1. science
2. mathematics

REPUBLIC OF RWANDA
MINISTRY OF EDUCATION
MATHEMATICS SYLLABUS FOR ORDINARY LEVEL S1-S3
Kigali, 2015
RWANDA EDUCATION BOARD
P.O Box 3817 KIGALI
Telephone : (+250) 255121482
E-mail: info@reb.rw
Website: www.reb.rw
MATHEMATICS SYLLABUS FOR
ORDINARY LEVEL S1-S3
Kigali, 2015
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© 2015 Rwanda Education Board
All rights reserved
This syllabus is the property of Rwanda Education Board, Credit must be provided to the author and source of the document
when the content is quoted.
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FOREWORD
The Rwanda Education Board is honored to avail Syllabuses which serve as official documents and guide tocompetencebased teaching and learning in order to ensure consistency and coherence in the delivery of quality education across all
levels of general education in Rwandan schools.
The Rwandan education philosophy is to ensure that young people at every level of education achieve their full potential in
terms of relevant knowledge, skills and appropriate attitudes that prepare them to be well integrated in society and exploit
employment opportunities.
In line with efforts to improve the quality of education, the government of Rwanda emphasizes the importance of aligning the
syllabus, teaching and learning and assessment approaches in order to ensure that the system is producing the kind of
citizens the country needs. Many factors influence what children are taught, how well they learn and the competencies they
acquire, among them the relevance of the syllabus, the quality of teachers’ pedagogical approaches, the assessment strategies
and the instructional materials available. The ambition to develop a knowledge-based society and the growth of regional and
global competition in the jobs market has necessitated the shift to acompetence-based syllabus. With the help of the teachers,
whose role is central to the success of the syllabus, learners will gain appropriate skills and be able to apply what they have
learned in real life situations. Hence they will make a difference not only to their own lives but also to the success of the
nation.
I wish to sincerely extend my appreciation to the people who contributed towards the development of this document,
particularly REB and its staff who organized the whole process from its inception. Special appreciation goes to the
development partners who supported the exercise throughout. Any comment of contribution would be welcome for the
improvement of this syllabus.
Mr. GASANA Janvier,
Director General REB.
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ACKNOWLEDGEMENT
I wish to sincerely extend my special appreciation to the people who played a major role in development of this syllabus. It
would not have been successful without the participation of different education stakeholders and financial support from
different donors that I would like to express my deep gratitude.
My thanks first goes to the Rwanda Education leadership who supervised the curriculum review process and Rwanda
Education Board staff who were involved in the conception and syllabus writing. I wish to extend my appreciation to
teachers from pre-primary to university level whose efforts during conception were much valuable.
I owe gratitude to different education partners such as UNICEF, UNFPA, DFID and Access to Finance Rwanda for their
financial and technical support. We also value the contribution of other education partner organisations such as CNLG, AEGIS
trust, Itorero ry’Igihugu, Gender Monitoring Office, National Unit and Reconciliation Commission, RBS, REMA, Handicap
International, Wellspring Foundation, Right To Play, MEDISAR, EDC/L3, EDC/Akazi Kanoze, Save the Children, Faith Based
Organisations, WDA, MINECOFIN and Local and International consultants. Their respective initiative, co- operation and
support were basically responsible for the successful production of this syllabus by Curriculum and Pedagogical Material
Production Department (CPMD).
Dr. Joyce Musabe,
Head of Curriculum and Pedagogical Material Production Department,
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LIST OF PARTICIPANTS WHO WERE INVOLVED IN THE ELABORATION OF THE SYLLABUS
Rwanda Education Board Staff
1. Dr. MUSABE Joyce, Head of Department ,Curriculum and Pedagogical Material Department (CPMD)
2. Mr. RUTAKAMIZE Joseph, Director of Science and Art Unit,
3. Mr. KAYINAMURA Aloys , Mathematics Curriculum Specialist : Team leader,
4. Madame NYIRANDAGIJIMANA Anathalie: Specialist in charge of Pedagogic Norms.
Teachers and Lecturers
1. HABINEZA NSHUTI Jean Clément, Mathematics teachers at Ecole Secondaire de Nyanza
2. NKUNDINEZA Felix, Mathematics teachers at G.S. KIMIRONKO I
3. NSHIMIRYAYO Anastase, Mathematics teachers at NYAGATARE Secondary School
4. NYIRABAGABE Agnès, Mathematics teachers at Lycée Notre Dame de Citeaux
5. UNENCAN MUNGUMIYO Dieudonné, Mathematics teachers at Lycée de Kigali
Other resource persons
Mr Murekeraho Joseph, National consultant
Quality assurer /editors
Dr Alphonse Uworwabayeho (PhD), University of Rwanda (UR), College of Education.
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Table of Contents
FOREWORD ................................................................................................................................................................................................................ 3
ACKNOWLEDGEMENT .............................................................................................................................................................................................. 4
LIST OF PARTICIPANTS WHO WERE INVOLVED IN THE ELABORATION OF THE SYLLABUS....................................................................................... 5
1.
2.
3.
INTRODUCTION ................................................................................................................................................................................................. 8
1.1.
BACKGROUND TO CURRICULUM REVIEW ................................................................................................................................................. 8
1.2.
RATIONALE OF TEACHING AND LEARNING MATHEMATICS ............................................................................................................... 8
1.2.1.
MATHEMATICS AND SOCIETY.......................................................................................................................................................... 8
1.2.2.
MATHEMATICS AND LEARNERS ...................................................................................................................................................... 9
1.2.3.
COMPETENCES .................................................................................................................................................................................. 9
PEDAGOGICAL APPROACH ............................................................................................................................................................................. 12
2.1.
ROLE OF THE LEARNER .......................................................................................................................................................................... 12
2.2.
ROLE OF THE TEACHER .......................................................................................................................................................................... 13
2.3.
SPECIAL NEEDS EDUCATION AND INCLUSIVE APPROACH ................................................................................................................ 14
ASSESSMENT APPROACH ............................................................................................................................................................................... 14
3.1.
TYPES OF ASSESSMENTS ........................................................................................................................................................................ 15
3.1.1.
FORMATIVE ASSESSMENT: ............................................................................................................................................................ 15
3.1.2.
SUMMATIVE ASSESSMENTS: .......................................................................................................................................................... 15
3.2.
RECORD KEEPING ................................................................................................................................................................................... 16
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4.
5.
3.3.
ITEM WRITING IN SUMMATIVE ASSESSMENT ..................................................................................................................................... 16
3.4.
STRUCTURE AND FORMAT OF THE EXAMINATION ............................................................................................................................ 17
3.5.
REPORTING TO PARENTS....................................................................................................................................................................... 18
RESOURCES ...................................................................................................................................................................................................... 18
4.1.
MATERIALS NEEDED FOR IMPLEMENTATION .................................................................................................................................... 18
4.2.
HUMAN RESOURCE ................................................................................................................................................................................. 18
SYLLABUS UNITS ............................................................................................................................................................................................. 19
5.1.
PRESENTATION OF THE STRUCTURE OF THE SYLLABUS UNITS ...................................................................................................... 19
5.2.
MATHEMATICS PROGRAM FOR SECONDARY ONE .............................................................................................................................. 20
5.2.1.
KEY COMPETENCIES AT THE END OF SECONDARY ONE ............................................................................................................ 21
5.2.2.
MATHEMATICS UNITS FOR SECONDARY ONE ............................................................................................................................ 22
5.3.
MATHEMATICS PROGRAM FOR SECONDARY TWO ............................................................................................................................. 31
5.3.1.
KEY COMPETENCIES AT THE END OF SECONDARY TWO ........................................................................................................... 31
5.3.2.
MATHEMATICS UNITS FOR SECONDARY TWO ........................................................................................................................... 32
5.4.
MATHEMATICS PROGRAM FOR SECONDARY THREE.......................................................................................................................... 43
5.4.1.
KEY COMPETENCIES AT THE END OF SECONDARY THREE....................................................................................................... 43
5.4.2.
MATHEMATICS UNITS FOR SECONDARY THREE ......................................................................................................................... 44
6.
REFERENCES .................................................................................................................................................................................................... 57
7.
APPENDIX: SUBJECTS AND WEEKLY TIME ALLOCATION FOR O’ LEVEL (S1-S3)..................................................................................... 59
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1. INTRODUCTION
1.1. BACKGROUND TO CURRICULUM REVIEW
The motive of reviewing the Mathematics syllabus of ordinary level was to ensure that the syllabus is responsive to the needs
of the learner and to shift from objective and knowledge-based learning tocompetence-based learning. Emphasis in the
review is put more on skills and competencies and the coherence within the existing content by benchmarking with syllabi
elsewhere with best practices.
The new Mathematics syllabus guides the interaction between the teacher and the learners in the learning processes and
highlights the competencies a learner should acquire during and at the end of each learning unit.
Learners will have the opportunity to apply Mathematics in different contexts, and discover its important in daily life.
Teachers help the learners appreciate the relevance and benefits for studying this subject.
The new Mathematics syllabus is prepared for all learners in ordinary level and it has to be taught in six periods per week.
1.2. RATIONALE OF TEACHING AND LEARNING MATHEMATICS
1.2.1. MATHEMATICS AND SOCIETY
Mathematics plays an important role in society through abstraction and logic, counting, calculation, measurement, systematic
study of shapes and motion. It is also used in natural sciences, engineering, medicine, finance and social sciences. The applied
mathematics like statistics and probability play an important role in game theory, in the national census process, in scientific
research,etc. In addition, some cross-cutting issues such as financial awareness are incorporated into some of the
Mathematics units to improve social and economic welfare of Rwandan society.
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Mathematics is key to the Rwandan education ambition of developing a knowledge-based and technology-led economy
since it provide to learners all required knowledge and skills to be used in different learning areas. Therefore, Mathematics
is an important subject as it supports other subjects.This new curriculum will address gaps in the current Rwanda Education
system which lacks of appropriate skills and attitudes provided by the current education system.
1.2.2. MATHEMATICS AND LEARNERS
Learners need enough basic mathematical competencies to be effective members of the Rwandan society, including the
ability to estimate, measure, calculate, interpret statistics, assess probabilities, and read the commonly used mathematical
representations and graphs. For example, reading or listening to the news requires some of these competencies, and
citizenship requires being able to interpret critically the information one receives.
Therefore, Mathematics equips learners with knowledge, skills and attitudes necessary to enable them to succeed in an era of
rapid technological growth and socio-economic development. Mastery of basic Mathematical ideas and operations makes
learners being confident in problem-solving. It enables the learners to be systematic, creative and self confident in using
mathematical language and techniques to reason; think critically; develop imagination, initiative and flexibility of mind.
Mathematics has a high profile at all levels of study where learning needs to include practical problem-solving activities with
opportunities for learners to plan their own investigations and develop their confidence towards Mathematics.
1.2.3. COMPETENCES
Competence is defined as the ability ability to perform a particular task successfully, resulting from having gained an
appropriate combination of knowledge, skills and attitudes
The Mathematics syllabus gives the opportunity to learners to develop different competencies, including the generic
competencies .
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Basic competencies are addressed in the stated broad subject competences and in objectives highlighted year on year basis
and in each of units of learning. The generic competencies, basic competences that must be emphasized and reflected in the
learning process are briefly described below and teachers will ensure that learners are exposed to tasks that help the
learners acquire the skills.
GENERIC COMPETENCIES AND VALUES
Critical and problem solving skills: Learners use different techniques to solve mathematical problems related to real life
situations.They are engaged in mathematical thinking, they construct, symbolize, apply and generalize mathematical ideas.
