i
Mathematics
Activities
Teacher’s Guide
Grade 3
T. Mukhuri
M. Okello
M. Mwimani
J. Mwaniki
S. Ndinwa
ii
Published by
Longhorn Publishers Ltd.,
Funzi Road, Industrial Area,
P. O. Box 18033-00500,
Nairobi, Kenya.
Longhorn Publishers (Uganda) Ltd.,
Plot 4 Vubyabirenge, Ntinda
P. O. Box 24745
Kampala, Uganda
Longhorn Publishers (Tanzania) Ltd.,
New Bagamoyo/Garden Road
Mikocheni B, Plot No. MKC/MCB/81,
P O Box 1237
Dar es Salaam, Tanzania.
Longhorn Publishers (Rwanda) Ltd.,
Remera opposite COGE Bank
P.O. Box 5910
Kigali, Rwanda
© T. Mukhuri, M. Okello, M. Mwimani, J. Mwaniki, S. Ndinwa, 2018
e moral rights of the authors have been asserted.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system
or transmitted in any form or by any means, electronic, mechanical, photocopying, recording
or otherwise without the prior written permission of the copyright owner.
First published 2018
ISBN 978 9966 64 046 8
Printed by Ramco Printing Works Ltd,
Unit 2, Ramco Industrial Complex,
Before Imara Daima Turn o, Mombasa Road,
P. O. Box 27750 - 00506,
Nairobi, Kenya.
iii
CONTENTS
PART ONE: METHODOLOGY AND THE SUBJECT ......................................... 1
Introduction ....................................................................................................................... 1
How the syllabus is approached in this course ............................................................... 1
e Mathematics Teacher’s Guide.................................................................................... 6
SCHEMES OF WORK ...................................................................................................... 14
LESSON PLAN .................................................................................................................. 17
Assessment and evaluation ............................................................................................... 20
Emerging issues.................................................................................................................. 24
PART TWO: TEACHING GUIDELINES
Strand 1: Numbers
Sub-Strand 1: Number Concept .................................................................... 31
Sub-Strand 2: Whole Numbers...................................................................... 35
Sub-Strand 3: Fraction.................................................................................... 51
Sub-Strand 4: Addition................................................................................... 57
Sub-Strand 5: Subtraction .............................................................................. 71
Sub-Strand 6: Multiplication.......................................................................... 82
Sub-Strand 7: Division.................................................................................... 92
Strand 2: Measurement
Sub-Strand 8: Length..................................................................................... 98
Sub-Strand 9: Mass ........................................................................................ 104
Sub-Strand 10: Capacity ................................................................................. 110
Sub-Strand 11: Time ....................................................................................... 115
Sub-Strand 12: Money .................................................................................... 124
Strand 3: Geometry
Sub-Strand 13: Position & Direction............................................................. 132
Sub-Strand 14: Shapes .................................................................................... 135
iv
1
Part One
Methodology and the Subject
Introduction
How the syllabus is approached in
this course
is book is comprehensively designed
as a Teacher’s Guide in teaching/learning
Mathematics patterns for Grade 3.
Mathematics is the study of people and
the environment in which they live in,
and the relationship between measuring,
numerals and the quantities in the
environment. Mathematics is a dynamic
science subject that responds to constant
changes in skills, attitudes, knowledge,
values and quantities in the society and
the environment. It cuts across many
subject areas such as Science Activities,
Environmental activities, Religious
activities, Language activities, Psycho-
motor activities and Creative Activities.
Mathematics background, nature and
scope on new curriculum
Mathematics is the science of working
with numerals, how they relate to each
other and how they can be applied in the
environment. is environment includes
social, physical, spiritual and emotional
world. is consists of living and
non-living things. is involves use of
numbers to measure certain models,
values and experiences we come across in
our day to day real-life situations.
Mathematics is a science which is based
on key inquiry questions on why and how
things happen and exist the way they are.
e Structure of the syllabus
Mathematics subject is taught and learned
at all levels as a core subject. At every
grade, the syllabus is structured in strands
and further broken down into sub-
strands.
Each sub-strand:
• Is aligned with the number of lessons.
• Has key outcome competence
whose achievement is pursued by
all teaching and learning activities
undertaken by both the teacher and
the learners.
• Key competence is broken into three
types of learning outcomes as namely:
(a) Knowledge I: Learning
Objectives relating to knowledge and
understanding. ese are associated
with Lower Order inking Skills
(LOTS).
(b) Skills II and Type III: ese
learning objectives relate to
acquisition of skills, Attitudes and
Values. ey are associated with
Higher Order inking Skills
(HOTS). – ese learning objectives
are actually considered to be the ones
targeted by the present reviewed
syllabus.
2
that will enable them interact with the
environment by doing practical activities.
It is from this background that the Math-
ematics syllabus for Grade 3 was reviewed
to ensure that it is responsive to the needs
of the learner shi from knowledge-based
learning to competence-based learning.
Competence-based learning refers to
systems of instruction, assessment,
upgrading, and academic reporting that
are based on learners to demonstrate that
they have acquired and learnt the
pre-requisite knowledge, skills and
attitudes as they progress from lower
level to high level of education. Apart
from being integrative, the newly revised
syllabus guides the interaction between
the teacher and the learner in the learning
process. It further puts greater emphasis
on skills a learner should acquire during
each unit of learning. As a competency-
based syllabus, it elaborates on the three
aspects of knowledge, skills and attitudes
in Mathematics.
Teaching and Learning Mathematics
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 national census process,
scientific research, etc. In addition, some
partinent and contemporary issues such
as citizenship are incorporated into some
of the mathematical units to enhance
partrotism and social cohesion in the
Kenyan society.
• Has a content area which indicates the
scope of coverage of what a teacher
should teach and learner should learn
in line with stated learning objectives.
• suggests learning activities that are
expected to engage learners in an
interactive learning process as much
as possible (learner-centered and
participatory approach).
• is linked to other subjects, its
assessment criteria and the materials
(or Resources) that are expected to be
used in teaching and learning process.
