

Explain the arrangement of elements in the Periodics Table

Sub-topic: Metals, Non-metals and Metalloids
Key Stage 3•

Classify elements as metals, non-metals and metalloids based on their
physical properties

Sub-topic: Glass, Ceramics, Plastics and Fibres
Key Stage 3•

Classify a number of common everyday materials based on their properties•

Use data on the properties of different materials to make evaluative
judgments about their uses•

Appreciate the existence and uses of various substances with different
properties

123Chapter 8

Topic: Water as Matter
Sub-topic: Water Cycle
Key Stage 2•

Investigate and explain the processes in the water cycle

Key Stage 3•

Investigate the processes of evaporation and condensation•

Relate the changes in the state of water with the formation of clouds and rain•

Give examples of natural phenomena related to the water cycle

Sub-topic: Impact of Water Pollution
Key Stage 3•

Describe the impact of water pollution on the Earth’s water resources

Sub-topic: Importance of Water Cycle in Life Processes
Key Stage 3•

Elaborate on the importance of maintaining the cleanliness of water
resources•

Describe the uses of water in homes and industries

Sub-topic: Conservation of Water and Water Purification
Key Stage 3•

Explore and explain ways of water conservation and the preservation ofwater quality•

Show appreciation that water is a precious resource and instil awarenessof water conservation•

Perform methods of water purification and preservation of water quality

124Chapter 8

Sub-topic: Solutions, Mixtures and Suspensions
Key Stage 3•

Distinguish between solute, solvent and solution•

Differentiate the solids which are soluble and insoluble in water•

Understand that some gases can also dissolve in water to form a solution•

Classify mixtures into solutions, colloids and suspensions•

Conduct simple experiments on solutions and suspensions

Sub-topic: Factors Affecting Solubility and Rate of Dissolving Substances
Key Stage 3•

Investigate the factors that affect the quantity of solid that dissolves in water•

Investigate the factors that affect the solubility and rate of dissolving
substances

Sub-topic: Separation Technique
Key Stage 3•

Use separation techniques such as filtration, distillation and paper
chromatography to separate mixtures and show awareness of the basic
principles involved•

Select appropriate techniques for separating constituents of mixtures•

Interpret a chromatogram in terms of the number of different dyes present•

Explain the techniques involved in obtaining pure water from sea waterin desalination plants

125

Chapter 8

Topic: Acids, Bases and Salts
Sub-topic: Properties of Acids, Bases, and Alkalis
Key Stage 3•

Classify everyday substances as acids or bases based on their properties•

Understand that both acids and bases react with indicators to produce
different colours•

Conduct an activity to investigate the properties of acids and alkalis interms of:•

pH value

effect on litmus paper

Investigate the effects of acids, alkalis and neutral solutions on:


Red/Blue Litmus paperpH paper

Universal IndicatorNatural Indicator•

Prepare natural indicators (obtained from plants) as an acid-base indicator•

List some common acids and bases used at home and in industry

Sub-topic: Neutralisation
Key Stage 3•

Recognise that acids and bases neutralise each other•Define neutralisation as a chemical reaction where an acid and an alkali
react to form salt and water only•

Write a word equation for neutralisation•

Write simple equation for neutralisation•

Describe neutralisation in daily life

126

Chapter 8

Topic: Chemical Reactions
Sub-topic: Chemical Change
Key Stage 3•

Understand different types of chemical reactions•

Understand chemical reactions that occur in the presence of light(e.g. photosynthesis)

Sub-topic: Chemical Compounds
Key Stage 3•

Classify different types of compounds (ionic or covalent) from their physicalproperties like melting point, hardness, polarity, electrical and thermal
conductivity•

List names of organic compounds and their uses

Topic: Aqueous Solutions and Ions
Sub-topic: Electrolysis
Key Stage 3•

Understand electrolysis of aqueous solutions•

Identify electrolyte and non-electrolyte•

Conduct an experiment on electrolysis of water•

Explain the importance of electrolysis in daily life and industries

Sub-topic: Chemical Cells
Key Stage 3•

Understand chemical cells•

Conduct a simple experiment to understand the production of electricalenergy from chemical reactions•

Appreciate the innovative efforts in the design of equipment using chemical
reactions as source of energy127

Chapter 9

Chapter 9

Energy and Change
Strand Description
This strand aims to develop understanding of scientific concepts and principles
related to the big idea of energy. It includes energy changes and transfers, energy
calculation of fuel uses and costs, energy changes in systems, observed waves,sound waves, energy and waves, light waves, use of lenses, heat, stability,
forces, motion, pressure in fluids, balanced forces, simple machines, current
electricity, static electricity, magnetism, electromagnetism, particle model ofmatter, energy in matter, space and nuclear physics.
In carrying out scientific activities, students are expected to engage
collaboratively with other peers to develop interest and inculcate positive values
about scientific learning. The use of challenging activities should encourage thedevelopment of higher order thinking and deep understanding of the science
introduced. Students should be encouraged to solve real-world problems.
Students should develop own ideas from hands-on experience including theuse of scientific models. This can be achieved through the use of appropriate
ICT and other representations. The use of scientific activities should encourage
students to take responsibility for their learning and develop confidence andinformed decision making relating to energy sources, energy transformations
and conservation.