The acquisition of such skills will help learners to think imaginatively and broadly to evaluate and find solutions to problems
encountered in all situations.
Creativity and innovation :The acquisition of such skills will help learners to take initiatives and use imagination beyond
knowledge provided to generate new ideas and construct new concepts. Learners improve these skills through Mathematics
contest, Mathematics competitions,etc.
Research: This will help learners to find answers to questions basing on existing information and concepts and to explain
phenomena basing on findings from gathered information.
Communication in official languages: Learners communicate effectively their findings through explanations, construction
of arguments and drawing relevant conclusions.
Teachers, irrespective of not being teachers of language, will ensure the proper use of the language of instruction by learners
which will help them to communicate clearly and confidently and convey ideas effectively through speaking and writing and
using the correct language structure and relevant vocabulary.
Cooperation, inter personal management and life skills: Learners are engaged in cooperative learning groups to promote
higher achievement than do competitive and individual work.
This will help them to cooperate with others as a team in whatever task assigned and to practice positive ethical moral values
and respect for the rights, feelings and views of others. Perform practical activities related to environmental conservation
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and protection. Advocating for personal, family and community health, hygiene and nutrition and Responding creatively to
the variety of challenges encountered in life.
Lifelong learning:The acquisition of such skills will help learners to update knowledge and skills with minimum external
support and to cope with evolution of knowledge advances for personal fulfillment in areas that need improvement and
development
BROAD MATHEMATICS COMPETENCIES
During and at the end of learning process, the learner can:
1.
2.
3.
4.
5.
Use correctly specific symbolism of the fundamental concepts in Mathematics;
Develop clear, logical, creative and coherent thinking;
Apply acquired knowledge in Mathematics in solving problems encountered in everyday life;
Use the acquired concepts for easy adaptation in the study of other subjects ;
Deduce correctly a given situation from a picture and/or a well drawn out basic mathematical concepts and use them
correctly in daily life situations;
6. Read and interpret a graph;
7. Use acquired mathematical skills to develop work spirit, team work, self-confidence and time management without
supervision;
8. Use ICT tools to explore Mathematics (examples: calculators, computers, mathematical software,…).
MATHEMATICS AND DEVELOPING COMPETENCES
The national policy documents based on national aspirations identify some ‘basic Competencies’ alongside the ‘Generic Competencies’’
that will develop higher order thinking skills and help student learn subject content and promote application of acquired knowledge and
skills. Through observations, constructions, hand-on, using symbols, applying
and generalizing mathematical ideas, and
presentation of information during the learning process, the learner will not only develop deductive and inductive skills but also acquire
cooperation and communication, critical thinking and problem solving skills. This will be realized when learners make presentations
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leading to inferences and conclusions at the end of learning unit. This will be achieved through learner group work and cooperative
learning which in turn will promote interpersonal relations and teamwork.
The acquired knowledge in learning Mathematics should develop a responsible citizen who adapts to scientific reasoning and attitudes
and develops confidence in reasoning independently. The learner should show concern of individual attitudes, environmental protection
and comply with the scientific method of reasoning. The scientific method should be applied with the necessary rigor, intellectual
honesty to promote critical thinking while systematically pursuing the line of thought.
2. PEDAGOGICAL APPROACH
The change to acompetence-based curriculum is about transforming learning, ensuring that learning is deep, enjoyable and
habit-forming.
2.1. ROLE OF THE LEARNER
In thecompetence-based syllabus, the learner is the principal actor of his / her education. He/she is not an empty bottle to
fill. Taking into account the initial capacities and abilities of the learner, the syllabus lists under each unit, the activities which
are engaging learners to participate in the learning process .
The teaching- learning processes will be tailored towards creating a learner friendly environment basing on the capabilities,
needs, experience and interests. Therefore, the following are some of the roles or the expectations from the learners:
-
Learners construct the knowledge either individually or in groups in an active way. From the learning theory, learners
move in their understanding from concrete through pictorial to abstract. Therefore, the opportunities should be given
to learners to manipulate concrete objects and to use models.
Learners are encouraged to use hand-held calculator. This stimulates mathematics as it is really used, both on job and
in scientific applications. Frequent use of calculators can enhance learners’ understanding and mastering of
arithmetic.
Learners work on one competency at a time in form of concrete units with specific learning objectives broken down
into knowledge, skills and attitude.
Learners will be encouraged to do research and present their findings through group work activities.
A learner is cooperative: learners work in heterogeneous groups to increase tolerance and understanding.
Learners are responsible for their own participation and ensure the effectivness of their work.
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-
Help is sought from within the group and the teacher is asked for help only when the whole group agrees to ask a
question
The learners who learn at a faster pace do not do the task alone and then the others merely sign off on it.
Teacher ensure the effective contribution of each learner, through clear explanation and argumentation to improve
the English literacy and to develop sense of responsibility and to increase the self-confidence, the public speech
ability, etc.
2.2. ROLE OF THE TEACHER
In thecompetence-based syllabus, the teacher is a facilitator, organiser, advisor, a conflict solver, ...
The specific duties of the teacher in acompetence-based approach are the following:
-
-
-
-
He / she is a facilitator, his/her role is to provide opportunities for learners to meet problems that interest and
challenge them and that, with appropriate effort, they can solve. This requires an elaborated preparation to plan the
activities, the place they will be carried, the required assistance.
He/she is an organizer: his / her role is to organize the learners in the classroom or outside and engage them
through participatory and interactive methods through the learning processes as individuals, in pairs or in groups. To
ensure that the learning is personalized, active and participative , co-operative the teacher must identify the needs of
the learners, the nature of the learning to be done, and the means to shape learning experiences accordingly
He/she is an advisor: he/she provides counseling and guidance for learners in need. He/she comforts and encourages
learners by valuing their contributions in the class activities.
He/she is a conflict-solver: most of the activitiescompetence-based are performed in groups. The members of a group
may have problems such as attribution of tasks; they should find useful and constructive the intervention of the
teacher as a unifying element.
He/she is ethical and preaches by examples, by being impartial, by being a role-model, by caring for individual needs,
especially for slow learners and learners with physical impairments, through a special assistance by providing
remedial activities or reinforncement activities. One should notice that this list is not exhaustive.
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2.3. SPECIAL NEEDS EDUCATION AND INCLUSIVE APPROACH
All Rwandans have the right to access education regardless of their different needs. The underpinnings of this provision
would naturally hold that all citizens benefit from the same menu of educational programs. The possibility of this
assumption is the focus of special needs education. The critical issue is that we have persons/ learners who are totally
different in their ways of living and learning as opposed to the majority. The difference can either be emotional, physical,
sensory and intellectual learning challenged traditionally known as mental retardation.
These learners equally have the right to benefit from the free and compulsory basic education in the nearby
ordinary/mainstream schools. Therefore, the schools’ role is to enrol them and also set strategies to provide relevant
education to them. The teacher therefore is requested to consider each learner’s needs during teaching and learning
process. Assessment strategies and conditions should also be standardised to the needs of these learners. Detailed
guidance for each category of learners with special education needs is provided for in the guidance for teachers.
3. ASSESSMENT APPROACH
Assessment is the process of evaluating the teaching and learning processes through collecting and interpreting evidence of
individual learner’s progress in learning and to make a judgment about a learner’s achievements measured against defined
standards. Assessment is an integral part of the teaching learning processes. In the new competence-based curriculum
assessment must also be competence-based, whereby a learner is given a complex situation related to his/her everyday life
and asked to try to overcome the situation by applying what he/she learned.
Assessment will be organized at the following levels: School-based assessment, District examinations, National assessment
(LARS) and National examinations.
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3.1. TYPES OF ASSESSMENTS
3.1.1. FORMATIVE ASSESSMENT:
Formative assessment helps to check the efficiency of the process of learning. It is done within the teaching/learning process.
Continuous assessment involves formal and informal methods used by schools to check whether learning is taking place.
When a teacher is planning his/her lesson, he/she should establish criteria for performance and behavior changes at the
beginning of a unit. Then at the end of every unit, the teacher should ensure that all the learners have mastered the stated
key unit competencies basing on the criteria stated, before going to the next unit. The teacher will assess how well each
learner masters both the subject and the generic competencies described in the syllabus and from this, the teacher will gain a
picture of the all-round progress of the learner. The teacher will use one or a combination of the following: (a) observation
(b) pen and paper (c) oral questioning.
3.1.2. SUMMATIVE ASSESSMENTS:
When assessment is used to record a judgment of a competence or performance of the learner, it serves a summative
purpose. Summative assessment gives a picture of a learner’s competence or progress at any specific moment. The main
purpose of summative assessment is to evaluate whether learning objectives have been achieved and to use the results for
the ranking or grading of learners, for deciding on progression, for selection into the next level of education and for
certification. This assessment should have an integrative aspect whereby a student must be able to show mastery of all
competencies.
It can be internal school based assessment or external assessment in the form of national examinations. School based
summative assessment should take place once at the end of each term and once at the end of the year. School summative
assessment average scores for each subject will be weighted and included in the final national examinations grade. School
based assessment average grade will contribute a certain percentage as teachers gain more experience and confidence in
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assessment techniques and in the third year of the implementation of the new curriculum it will initialy contribute 10% of
the final grade, but will be progressively increased. Districts will be supported to continue their initiative to organize a
common test per class for all the schools to evaluate the performance and the achievement level of learners in individual
schools. External summative assessment will be done at the end of P6, S3 and S6.
3.2. RECORD KEEPING
This is gathering facts and evidence from assessment instruments and using them to judge the student’s performance by
assigning an indicator against the set criteria or standard. Whatever assessment procedures used shall generate data in the
form of scores which will be carefully be recorded and stored in a portfolio because they will contribute for remedial actions,
for alternative instructional strategy and feed back to the learner and to the parents to check the learning progress and to
advice accordingly or to the final assessment of the students.
This portfolio is a folder (or binder or even a digital collection) containing the student’s work as well as the student’s
evaluation of the strengths and weaknesses of the work. Portfolios reflect not only work produced (such as papers and
assignments), but also it is a record of the activities undertaken over time as part of student learning. Besides, it will serve as
a verification tool for each learner that he/she attended the whole learning before he/she undergoes the summative
assessment for the subject.
3.3. ITEM WRITING IN SUMMATIVE ASSESSMENT
Before developing a question paper, a plan or specification of what is to be tested or examined must be elaborated to show
the units or topics to be tested on, the number of questions in each level of Bloom’s taxonomy and the marks allocation for
each question. In a competency based curriculum, questions from higher levels of Bloom’s taxonomy should be given more
weight than those from knowledge and comprehension level.
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Before developing a question paper, the item writer must ensure that the test or examination questions are tailored towards
competency based assessment by doing the following:

Identify topic areas to be tested on from the subject syllabus.

Outline subject-matter content to be considered as the basis for the test.

Identify learning outcomes to be measured by the test.

Prepare a table of specifications.

Ensure that the verbs used in the formulation of questions do not require memorization or recall answers only but
testing broad competencies as stated in the syllabus.
3.4. STRUCTURE AND FORMAT OF THE EXAMINATION
There will be one paper in Mathematics at the end of Primary 6. The paper will be composed by two sections, where the first
section will be composed with short answer items or items with short calculations which include the questions testing for
knowledge and understanding, investigation of patterns, quick calculations and applications of Mathematics in real life
situations. The second section will be composed with long answer items or answers with simple demonstrations,
constructions , calculations, simple analysis , interpretation and explanations. The items for the second section will
emphasize on the mastering of Mathematics facts, the understanding of Mathematics concepts and its applications in real life
situations. In this section, the assessment will find out not only what skills and facts have been mastered, but also how well
learners understand the process of solving a mathematical problem and whether they can link the application of what they
have learned to the context or to the real life situation. The Time required for the paper is three hours (3hrs).