In all, the Mathematics syllabus for Grade
3 has three strand areas namely:
• Numbers
• Measurement
• Geometry
e topic areas are sub-divided into 14
sub-strands, namely:
1. Number Concept
2. Whole numbers
3. Fraction
4. Addition
5. Subtraction
6. Multiplication
7. Division
8. Length
9. Mass
10. Capacity
11. Time
12. Money
13. Position & Direction
14. Shapes
Background Information on new
Curriculum
e aim of a competence-based curriculum
is to develop in the learners competences
3
of non-formal activities applied here for a
Grade 3 Learner are:
• Tree planting in schools.
• Measuring mass of items.
• Measuring containers of water.
• Taking turns in playing games.
• Counting trees in school compound.
• Sharing of library books.
• Cleaning the school compound
• Play games involving multiplication,
division, addition, subtraction and
number concept.
Whole numbers, length, money, mass,
capacity, time, shape, position and
direction.
• Watering owers and trees in the
school compound.
• Measuring length of buildings in
schools.
• Measuring and marking play grounds
for games.
• Time keeping during games or sports
or lesson attendance.
• Participating in games activities and
scouting.
• Marking of the games and sports
elds.
(d) Mathematics is linked to establishing
learner’s ability and values.
• Responsibility
• Unity
• Integrity
• Respect
• Patriotism
• Love
Mathematics is the key to the Kenyan
education vision 2030 of developing a
knowledge-based and technology-led
economy since it provides all the required
knowledge and skills to be used in different
learning areas. Therefore, Mathematics
is an important subject as its linked to
other subjects. This new curriculum
will address gaps in the current Kenya
Education System
Competence-based learning areas
(a) Mathematics focuses on development
of core competences as designed
below:
(i) Learning to learn
(ii) Communication and
collaboration
(iii) Imagination and creativity
(iv) Self-eciency
(v) Critical thinking
(vi) Citizenship
(vii) Digital numeracy
(b) Mathematics draws its content from
various duties to other subjects such
as:
(i) Environmental activities
(ii) Religious activities
(iii) Language activities
(c) Mathematics involves other non-
formal activities which supports
learning in the school environment.
ese non-formal activities are designed
to assist the learner to understand the
relationship of human beings with the
activities in the surrounding environment
of the past, present and future. Examples
4
information to the learners so that they are
aware!
Links to attitudes and values
Values are standards that guide an
individual on how to respond or behave
in a given circumstance. e teaching
of values will facilitate the achievement
of the curriculum reforms’ vision with
respect to moulding ethical citizens.
Truly engaging with the learning, requires
appropriate attitudes and values that relate
to the lesson.
Attention to Special Education Needs
is section provides a way that the
teacher can cater for the dierent special
education needs with a consideration to
the nature and requirements of the lesson.
Suggested Community Service Learning
e learner is part of a larger community
and therefore, education should lead
the youth of the country to accept
membership of this community with all
the obligations and responsibilities, rights
and benets that this membership entails.
Working collectively in assisting the
community in various development and
environmental activities.
Types of competences and their
acquisition
Competences are statements of the
characteristics that learners should
demonstrate which indicate they are
prepared and have the ability to perform
independently in professional practice.
Types of competences incorporated in this
curriculum are:
Core Competences to be
developed:
A competence-based approach enables
meaningful connections within and
between subject areas. e seven core
competences to be achieved by every
learner are:
• Communication and collaboration
• Self-ecacy
• Critical thinking and problem solving
• Citizenship
• Digital literacy
• Learning to learn
• All these will be achieved once learners
have met all the learning objectives in
the lesson.
Key inquiry questions
e question statement is a comprehensive
learning statement presented as a starting
point. It is a question that is meant to make
the learners want to nd out the solutions
in the course of the lesson.
Links to PCIs
Instructions should set out approach
to Pertinent and contemporary issues.
Examples are life skills, citizenship skills,
animal welfare, environmental education
and many more.
Links to other subjects
It is important for learners to gain an
understanding of the interconnections
between dierent subjects so that learning
in each subject is reinforced across the
curriculum. is platform does exactly
that. It prepares the teacher to pass this
5
help learners to take initiatives and
use imagination beyond knowledge
provided in classroom to generate new
ideas and construct new concepts.
5. Research skills
is will help learners to nd answers
to questions based on existing
information and concepts and use it
to explain phenomena from gathered
information.
6. Communication in ocial languages
Teachers, irrespective of being language
teachers should ensure the proper
use of the language of instruction by
learners (which is English at O- level).
e teachers should communicate
clearly and condently and convey
ideas eectively through spoken and
written English by applying appropriate
grammar and relevant vocabulary.
7. Co-operation, inter-personal
management and life skills
is will help the learner to co-operate
in a team in whatever task assigned
and to practice positive ethical moral
values while respecting rights, feelings
and views of others. Perform practical
activities related to environmental
conservation and protection. Advocate
for personal, family and community
health, hygiene and nutrition and
responding creatively to a variety of
challenges encountered in life.
8. Lifelong learning to learn
e acquisition of such skills will help
learners to update knowledge and skills
1. Numeracy
• Computing accurately using the four
mathematical operations.
• Manipulating numbers, mathematical
symbols, quantities, shapes, and
gures to accomplish a task involving
calculations, measurements and
estimations.
• Use numerical patterns and
relationships to solve problems related
to everyday activities like commercial
context and nancial management.
• Interpreting basic statistical data using
tables, diagrams, charts, and graphs.
2. ICT and digital competences
• Locating, extracting, recording and
interpreting information from various
sources.
• Assessing, retrieving and exchanging
information via internet or cell phones.
• Using cell phones and internet for
leisure and for money transactions.
• Using computer keyboard and mouse
to write and store information.
• Using information and communication
technologies to enhance learning and
teaching (all subjects).
3. Critical thinking and problem solving
skills
e acquisition of such skills will
help learners to think imaginatively,
innovatively and broadly and be able to
evaluate and nd solutions to problems
encountered in their surroundings.
4. Creativity and innovation
e acquisition of such these skills will
6
be applied with the necessary rig or,
intellectual honesty to promote critical
thinking while systematically pursuing the
line of thought.
e Mathematics Teacher’s Guide
is Teacher’s Guide is written to help you
use the pupil’s Book appropriately and
teach eciently. Both the Teacher’s Guide
and the Pupil’s Book are closely related
and follow the new syllabus.