Topic: Sound
Sub-topic: Sources, Properties, Harmful Effects of Loud Sound, Hearing
Sound Waves
Key Stage 1•

Identify the sources of sound•Differentiate sources of sound in terms of loudness and tone•

Appreciate the need to avoid harmful effects of loud sounds

Key Stage 2•

Infer through investigation that sounds are produced due to a vibrating
source•Infer through investigation that sound needs a medium through whichto travel•

Discuss the harmful effects of loud sounds
128Chapter 9

Key Stage 3•

Explain that sounds are produced due to interactions between particles ofa medium caused by a vibrating source•

Explain the generation of sound waves, sound intensity, hearing, and soundquality, and apply the knowledge•

Differentiate the properties of sound in terms of pitch, volume, andamplitude•

Relate the pitch of a sound to its frequency, and loudness to its amplitude•

Investigate the effect of different materials on the transmission of sound•Explain how the ear detects sounds in terms of the vibrations of the eardrum
and ear bones, and the subsequent interpretation of sound by the brain•

Recognise how the property of sound waves can be used to explain common
real-life phenomena

Topic: Light
Sub-topic: Sources, Properties /Characteristics, Behaviour of Light onMaterials, How We See Things
Key Stage 1•

List the various sources of light•

Demonstrate the formation of shadows

Key Stage 2•

Demonstrate that light travels in straight line•

Differentiate the characteristics of ‘transparent’,’ translucent’ and ‘opaque’materials•

Investigate the variables that affect shadow formation

Key Stage 3•

Describe different properties and characteristics of light•Show an understanding that the ray model represents the path taken by light•

Explain how a person sees things•

Relate how light affects the behaviour of humans and other living things

129Chapter 9

Sub-topic: Reflection
Key Stage 1•

Find out that light reflects on the mirror

Key Stage 2•

Identify examples of reflection of light observable in daily life

Key Stage 3•

Explain how reflection is affected by a smooth and rough surface•

Investigate the characteristics of the image formed by a plane mirror•

Apply the properties of reflection of light for everyday uses (e.g. plane andcurved surfaces)

Sub-topic: Refraction and Lenses
Key Stage 2•

Define the meaning of refraction•

Identify examples of refraction of light observable in daily life

Key Stage 3•

Investigate the effects of refraction of light•

Explain refraction in terms of the speed of light in a medium•

Apply ray diagrams to describe the characteristics and positions of theimage formed by lenses•

Compare images formed by different types of lenses (e.g. convex andconcave lenses)•

State the uses/benefits of convex and concave lenses•

Appreciate the benefits of optical instruments to daily life and for theadvancement of society (e.g. eyeglasses, mirrors, binoculars, telescopes
and microscopes)

130Chapter 9

Sub-topic: Colours of Light
Key Stage 2•

Investigate the component colours of white light•

Describe the dispersion of white light by a prism

Key Stage 3•

Analyse dispersion of light•Experiment and explain absorption of coloured light, colour vision, andapply the knowledge•

Analyse the principle of subtraction of colour of light to explain theappearance of coloured objects•

Explain how we see the colour of objects in white light and coloured lightsuch as red, blue and green•

Appreciate the importance of colour in daily life

Sub-topic: Light Intensity and Colour
Key Stage 3•

Demonstrate an understanding of the characteristics of light intensity or
brightness and colour•

Explain the effects of brightness of light on humans and other living things

Topic: Waves
Sub-topic: Properties of Mechanical Waves
Key Stage 3•

Describe what is meant by wave motion as illustrated by vibrations in ropes
and springs and by waves in a ripple tank•

Explain the relationship between speed, frequency and wavelength ofmechanical waves•

Compare transverse and longitudinal waves and give suitable examplesof each131

Chapter 9

Sub-topic: Electromagnetic Waves
Key Stage 3•

Demonstrate an understanding that all electromagnetic waves are transverse
waves that travel with the same speed in vacuum•

Describe the main components of the electromagnetic (EM) spectrum•

Explain the benefits and the harmful effects of EM radiation on living cells
and tissues

Topic: Electricity
Sub-topic: Sources, Conductors, Insulators, Circuits, and Electrical System
Key Stage 1•

Identify the various sources of electricity•

Differentiate between closed/complete and open/incomplete circuits•

Differentiate between electrical conductors and insulators

Key Stage 2•

Analyse the direction of electric current•

Differentiate between series and parallel circuits•

Recognise the components of an electrical system which consists of anenergy source and other circuit components•

Investigate how different brightness of light bulbs and volume of sounds
are produced by using different number and arrangement of batteries

Key Stage 3•

Associate the symbols with the respective components of an electrical circuit•

Draw and interpret circuit diagrams and set up circuits containing electricalsources, switches, lamps, resistors (fixed and variable), ammeters andvoltmeters•

Set up simple electric circuits in series and parallel•

Describe the function of diode, transistor and capacitor•

Set up a working electric circuit consisting of diode, transistor or capacitor

132

Chapter 9

Sub-topic: Current, Voltage and Resistance
Key Stage 3•

State that electric current is the flow of electrons•

State that ampere (A) and volt (V) are the units of current and voltage
respectively•

Investigate the relationships between current, voltage and resistance inseries circuits•

Investigate the relationship between current, voltage and resistance inparallel circuits•

Recognise that the resistance of a circuit can be varied by arranging resistors
in series or parallel

Sub-topic: Electrical Hazards, Safety Precautions and Devices at HomeKey Stage 1•

Name different types of electrical appliances•

Recognise the need for safety precautions when handling electricalappliances

Key Stage 2•

Recognise the need to conserve electricity (e.g. by using more energyefficient appliances)•

Practise safe and economical connection of household electrical circuits

Key Stage 3•

Explain the importance of a fuse, circuit breaker and grounding in the safeuse of electrical appliances