The following topic areas have to be assessed: algebra; metric measurements (money & its application); proportional
reasoning; geometry; statistics and probability. Topic areas with more weight will have more emphasis in the second section
where learners should have the right to choose to answer 3 items out of 5.
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3.5. REPORTING TO PARENTS
The wider range of learning in the new curriculum means that it is necessary to think again about how to share learners’
progress with parents. A single mark is not sufficient to convey the different expectations of learning which are in the
learning objectives. The most helpful reporting is to share what students are doing well and where they need to improve.
4. RESOURCES
4.1. MATERIALS NEEDED FOR IMPLEMENTATION
The following list shows the main materials/equipments needed in the learning and teaching process:

Materials to encourage group work activities and presentations: Computers (Desk tops&lab tops) and projectors;
Manila papers and markers

Materials for drawing & measuring geometrical figures/shapes and graphs: Geometric instruments, ICT tools such as
geogebra, Microsoft student ENCARTA, ...

Materials for enhancing research skills: Textbooks and internet (the list of the textbooks to consult is given in the
reference at the end of the syllabus and those books can be found in printed or digital copies).

Materials to encourage the development of Mathematical models: scientific calculators, Math type, Matlab, etc
The technology used in teaching and learning of Mathematics has to be regarded as tools to enhance the teaching and
learning process and not to replace teachers.
4.2. HUMAN RESOURCE
The effective implementation of this curriculum needs a joint collaboration of educators at all levels. Given the material
requirements, teachers are expected to accomplish their noble role as stated above. On the other hand school head teachers
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and directors of studies are required to make a follow-up and assess the teaching and learning of this subject due to their
profiles in the schools. These combined efforts will ensure bright future careers and lives for learners as well as the
contemporary development of the country.
In a special way, the teacher of Mathematics at ordinary level should have a firm understanding of mathematical concepts at
the leavel he / she teaches. He/she should be qualified in Mathematics and have a firm ethical conduct. The teacher should
possess the qualities of a good facilitator, organizer, problem solver, listener and adviser. He/she is required to have basic
skills and competency of guidance and counseling because students may come to him or her for advice.
Skills required for the Teacher of Religious Education
The teacher of Mathematics should have the following skills, values and qualities:
-
Engage learners in variety of learning activities
Use multiple teaching and assessment methods
Adjust instruction to the level of the learners
Have creativity and innovation the teaching and learning process
Be a good communicator and organizer
Be a guide/ facilitator and a counsellor
Manifest passion and impartial love for children in the teaching and learning process
Make useful link of Mathematics with other Subjects and real life situations
Have a good master of the Mathematics Content
Have good classroom management skills
5. SYLLABUS UNITS
5.1. PRESENTATION OF THE STRUCTURE OF THE SYLLABUS UNITS
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Mathematics subject is taught and learnt in lower secondary education as a core subject, i.e. in S1, S2 and S3 respectively. At
every grade, the syllabus is structured in Topic Areas, sub-topic Areas where applicable and then further broken down into
Units to promote the uniformity, effectivness and efficiency of teaching and learning Mathematics. The units have the
following elements:
1. Unit is aligned with the Number of Lessons.
2. Each Unit has a Key Unit Competency whose achievement is pursued by all teaching and learning activities
undertaken by both the teacher and the learners.
3. Each Unit Key Competency is broken into three types of Learning Objectives as follows:
a. Type I: Learning Objectives relating to Knowledge and Understanding (Type I Learning Objectives are also
known as Lower Order Thinking Skills or LOTS)
b. –Type II and Type III: These Learning Objectives relate to acquisition of skills, Attitudes and Values (Type II
and Type III Learning Objectives are also known as Higher Order Thinking Skills or HOTS) – These Learning
Objectives are actually considered to be the ones targeted by the present reviewed curriculum.
4. Each Unit has a Content which indicates the scope of coverage of what to be tought and learnt in line with stated
learning objectives
5. Each Unit suggests a non exhaustive list of Learning Activities that are expected to engage learners in an interactive
learning process as much as possible (learner-centered and participatory approach).
6. Finally, each Unit is linked to Other Subjects, its Assessment Criteria and the Materials (or Resources) that are
expected to be used in teaching and learning process.
The Mathematics syllabus for ordinary level has got 6 Topic Areas: Algebra, Measures, Proportional reasoning,
Geometry, Statistics and Probability. As for units, they are 9 in S1, 11in S2 and 13 in S3
5.2. MATHEMATICS PROGRAM FOR SECONDARY ONE
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5.2.1. KEY COMPETENCIES AT THE END OF SECONDARY ONE
After completion of secondary one, the mathematics syllabus will help learner to:
1. Use correctly simple language structure, vocabulary and suitable symbolism for Ordinary Level Mathematics;
2. Carry out correctly numerical calculations;
3. Solve simple equations of an unknown in , , ID and ;
4. Use methodical and coherent reasoning in solving mathematical problems;
5. Solve problems related to percentage, unitary method, movement, interest, division, surface area and volume of
figures;
6. Draw correctly figures by using geometrical instruments and describe them using appropriate terms;
7. Locate area position from numerical data;
8. Make simple chart, graph or diagram from series of a statistical data.
9. Interpret simple diagrams and statistics, recognising ways in which representations can be misleading.
10. Determine the probability of an event happening under equally likely assumption.
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5.2.2. MATHEMATICS UNITS FOR SECONDARY ONE
Topic Area:ALGEBRA
S1 Mathematics
Unit 1: SETS
No. of lessons:30
Key Unit Competency: To be able to use sets, Venn diagrams and relations to represent situations and solve problems.
Learning Objectives
Knowledge and
understanding
Skills
- Define and give examples
of sets
- Indicate what a specified
region in a Venn diagram
represents, using
connecting words (and,
or, not) or set notation
- Show how sets are used in
representation of a given
information
- Observe a contextual
problem that involves
sets, record the solution,
using set notation and
give explanations
- Demonstrate algebraic
and graphical reasoning
through the study of
relations
- Identify different types of
relations between sets
- Use sets to group
and classify
according to given
conditions
- Use Venn diagrams
to represent
information.
- Find intersection,
union, complement,
difference and
symmetrical
difference on sets
- Represent relations
between sets as
mappings and
graphs
- Use sets and
relations to solve
problems
Content
Learning Activities
Attitudes and
values
Appreciate how sets,
Venn
diagrams
and relations
can be used
to represent
situations
mathematica lly
Set Concept: definition of set,
notation,examples (subsets of
natural numbers like even
numbers,odd numbers,prime
numbers, etc), cardinal number, Venn diagrams, complement,
intersection, union, set
difference, symmetric difference
Relations:mappings, ordered
pair,Cartesian product, domain
and range,graphof a
relation,equivalence
relation(reflexive,symmetric,
and transitive),particular
relations(function, mapping,
injection/ one to one,
surjection/ onto, bijections/ one
to one and onto)
- Inverse relation,composite
relations
-
The class act out various Venn diagrams with rules
for sets (e.g. students are numbered and sort
themselves according to different rules like even
numbers,odd numbers,prime numbers,etc)
Represent practical experiences in Venn diagrams
and using the notation and symbols of sets, including,
union ( ), intersection ( ), subset (  ),
complement, difference, symmetrical difference (  )
In pairs, create sets of ordered pairs using the
Cartesian product
In pairs explore relations between sets (objects,
shapes, and numbers) define domain and range,
create mappings.
Individually, for given relation between sets of
numbers, illistrate it using a cartesian plane and
show its elements in terms of couples / ordered
pairs.
In group, investigate when inverse relations are
possible and identify the criteria.
In pairs, verify if a given relation is an equivalence
relation or a composite one.
Links to other subjects: Any subject where classification is important e.g. biology, geography, physics, financial education,...
Assessment criteria: Use sets, Venn diagrams and relations to represent situations and solve problems.
Materials: cards for acting out scenarios …
Page 22 of 60
Topic Area: ALGEBRA
S1 Mathematics
Unit 2: SETS OF NUMBERS
No. of lessons: 36
Key Unit Competency: Use operations to explore properties of sets of numbers and their relationships
Learning Objectives
Knowledge and
understanding
- Identify sets of numbers
(natural, integer, rational
and real) and know the
relationships between
them
- Illustrate different set of
numbers on a number line
- Show that irrational
numbers cannot be
expressed exactly as a
decimal
Skills
- Curry out mathematical operations on sets of
numbers
- Work systematically to
determine the operation
properties of sets of
numbers
- Determine the
hierarchy of sets of
numbers and explain its
relationship with
operations
- Convert between
decimal and fraction
representations of
rational numbers
Content
Learning Activities
Attitudes and values
Appreciate that
rational numbers can
be represented exactly as a fraction or a
decimal which may
terminate or recur.
Appreciate that the
number line is
incomplete without the
irrationals which
cannot be written
exactly as a decimal
Vocabularies and notation
 In groups, add, subtract, multiply and
for different sets of numbers
divide pairs of natural numbers – for
Set of numbers and its
which operation(s) is the answer
subsets : natural numbers,
always/sometimes/never a natural
integers, rational numbers,
number?
Irrational numbers and real
- Repeat for integers
numbers
- Repeat for rational numbers
Four operations and
- Repeat for real numbers
Properties on sets of
 Individually, construct a Venn diagram
numbers
to illustrate the relationship between
The relationship between
two or more sets of numbers.
sets of numbers
 In pairs, investigate the decimal
representation of rational numbers
and determine why the decimal is
terminating or recurring
Links to other subjects: It is linked with biology, English,computerscience,geography,chemistry,physics.economics,finance,accounting, construction, etc.
Assessment criteria: Use operationsto explore properties of sets of numbers and their relationships.
Materials: Text books, manila paper, calculators,.
Page 23 of 60
Topic Area:ALGEBRA
S1 Mathematics
Unit 3: Linear Functions, Equations and Inequalities
No. of lessons:36
Key Unit Competency:Represent and interpret graphs of linear functions and apply them in real life situations. Solve linear equations and inequalities,
appreciate the importance of checking their solution, and represent the solution
Learning Objectives
Knowledge and
understanding
- Define a linear
function and
recognize its graph
- Illustrate that the
linear function
iswritten in the form
, c is the yintercept, m is a
measure of steepness
and the solution of the
equation
is the x-intercept
- Explain what is meant
by the solution of a
linear equation and
inequality
Skills
- Plot linear functions on the
Cartesian plane
- Interpret the graph of a linear
function linking the parameters of
the function with the features of
the graph, including intercepts
and steepness
- Solve linear equations
representing the solution
graphically
- Solve linear inequalities in one
unknown representing the
solution on a number line
- Check solutions to equations and
inequalities by substituting into
one side of the original equation
- Use linear functions, equations
and inequalities to model
situations and solve problems
Content
Learning Activities
Attitudes and
values
Appreciate the
importance of
checking the
solution when
solving an equation
or inequality and
represent on a
graph (equation
only) and number
line
- In groups,systematically
 Linear functions:
- Definition, notation and examples: investigate different values of m
and c in
(best done
- Cartesian plane and coordinates
using graph plotting software)
- Graph of linear function and its
to develop intuitive
features (intercepts, steepness)
understanding. Generalize how
to find intercepts and determine
 Equations and inequalities with one
steepness. Plot some examples
unknown:
by hand to illustrate findings
- Solve linear equations with one
- In pairs, solve linear equations
unknown and represent the
and relate the solution to a
solution graphically
graph
- Solve linear inequalities in one
- In pairs, solve linear inequalities
unknown and represent the
and record solutions on a
solution on a number line
number line
- Model and solveproblems using
- In groups,research contexts
linear functions, equations and
where linear functions,
inequalities
equations and inequalities are
relevant – present to class
Links to other subjects: Linear functions, equations and inequalities arise in science and economics
Assessment criteria: Can represent and interpret graphs of linear functionsand apply them in real life situations. Solve linear equations and inequalities,
Page 24 of 60
appreciate the importance of checking their solution, and represent the solution
Materials:Digital technology including graph plotting software
Topic Area:
METRIC MEASUREMENTS (MONEY)
S1 Mathematics
Unit 4: PERCENTAGE, DISCOUNT, PROFIT AND LOSS
No. of lessons:12
Key unit competency: To solve problems that involve calculating percentage, discount, profit and loss and other financial calculations.