Organisation of the lessons/activity
e Teacher’s Guide follows the syllabus
and has a suggested lessons/activities for
each strand, sub-strand. Each lesson has:
1. Preparation
2. Title of the activity
3. Specic learning outcomes
4. Suggested number of lessons (time)
5. Background information
(Pre-requisite to the current activity
being taught.)
6. Knowledge, skills, attitudes and values
to be acquired and be developed
7. Teaching and learning resources
8. Guideline to lesson/activity
development
9. Assessment
10. Answers
Specic learning outcomes
ese are taken from the syllabus and help
to focus the lesson concept development.
All the specic learning outcomes for the
whole year are covered in this course.
with minimum external support.
e learners will be able to cope with
evolution of knowledge advances for
personal fulllment in areas that are
relevant to their improvement and
development.
Mathematics and developing
competences
e national policy documents based
on national needs identify competences
that will develop higher order thinking
skills and help the pupils learn subject
content and promote application
of acquired knowledge and skills.
rough observations, constructions,
manipulation-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
co-operation and communication,
critical thinking and problem-solving
skills. is will be realised when learners
make presentations leading to inferences
and conclusions at the end of learning a
sub-strand. is will be achieved through
learner group work and cooperative
learning that in turn will promote
interpersonal relations and teamwork.
e acquired knowledge in learning
Mathematics should develop a responsible
citizen who adapts to scientic reasoning
and attitudes and develops condence
in reasoning independently. e learner
should show concern of individual
attitudes, environmental protection and
comply with the scientic method of
reasoning. e scientic method should
7
Generally teaching and learning resources
could include materials such as:
• Illustrations, ashcards, number cards,
photographs, cut-outs
• Mathematics Pupil’s textbooks
• Other reference textbooks, newspapers
and magazines
• Field visits
• Resource persons
• Any published and unpublished
information
• Dictionaries
• You can also access important current
information from the internet. You
can browse the internet, download
information and use it as reference
material for teaching. However, always
verify the information you download
from the internet, as some of it may not
be accurate.
Knowledge, skills to be developed,
attitudes and values to be acquired
Every sub–strand in the syllabus is
designed to instill, develop and promote
certain knowledge, skills and attitudes and
values in the pupil. Under every SUB-
STRAND heading, a list of knowledge,
skills, attitudes and values have been
provided to enable you to emphasize their
development as you progress through the
lesson activity
e national goals of education
emphasises this in length as stated here:
• Promote sound moral and religious
values.
• Foster nationalism, patriotism and
promote national unity.
Background information
(Pre-requisite is the current lesson
topic)
is gives you a brief outline and, in
some cases, more detail of what you are
expected to cover in the lesson, as the
information given in the Pupil’s Book is
limited to the level of understanding of
the learners.
Teaching and learning resources
Reference materials
ese are teaching resources which contain
written materials that will assist you to
gain deeper knowledge to disseminate to
the pupils. is is a list of teaching and
learning resources given under every sub-
strand heading to supplement and ease the
acquisition of knowledge, skills, attitudes
and values through the pupils’ activity.
Other materials listed are meant to enrich
the lesson. e list is by no means limited
and therefore you are encouraged to collect
more where necessary.
Teaching Aids
Learning resources are basically readily
and easily available within or around
the school environment. ey include
material that assist teaching and learning
through explanations, demonstrations,
imitations, observations, modeling and
other teaching approaches. ese teaching
and learning resources include, models,
equipment, tools, photographs, cut-outs,
illustration, charts, diagrams resource
persons, environment and other materials
that can help the learners to understand
the concept being taught.
8
e nature of the scientic method
demands learners to be honest with
themselves as they record results and
make unbiased conclusions. ey should
be aware of the danger involved in
generalising out of limited information.
ey should be open-minded and able
to distinguish between propaganda and
truth.
Some of the attitudes that learners should
develop include:
• Responsibility – A learner should
be responsible enough to eect tasks
apportioned and take good care
of apparatus during and aer an
investigation.
• Co-operation – Learners will oen be
working in groups while carrying out
investigations and need therefore to
co-operate with all other members of
the group.
• Curiosity – Learners should have a
curious attitude as they observe things
and events around them. is is the
rst step towards solving a problem.
• Self-condence – Learners should have
the will to attempt to solve a problem.
e feeling of self-condence can be
strengthened in young learners if they
experience many small successes that
win approval and encouragement from
the teacher. e problems that learners
attempt to solve should not be so
dicult that they lead to frustration.
• Honesty – As they make observations,
record, analyse results and draw
conclusions.
• Patience – Learners should be patient
for the results of an experiment that
may take time to manifest.
• Promote individual development and
self-fulllment.
• Promote respect for and development
of Kenya’s rich and varied cultures.
• Promote international consciousness
and foster positive attitude towards
other nations.
• Promote positive attitudes towards
health and environmental protection.
erefore, under this heading , a list of
values and positive attitudes have been
provided for you to use as a checklist to see
whether the specied National Goals are
being achieved.
Important attitudes for eective
learning Mathematics
Attitude refers to the orientation of the
mind with regard to a thing or a person.
It determines one’s behaviour or reaction
to the thing or person. In a classroom
situation, the attitudes of the teacher
and the learners determine the level and
eectiveness of the interactions between
them, which in turn aect learning. Good
attitudes in the learners and teachers is
particularly important in the delivery of a
competence based curriculum that require
high level interactions and co-
operation between learners, as they use
discovery approach to acquire knowledge
and competences, with the teacher as the
facilitator.
(a) In learners
ere are certain useful attitudes, which
the teacher should help develop in the
learners as they carry out investigations in
Mathematics. Mathematics as a problem
solving discipline is expected to make an
impact on a learner’s general behaviour.
9
taught activity to establish how much
background knowledge the pupil already
have on the sub-strand they learned in
relation to the one they are going to learn
in order to start at an appropriate point.
It may also be used to quickly assess how
much they remember from the previous
lesson. At this stage you are at your own
choice to organize your learners into
suggested pairs or groups depending
on the number of learners you have in
class. Simple and short songs can also be
involved here to open the lesson tone with
high mood of learning.
Step II: Content development
At this stage you are guided on the I
DO, WE DO and YOU DO process.
e teacher is provided with actual
information to present to the learners.