133Chapter 9

Sub-topic: Power and Electrical Energy
Key Stage 2•

Identify through experimentation the conversion of electrical energy toother forms of energy•

Analyse how the amount of electrical energy affects heat, brightness of lightor volume of sound produced•

Identify through experimentation the different electrical appliances andthe energy output in them•

Identify ways by which energy is used wisely

Key Stage 3•

Explain the meaning of power and its unit•

Explain electrical energy using the concept of power (e.g. by comparing
power ratings of different electrical appliances)•

Analyse the cost of electrical usage•

Calculate electrical energy consumption of electrical appliances•

Describe how electricity is generated and distributed from the generating
plant to household users•

Cite the importance of distribution grids in the transmission of electricity•

Justify the need to conserve electrical energy•

Practise the conservation of electrical energy

Sub-topic: Static Electricity
Key Stage 1•

Produce electrical forces by rubbing two objects together

Key Stage 2•

Differentiate static from current electricity

Key Stage 3•

Explain how static electricity is formed using the concept of charges•

Apply Coulomb’s Law in describing the amount of electrical forces between
charges134

Chapter 9

Topic: Magnetism
Sub-topic: Properties of Magnets/Magnetic Field and Electromagnets
Key Stage 1•

Differentiate between magnetic and non-magnetic materials•

Demonstrate the properties of magnetic attraction and repulsion•

Compare the strength of different types of magnets•

Recognise simple applications of magnets in daily life

Key Stage 2•

Investigate the properties of a magnet•

Investigate the relationship between strength of the magnetic force and the
distance from a magnet or magnets of different sizes•

Observe and draw magnetic field patterns using iron filings around amagnet•Create a magnet using the stroke or electrical method•

Create simple toys using the properties of magnets to serve a particularpurposeKey Stage 3•

Infer through experimentation that a current carrying wire produces amagnetic field around it•

Analyse the magnetic field around an electromagnet•

Investigate the factors affecting the strength of an electromagnet•

Construct a simple DC motor•

Investigate and discuss the factors affecting the strength of the turning
effect of a motor•

Describe the design of a simple generator•

Recognise the applications of electromagnets in daily life

135

Chapter 9

Topic: Force and Motion
Sub-topic: Forces and Their Effects
Key Stage 1•

Demonstrate the effect of different forces on an object and its motion•

Differentiate the different types and strengths of forces (e.g. squashing,bending, twisting and stretching) and their effects on objects

Key Stage 2•

Classify forces as contact and noncontact•

Carry out an experiment and describe the effects of forcesOn the state of rest or motion of a bodyOn the size of a body•

Identify some examples of forces, including gravitational force, frictional
force, magnetic force and predict their effects on an object•

Use the Newton as the SI unit of force•

Cite the effects of varying amounts of force to the speed of an object

Key Stage 3•

Identify the relationship between force, mass and acceleration of an object•

Perform investigations that show the effect of the varying amounts of force
on the acceleration of an object•

Determine the magnitude and direction of the resultant force of several
co-planar forces acting in an object•

Experiment and explain static and kinetic frictions and relationships
between frictional force and characteristics of contact surfaces and reaction
force perpendicular to the surfaces•

Apply knowledge of frictional force in daily life•

Identify action-reaction pairs in a system•

Experiment and explain action and reaction forces, and apply the knowledge•

Demonstrate understanding of Newton’s three laws of motion throughexperiments•

Solve real life problems by applying knowledge and understanding of
Newton’s laws of motion

136

Chapter 9

Sub-topic: Distance/Time, Displacement, Speed/Velocity, and Acceleration
Key Stage 1•

Measure the distance travelled by an object

Key Stage 2•

Explain the motion of an object using speed, distance and time•

State the relationships between distance, speed and time•

Perform activities that describe the motion of an object•

Measure the period of pendulum•

Experiment and explain distance, speed, displacement and velocity ofobjects in motion

Key Stage 3•

Differentiate quantities using concepts of distance vs. displacement,
speed vs. velocity and acceleration•

Explain acceleration and effects of a resultant force acting on an object•

Give daily life examples of force, mass, acceleration, work and force•

Solve real-life problems by applying knowledge and understanding of
distance, time, speed, velocity and acceleration

Sub-topic: Inertia/Momentum
Key Stage 3•

Demonstrate understanding of projectile motion, impulse, momentum andconservation of momentum•

Cite examples that obey the law of conservation of momentum•

Determine the factors that affect the value of momentum of a body•

Apply the concepts of momentum•

Explain the concept of inertia

137

Chapter 9

Sub-topic: Simple Machines and Moment of ForceKey Stage 2•

Demonstrate and explain how levers , pulleys, gears, and inclined planes
work•

Analyse levers through investigation•

Explain the condition for a lever in a balanced state in relation to themoment of force•

Calculate the moment of a force using the equation: moment of a force
about a point = force x perpendicular distance from the pivot to the lineof action of the force•

List uses of levers, pulleys, gears, and inclined planes in daily life

Key Stage 3•

Identify the different classes of levers•

Determine through experimentation the mechanical advantage of different
simple machines•

Explain what is meant by moment of a force•

Appreciate the innovative efforts in the design of simple machines tosimplify work•

Define centre of gravity•

Investigate how the centre of gravity affects stability•

Identify the different types of equilibrium based on the location of thecentre of gravity•