Learning Objectives
Knowledge and
understanding
Explain how to calculate
discount, commission,
profit and loss, simple
interest, tax
Skills
- Use percentages to
calculate discount,
commission, profit, loss,
interest, taxes
- Solve problems involving
- Discount
- Commission
- Profit and loss
- Loans and savings
- Tax and insurance
Content
Learning Activities
Attitudes and values
- Appreciate the role
money plays in our life
- Be honest in managing
and using money
- Appreciate that saving
and investing money can
increase its value
- Appreciate the
importance of paying
taxes
-
Percentages
Discount
Commission
Profit and loss
Loans and savings
(simple interest only)
Tax and insurance
- In groups research, discuss the use of
percentages in business, household
and personal finance – prepare a
poster
- In groups,determine the best value for
money with different discount
arrangements
- In pairs, solve problems involving
simple interest, discount, profit and
loss
Links to other subjects: Personal finance calculations inEconomics, Entrepreneurship, Finance, Accounting, Business Administration and other related fields.
Assessment criteria:Able to solve problems that involve calculating percentage, discount, profit and loss and other financial calculations
Materials: coins, bills, receipt papers, Electronic materials, ATM cards.
Page 25 of 60
Topic Area:
PROPORTIONAL REASONING
S1 Mathematics
Unit 5: RATIO AND PROPORTIONS
No. of lessons:12
Key Unit Competency:To be able to solve problems involving ratio and proportion
Learning Objectives
Knowledge and
understanding
Skills
- Express ratios in their - Compare quantities using
simplest form
proportions
- Share quantities in a given
- Identify a direct and
proportion or ratio
indirect proportion.
- Apply ratio and unequal
- Differentiate direct
sharing to solve given
from indirect
problems
proportion
- Solve real life problems
involving direct and indirect
proportion using tables and
graphs
- Interpret ratio and
proportions in practical
contexts.
Content
Learning Activities
Attitudes and values
Appreciate the
- Ratio, proportion and - In groups, solve problems involving direct
sharing
and inverse proportion, ratios and sharing
importance of
adjust recipe amounts for different numbers
multiplication when - Applying ratio and
proportion in
of people
working with ratio
practical and
- In pairs, match different representations of
and proportion
everyday contexts
ratios and proportions including simplest
- Direct and indirect
form
proportional
- In groups, interprete and explain the ratio and
relationships in
proportion in maps and scale
practical contexts
drawings/models
- In pairs, solve problems in practical contexts
involving direct and indirect proportion using
tables of values and graphs
Links to other subjects: Any subject where proportional reasoning is required e.g. biology, physics, computer science, chemistry, economics, personal
finance etc.
Assessment criteria: can solve problems involving ratio and proportion in a variety of contexts
Materials: calculators and electronic materials
Page 26 of 60
Topic Area:GEOMETRY
S1 MATHEMATICS
Unit 6: POINTS, LINES AND ANGLES
No. of lessons:36
Key Unit Competency:To be able to construct mathematical arguments using the angle properties of parallel lines
Learning Objectives
Knowledge and
understanding
- Recognize the
position of an angle
at a point sum to
360o; angles at a
point on straight line
sum to 1800
- Distinguish and
recognize vertically
opposite,
corresponding,
alternate and
supplementary
angles
Skills
Content
Learning Activities
Attitudes and values
- Use knowledge of - Appreciate the need - Segments, rays, lines - Practical – fold a paper triangle to bring all angles
angle properties of to give reasons when
and acute, right,
together at a point - in groups discuss why this works
parallel lines and
developing solutions
obtuse and reflex
shapes to
to missing angle
angles
construct
problems
- Parallel and
arguments when - Value a variety of
transversal lines and
finding missing
different approaches
their properties.
angles in
to reach the same
- Constructing
- Inpairs,draw two parallel lines and a transversal, identify
geometric
conclusion
mathematical
all angles that are equal (measure to check) – identify
diagrams
arguments using
vertically opposite, corresponding, alternate and
- Construct and
angle properties of
supplementary angles and write their own glossary
calculate angles
parallel lines and
In groups, solve missing angle problems, giving reasons
shapes
for each step in the process
Links to other subjects: Physics, construction, engineering, geography, fine arts, scientific drawing.
Assessment criteria:construct mathematical arguments using the angle properties of parallel lines
Materials:Manila papers,geometrical instruments, Electronic materials.
Page 27 of 60
Topic Area:
GEOMETRY
Mathematics S1
Unit 7: SOLIDS
No. of lessons: 24
Key unitcompetency:To be able to select and use formulae to find the surface area and volume of solids.
Learning Objectives
Knowledge and
understanding
Skills
Content
Learning Activities
Attitudes and
values
- Explain the
- Derive the surface
- Appreciate the - Components of
- In small groups, count the number of faces (f), number of vertices(v)
surface area of a
area for prism and
difference
solids: faces,
and number of edges(e) for a variety of solid figureswith polygonal
solid as the area
cylinder
between
vertices and
faces and look for relationships (e.g. Euler’s rule(f+v=e+2)
of the net
- Calculate the surface
surface area
edges
- In groups, investigate the relationship between the surface area of
- Illustrate the
area and volume of
and volume and - Surface area and
cuboids, prisms, pyramids, cylinders and their nets. Generalize.
volume as the
common geometrical recognize
volume of a prism, - Practically in pairs(or teacher demonstration) measure the diameter
space occupied by solids, using formulas solids in the
pyramid, cylinder, of an orange then peel carefully and arrange the peel into circles with
a solid
where necessary
environment
cone and sphere
the same diameter as the orange. How many circles does the peel fill?
- Distinguish
- Distinguish between
- Formulae for
(Roughlyfour). Relate to formula
between surface
surface area and
surface area and
- In groups, select appropriate methods and units when solving
area and volume
volume and select
volume
problems concerning the volume and surface area of solids e.g. design
and know the
appropriate formulae
solids with a volume of 1000cm3, minimizing their surface area; what is
correct units
and units to use in
the greatest volume cylinder that can be made from a sheet of A4 paper
various contexts
Links to other subjects: Where volume and area calculations may be needed e.g. physics, construction, engineering, geography, fine arts, scientific
drawing etc.
Assessment criteria:Able to select and use formulae to find the surface area and volume of solids
Materials: solid figures for practical work, paper, scissors, glue, calculators, oranges
Page 28 of 60
Topic Area: STATISTICS AND PROBABILITY
SENIOR1 MATHEMATICS
Unit8: STATISTICS (ungrouped data )
No. of lessons:24
Key Unit Competency: To be able to Collect, to represent, and to interpret quantitative discrete data appropriate to a question or problem.
Learning Objectives
Knowledge and
understanding
- Define
quantitative data
and qualitative
data
- Differentiate
discrete and
continuous data
- Present data on a
frequency
distribution
- Define mode and
median of given
statistical data
- Recognize
formulae used to
calculate the
mean and median
- Read diagram of
statistical data.
Skills
- Apply data
collection to carry
out a certain
research.
- Represent statistical
information using
frequency
distribution table,
bar chart,
Histogram, Polygon,
Pie chart or
pictogram.
- Determine the
mode, mean and
median of statistical
data
- Interpret correctly
the graphs involving
statistical data
Content
Learning Activities
Attitudes and
values
- Help in decision - Definition of data.
making and
- Types of data (qualitative,
draw conclusion quantitative, discret and
- Self confidence
continuous data
and
- Collecting data
determination - Frequency distribution
- Develop
- Measures of central
competitiveness tendency: mode, Mean,
- Appreciate the
median, quartiles (1st , 2nd,
importance of
3rd quartiles, interorder in daily
quartile range)
activities.
- Data display: Bar chart,
- Develop
Histogram, Frequency
research and
Polygon, Pie chart,
creativity.
Pictogram
- Respect each
- Reading statistical graphs
other.
- Converting statistical
graphs into frequency
tables
In groups, collect data for a given situation such as heights,
weight, colors, blood group, ages, marks etc
Discuss whether it is quantitative or qualitative data,
continuous or discrete data. Hence make a frequency
distribution table for each case
In groups, observe and collect data for a given situation such
as height, weight, ages, marks etc. then determine, mode,
mean and median.
In groups, draw a bar chart, a histogram, frequency polygons
and a pie chart corresponding to the data collected and
compare results
In pairs, calculate the quartiles, the inter-quartile range and
represent them graphically
Individually, in the given bar chart, histogram, polygon, pie
chart identify mode, draw frequency table and hence find
mean and median. work in group
Given a graph, indicate/estmate where the mode, Mean,
median can be found.
Links to other subjects: Any subject where data collection, data representation, and data interpretation are important e.g. biology,geography, physics,
computer science, finance, economics,engineering, etc.
Assessment criteria:Consistently make appropriate data collection and data representation to solve a problem, and thendraw conclusions consistent with
findings.
Materials:Text books, papers, geometrical instruments, Electronic materials
Page 29 of 60
Topic Area: STATISTICS AND PROBABILITY
Mathematics S1
Unit 9: PROBABLITY
No. of lessons:6
Key Unit Competency:To be able to determine the probability of an event happening using equally likely events or experiment.
Learning Objectives
Knowledge and
understanding
- Define event and explain why
the probabilities can only be
between 0 (impossible) and
1 (certain).
- Explain that probabilities can
be calculated using equally
likely outcomes (e.g. tossing
a coin or dice, drawing a card
from a pack) or estimated
using experimental data (e.g.
weather, sport, arriving late
to school)
- Demonstrate that the more
data is collected; the better is
the estimate of the
probability.
Skills
Content
Learning Activities
Attitudes and values
- Calculate the
- Appreciate that the
probability of an
chance of an event
event where
happening is given
there are equally
by its probability
likely outcomes
which is number
e.g. heads or tails
between 0
on a coin, a score
(impossible) and 1
on a dice
(certain)
- Estimate
- Distinguish when an
probabilities
experiment is
using data
necessary to find a
probability and that
more data improves
the estimate
- Definition of event
In groups:Think and debate chance situations
and outcome
such as playing cards, tossing a coin, rolling dice –
- Examples of random
what are the chances of getting a particular
events
outcome? Introduce probability scale.
- Probability of equally
- Consider playing football, basketball ball, volley
likely outcomes
ball, hand ball or any other game.Discuss the
through experiments
chance ofwin, lose or draw.Use results to estimate
like tossing a coin or
probabilities.
dice, etc
- Investigate the relationship between
- Estimation of
experimental and calculated probability by
probabilities where
tossing a dice or coin many times and estimating
experimental data is
the probability of a particular outcome – plot a
required
graph to show the experimental probability and
note how that tends to the calculated probability
Links to other subjects: Any subject where probability is important e.g.economics, finance, physics chemistry,biology.
Assessment criteria:Use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations.