You are rst referred to the Pupil’s
Book, relevant sub-strand and the page
reference.
I do- this is where you are advised to
use your own knowledge to demonstrate,
explain on various examples and enrich
the lesson from any other relevant
information from the environment
while the learners listen, observe and
ask questions where necessary. You are
advised to make a summary of the key
points and steps on the chalkboard as you
teach this part.
We do- this is the stage where the
teacher together with the learner are
involved in the activities. However, at
this stage the learners do most of the
activities in pairs or in group work while
the teacher guides, directs and supervises
the learners.
• Practical approach to problem solving.
Learners should seek answers to their
questions and problems by carrying
out investigations wherever possible.
(b) In Teachers
A good teacher should make the following
capabilities:
• Engage students in variety of learning
activities.
• Apply appropriate teaching and
assessment methods.
• Adjust instructions to the level of the
learner.
• Creativity and innovation.
• Makes connections/relations with
other subjects.
• Show a high level of knowledge of the
content.
• Develop eective discipline skills
manage adequately the classroom
• Good communicator.
• Guide and counsellor.
• Passion for children teaching and
learning.
Guideline to lesson/activity
development
e suggested lesson/activity development
is meant to be a guideline to the teacher
as you teach the learners at the classroom
level.
e lesson/activity is divided into the
following steps:
Step I: Introduction
is is the stage the teacher and the
learners do quick review of the previous
10
pupil has absorbed from the content. For
faster and brighter pupils, you could have
extra work set to challenge them.
Step V: Conclusion
is is the stage where you do quick
review of the content taught. is is where
you highlight the main points of the
lesson. You can decide to do this yourself
through statements or by asking pupils
quick and precise oral questions whose
responses will always give the key point of
the lesson.
Answers to exercises
Answers to all the activities and exercises
are placed at the end of the sub-strand
development.
(a) Learner’s role in learning
Mathematics
Learning takes place only when the
learner assimilates the material to be
learnt as is actively engaged in the
learning exercise.
For active participation in learning, the
learner must:
(a) Develop the curiosity, powers of
observation and inquiry by exploring
the local environment.
(b) Raise questions about what is
observed.
(c) Suggest solutions to those questions
and carry out investigations to search
for answers.
(d) Manipulate a variety of materials in
search of patterns and relationships
while looking for solutions to
problems.
e approaches and activities used in
this stage may include: Demonstrations,
Drawing, Group discussions, Role-
playing, Pupils class exercises, Classifying,
Sorting , Grouping, Pairing , Writing
notes, Reciting, Singing, Modeling,
Planting owers, trees……, Watering
ower, trees…., Presentations and
displays, Environmental and digital
games, Field activities and trips near the
school and to other important educational
sites.
Step III: Class work/assessment
You do-is is the stage when the pupils
do much of the learning on their own
but under your guidance. is book
has taken all the aspects of relevant and
interesting activities which encourage the
learners to develop genuine interest and
quickly understand the concept. Here is
where the learners attempt the exercises
given in the Pupil’s Book to enrich their
understanding.
It is at the class work that you will get
to identify the learner’s expectations and
note the progress of the fast, moderate and
slow learners. You are therefore advised
to prepare adequately by having extra
work for fast pupils and organize remedial
session for slow learners. Encourage
pupil’s to learn, communication and
collaboration, imagination and creativity,
self-eciency, critical thinking and
Citizenship and group activities to teach
the learners the importance of working
together.
In the Pupil’s Book, the exercises are
placed at the end of every lesson activity.
ey are meant to assess how much each
11
• Using and developing skills of
organizing and interpreting data,
reasoning, proposing explanations,
making predictions based on what they
think or nd out.
• Working collaboratively with others,
communicating their own ideas and
considering others’ ideas.
• Expressing themselves using
appropriate mathematical terms and
representations in writing and talk.
• Engaging in lively public discussions in
defense of their work and explanations.
• Applying their learning in real-life
contexts.
• Reecting self-critically about the
processes and outcomes of their
inquiries.
During this reciprocal interaction, what
learners will acquire is not only content
knowledge, but a number of skills
including how to approach a problem,
identify important resources, design
and carry out hands-on investigations,
analyze and interpret data, and, perhaps
most importantly, recognise when they
have answered the question or solved the
problem.
(b) Teacher’s role in learning and
teaching
e teacher will rather be “the guide on
the side” who acts as facilitator in a variety
of ways which include:
• Encouraging and accepting learner
autonomy and initiative.
• Using raw data and primary sources,
along with manipulative, interactive,
and physical materials.
e competence-based approach
considers the learning process to involve
the construction of meaning by learners.
Simply, it emphasises the need for children
to think about mathematical activity in
order to understand the Mathematics
concepts being introduced. In this new
dispensation, learners are in the driver’s
seat, which implies that they will construct
their knowledge by posing questions,
planning investigation, conducting
their own experiments, analysing and
communicating results. More specically,
when engaging in inquiry, learners will
describe objects and events, ask questions,
construct explanations, test those
explanations against current knowledge,
and communicate their ideas to others. By
so doing, the learners will take ownership
of the learning process.
Learners’ activities are indicated against
each learning unit reecting their
appropriate engagement in the learning
process. Even though they do not
necessarily take place simultaneously
in each and every Mathematics lesson
and for all levels, over time learners get
involved in the following activities:
• Observing and where possible,
handling and manipulating real
objects.
• Pursuing questions which they
have identied as their own even if
introduced by the teacher.
• Taking part in planning investigations
with appropriate controls to answer
specic questions.
• Using and developing skills of
gathering data directly by observation
or measurement and by using
secondary sources.
12
learning. e teacher must make an eort
to teach the learners how to team up but
still have each learner directly involved
in working with materials, consulting
with the teacher and with fellow learners.
Remember that whatever you do during
the class, the interests of the learner
remain paramount! erefore the teacher
should allow and encourage the learners
to:
• Explore their local environment.
• Ask questions about things and events.
• Make observations.
• Perform simple investigations research
and experiments to seek answers to
their questions.
• Talk to each other and to the other
learners about their experiences,
interests, problems, successes and even
frustrations.
• Play and make models of things that
interest them.