Appreciate the importance of stability in real life situations

Topic: Pressure
Sub-topic: Relate Pressure to Force and Area
Key Stage 3•

Explain the relationship of force, pressure and area•

Calculate pressure using the equation: pressure = force/area•

State that the SI unit of pressure is Newton per square meter or Pascal (Pa)•

Describe examples of daily life phenomena related to pressure

138

Chapter 9

Sub-topic: Fluid Pressure
Key Stage 3•

Perform experiments that identify the factors affecting liquid pressure•

Measure atmospheric pressure using appropriate instruments•

Relate the value of atmospheric pressure to altitude•

Describe examples of daily life phenomena associated with atmosphericpressure

Sub-topic: Hydraulic System in Daily Life
Key Stage 3•

Explain Pascal’s principle•

Describe and explain the transmission of pressure in hydraulic systems•

Cite examples of equipment that use hydraulic systems in everyday life•

Apply the principle of hydraulic systems in everyday life

Sub-topic: Buoyant Force of Liquid
Key Stage 3•

Explain the buoyant force of a liquid acting upon objects•

Define the buoyant force and relate it to Archimedes’ Principle•

Carry out experiment and describe the design of ships and submarines interms of buoyant force

Topic: Energy, Work and Power
Sub-topic: Common Forms, Sources, Uses of Energy, and Renewable and
Non-Renewable Energy
Key Stage 1•

Recognise that the Sun is the primary source of light and heat energy•

Investigate the movement of an object which is moved by wind, water flow,
falling object or rubber

Key Stage 2•

Identify the common sources and uses of energy•

Describe different forms of energy (e.g. sound, light, heat, kinetic, potential,
electrical, etc.)139Chapter 9

Key Stage 3•

Identify the various forms of potential energy (e.g. gravitational, elastic,
electrical)•

Differentiate between kinetic energy and potential energy•

Identify renewable and non-renewable sources of energy•

Evaluate the benefits and risks when using various sources of energy(e.g. geothermal, biofuels, fossil fuels, solar, hydro-electric, wind, nuclear)to generate electricity and consider their impact to the environment

Sub-topic: Conversion of Energy, Law of Energy Conservation
Key Stage 2•

Investigate and explain energy conversion from one form to another•

Identify the energy conversions in everyday household appliances

Key Stage 3•

Investigate and explain that energy can be transformed from one form
to another, taking reference to the law of energy conservation, to various
situations (e.g. pendulums, balls on an inclined plane)•

Recognise energy losses in mechanical systems due to friction•

Perform mathematical calculations involving conversion of energy•

Design and perform investigations that demonstrates the law ofconservation of energy

Sub-topic: Work and PowerKey Stage 3•

State joule as the unit of energy•

State that energy is the capacity to do work•

Identify the unit of work as the joule (J)•Show an understanding that work is done when an object moves in thesame direction as the applied force•

Compare between situations involving forces where work is done andwhere work is not done•

Carry out an experiment and calculate work done by a force using:work done = force x distance moved in the direction of the force

140Chapter 9•Show an understanding of power as the rate at which work is done•

Establish the relationship between force, distance, work, energy and power

Topic: Heat
Sub-topic: Heat-Temperature Relationship
Key Stage 1•

Identify sources of heat in daily life•

Demonstrate the ways of producing heat

Key Stage 2•

State heat as a form of energy•

State that temperature of an object is a measurement of the degree of hotness
or coldness of the object•

Differentiate between heat and temperature•

Use a thermometer to measure temperature•

Identify different units of temperature and convert temperature
measurements from one unit to another•

Infer that heating an object can increase its temperature

Key Stage 3•

Identify the effects of heat gain/loss in everyday life (e.g. change of stateof matter, contraction and expansion of objects)

Sub-topic: Conduction, Convection and Radiation
Key Stage 2•

Demonstrate that heat can be transferred from one object to another•

Carry out an experiment to show an understanding that heat flows froma hotter to a colder object or region until both reach the same temperature•

Investigate the difference of heat transfer between solid and fluid

Key Stage 3•

Investigate and explain heat transfer by conduction, convection andradiation•

Identify and explain applications of heat conduction, convection andradiation (e.g. in cooling, heating, insulation and solar radiation) in daily life

141

Chapter 9•

Deduce from experiments that different materials have different rates ofheat flow•

Investigate the factors affecting the rate of heat loss or gain by a bodythrough radiation (e.g. nature of the surface)•

Solve real world problems through the application of knowledge andunderstanding of conduction, convection and radiation

Sub-topic: Thermal Expansion and Contraction
Key Stage 2•

Investigate the effect of heat on the expansion and contraction of matter

Key Stage 3•

Infer from experimentation that generally, solids, liquids and gases expand
when heat is absorbed and contract when heat is given off•

Infer from experimentation that thermal expansion results in a change involume of the substance and therefore the density of the substance•

Deduce from experiments that different materials have different values of
specific heat capacities•

Explain the effects of expansion and contraction of matter in everyday
situations

Topic: Nuclear Physics
Sub-topic: Radiation
Key Stage 3•

Explain the types and properties of radiation from radioactive elements•

Cite applications of radiation in industry, medicine and radioactive dating•

Explain the cause of radioactivity and identify methods for detection ofradiation in the environment, their applications, and effects on living things
and the environment•

Be made aware of the need for proper handling of radioactive substance142

Chapter 9

Sub-topic: Atomic Structure
Key Stage 3•

Understand the structure of an atom•

Apply the idea of proton number and nucleon number in atoms of elements•

Relate that atoms and molecules in matter are in constant motion and thedifferences in relative motion and distance between particles in solids,
liquids and gases•

Apply knowledge about the movement of and distance between atoms andmolecules to explain the physical properties of solids, liquids, and gases(volume, shape, density and compressibility)