Materials:Dice, coins, playing cards,graph paper
Page 30 of 60
5.3. MATHEMATICS PROGRAM FOR SECONDARY TWO
5.3.1. KEY COMPETENCIES AT THE END OF SECONDARY TWO
After completion of secondary two, the mathematics syllabus will help learner to:
1. Use correctly the simple language structures, vocabulary and the symbols found in the second year mathematics
program;
2. Carry out efficiently numerical and literal calculations;
3. Solve the equations and inequalities of the first degree in ℝ
4. Recognize and justify congruent shapes.
5. Calculate the component of a vector.
6. Identify the image of a figure under a transformation and use the properties of transformations to solve
related problems.
7. Use methodical and coherent reasoning in solving mathematical problems;
8. Collect quantintative data appropriate to the problem or investigation, taking into account possible bias and extend the
knowledge to grouped data.
Page 31 of 60
5.3.2. MATHEMATICS UNITS FOR SECONDARY TWO
Topic Area:
ALGEBRA
S2 MATHEMATICS
Unit 1: INDICES AND SURDS
No. Of lessons: 18
Key unit competency: To be able to Calculate with indices and surds, use place value to represent very small and very large numbers.
Learning Objectives
Knowledge and
understanding
Skills
-Recognize laws of
indices
-Represent very
small number or
large number in
standard form
-Define and give
examples of
surds
-Identify
properties of
surds
-Recognize the
conjugates of
surds.
- Perform operations on
indices and surds.
- Solve simple equations
involving indices and
surds.
- Use standard form to
represent a number.
- Apply properties of
indices to simplify
mathematical expressions
- Apply Properties of surds
to simplify radicals.
- Compute rationalisation
of denominator on surds.
Attitudes and
values
Learning Activities
Content
Appreciate the  Indices/powers or exponents.
importance of
o Definition
indices and
o Properties indices.
surds in solving o Applications of indices:
mathematical
- Simple equations involving indices.
problems.
- Standard form
Show concern of  Surds/ radicals
self-confidence, o Definition and examples
determination,
o Properties of surds
and group work o Simplification of surds
spirit.
o Operations on surds
o Rationalisation of denominator.
 Square roots calculation methods:
o By factorization
o By general method.
o Estimation method
- In pairs, learners think themselves two
numbers or more having different powers
but the same base, multiply and divide
them.Then draw conclusion.
- In groups, express the given larger numbers
or smaller numbers in standard form.
- Solve given equations involving indices
- Individually, simplify surds by rationalizing
the denominators
- In groups, express each of the given surd as
the square root of a single number
- In groups, discuss and reduce surds to the
simplest possible surd form
- find the square roots of given numbers by
using Square roots methodsand calculators
Links to other subjects: Physics, Chemistry, Biology, Computer science, Economics, Finance, etc.
Assessment criteria: Use rules of indices and surds to simplify mathematical situation involving indices and surds
Materials: Calculator.
Page 32 of 60
Topic Area: ALGEBRA
S2 MATHEMATICS
Unit 2: POLYNOMIALS
No. of lessons: 30
Key Unit Competency: To be able to perform operations, factorise polynomials and solve related problems
Learning Objectives
Knowledge and
understanding
- Define polynomial
- Classify polynomials by
degree and number of terms.
- Recognize operation
properties on polynomials
- Give common factor of
algebraic expression
Skills
- Perform operation of polynomials
- Expand algebraic
expression by removing
bracket and collecting
like terms
- Apply operation
properties to carry out
given operation of
polynomials.
- Factorize a given
algebraic expression
using appropriate
methods.
- Expand algebraic
identities
Content
Attitudes and values
Appreciate the role of numerical
values of polynomials.
and algebraic identities in
simplifying mathematical
expressions.
Develop critical thinking and
reasoning
Ability to classify and able to
follow order to perform a given
task.
Learning Activities
- Definition and classification of
polynomials including homogenious
polynomials (monomials,binomials, and
trinomials, polynomial of four terms)
- Operations on polynomials.
- Numerical values of polynomials.
- Algebraic identities
- Factorization of polynomials by :
o Common factors
o Grouping terms
o Algebraic identities
o Zeros (roots) of polynomials
o Factorization of quadratic
expressions(Sum and Product)
In groups:
- Classify
polynomials
according :
to their degree or
to the number of
terms.
- Discuss and
perform
operations on
polynomials
- Expand and
factorize given
mathematical
expressions
Links to other subjects: Any subject where polynomials are important like in Physics, Chemistry, etc.
Assessment criteria: Perform operations, factorise polynomials and solve related problems.
Materials: Text book, Papers, calculators
Page 33 of 60
Topic Area: ALGEBRA
S2 MATHEMATICS
Unit 3: SIMULTANEOUS LINEAR EQUATIONS , INEQUALITIES
No. of lessons: 30
Key unit Competency: To be able to solve problems related to simultaneous linear equations, inequalities and represent thesolution graphically.
Learning Objectives
Knowledge and
understanding
Skills
Attitudes and values
Content
Learning Activities
- Define simultaneous - Solve
- Appreciate the
- Definition and examples of simultaneous linear equations - In pairs, show whether a
linear equations and simultaneous
importance of solving in two variables and inequalities in one variable.
given system of 2 linear
give examples.
linear equations
problems related to
- Types of simultaneous linear equations (independent
equations is independent,
- Show whether a
in two variables
simultaneous linear
simultaneous linear equations, dependent simultaneous
dependent, or inconsistent
given simultaneous - Model and solve
equations, inequalities. linear equations, and inconsistent/incompatible
- In group, discuss different
linear equtions is
mathematical
- Be accurate in solving simultaneous linear equations)
methods for solving
independent,depen
word problems
system of linear
- Solving simultaneous linear equations in two unknowns
simultaneous linear
dent or inconsistent
using
equations, inequalities. using algebraic methods:Substitution method,
equations and use one of
- Recognize the forms simultaneous
- Developing self
Comparison method, Elimination method, and
them(on your choice) to
of compound
equations
confidence in solving
Cramer’s rule.
solve a given simultaneous
inequalities with
- Solve compound
system of linear
linear equations.
- Inequalities of the types:
,
,
one unknown and
inequalities in
equations/ inequalities ,
Individually, solve problems
,
give examples
one variable.
in one variable.
involving simultaneous
,
equations.
In pairs, solve given
- Compound inequalities or systerm of two inequalities in
simultaneous inequalities in
one unknown.
two unknowns and given
compound inequalities.
Links to other subjects: Any subject where simultaneous linear equations and inequalities are needed.
Assessment criteria: Solve problems related simultaneous linear equations, inequalities and represent the solution graphically.
Materials: Calculators, text book, papers.
Page 34 of 60
Topic Area: ALGEBRA (PROPORTIONS REASONING)
S2 MATHEMATICS
Unit 4: MULTIPLIER FOR PROPORTIONAL CHANGE
No. of lessons: 12
Key Unit Competency: To be able to use a multiplier for proportional change
Learning Objectives
Knowledge and
understanding
- Recognize the
properties of
proportions
- Express ratio in their
simplest form
- Share quantities in a
given proportion or
ratio.
Skills
Content
Learning Activities
Attitudes and values
- Solve problems in real life
- Be honest in sharing
involving multiplier proportion with other.
change
- Develop critical
- Apply multipliers for
thinking in terms
proportional change to solve
proportion multiplier given problem
for proportional change
- Use multiplier for proportional
change to find the new
quantities
- Use “Decreased by n%”
and “Increased n%”
Increasing quantities by - In group, solve problems involving multiplier
n%
for proportional change
Decreasing quantities by - Individually , solve problems involving
n%
Decreased by n% and
Calculation of
Increased by n%
proportional change
using multiplier
Links to other subjects: Economics, Entrepreneurship, Finance, Accounting, Business Administration and other related fields.
Assessment criteria: Explain the importance of money in connection to real life.
Materials: Text books, coins, bills, geometrical instruments, receipt papers, Electronic materials, ATM cards.
Page 35 of 60
Topic Area: GEOMETRY
S2 MATHEMATICS
Unit 5: THALES THEOREM
No. of lessons:12
Key Unit Competency: Use Thales’ theorem to solve problems related to similar shapes, and determines their lengths and areas.
Learning Objectives
Knowledge and
understanding
- Identify and name triangles
or trapezium from parallel
and transversals
intersecting lines
- State Thales’ theorem and
its corollaries
Skills
Content
Learning Activities
Attitudes and values
- Associate extended
- Develop participation, self- Midpoint theorem
proportions in the
confidence, determination, and
- Thales’ theorem and its
triangles
team spirit.
converse
- Apply Thales’ theorem - Appreciate the importance of
- Application of Thales‘
and its corollaries to
solving daily activities involving
theorem in calculating
solve problems on
midpoint theorem,
lengths of proportions
proportions of triangles, Thales’ theorem and its converse
segments (in triangles,
trapezium
and application of Thales‘theorem. trapezium)
- Discuss the converse of
Thales’ theorem
- In groups, solve problems
involving midpoint theorem for a
given situation.
- In group, discuss and solve
mathematical problems involving
the applications of
Thares’theorem.
Links to other subjects: Technical drawing, Scientific drawing, Light Physics etc.
Assessment criteria: Use Thales’ theorem to Solve problems related to similar shapes, and determines their lengths and areas.
Materials: Geometrical instruments.
Page 36 of 60
Topic Area: GEOMETRY
S2 MATHEMATICS
Unit 6: PYTHAGORAS’ THEOREM
No. of lessons: 12
Key units Competency: To be able tosolve problems of lengths in right angled triangles by using Pythagoras’ theorem.
Learning Objectives
Knowledge and
understanding
Skills
- State Pythagoras’
- Use Pythagoras’
theorem
theorem to find
- Identify the
lengths of sides of
hypotenuse in three
right angled triangle
sides of a right angled - Apply Pythagoras’
triangle
theorem to solve
- List properties of a
problems in range of
right angled triangle
contexts
- Demonstrate
Pythagoras’ theorem
practically
Content
Learning Activities
Attitudes and values
- Appreciate the role of - Pythagoras’ theorem
- In groups, find the squares of given sides of a triangle,
Pythagoras’ theorem - Demonstration of Pythagoras’
verify relationship between the sum of the squares of
in solving daily life
theorem
shorter sides and the square of the longer side.
activities.
- Applications of Pythagoras’
Hence, discuss whether a triangle is right-angled given
- Develop confidence
theorem in the calculation of
the length of sides and give the properties.
and accuracy in
any side of right angled
constructing shapes.
triangle , word problems
- Individually, using Pythagoras’ theorem, find the
- Develop team work
length of the hypotenuse, if the other sides of the right
spirit and respect
angle are given.
analytically the views
- In groups, learners can practically, demonstrate
of others.
Pythagoras’ theorem by :
 Measuring the areas of squares on sides of the
right angled triangles
 Exploring phythagorean dissections by cutting
and reassembling parts
Links to other subjects: Technical drawing, Scientific drawing, Optics,etc.
Assessment criteria: Solve problems of lengths in right angled triangles by using Pythagoras’ theorem.
Materials: Geometrical instruments, Calculators
Page 37 of 60
Topic Area: GEOMETRY
S2 MATHEMATICS
Unit 7: VECTORS
No. of lessons: 18
Key unit competency: To be able to solve problems using operation on vectors.
Learning Objectives
Knowledge and
understanding
- Define a vector
- Represent a vector in a
Cartesian plane
- Differentiate between vector
quantities and scalar
quantities.
- Show whether vectors are
equal.
Skills
Attitudes and values
- Use vector notations
correctly and perform
operations on vectors
- Appreciate the importance of
vectors in motion.