(a) Classroom as a learning environment
Classroom generally refers to the place
where learning takes place. Pupils learn
from everything that happens around
them, from those that they hear, see,
touch, taste, smell and play with etc. It
is therefore important for the teacher
to make his classroom environment
attractive and stimulating. is can be
done by:
• Carefully arranging the furniture and
desks.
• Putting up learning and teaching aids
on the walls. Examples are wall charts
or pictures or photographs.
• Displaying models.
• Using cognitive terminology such as
classify, analyse, predict, and create
when framing tasks.
• Allowing pupil responses to drive
lessons, shi instructional strategies,
and alter content.
• Familiarizing themselves with pupil’s
understanding of concepts before
sharing their own.
• Encouraging students to engage in
dialogue, both with the teacher and one
another.
• Engaging learners in experiences that
pose contradictions to their initial
hypotheses and then encouraging
discussion.
• Providing time for the learners to
construct relationships and create
metaphors.
• Nurturing learners natural curiosity.
• Organising the classroom to create a
suitable learning environment.
• Preparing appropriate materials for
learning activities.
• Motivating learners to make them
ready for learning.
• Coordinate pupils’ activities so that the
desired objectives can be achieved.
• Assessing learners’ activities and
suggest solutions to their problems.
• Assist learners to consolidate their
activities by summarising the key
points learnt.
From time to time, the teacher should
interact with the learners individually or
in groups to diagnose their weaknesses
and frustrations, appraise their eorts,
imagination and excitement. is will
assist and guide them in the task of
13
communicate with all the learners,
and also have a general view of the
whole class.
Grouping learners for learning
Most of the Mathematical activities are
carried out in groups and therefore the
teacher should place 2 or 3 desks against
each other and then have a group of
learners sitting around those desks.
In certain activities, the teacher may
wish to carry out a demonstration. In
this case, the learners should be sitting
or standing in a semicircle, or arranged
around an empty shape of letter “U” such
that each learner can see what the teacher
is doing clearly and without obstruction
or pushing. If the learners are involved in
individual work, each learner can work on
the oor or on the desk or a portion of the
desk if they are sharing. In this case, they
need not face each other.
Grouping learners for learning has
increasingly become popular in recent
years. In fact, the shi from knowledge-
based to competence curriculum will
make grouping the norm in the teaching
learning process. Grouping learners can
be informed by one or all of the following:
(a) Similar ability grouping.
(b) Mixed ability grouping.
(c) Similar interests grouping.
(d) Needs grouping.
(e) Friendship grouping.
(f) Sex grouping.
Grouping learners in a Mathematics class
has several advantages that include:
(a) e individual learner’s progress and
needs can easily be observed.
• Providing objects for play for example
toys.
• Having a display corner in the
classroom where learners display their
work.
• Securing a storage area.
e materials in the classroom should get
the learners thinking and asking questions
about what is around them and encourage
them to do worthwhile activities.
Classroom organisation
A well organised classroom is an asset to
good teaching of Mathematics but there is
no one correct style to suit all classrooms
and situations. However, the teacher
should consider the following factors
when organising the classroom:
(a) Furniture should be well arranged so
as to allow free movement of learners
and the teacher.
(b) Set a corner for storing materials so
as not to obstruct learners or distract
them.
(c) e number of learners in the class
and their ages.
(d) Learners should be reasonably spread
out so that they do not interfere with
one another’s activities.
(e) e series of lessons or activities
going on for a number of days or
weeks such as individual or group
work or whole class.
(f) Classroom itself, that is, positions of
windows, doors such that learners
face the lighted areas of the room.
(g) Personal preferences, though these
should be in the interest of the
learners for example while in class
teaching, you should be able to
14
depending on the nature of the content
being taught at the time.
SCHEMES OF WORK
A scheme of work is a systematic plan of
activities, for a whole term for content to
be covered during the teaching/learning
of a given subject. It is prepared for a
particular class and it contains all the
work to be covered within a specic time.
e scheme of work is derived from the
syllabus and has the following elements:
• Week
• Lesson number
• strand
• sub-strand
• Specic learning outcomes
• Teaching/ learning experiences
• Key inquiry questions
• Teaching / learning resources
• Assessment
• Remarks
When making a scheme of work, you need
to take into consideration factors such
as , holidays, sports, drama and music
festivals. e scheme of work needs to be
comprehensive and clear, so that any other
teacher taking over at any time in the
course of the term can easily continue and
can maintain continuity in the learning
process. Remember the scheme of work
is the property of the school and must be
le behind in case you are transferred to
another school. A sample scheme of work
is shown below:
(b) e teacher-learner relationship is
enhanced.
(c) A teacher can easily attend to the
needs and problems of a small group.
(d) Materials that were inadequate for
individual work can now easily be
shared.
(e) Learners can learn from one another.
(f) Co-operation among learners can
easily be developed.
(g) Many learners accept correction from
the teacher more readily and without
feeling humiliated when they are in
a small group rather than the whole
class.
(h) Learners’ creativity, responsibility
and leadership skills can easily be
developed.
(i) Learners can work at their own pace.
e type of “grouping” that a teacher may
choose depends on:
(a) e topic or task to be tackled.
(b) e materials available.
(c) Ability of learners in the class (fast,
average, slow).
However, the teacher must be exible
enough to adjust or change his/her type of
grouping to cope with new situations.
ere is no xed number of learners
that a group must have. is again will
be dictated by such factors as the task to
be done, the materials, characteristics
of learners in your class, size and the
space available. However, groups should
on average have between four to ve
learners. You can also resort to pair work
15
SAMPLE SCHEME OF WORK
CLASS: GRADE 3
SUBJECT: MATHEMATICS TERM: 1
WK Lesson Strand/
eme
Sub-
strand
Specic
learning
outcomes
Learning
experience
Key
inquiry
questions
Teaching/
learning
resources
Assessment Remarks
1 2 Numbers By the end
of the lesson,
the pupils
should be
able to:
Pupil’s
Book 3
pages
Teaching methods
ere is a variety of possible ways in which a teacher can help the learners to learn.
ese include :
(a) Direct exposition
(b) Discovery or practical activity
(c) Group, class or pair discussion
(d) Project method
(e) Educational visit/ eld trips
(f) Teacher demonstration
(g) Experimentation/ Research
e particular technique that a teacher may choose to use is inuenced by several
factors such as:
• e particular group of learners in the class.