Sub-topic: Nuclear Reaction, Nuclear Power and Its Uses
Key Stage 3•

Explain nuclear reaction, fission, fusion and the relationship between massand energy•

Carry out research and discuss outcomes of research about nuclear power
plants, and apply the knowledge•

Describe the process how a nuclear power plant generates electricity•

Express ideas, opinions or viewpoints on the pros and cons of generating
electricity through nuclear power plants•

Search for information on energy generated from nuclear reactions and its
effects on living organisms and the environment143

Chapter 10

Chapter 10

Earth and Space
Strand Description
This strand encompasses the topics of soil, water, atmosphere, weather andclimate, earthquakes and volcanic eruptions, Earth, solar system and universeand space technology. Through scientific activities, it is expected that students
will develop creative and critical thinking skills, creativity, collaboration,
teamwork, communication skills and ICT skills. It is also expected that students
will be engaged in applying, modelling and exemplifying.
In carrying out scientific activities, students are expected to engage
collaboratively with other peers to develop interest and inculcate positive values
about scientific learning. The use of challenging activities should encourage thedevelopment of higher order thinking and deep understanding of the science
introduced. Students should be encouraged to solve real-world problems.
Students should develop own ideas from hands-on experience including theuse of scientific models. This can be achieved through the use of appropriate
ICT and other representations. The use of scientific activities should encourage
students to take responsibility for their learning and develop confidence andinformed decision.

Topic: Soil
Sub-topic: Soil and Growth of Plants
Key Stage 1•

Identify through experimentation the different types of soil, such as clay,
garden soil and sand

Key Stage 2•

Explore and classify soil using physical properties as criteria, and apply
the knowledge•

Investigate and sequence the types of soil based on the ability for water toflow through them•

Explore, experiment and explain the components and physical properties
of soil in the local area•

Determine different types of soil to support different types of plants throughobservation using multiple media

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Chapter 10

Key Stage 3•

Identify common sources of soil pollution and action taken to reduce soil
pollution•

Conduct a local investigation on the different types of soil and the vegetationthat thrive in them

Topic: Water
Sub-topic: Water Resources, State of Water and the Environment
Key Stage 1•

Identify the natural water resources

Key Stage 2•

Explore and explain the physical properties of water from sources in thelocal area•

Explain the importance of water in daily activities•

Identify common sources of water pollution and action taken to reducewater pollution•

Describe the impact of water pollution on Earth’s water resources•

Understand the water supply system

Key Stage 3•

Design a water supply system model

Topic: Solid Earth
Sub-topic: Physical Structure, Components and Layers of Earth
Key Stage 2•

Describe the different layers of the Earth•Identify and describe the different land forms

Key Stage 3•

Illustrate how some human activities affect ecosystems•

Recognise that soil, water, rocks, coal and other fossil fuels are Earthmaterials•

Recognise that Earth materials provide many of our resource•

Identify and describe common Earth materials and explain theircomposition, origin and uses
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Chapter 10

Sub-topic: Plate Tectonic Theory
Key Stage 3•

Discuss the theory of plate tectonics•

Identify the different evidences that can be used to understand the
movement of the lithospheric plates over geological time•

Demonstrate the mechanisms of crustal growth and transfer of heat at
spreading ocean ridges•

Discuss the difference between relative and true plate motion•

Relate plate tectonics theory to seafloor spreading•

Describe and locate fault lines in the graphs of the ‘Pacific Rim of Fire’ using
models or illustrations•

Explain how movement along faults generate earthquakes

Sub-topic: Earth’s Processes, Cycles and Geological Events
Key Stage 2•

Define weathering and erosion and identify the different factors affectingthem•

Describe how weathering and erosion help shape the surface of the earth

Key Stage 3•

Describe the fundamental Earth systems and cycles including how they
integrate sub-disciplines and cross traditional discipline boundaries andexplain how they truly benefit society•

Explain the processes operating at and beneath the Earth’s surface,
how those processes create the Earth’s landscape, and how humans affectand are affected by the processes•

Discuss and demonstrate the geological processes, and interactions between
the various physical and biological components of the Earth system•

Discuss and explain the Earth system relating to mining and managementof Earth’s resources•

Research and discuss and describe the geologic time and major events inthe evolution of Earth•Analyse, interpret and report on laboratory and field findings using
appropriate statistical techniques and computer applications•

Discuss how geological processes cause changes in the geomorphology of
the Earth’s surface
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Chapter 10

Topic: AtmosphereSub-topic: Layers of Earth’s Atmosphere and Important Gases
Key Stage 2•

Identify and describe the different elements of weather (temperature,pressure, humidity, precipitation, wind systems, etc.)

Key Stage 3•

Describe the different layers of the atmosphere•

Describe how different weather systems affect the land and sea and how
land and sea affect weather systems•

Show how waves are generated by wind events, and the principles thatgovern wave energy propagation, and of the transformation/dissipationof waves in the coastal zone•

Illustrate how human activities affect the atmosphere and the build-up of
greenhouse gases (GHGs)•

Discuss and explain how energy from the Sun enters the atmosphere andhow the atmospheric gases react and transform•Interpret and explain how global temperature affects the atmospheric gases
and alter the atmospheric functionalities•

Research and explain the effect of sea temperature focusing on El Nino and
La Nina phenomenon

Sub-topic: Changes in Atmospheric Conditions
Key Stage 3•

Research, discuss and explain how the atmosphere protects and maintains
global temperature to maintain life forms in the ecosystem•