- Show self-confidence; and,
determination while solving
- Find the components of problems on vectors.
a vector in the Cartesian
plane
- Find the magnitude of a
vector
Content
- Concept of a vector :
definition and properties
of a vector, notation
- Vectors in a Cartesian
plane
- Components of a vector in
the Cartesian plane
- Equality of vectors
- Operations on vectors :
o Addition
o Subtraction
o Multiplication by a
scalar
- Magnitude of a vector as
its length.
Learning Activities
In groups, graphically add and
subtract given consecutive or any
vectors using parallelogram rule.
Graphically multiply a given vector
by a scalar individually or in
groups.
In groups, perform multiplication
of vectors by a scalar, addition or
subtraction of vectors given their
components.
Individually, calculate the
magnitude of vectors given their
components
Links to other subjects: Physics (forces) ,...
Assessment criteria: Solve problems using operation on vectors.
Materials: Geometrical instruments and calculators
Page 38 of 60
Topic Area: GEOMETRY
S2 MATHEMATICS
Unit 8: PARALLEL AND ORTHOGONAL PROJECTIONS
No. of lessons: 12
Key unit Competency: To be able to transform shapes under orthogonal or parallel projections
Learning Objectives
Knowledge and
understanding
- Identify an image of a figure
under Parallel projection
- Identify an image of a figure
under orthogonal projection
Skills
Content
Learning Activities
Attitudes and values
- Construct an image of - Show the importance of parallel - Definition of :
an object or geometric
and orthogonal projection in
o Parallel projection
shape under :
various situations.
o Orthogonal projection
o Parallel projection - Develop critical thinking and
- Properties of:
o Orthogonal
reasoning while transforming
o Orthogonal projection
projection.
shapes under parallel or
o parallel projections
orthogonal projection.
- Image of geometric shape
- Be accurate in construction of
under:
figures and their images under o Parallel projection
parallel or orthogonal
o Orthogonal projection
projection
- Develop confidence in solving
problems related to
transformation of shapes under
parallel or orthogonal
projection.
o In groups, observe drawings of
different objects and their images
involving parallel or orthogonal
projection. Discuss and deduce
properties and type of projection
used.
Links to other subjects: Technical drawing, scientific drawing,...
Assessment criteria: make image of figures using parallel projections
Materials: Geometrical instruments, calculators.
Page 39 of 60
Topic Area: GEOMETRY
S2 MATHEMATICS
Unit 9: ISOMETRIES
No. of lessons: 30
Key Unit Competency: To be able to transform shapes using congruence (central symmetry, reflection, translation and rotation).
Learning Objectives
Knowledge and
understanding
Content
Skills
- Identify an image of - Construct the image of a
a figure under:
point, a segment, a
o Central
geometric shape, under:
symmetry
o Central symmetry
o Reflection
o Reflection
o Translation
o Translation
o Rotation
o Rotation
- Find the coordinates of
image of an object
under:
o Central symmetry
o Reflection
o Translation
o Rotation
Learning Activities
Attitudes and values
- Appreciate that
- Definition of:
- In groups, construct the image of a given object
translation, rotation and
o Central symmetry
under central symmetry , then compare the
reflection play important
o Reflection
image to the initial, and then discuss and
role in various situations.
o Translation
deduce the applied properties.
- Develop team work spirit
o Rotation
- Repeat the above activity for reflection ,
- Develop confidence in
- Construction of an image of an translation or rotation
construction of the image object / geometric shape under : - In pairs, given an object and its image find: the
of a point, a segment, a
o Central symmetry
center of symmetry, line of symmetry or the
geometric shape under
o Reflection
translation vector, the center of rotation and
any isometry
o Translation
angle of rotation.
- Develop accuracy in
o Rotation
- Individually, construct the images of a given
constructing shapes
- Properties and effects of:Central object under successive transformations .
under isometries
symmetry
Reflection
o Translation
o Rotation
- Composite transformations up
to three isometries
Links to other subjects: Physics, ICT, Engineering, technical drawing, scientific drawing,…
Assessment criteria: Transform shapes using congruence (central symmetry, reflection, translation and rotation).
Materials: Geometrical instruments, calculators.
Page 40 of 60
Topic Area: STATISTICS AND PROBABILITY
S2 MATHEMATICS
Unit10: STATISTICS (grouped data )
No. of lessons: 30
Key Unit Competency: To be able to collect, represent and interpret grouped data.
Learning Objectives
Knowledge and
understanding
- Define grouped data
and represent
grouped data on a
frequency
distribution
- Identify mode,
middle class, modal
class and median of
given grouped
statistical data
- Read diagram of
grouped statistical
data
Skills
Content
Learning Activities
Attitudes and values
- Apply data collection - Appreciate how
to carry out a certain data collection, data
research.
representation and
- Represent grouped
data interpretation
statistical information can be used for
using: histogram,
solving real life
polygon, frequency
situations.
distribution table and - Appreciate the
pie chart.
importance of data
- Calculate the mode,
in culture of
mean and median of
investigation
statistical data
and decision making.
- Interpret correctly
- Team work spirit
the graph of grouped and respect the
statistical data
views of others.
- Develop accuracy in
reading graphs
- Definition and examples of grouped data
- Grouping data into classes
- Frequency distribution table for grouped
data.
- Cummulative frequency distribution table.
- Measures of Central tendency for grouped
data:
o Mean, Median , Mode, and range for
grouped data
- Graphical representation of grouped data:
o polygon
o Histogram
o Superposed polygon
-
In groups:
- Collect data for a given situation such as
height, weight, ages, or marks in any
subject, group them in a given interval,
and then represent them in a frequency
distribution table.
- Collect data for a given situation such as
their height, weight, ages, marks in any
subject then group them into classes in
given interval, determine the middle class,
modal class, class mean and median class.
Then draw histogram, frequency polygons
and a superimposed frequency polygon
and interpret the result then infer
conclusion.
- Converting statisticalgraphs into
frequency tables and finding measures of
central tendency using graphs
Links to other subjects: History, Biology, Geography, Physics, Computer Science, Finance, Etc
Assessment criteria: Collect, represent and Interpret grouped data.
Materials: Calculators, graph papers.
Page 41 of 60
pic Area: STATISTICS AND PROBABILITY
S2 MATHEMATICS
Unit11: TREE AND VENN DIAGRAMS AND SAMPLE SPACE
No. of lessons: 12
Key unit Competency: To be able to determine probabilities and assess likelihood by using tree diagrams
Learning Objectives
Knowledge and
understanding
Skills
Content
Learning Activities
Attitudes and values
- Define mutually
- Construct and
- Appreciate the
exclusive and
Interpret correctly importance of
independent events
the tree diagram
probability to find
- Count the number of - Use tree and Venn chance for an event to
branches and total
diagrams to
happen.
number of outcomes
determine
- Show curiosity to
on a tree diagram
probability.
predict what will
happen in future.
- Promote team work
spirit and selfconfidence.
- Tree diagram.
In groups:
- Total number of
- For a given task, construct a tree diagram corresponding to that
outcomes
situation and determine the number of branches. Hence
- Determining
calculate required probability
probability using:
- Analyze a given situation, present it using Venn diagram and
o Venn diagram
then find probability. e.g. in the venn diagram E= {pupils in class
o Tree diagram
of 15}, G={girls}, S={Swimmers} , F={Pupils who are christians}.
- Mutually exclusive
A pupil is chosen at random . find the
and independent
probability that the pupil :
events.
a) Can swim
b) Is a girl swimmer
c) Is a boy swimmer who is christian
Two pupils are chosen at random .
find
the probability that :
d) both are boys
e) neither can swim
f) both are girls swimmers who are chritians
- For given tasks on events , suggest whether events aremutually
exclusive or independent or neither.
Links to other subjects: Financial education, Physics, Chemistry, Biology, Physical Education and Sport, Etc.
Assessment criteria: Determine probabilities and assess likelihood by using tree diagrams
Materials: Dice, Coins, Playing Cards, Calculators, Balls,
Page 42 of 60
5.4. MATHEMATICS PROGRAM FOR SECONDARY THREE
5.4.1. KEY COMPETENCIES AT THE END OF SECONDARY THREE
1. Carry out efficiently numerical and literal calculations;
2. Solve problems that involve sets of numbers using Venn diagram;
3. Represent graphically a function of the first degree, a function of the second degree point by point;
4. Solve equations, inequalities and the systems of the first degree in two unknowns;
5. Apply compound interest in daily life situations;
6. Calculate the side lenghts, angles in a right triangles and areas of geometric shapes.
7. Represent and interpret graphs to linear and quadratic functions
8. Construct mathematical arguments using circle theorems
9. Construct the image of a geometric figure under composite transformations.
10. Collect bivariate data to investigate possible relationships through observations.
Page 43 of 60
5.4.2. MATHEMATICS UNITS FOR SECONDARY THREE
Topic Area: ALGEBRA
S3 MATHEMATICS.
Unit 1: PROBLEMS ON SETS
No. of lessons: 6
Key Unit Competency: To be able to solve problems involving sets.
Learning Objectives
Knowledge and
understanding
- Express a mathematical
problem on set using a
venn diagram
- Represent a mathematical
problem on venn diagram
Skills
Attitudes and values
- Use Venn diagram to - Develop clear, logical and
represent a
coherent thinking in solving real
mathematical
life problems involving sets.
problem on sets
- Appreciate the importance of
- Interpret , model , and representing , and solving a
solve a mathematical
mathematical problem on sets
problem on sets
using venn diagram
Content
Learning Activities
- Matheatical Problems involving
In groups
sets:
- Observe information
o Analysis and
given in the Venn
interpretation of a
diagram and solve
problem using set
related questions
language (intersection,
- Discuss on a given
union,...)
situation involving set
o Representation of a
theory, represent it
problem using venn
using Venn diagram,
diagram ,
form an equation and
o Modeling and Solving a
solve related questions
problem
Links to other subjects: Any subject where classification is important e.g. biology, geography, physics, financial education, ....
Assessment criteria: Solve problems involving sets.
Materials: Calculators.
Page 44 of 60
Topic Area: ALGEBRA
S3 MATHEMATICS
Unit 2: NUMBER BASES
No. of lessons: 12
Key Unit Competency: To be able to represent numbers in different number bases and solve related problems.
Learning Objectives
-
Knowledge and
understanding
Skills
List the digits used in a
given base
Convert number from
base ten to any other
base and vice versa.
- Carry out addition
and subtraction
multiplication and
division on numbers
bases
- Solve equations
involving bases.
Content
Learning Activities
Attitudes and values
- Develop clear, logical and - Definition and
- In group: Convert a given number from
coherent thinking while
examples of different
base ten to any other base and vice versa.
solving problems on sets
number bases.
Convert numbers from any base diffrent
- Appreciate the importance - Converting a number
from ten to another.
of bases in various
from base ten to any
- Discuss and carry out operations on
contexts.
other base like base 2,
number bases
3, or 5 and vice versa
- In groups, solve equations involving bases
- Converting a number
from one base to
another (e.g. base 2 to
base 3, etc).
- Addition and
substraction on
number bases
- Multiplication and
division on number
bases
- Solving equations
involving number bases
Links to other subjects: ICT, etc
Assessment criteria: Represent numbers in different number bases and solve related problems.
Materials: Calculators.
Page 45 of 60
Topic Area: ALGEBRA
S3 MATHEMATICS
Unit 3: Algebraic fractions
No. of lessons:24
Key Unit Competency: To be able to perform operations on rational expressions and use them in different situations.