• e skills, attitudes and knowledge to be learnt.
• Learning and teaching aids available in the local environment.
• e teacher’s personal preference.
• e prevailing weather.
• e requirements of mathematical syllabus.
(a) Direct exposition
is is the traditional way of teaching whereby the teacher explains something while the
learners listen. Aer the teacher has nished, the learners may ask questions. However,
remember that in competence-based curriculum, this technique should be used very
minimally.
16
(d) Project method
In this approach, the teacher organises
and guides a group of learners or the
whole class to undertake a comprehensive
study of something in real life over a
period of time such as a week or several
weeks.
Learners using the project method of
studying encounter real-life problems
which cannot be realistically brought
into a normal classroom situation. A
project captures learners’ enthusiasm,
stimulates their initiative and encourages
independent enquiry. e teacher, using
the project method, must ensure that
the learners understand the problem to
be solved and then provides them with
the necessary materials and guidance to
enable them carry out the study.
Disadvantages
If a project is not closely supervised,
learners easily get distracted and therefore
lose track of the main objective of their
study. Studying by the project method
does not work well with learners who have
little or no initiative.
(e) Educational visits and trips/nature
walks
is is a lesson conducted outside the
school compound during which a teacher
and the learners visit a place relevant to
their topic of study. An educational visit/
nature walk enables learners to view their
surroundings with a broader outlook that
cannot be acquired in a classroom setting.
It also allows them to learn practically
through rst-hand experience. In all
“educational visit/nature walk lessons”,
learners are likely to be highly motivated
(b) Guided Discovery
In this technique, the teacher encourages
learners to nd out answers to problems
by themselves. e teacher does this by:
• Giving learners specic tasks to do.
• Giving learners materials to work with.
• Asking structured or guided questions
that lead learners to the desired
outcome.
Sometimes learners are given a problem to
solve and then le to work in an
open-ended manner until they nd out
for themselves.
With the introduction of the new
curriculum, this is the preferred method
of teaching.
(c) Group or class discussion or pair
work
In this technique, the teacher and
learners interact through question and
answer sessions most of the time. e
teacher carefully selects his questions
so that learners are prompted to think
and express their ideas freely, but along
a desired line of thought. Discussion
method should take learners from known
to unknown in a logical sequence; and
works well with small groups of learners.
e disadvantage of this method is that
some learners shy o from sharing air
their opinions freely in front of the
teacher or their peers. is may give
them more condent learners a chance
to dominate the others. However, the
method should be embraced as it intends
to eliminate the lack of condence in
learners. Further, it is hoped that it
will help improve interpersonal and
communication skills in learners.
17
• e apparatus and materials involved
are delicate for learners to handle.
• Apparatus and equipment are too few.
LESSON PLAN
e lesson plan should contain the
following components:
• Draw the lesson plan administration
template.
• Write down the strand, sub-strand and
the content title as it appears in the
Pupils Book.
• Write down how many lessons each
activity in the sub-strand will take.
• Identify, collect and list down the
necessary teaching/learning resources
required to teach the topic.
• ink of many relevant learning
activities to involve the pupils
individually, in pairs or in groups.
For example, discussion, sorting
out, pairing, counting, role- playing,
drawing, writing, pattern making.
• Decide on the amount of time to
be spent on each step in the lesson
development.
• Decide how to introduce, demonstrate,
develop and explain the content.
• Decide how you will assess the
learning.
• Make self- evaluation from the lesson
presentation.
• e lesson plan must be drawn up from
the schemes of work.
and the teacher should exploit this in
ensuring eective learning. However,
educational visits are time consuming and
require a lot of prior preparation for them
to succeed. ey can also be expensive to
undertake especially when learners have
to travel far from the school.
(f) Demonstration lessons
In a demonstration, the teacher shows
the learners an experiment, an activity
or a procedure to be followed when
investigating or explaining a particular
problem. e learners gather around the
teacher where each learner can observe
what the teacher is doing. It is necessary
to involve the learners in a demonstration,
for example by:
• Asking a few learners to assist you in
setting up the activity.
• Requesting them to make observations.
• Asking them questions as you progress
with the demonstration.
is will help to prevent the
demonstration from becoming too
teacher-centred.
When is a demonstration necessary?
A teacher may have to use a
demonstration, for example when:
• e experiment/procedure is too
advanced for learners to perform.
• e experiment/ procedure is
dangerous.
18
Preparing ourselves
Suggested teaching aids
1. Counters – Stones, leaves, straws, small wooden blocks, bottle tops, empty match
boxes, beads, beans seeds, maize seeds, buttons sticks, fruits rulers, spoons, erasers,
chairs, tables.
2. Place value chart – Place value pockets, place value charts, place value tray, place
value abacus, wooden cubes, blocks.
3. Flash cards – Picture ash cards for addition, multiplication and subtraction, sign
cards, number cards.
4. Number lines – drawn on the chalkboard, ground, oor, on a chart.
5. Measuring materials – Beam balance, strings, rope, paper strips, metre, sticks, tins,
containers. Body parts-footsteps, strides, armspan, handspan, metre rule, wall
clock, wrist watch digital watch, improvised clock face.
6. Geometric cut outs – square paper cut out, rectangular, circular, triangular, oval,
plasticines, clays, models.
7. Games – digital games, two number games, seek and hiding games, card game,
what I am thinking, Hop scotch, Number Bingo, visiting the market, catching the
beam bag, skittles, nd my mistake.
8. Wall charts – Number chart, Addition and subtraction chart, bundle chart,
multiplication and division charts, animal charts, lines and shapes chart, Beam
balance charts, clock face charts.
A suggested sample lesson plan
Lesson plan template: Administrative details
SUBJECT GRADE/CLASS DATE TIME ROLL
Mathematics 3 25/01/2018 8.50-9.20 am 52
Strand: Numbers
Sub strand: Whole numbers
Content Tittle: Counting numbers in twos and in ves
Pupil’s Book pages 1–3
Specic learning outcomes
By the end of the lesson, the learner should be able to:
(a) Count numbers forward and backwards from 1 to 1000.