Interpret and explain how solar radiation heats up the Earth’s surface andinfluence the changes in atmospheric structure

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Chapter 10

Topic: Weather and Climate
Sub-topic 1: Weather Disturbances and Safety Measures
Key Stage 1•

Observe, record and describe patterns of daily weather at different timesof the day

Key Stage 2•

Observe, identify and describe different kinds of weather•

Explain the difference between the terms “weather” and “climate”

Key Stage 3•

Demonstrates understanding of the types of weather, characteristics ofweather changes and how these relate to daily activities, health and safety•

Explain the different weather disturbances such as storm and typhoons•

Give reasons for the occurrence of the intertropical convergence zones•

Explain how landforms and bodies of water affect typhoons•

Trace the path of typhoons using topographic maps and tracing data•

Identify and explain the different technological advancement in the analysis
and prediction of weather•

Make suggestions with regard precautions and actions that communities
could take in preparation for weather disturbances such as storms andtyphoons

Sub-topic: Weather Phenomena Affect Humans and Living Things
Key Stage 3•

Observe, analyse, and discuss weather phenomena affecting humans•

Understand the different weather disturbances such as storm and typhoons•

Research, analyse and explain effects of the weather on the communities
and the environment•

Research, analyse and explain the natural factors and human actions
affecting changes of the Earth’s temperature, ozone holes, and acid rain•

Discuss how human activities contribute to or reduce ozone depletion andglobal warming•

Suggest solutions to problems associated with pollution, global warming,
and water resources
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Chapter 10

Sub-topic: Seasons
Key Stage 1•

Through observation give examples of seasonal weather changes•

Identify and explain the type of clothing that is appropriate to wear during
different seasons

Key Stage 2•

Compare pictures of the different seasons•

Discuss experiences and knowledge of the different seasons•

Demonstrate by using simple models to show that movement and tilt ofEarth produce seasons

Key Stage 3•

Use models to explain the effects of the following:

the tilt of the Earth on the length of daytimethe length of daytime to the amount of energy received



the position of the Earth in its orbit to the height of the Sun in the sky

the tilt and movement of the Earth to the height of the Sun in the sky

the height of the Sun in the sky to the amount of energy received

the latitude of an area to the amount of energy the area received

Sub-topic: Effects of Seasons on Livelihood and Human Health
Key Stage 1•

Explain the effects of seasons to human health

Key Stage 2•

Describe the seasons and their effects on livelihood and the health of people
in the community

Key Stage 3•

Discuss the different government programmes that mitigate the effect ofchanging seasonal weather conditions to economy and human health149

Chapter 10

Topic: Faults, Volcanic Eruptions, Earthquakes and Disaster Management
Sub-topic: Faults
Key Stage 3•

Use models and illustrations to explain how movements along faults
generate earthquakes and form mountains

Sub-topic: Volcanic Eruptions and Warning Signs
Key Stage 2•

Describe the different volcanic structures and eruptive styles•

Characterize the different materials extruded during volcanic eruptions•

Describe common warning signs that a volcano is about to erupt•

Identify volcanic hazards•

Describe different volcanic monitoring activities•

Make an emergency plan with the family for earthquakes, tsunami andvolcanic eruptions

Key Stage 3•

Use models and illustrations to explain how volcanoes erupt•

Illustrate different types of volcanism at different plate boundaries

Sub-topic: Earthquakes
Key Stage 3•

Differentiate the epicenter of an earthquake from its focus•

Differentiate types of earthquake waves•

Discuss and explain how the process by which the epicenter of anearthquake is located•

Discuss and explain how tsunami relates to an earthquake•

Differentiate the intensity of an earthquake from its magnitude

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Chapter 10

Sub-topic: Disaster Preparedness during Earthquakes, Tsunamis andVolcanic Eruptions
Key Stage 2•

Understand and explain the disaster safety precautions taken before, during
and after earthquakes, tsunamis and volcanic eruptions•

Make informed decisions about what safety precautions to take before,
during and after earthquakes, tsunamis and volcanic eruptions

Key Stage 3•

Be aware and participate in disaster management activities

Topic: Earth, Solar System and the Universe
Sub-topic: Earth as a Member of the Solar System and the Universe
Key Stage 1•

State that there are the Sun, the Moon and the stars in the sky•

Observe, describe and ask questions about movement of the Sun•

Observe, describe and ask questions about the changes in temperature on
different times of the day•

State that the Sun is a star and explain its importance•

Demonstrate understanding of the benefits as well as harmful effects of
the Sun•State that planets rotate on their own axis and at the same time revolvearound the Sun at their own orbit through observation from various media•

Draw diagrams to show the orbit of the planets around the Sun•

State that the Sun, Earth, planets and satellites are part of the Solar System

Key Stage 2•

Estimate the relative distance of Earth to Sun compared to the relative
distance of Earth to Moon•

Describe that Moon does not emit light but reflects Sun’s light•

Describe and explain that the Earth rotates and revolves in aspects ofdirection and time by carrying out simulations•

Observe and explain that rotation of the Earth causes the rising and settingof the Sun and the Moon and the occurrence of days and nights

151

Chapter 10•

Construct a simple model to show the rotation of the Earth•

Explain the events of day and night through simulation•

Observe and explain that Moon appears to have in different shapes atdifferent periods of the month•Differentiate size and the relative distance between Earth, Moon and Sun•

List the planets of the Solar System and their location•

Construct a model of the Solar system•

State that a constellation is a group of stars that form a certain pattern•

Locate and identify shapes of constellations such as Big Dipper, Southern
Cross, Scorpion, Orion•