Learning Objectives
Knowledge and understanding
- Define an algebraic fraction
- State the restriction on the
variable in algebraic fraction
- Recognize the rules applied for
addition, subtraction,
multiplication or division and
simplification of algebraic
fractions.
Skills
Content
Learning Activities
Attitudes and values
- Perform operations
- Develop clear, logical and
on algebraic fractions
coherent thinking while
- Solve rational
working on algebraic fractions
equations with linear - Show concern of patience,
denominators
mutual respect, tolerance, team
- Simplify algebraic
sprit and curiosity in group
fractions
activities while solving and
discussing about mathematical
situations involving algebraic
fractions.
- Definition and examples of In groups,
an algebraic fraction
- State the restrictions on
- Restrictions on the variable
the variable given
or conditions of existence of
algebraic fractions
an algebraic fraction.
- Carry out different
- Simplification of algebraic
operations for given
fractions
algebraic fractions and
- Addition or substraction of
simplify. Then present
algebraic fractions with
and explain the findings
linear denominators
- Multiplication or division
Individually, Solve given
and simplification of two
rational equations.
algebraic fractions
- Solution of rational
equations with linear
denominators
.
Links to other subjects: Physics (Distance problems, Motion problems…), work problems…
Assessment criteria: Perform operations on rational expressions and use them in different situations
Materials: Calculators.
Page 46 of 60
Topic Area:
ALGEBRA
S3 MATHEMATICS
Unit 4: Simultaneous Linear Equations and inequalities
No. of lessons : 18
Key Unit Competency: To be able to solve word problems involving simultaneous linear equations.
Learning Objectives
Knowledge and
understanding
- Define simultaneous
linear inequalities in
two unknowns
- Give examples of
simultaneous linear
inequalities in two
unknowns
- Show solution set of
simultaneous linear
equations /inequalities
in two unknowns given
their graphs
Skills
- Solve graphically simultaneous
linear equations
/ inequalities in
two unknowns
- Interpret
graphical
solution of
simultaneous
linear equations
/inequalities in
two unknowns
- Solve word
problems leading
to simultaneous
linear equations
Content
Learning Activities
Attitudes and values
Appreciate how simultaneous linear
- Graphical solution of
equations in two unknowns is important simultaneous linear equations in
to represent and solve mathematical
two unknowns
word problems
- Solving word problems
Develop clear, logical and coherent
involving simultaneous linear
thinking while solving simultaneous
equations in two unknowns (
linear equations /inequalities in two
graphically or algebraically)
unknowns
- Definition and examples of
Show concern of patience, mutual
simultaneous linear inequalities
respect, tolerance, team sprit and
in two unknowns.
curiosity in group activities while solving - Solving simultaneous linear
and discussing about mathematical
inequalities in two unknowns
situations involving simultaneous linear
equations / inequalities in two unknowns
In group:
Solve given simultaneous
linear equations /
inequalities in two
unknowns graphically.
Solve word problems
involving simultaneous
linear equations.
Obseve a given graphical
representation of
simultaneous linear
equations/ inequalities in
two unknowns and
deduce or show the
solution set
Links to other subjects: Physics, Financial education …
Assessment criteria: Solve word problems involving simultaneous linear equations.
Materials: Geometrical instruments, Calculators.
Page 47 of 60
Topic Area: ALGEBRA
S3 MATHEMATICS
Unit 5: QUADRATIC EQUATIONS
No. of lessons: 24
Key unit competency: To be able to solve quadratic equations.
Learning Objectives
Knowledge and
understanding
- Define quadratic
equations
- State methods
used to solve a
quadratic
equation.
Skills
Content
Learning Activities
Attitudes and values
- Solve quadratic
- Develop clear, logical and coherent
equations
thinking in solving quadratic
- Model and solve
equations
problems involving - Appreciate the importance of
quadratic equations. quadratic equations in solving word
- Solve equations
problems involving quadratic
reducible to
equations.
quadratic
.
- Promote team work spirit when
working in group while solving
quadratic equations
- Show concern of patience, mutual
respect, tolerance and curiosity
when discussing and solving
problems involving quadratic
equations in groups
- Definition and example of
In groups:
quadratic equation
- Solving quadratic equations - Discuss and use factorization or any
othor method to solve given
by:
quadratic equations
o Factorization
o graph
- Model given mathematic problems
o Completing squares.
using quadratic equations and solve
o Quadratic formula
them.
o Synthetic division
- Problems involving quadratic - Solve given equations reducible to
quadratic by using:
equations.
o Factorization
- Solution of equations
o Synthetic division (Horner’s
reducible to quadratic by:
method)
o Factorization
o Horner’s method
Links to other subjects: Physics, Financial education …
Assessment criteria: Solve word problems involving quadratic equations.
Materials: Geometrical instruments, Calculators.
Page 48 of 60
Topic Area: ALGEBRA
S3 MATHEMATICS
Unit 6: LINEAR AND QUADRATIC FUNCTIONS
No. of lessons: 24
Key Unit Competency: To be able to solve problems involving linear or quadratics functions and interpret the graphs of quadratic functions.
Learning Objectives
Knowledge and
understanding
- Define a Cartesian
equation of a
straight line.
- Define quadratic
function
- List the
characteristics of
linear or quadratic
function.
- Diffentiate linear
from quadratic
function
Skills
- Determine:
o Cartesian equation of
straight line
o Coordinates of vertex
o The equation of axis of
symmetry
- Determine the intercepts of
a quadratic function.
- Sketch and draw graphs
from a given function
- Use linear or quadratic
function to solve problems
in various situations and
interpret the results.
Content
Learning Activities
Attitudes and values
Develop clear, logical and
coherent thinking in working
out on linear and quadratic
functions
Appreciate the importance of
linear and quadratic
functions in learning other
subjects.
Show concern on patience,
mutual respect, tolerance,
team work spirit, and
curiosity in solving and
discussions about problems
involving linear and
quadratic functions
Linear functions:
- In group, determine the equation of
o Slopes
straight line passes through:
o Cartesian
equation
o a point and given its slope
o Conditions for
o two points
lines to be
o a point and parallel to a given line
parallel or
o a point and perpendicular to a
perpendicular
given line
line
- Individually, given a quadratic
Quadratic functions
function, say whether its graph is
o Table of values
concave up or down and determine
o Vertex of
the intercepts, the vertex, then make a
parabola
o Axis of symmetry table of values hence sketch the
parabola.
o Intercepts
o Graph in
Cartesian plane
Links to other subjects: Physics (linear motion), …
Assessment criteria: Solve problems involving linear or quadratics functions and interpret the graphs of quadratic functions.
Materials: Geometrical instruments, Calculators.
Page 49 of 60
Topic Area: ALGEBRA (MONEY )
S3 MATHEMATICS
Unit 7: Compound interest , reverse percentage and compound proportional
change
No. of lessons: 20
Key unit Competency: To be able to solve problems involving compound interest, reverse percentage and proportional change using multipliers
Learning Objectives
Knowledge and
understanding
Skills
Attitudes and values
Content
Learning Activities
- Define compound
- Solve problems involving
- Appreciate the role of compound
- Reverse percentages
In group:
interest, reverse
reverse percentages and
interest in banking, in financial
- Compound interest
- Solve given problems
percentage , compound
compound interest
activities
and its applications in
involving reverse
proportional change and - Apply compound interest in - Appreciate that in case of
contextual situations (
percentages and compound
continued proportional
solving mathematical
compound interest , saving and
e.g. in banking, in
interest
- Find a reverse
problems involving savings
investing money can increase its
financial activities...)
- Compare the overall values
percentages in a given
or calculations in any other
value.
of given different goods,
mathematical problem
financial activity.
- Show concern of paying taxes and - Compound
hence draw conclusion.
- Determine a compound - Apply reverse percentage
being honest in daily activities
proportional change or - In group, solve problems
interest in a given
and compound proportional involving money.
Continued proportions involving compound
mathematical problem
change in solving real life - Develop logical and critical thinking
proportional change or
- Simplify ratio in their
mathematical problems
while solving problems involving
continued proportions
simplest form
compound interest, reverse change,
and continued proportional change
Links to other subjects: The unit is linked with Economics, Entrepreneurship, Financial education and other related fields.
Assessment criteria: Use mathematical concepts and skills to solve problems involving compound interest, reverse percentage and proportional change
Materials: Text books, coins, bills, geometrical instruments, receipt papers, Electronic materials, ATM cards, Calculators.
Page 50 of 60
Topic Area: GEOMETRY
S3 MATHEMATICS
Unit 8: RIGHT ANGLED TRIANGLES
No. of lessons: 18
Key Unit Competency: to be able to find side lengths and angles in right angled triangles using trigonometric ratios
Learning Objectives
Knowledge and
understanding
-
-
Give and define
the elements of
a right angled
triangle
Show
relationship
between the
elements of a
right angled
triangle.
Skills
Attitudes and values
- Use Pythagoras’
- Appreciate the
theorem to find
importance of right
relationship
angled triangles in
between the
various situations.
elements of a right
- Promote team work
angled triangle.
spirit.
- Solve problems about - Show concern on
right angled triangle
patience, mutual
using the properties
respect, tolerance and
of elements of a right
curiosity in the solving
angled triangle and
and discussion about
Pythagoras theorem.
problems involving
right angled triangles
Content
- Median through the vertex of the
right angle
- Height through the vertex of a
right-angled triangle and the sides
of the right angle
- Height through the vertex of a
right-angled triangle and the
lengths of the segments on the
hypotenuse
- Determination of the sides of
right angled triangle given their
orthogonal projection on the
hypotenuse.
- Trigonometric ratios in a right
angled triangle: Sine, cosine and
tangent
Learning Activities
-
-
-
-
In group, find the missing sides of a triangle
in each case draw the clear diagram before
starting to calculate
In pairs, given two sides of right angled
triangle but not hypotenuse. Find the
length of hypotenuse and then calculate the
length of height and the median
corresponding to that hypotenuse
In groups, given lengths of segments
defined by the height on hypotenuse, find
length of sides of that triangle, the height
and the median
Individual, given acute angle and length of
one side; use sine, cosine and tangent to
find the length of other sides.
Links to other subjects: Technical drawing, scientific drawing…
Assessment criteria: Construct mathematical arguments about right angled triangle to solve related problems.
Materials: Calculators, geometrical instruments.
Page 51 of 60
Topic Area: GEOMETRY
S3 MATHEMATICS
Sub-topic Area: SHAPE AND ANGLES
Unit 9: CIRCLE THEOREMS
No. of lessons: 18
Key Unit Competency: To be able to construct mathematical arguments about circle and use circle theorems and disk to solve related problems.
Learning Objectives
Knowledge and
understanding
- Recognise and
identify the
elements of a
circle
- Identify angle
properties in a
circle.
Skills
- Find the length of
elements of a circle
- Calculate the area
of disk and its
sector.
- Use the angle
properties of lines
in circles to solve
problems
- Use tangent
properties to solve
circle problems
Content
Learning Activities
Attitudes and values
-
-
Develop clear, logical
and coherent thinking
Appreciate the
importance of circle
theorems in dividing
into sectors
Promote team work
spirit when working
in group.
Show concern on
patience, mutual
respect, tolerance and
curiosity in the solving
and discussion about
problems involving
circle theorems and
disk
-
Elements of a circle and disk: center, radius,
diameter, circumference, area, chord, tangent,
secant, sector.
Circle theorems:
First circle theorem: angles at the centre and at
the circumference.
Second circle theorem: angle in a semicircle.
Third circle theorem: angles in the same
segment.
Fourth circle theorem: angles in a cyclic
quadrilateral.
Fifth circle theorem: length of tangents.