(b) Identify the counting numbers in twos and in ves.
(c) Count numbers of objects in the environment at home and in schools.
19
Teaching and learning resources: Counters, sticks, bottle tops, charts, pictures in the
Pupil’s Book
Lesson/ Activity development
Time Introduction Learning experience T/ learning
activities
T/learning
resources
5 min Introduction
and Inquiry
Questions
• Organize learners into
groups.
• Let pupils handle various
counters to gure out what
they are, their elements and
how they are going to use
them.
• Ask pupils to brainstorm
over the meaning of counting
backward concept.
Name the things
they see in the
picture in the
Pupil’s Book, page
1
Number cards,
straws, sticks,
reeds, stones,
bottle tops,
picture in the
Pupils Book.
Wall charts.
10 min Content
Development
and
Explanations
• Read and discuss with pupils
about the content and
examples in the Pupil’s Book
pages 1-3
• Guide them to work out the
examples on the chalkboard.
• Dene counting backwards
and ask pupils to write the
denition in their exercise
books.
• Write notes on the
chalkboard for pupils to copy
in their Exercise books.
Listen and follow
the example
explanation as
drawn.
Ask where you
don’t understand.
Work out
questions on the
chalkboard from
the Pupil’s Book
in Activity on
page 2.
Straws, sticks,
reeds, stones,
bottle tops,
pupils text
book.
Chalkboard.
Body parts
(ngers)
10 min Class work
Activities
• Go round the classroom to
observe how learners are
doing the exercises.
• Assist the weaker ones and
slow learners.
• Mark their work and do
corrections with them where
necessary.
Do Exercise 2A in
the Pupil’s Book
on page 2.
Ask questions
where they don’t
understand.
Work together
and assist one
another in groups.
Pupils text
book
Counters
20
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
behaviour changes at the beginning of
a unit. en at the end of every unit,
the teacher should ensure that all the
learners have mastered the stated key unit
competences basing on the criteria stated,
before going to the next unit. e teacher
will assess how well each learner masters
both the subject matter and the generic
competences described in the syllabus and
from this, the teacher will gain a picture of
the all-round progress of the learner. e
teacher will use one or a combination of
the following:
• Observation to judge the extend of skill
acquisition
• Written tests
• Oral questions
• Project work
• Attitude change – this can be done by
asking probing questions and checking
body language as learners respond to
the questions.
(i) Written tests
Under this, learners are given questions
or tasks and are required to respond in
writing. Examples of written tests are:
short answer type questions, structured
5 min Conclusion
• Summarize key points on the
chalkboard.
• Conclude the lesson by
asking oral questions.
chalkboard
summary
Answer questions
Assessment and evaluation
Assessment is the process of trying to
measure the extent of success achieved
in any given lesson, unit or course.
Successful assessment has two parts, as
discussed below.
• Self-assessment, where the teacher
measure his or her own classroom
performance in terms of meeting the
content specic learning outcomes in
the stipulated time.
• Pupil assessment, where the teacher
tries to evaluate the extent of progress
and achievement made by the
learners, their content understanding,
knowledge development, attitude
acquired and application of the relevant
skills into real-life experience in school
and outside the school environment.
Assessment is a continuous process of
measuring and recording the extent
to which key objectives and main
components of the syllabus are being
achieved.
Types of assessment
e two types of assessment that will
be employed in the new curriculum is
formative and summative assessment.
(a) Formative and continuous
assessment (assessment for learning)
Formative or continuous assessment
21
(vi) Project work
In a project, learners undertake a
comprehensive study of something in real
life over a period of time such as several
weeks or even months aer which they
present a report. In project work, let
learners begin from planning stage (come
up with a schedule of events), execute the
plan, analyse the results and look back
( reect on the challenges encountered
during the project and come up with
solutions to those challenges (problem-
solving skills).
A teacher can use one or several of these
assessment methods depending on the
sub-strand being studied or the purpose
for which assessment is required.
(b) Summative assessment
(assessment of learning)
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 specic moment. e 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 certication.
is assessment should have an integrative
aspect whereby a student must be able to
show mastery of all competences.
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.
type questions, lling blanks, multiple
choice questions, true-false questions and
matching items.
(ii) Practical work or Activity
In this category, learners are required
to perform a task or solve a problem
practically. e teacher then assesses the
nished work by looking at the materials
used, procedures followed, whether it
works or not or whether it is nished. He
or she then awards marks accordingly.
(iii) Observation
is involves the teacher observing the
learners as they perform a practical task
to assess acquisition of skills and attitude
change. e teacher checks ability of the
learner to measure, classify, communicate
ndings, etc. He or she also assesses the
learner’s curiosity, patience, team and
co-operation spirit among others.
(iv) Oral questions or interviews
Asking learners questions which require
a verbal response such as naming parts
of human body, a system or short
explanations of a process such as digestion
can also be used to assess a learner’s level
of competence.
(v) Drawing
is involves asking learners to draw
something they have observed or learnt
about. ey can also collect data and draw
graphs and interpret the graph and give
conclusions. is helps to assess their skill
in communication through recording.
22
to impart knowledge through passing
information to the pupils. You can assess
the pupil to establish whether they have
assimilated the information and knowledge
through:
• Periodic observations of the pupils
exercise books.
• Weekly or end-of-lesson or end-of-
course tests and quizzes.
• Individual pupil or group discussion,
debates or interviews.
• Group competitions.
2. Assessment of acquired attitudes and
values by comprehending information
Attitude and values that pupils acquire in
the process of learning can be evaluated
most appropriately by using a checklist.
3. Assessment of development of skills
by application of the information
Evaluation of skills can be undertaken by
the teacher through keeping a record of
what skills the teacher aims at imparting
to pupils. In mathematics the key skills for
emphasis are reading, counting, recording,
recalling, organization, representation,
drawing, interpretation and relating.
Assessment records
1. Progress records
Progress records are essential components
of the evaluation process. You should
design test, quizzes and other forms of
assessment. is can be done weekly, aer
a fortnight, monthly, or at the end of a sub-
strand or course. A pupil’s progress should
then be assessed aer every lesson is taught
and results entered into a progress record.