Describe lunar and solar eclipse phenomena with the assistance of sketches
based on the position of the Moon, Earth and Sun and the properties of light

Key Stage 3•

Differentiate an asterism from a constellation and identify examples•

Explain the use of constellations to indicate directions and indicate seasons•

Explain how tides are affected by the positions of Earth, Moon and Sun•

Understand the physical characteristics of the planets of the Solar System•

Compare and contrast comets, meteors and asteroids•

Predict the appearance of comets based on recorded data of previous
appearances•

Explain the regular occurrence of meteor showers

Topic: Space Technology
Sub-topic: Advancement and Benefits of Space Technology
Key Stage 2•

Research, discuss and present the understanding of the advancement andbenefits of space technology

Key Stage 3•

Research ( including ICT), discuss and present understanding ofadvancement in space technology for exploration of space, celestial objects,
weather conditions, agriculture, navigation, and communication•

Research ( including ICT), discuss and present understanding of applications
and benefits of launching rockets, satellites, space crafts and space stations
152

Chapter 11

Chapter 11

Science, Engineering and Technology for a
Sustainable Society
Strand Description
In order to develop a sustainable society, we need to be innovative and solve
real-world problems relating to conservation of natural resources, environmental
conservation, water and energy resources, pollution and wastes, health anddiseases, drugs, ethical , moral and social issues in science, technology andengineering, ICT and cybercrimes. Thus this strand engages students to solve
problems key measures of sustainable development and developing solutions
associated with these issues. It also engages students in developing good practicewith regard to sustainable development and global citizenship.
In carrying out scientific activities, students are expected to engage
collaboratively with other peers to develop interest and inculcate positive values
about scientific learning. The use of challenging activities should encourage thedevelopment of higher order thinking and deep understanding of the science
introduced. Students should be encouraged to solve real-world problems.
Students should develop own ideas from hands-on experience including theuse of scientific models. This can be achieved through the use of appropriate
ICT and other representations. The use of scientific activities should encourage
students to take responsibility for their learning and develop confidence andinformed decision.

Topic: Environment and Conservation of Natural Resources
Sub-topic: A Healthy Environment
Key Stage 1•

Share experience of good and healthy environment

Key Stage 2•

Suggest ways to maintain a healthy environment•

Practise the habit of maintaining a healthy environment

Key Stage 3•

Investigate any issues related to real life context about the environment

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Chapter 11

Sub-topic: Impact of Human Activities on the Environment
Key Stage 2•

Gather information using available resources and ICT the impact of humanactivities on the environment•

Discuss causes and effects of human activities on the environment•

Suggest ways to address the negative effects of human activities on theenvironment

Key Stage 3•

Conduct research and suggest ways to address the negative effects of humanactivities on the environment

Sub-topic: Impact of Modernisation on the Environment
Key Stage 2•

Suggest possible solutions to overcome the negative impact of modernisationon the society and on environment

Key Stage 3•

Debate the positive and negative impacts of modernisation on environment•

Design products related to the solution of problems associated with theimpact of modernization on the environment

Sub-topic: Impact of Human Activities on Air Quality
Key Stage 2•

Analyse the composition of polluted air and the effects of various air
pollutants•

Research and report on human activities which affect air quality

Key Stage 3•

Evaluate human activities affecting air quality•

Design a model to decrease the effects of air pollutants154

Chapter 11

Sub-topic: Acid Rain
Key Stage 2•

Explain the causes of acid rain•

Investigate the formation of acid rain

Key Stage 3•

Evaluate the impact of acid rain

Sub-topic: Wise Use and Consumption of Natural Resources
Key Stage 2•

Evaluate the availability of food and natural resources•

Suggest ways to optimize the use of natural resources

Key Stage 3•

Evaluate the different methods of conserving natural resources•

Innovate alternatives to natural resources

Sub-topic: Conservation of Water and Energy
Key Stage 1•

Compare the quality of drinking water from different sources

Key Stage 2•

Inculcate the awareness of water and energy shortage•

Suggest ways of conserving water and energy supply

Key Stage 3•

Conduct research and make informed decisions with regard alternative
sources of water and energy

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Chapter 11

Sub-topic: Renewable and Non-Renewable Energy Sources
Key Stage 2•

Analyse renewable and non-renewable sources of energy

Key Stage 3•

Suggest different potential energy sources•

Argue with scientific evidence the advantages and disadvantages ofdifferent energy sources•

Create a low cost model for alternative energy source

Sub-topic: Green Living
Key Stage 1•

Appreciate green living in daily lives

Key Stage 2•

Practise and appreciate green living in daily lives

Key Stage 3•

Conduct research and make a presentation to illustrate evidence of green
living in real life context•

Design a model to implement practical green living in real life context

Topic: Ecosystem and Environmental Management
Sub-topic: Changes in the Components of Ecosystems
Key Stage 2•

Explain population, community, habitat and ecosystem•

Differentiate the biotic and abiotic components of an ecosystem•

Survey and report on the various ecosystems in the local area

Key Stage 3•

Identify factors and natural hazards affecting the changes of population
size in an ecosystem•

Gather information on how water supply, migration and population
changes affect the availability of resources

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Chapter 11

Sub-topic: Environmental Conservation and Use of Technology
Key Stage 2•

List the ways and justify the importance of conservation and preservationof environment

Key Stage 3•

Design and conduct project-based activities on the importance ofconservation and preservation of the environment•

Design ways to use technology to conserve the environment

Sub-topic: Responsible Attitudes in Proper Management of Natural
Resources
Key Stage 2•