Sixth circle theorem: angle between circle
tangent and radius.
Seventh circle theorem: alternate segment
theorem.
Eighth circle theorem: perpendicular from the
centre bisects the chord
 In group, discuss about and
solve problems involving two
concentric circles, such as areas,
lengths, ratios ...
 In pairs, for given circles
involving arcs, find minor arc
length, major arc length, minor
sector area and major sector
area.
 In group, discuss about the
properties of points in a cyclic
quadrilateral.
 In group, discuss about the
properties of chord through
given situation involving circle
theorem.
Links to other subjects: Technical drawing, scientific drawing…
Assessment criteria: Construct mathematical arguments about circle and use circle theorems and disk to solve related problems.
Materials: Calculators, geometrical instruments.
Page 52 of 60
Topic Area: GEOMETRY
S3 MATHEMATICS
Unit 10: COLLINEAR POINTS AND ORTHOGONAL VECTORS
No. of lessons: 6
Key Unit Competency: to be able to apply properties of collinearity and orthogonality to solve problems involving vectors.
Learning Objectives
Knowledge and
understanding
State the conditions
and properties of
collinearity and
orthogonality
Skills
- Use definition and
properties to show
whether:
o Three given points
are collinear or not.
o Two vectors are
orthogonal or not.
Attitudes and values
Content
Learning Activities
- Appreciate the use of properties of
- Conditions for:
In group,
collinearity and orthogonality to solve
o Points to be collinear
problems about vectors in two
o Vectors to be orthogonal -Discuss whether three
points are collinear in the
dimensions.
- Problems about points and
given situations
- Show concern on patience, mutual
vectors in two dimensions
Discuss
whether vectors
respect, tolerance and curiosity in the
are parallel ororthogonal.
solving and discussion about
problems involving vectors in two
dimensions
Links to other subjects: Technical drawing, scientific drawing, Physics (forces, motion, …), Chemistry, …
Assessment criteria: Solve problems involving points and vectors in two dimensions
Materials: Calculators, geometrical instruments.
Page 53 of 60
Topic Area: GEOMETRY
S3 MATHEMATICS
Unit 11: ENLARGEMENT AND SIMILARITY IN 2D
No. of lessons: 22
Key Unit Competency: To be able to solve shape problems about enlargement and similarities in 2D
Learning Objectives
Knowledge and
understanding
- Define enlargement
- Define similarity
- Identify similar
shapes
- List properties of
enlargement and
similarities.
Skills
- Determine the linear scale
factor of an enlargement
- Find centre of an
enlargement
- Construct an image of an
object under unlargement
- Use properties of
enlargement and
similarities to transform a
given shape.
- Find lengths of sides, area,
and volume of similar
shapes.
- Construct an image of an
object under composite
and inverse enlargement.
Attitudes and values
Content
Learning Activities
- Appreciate the
- Definition of enlargement.
- In group, construct the images of given
importance of
- Definition similarity.
shapes under given instructions related
enlargement and - Examples of similar shapes ( similar to enlargement and compare the images
similarities to
triangles, similar cylinder,etc)
to the initials. Discuss about the
transform shapes - Properties of enlargement and
properties of enlargement and
- Develop patience, similarities.
similarities used to transform those
mutual respect, - Determining linear scale factor of
shapes to their images.
tolerance and
enlargiment
- In pairs, construct an image of a given
team work spirit - Determining centre of enlargement. object under composite and inverse
in solving and
- Finding lengths of sides of similar
enlargement.
discussing
shapes using Thales theorem
- Individually, show similar shapes in
problems
- Areas of similar shapes
given different varieties of shapes and
involving
- Volumes of similar objects.
find the linear scale factor and center of
enlargement and - Composite and inverse
enlargement for each case.
similarities
enlargements
- In groups, find the area and volume of
given similar shapes and solids.
Links to other subjects: Physics, engineering, construction, technical drawing, scientific drawing, etc
Assessment criteria: Solve shape problems about enlargement and similarities in two dimension
Materials: Geometrical instruments.
Page 54 of 60
Topic Area: GEOMETRY
S3 MATHEMATICS
Unit 12: Inverse And Composite Transformations in 2D
No. of lessons: 12
Key Unit Competency: to be able to solve shape problems involving inverse and composite transformations.
Learning Objectives
Knowledge and
understanding
Skills
- State and explain
- Construct an image of an
properties of
object under composite
composite and
and inverse
inverse
transformation in 2D
transformations in
- Solve problems involving
2D
inverse and composite
- Identify type of
transformations in 2D
transformation used
in given drawings in
2D
- Show an image of an
object from different
transformed shapes
in 2D
Attitudes and values
Content
Learning Activities
- Appreciate the importance - Composite
- Individually, construct an image of a given
of inverse and composite
transformations:
object under inverse and composite
transformations to
o Composite
transformations in 2D
transform shapes
translations in 2D - In groups; observe, discuss and show
- Show concern on patience,
o Composite
images of objects from given different
mutual respect, tolerance
reflections in 2D transformed shapes in 2D and give the
and curiosity in the solving
o Composite
properties of inverse and composite
and discussion about
rotations in 2D
transformations used to transform those
problems involving
o Mixed
shapes.
inverse and composite
transformations - In pairs, construct image of objects under
transformations.to
in 2D
mixed transformations
transform
- Inverse
transformations in 2D
Links to other subjects: Physics, engineering, construction, technical drawing, scientific drawing.
Assessment criteria: Solve problems involving inverse and composite transformations of shapes in 2D
Materials: Geometrical instruments, etc
Page 55 of 60
Topic Area: STATISTICS AND PROBABILITY
S3 MATHEMATICS
Unit 13: STATISTICS (BIVARIATE DATA)
No. of lessons:12
Key unit Competency: To be able to Collect, represent and interpret bivariate data.
Learning Objectives
Knowledge and
understanding
- Define bivariate data
- Make a frequency
distribution table of
collected bivariate
data
- Interpret scatter
diagram
- Identify type of
correlation on a
scatter diagram
Skills
- Draw scatter diagram for
bivarite data and
indicate the type of
correlation.
- Analyze a scatter
diagram and infer
conclusion.
Content
Learning Activities
Attitudes and values
- Develop clear, logical and coherent
thinking while drawing
conclusion related to bivariate
data or scatter diagram .
- Appreciate the use of scatter
diagram to represent information.
- Show concern of patience, mutual
respect, tolerance, and curiosity in
the bivariate data collection,
representation and interpretation.
- Definition and examples of - In groups, Collect bivariate data
bivariate data
and organize them in frequency
- Frequency distribution table
distribution table and plot them
of bivariate data
on a scatter diagram.
- Scatter diagram.
- Types of correlation:
- In pairs, observe given
o Positive correlation
information on the graphs
o Negative correlation
(scatter diagrams), mention the
type of correlation, analyze,
interpret them and infer
conclusion.
Links to other subjects: All subjects
Assessment criteria: Solve problems involving Collection, representation and interpretation of bivariate data
Materials: Calculators, geometrical instruments.
Page 56 of 60
6. REFERENCES
1.
2.
3.
4.
5.
Alundria, I. & al (2009). Secondary Mathematics (student’s book2). MK publishersLtd.
Atkinson, C. & Mungumiyo, U. (2010). New general Mathematics: teacher’s guide. Pearson education ltd.
Ayres ,F. &al (1992). Mathématiques de base. McGraw-Hill Inc, Paris.
Backhouse, J.K. & Al (1985). Pure Mathematics 1(Fourth edition). Longman.
Ball, B. & Ball, D. (2011). Rich task Maths2 engaging mathematics for all learners. Association of Teachers of
Mathematics: England
6. Ball, D. (2003). Forty harder problems for classroom. Association of Teachers of Mathematics: England
7. Crawshaw, J. & Chambers, J. (2002). Advanced Level Statistics.Nelson Thornes Ltd.
8. Curriculum Planning and Development Division (2006). Secondary Mathematics Syllabuses. Ministry of
Education: Singapore
9. Hatch, G. (2004). What kind of Game is Algebra. Association of Teachers of Mathematics: England
10. Kamba, G. (2010). Secondary mathematics (student’s book3). MK publishersLtd.
11. Kasirye, S. & al (2009). Secondary Mathematics (student’s book1). MK publishersLtd.
12. Laufer, B. H. (1984). Discrete Mathematics and Applied Modern Algebra.PWS publishers.
13. Les Frères de l’Instruction Chrétienne (1961). Géométrie plane. La Prairie, P.Q, Ottawa.
14. Lyonga, E K. (2004). Mathematics for Rwanda: student book. Macmillan.
15. Macrae, M. & al (2010). New General Mathematics: student book1. Pearson education ltd.
16. Macrae, M. & al (2010). New General Mathematics: student book2. Pearson education ltd.
17. Macrae, M. & al (2010). New General Mathematics: student book3. Pearson education ltd.
18. Ministry of Education (2007). The New Zealand Curriculum. New Zealand
19. National curriculum Development Center (2006). Mathematics curriculum for ordinary Level.
Ministry of Education : Rwanda
20. National Curriculum Development Centre (2008). Mathematics Syllabus: Uganda Certificate of Education. Ministry
of Education and Sports: Uganda.
21. National Curriculum Development Centre (2013). Mathematics Learning Area Syllabus. Cambridge Education.
Uganda
22. Nichols & al (1992). Holt pre-algebra. Holt, Rinehart and Winston Inc.
23. Okot-Uma, R. & al (1997). Secondary school Mathematics: student book1. Macmillan: Uganda.
24. Okot-Uma, R. & al (1997). Secondary school Mathematics: student book2. Macmillan: Uganda.
Page 57 of 60
25. Okot-Uma, R. & al (1997). Secondary school Mathematics: student book3. Macmillan: Uganda.
26. Rayner, D. (2011). Extended Mathematics for Cambridge IGCSE. Oxford University Press.
27. Singh, M. (2002). Pioneer Mathematics. Dhanpat RAI&CO.(PVT).
28. University of Cambridge (2013). Cambrige IGCSE, International Mathematics. UCLES:UK
Page 58 of 60
7. APPENDIX: SUBJECTS AND WEEKLY TIME ALLOCATION FOR O’ LEVEL (S1-S3)
When learners go to secondary school, they study twelve ‘core’ subjects and an ‘elective’ subject, selected by the school. In
addition, there are three compulsory ‘co-curricular’ activities.
Core subjects
Weight
(%)
Number of Periods
(1 period = 40 min.)
S1
S2
S3
1. English
11
5
5
5
2. Kinyarwanda
7
3
3
3
3. Mathematics
13
6
6
6
4. Physics
9
4
4
4
5. Chemistry
9
4
4
4
6. Biology and Health Sciences
9
4
4
4
7. ICT
4
2
2
2
8. History and Citizenship
7
3
3
3
9. Geography and Environment
7
3
3
3
10. Entrepreneurship
4
2
2
2
11. French
4
2
2
2
12. Kiswahili
4
2
2
2
13. Literature in English
2
1
1
1
Page 59 of 60
Sub Total
41 periods
41 periods
41 periods
II. Elective subjects: Schools can choose 1 subject
Religion and Ethics
4
2
2
2
Music, Dance and Drama
4
2
2
2
Fine arts and Crafts
4
2
2
2
Home Sciences
4
2
2
2
Farming (Agriculture and Animal
husbandry)
4
2
2
2
Physical Education and Sports
2
1
1
1
Library and Clubs
2
1
1
1
100
45
45
45
30
30
30
1170
1170
1170
III. Co-curricular activities (Compulsory)
Total number of periods per week
Total number of contact hours per week
Total number of hours per year
(39 weeks)
Page 60 of 60