Cultivate responsible attitudes in the management of natural resources

Key Stage 3•

Report the management of natural resources through project-based activities•

Evaluate the management of natural resources

Sub-topic: Water, Carbon and Biogeochemical Cycles in Nature
Key Stage 3•

Illustrate and explain the process of decomposition and nutrient cycling•

Illustrate water, carbon and biogeochemical cycles in nature•

Explain the importance of the natural biogeochemical cycles in daily life

Sub-topic: Survival and Extinction of Endangered Species
Key Stage 3•

Elaborate on the survival and extinction of endangered species due to thechanging environment•

Evaluate the application of technology in protecting and conserving theendangered species

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Chapter 11

Sub-topic: Effects of Noise Pollution and Electro-Magnetic Waves on
Living Things
Key Stage 3•

Identify safe levels as well as the detrimental effects of noise andelectromagnetic waves

Sub-topic: Management of Solid Waste, Industrial Waste and Electronic
Waste
Key Stage 3•

List and evaluate the different ways to manage solid, industrial andelectronic wastes•

Present/Develop arguments on the environmental problems associatedwith the disposal of solid, industrial and electronic wastes•

Create an event to instil awareness on managing solid, industrial andelectronic wastes

Topic: Human Health and Management
Sub-topic: Awareness of Healthy Food and Diet
Key Stage 1•

Practise healthy eating habits

Key Stage 2•

Identify and justify healthy food•

Generate reasons for healthy and unhealthy food in relation to better health

Key Stage 3•

Gather information on the impact of food additives and processed foodon humans•

Produce and promote healthy food and diet158

Chapter 11

Sub-topic: Exercise to Keep Fit
Key Stage 1•

Implement regular exercise

Key Stage 2•

Explain and implement a healthy lifestyle through regular exercise

Key Stage 3•

Design a programme to promote a healthy lifestyle through exercise

Sub-topic: Preventing Heart Disease, High Blood Pressure, Diabetes andObesity
Key Stage 3•

Plan a programme/Construct precautionary steps to prevent heart disease,high blood pressure, diabetes and obesity

Sub-topic: Smoking and Lung Disease
Key Stage 2•

Recognise the harmful effects of smoking on the lungs

Key Stage 3•

Justify the harmful effects of smoking to human health•

Suggest ways of how to reduce smoking•

Create ads, posters on the harmful effects of smoking to human healthSub-topic: Prevention against Influenza, Measles, and Malaria
Key Stage 2•

Explain the causes of influenza, measles and malaria•

Describe the symptoms of influenza, measles and malaria•

Practise healthy habits to prevent the spread of influenza, measles andmalaria

Key Stage 3•

Plan project-based activities to prevent the spread of influenza, measles,
and malaria

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Chapter 11

Sub-topic: Preventing Harmful Effects of STDs and Controversial Practices
to the Reproductive System
Key Stage 3•

Use ICT to gather information and report on sexually transmitted diseases(STDs) and HIV-AIDS•

Critique the harmful consequences of STDs and HIV-AIDS•

Describe how to prevent the spread of STDs and HIV-AIDS•

Develop arguments on the issues relating to controversial practices ofabortion and pre-marital sex

Sub-topic: Impact of Drug/Substance Abuse and Solvents Including Alcoholon Humans and Society
Key Stage 3•

Use ICT to gather information relating to drug/substance abuse andsolvents including alcohol on humans and society•

Explain and justify the impact of drug/substance abuse and solvents
including alcohol on humans and society

Topic: Scientific, Technological and Engineering BreakthroughSub-Topic: Role of Science, Technology and Engineering to Improve theQuality of Life
Key Stage 1•

List current technological gadgets

Key Stage 2•

Examine the role of science, technology and engineering as a tool to improve
the quality of life•

Evaluate the application of science, technology and engineering to help
improve the quality of life•

Appreciate scientific, technological and engineering advancements

Key Stage 3•

Design a product using technology to improve the quality of life

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Chapter 11

Sub-topic: Ethical, Moral and Social Issues in Science, Technology andEngineering
Key Stage 2•

Justify the merits and demerits of science, technology and engineering insociety and the environment

Key Stage 3•

Plan project-based activities related to ethical, moral and social issues inapplying the knowledge of science, technology and engineering

Sub-topic: Use of Information and Communication Technology (ICT)Key Stage 1•

Explore the use of ICT tools (digital or electronic or mobile) tools tocommunicate and access information

Key Stage 2•

Explain the impact of (i.e. advantages and disadvantages) of ICT on society

Key Stage 3•

Implement usage of ICT to foster communication and networking•

Create or design an ICT gadget for a specific purpose that would benefit
society

Sub-topic: Awareness on Cyber Security and Safety Issues
Key Stage 2•

Develop arguments on the various issues concerning cyber security andsafetyKey Stage 3•

Conduct research and debate on cyber security and safety issues

161Chapter 11

Sub-topic: Ethical and Moral Issues on the Use of Technology in Genetic
Research
Key Stage 3•

Describe the application of technology on the growth and development ofplants and animals•

Use ICT to gather information on issues relating to genetic research•

Analyse the impact of genetic research on living organisms•

Develop arguments on the benefits and dangers of genetic research•

Assess and evaluate the usage of Genetically-Modified Organisms (GMO)

162

Chapter 11

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Mullis, I. V. S., & Martin, M. O. (Eds.) (2013). TIMSS 2015 Assessment Frameworks.
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National Curriculum in England. (2013). Science programmes of study: Key stages 1,
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