School-based summative assessment
average scores for each subject will be
weighted and included in the nal national
examinations grade. School-based
assessment average grade will contribute
a certain percentage as teachers gain more
experience and condence in assessment
techniques. In the new curriculum the
school-based assessment will contribute to
a certain percentage of the nal grade, but
will be progressively increased. Schools will
be supported to continue their initiative to
organize a common test per class for all the
classes to evaluate the performance and the
achievement level of learners in individual
schools.
It is important to note the following
points in assessment.
• Once a choice has been made of
the method to use in assessment, a
procedure is prepared to eect the
evaluation. Assessment is most aective
when carried out at the end of each
lesson, week, term, year or course.
• Various methods can be used to assess
the pupils work. ese include:
- Oral and written quizzes
- Exercises
- Asking questions in class
- Administering individual or group
assignments
- Setting tests that are administered
and marked aer class
- Observing learners doing the
activities
Assessment learning outcomes
1. Assessment of knowledge development
and assimilation of information
One of the key reasons for teaching is
23
learning abilities and disabilities. ese
records are important tools for multi-
ability assessment. ey can show a pupil
whose performance may be falling due
to personal or family problems and may
call for individual attention, guidance and
counseling.
All these two records should be done
and records eld together with all other
personal records in each pupil’s personal
le.
A progress record is essential because
it shows the pupils who are doing well in
class, those who are average and those who
are below average. It can act as a basis for
follow up for slow pupils who may require
extra attention to catch up with the others.
e slow pupils may require extra tuition
or take-home assignments in the evenings,
weekends and during holidays to improve
their performance.
2. Achievement record
Achievement record are also very
important for helping those with various
3. Assessment Record Checklist
e table below may help you in evaluating the assimilation, development and
acquisition of content, knowledge, attitudes and values on the part of pupils in
monitoring their progress and achievements in dierent learning areas and activities.
School………………………………………………………….Class/ Grade……………
Pupils name ……………………………………….. Admission number………………….
Age …………….. Term……………………… Year…………………
Subject/Activity area ……………………………………….
Pupil ability and expectations/
competencies
Weak Average Good Outstanding
1. Makes observations on learners
2. Asks oral questions in class
3. Answers questions orally in class
4. Recalls key concepts
5. Expresses self-esteem
6. Draws/ presents complete work
done
7. Makes correct interpretations
8. Relates things from known to
unknown
9. Makes correct analyses
10. Presents sustained reasonable
arguments
24
relieve stress and others because of peer
pressure to look and feel cool. Let the
pupils understand acceptable ways of
containing pressure, such as good social
groups, church membership, and sports
and games.
Care for the environment
is is a cross-cutting issue that you
must remember to bring out during your
lesson. You must try to develop a caring
and responsible attitude in the pupils so
that they learn to protect and conserve the
environment.
at means encouraging principals such
as environmental conservation, re-use,
recycling and use of alternative sources
of fuel, for example biogas. Use simple
activities such as asking the pupils to throw
rubbish away in the right place, planting
trees, and cleaning the classroom.
Gender disparity and parity
In most traditional African societies, there
was no equality between the boys and girls.
While this may have served some purpose
then, the government has now decided to
advocate gender equality. Boys and girls
should be given an equal opportunity in
life. is includes going to school, choice
of career, employment opportunities and
general social respect. You must repeatedly
bring this out during your lessons. In class,
gender parity means equal participation
in class discussion for boys and girls,
avoidance of sexist talk and jokes, and
encouragement of girls to excel. You may
also organize for gender integration by
putting boys and girls together in discussion
groups and moderating to ensure balanced
participation.
Emerging issues
ese are new issues that learners at this
young age must be aware of. ey are called
`Emerging issues`. e teacher should
guide the learners in a level of language
they can easily understand. Some of the
issues may appear to be mature for the
learners but you should make every eort
to expose them in simple steps and make
them assimilate the information positively.
Information and communication
technology
Due to very rapid advances in information
and communications technology, the
world has become what is commonly
referred to as a “global village”. rough
computers, email, internet and mobile
phone technology, people can instantly
communicate with each other all over
the world. As the world races towards the
information age, we should encourage
pupils to embrace technology and
technology education. You may do this
by pointing out the important benets of
technology and by using some of these
technologies in class or as reference for
teaching.
Drugs and substance abuse
e abuse of drugs among the youth has
become a major problem in this country.
Among the most abused drugs in Kenya are
cigarettes, bhang, miraa(khat) and alcohol.
In some urban areas, the youth have gone
into hard drugs such as cocaine or heroin.
Also drug abusers are irresponsible, violent
and undisciplined.
You must always stress the dangers of
drugs and drug abuse. Many take it to
25
lesson and activity as related to cultural
activities, citizenship, democracy and
human rights, law, peace and reconciliation
in accordance with the government of
Kenya.
Peace and conict resolution
With the world being a global village,
events in one part of the world also aect
other parts of the world. What happens in
one country or region aects other areas.
We can therefore no longer sit back and
do nothing when other people are locked
in bitter conict all around us. We must
all help prevent and control conicts.
e common causes of conict in our
country include poor leadership, problems
of communication, tribalism, scarcity of
resources, selshness and lack of proper
understanding of the need for peaceful
coexistence.
In the business environment, conicts
oen arise from interdepartmental rivalry,
perception of favoritism, sexual harassment,
nepotism and mismanagement. You must
bring out these pertinent issues during
your lessons. is will ensure development
of positive values and attitudes, practical
conict resolution skills and sensitivity
to the causes of misunderstanding and
conict.
Pupils with special learning needs
In your School every class is likely to have
pupils with special learning needs. You
need to know them wholesomely by their
abilities and needs to allow you identify
and cater for them adequately.
Human rights
In Mathematics children are informed of
their rights as children. Many children
are abused because of lack of knowledge
of their rights. Child rights protect the
children from abuse both at school and at
home. Some of the rights covered include
the right to identity, food, clothing, shelter,
schooling, medical care and protection.
is will ensure that children are able to
recognize any form of abuse both at home
and in school, and that they report such
cases to the relevant authorities.
HIV and AIDS
HIV and AIDS continue to kill many people
in our country. is aects the economy,
as highly trained human resources are lost
through sickness and death. Remember
that abstinence, faithfulness to a single
partner and use of condoms may help
to control the spread of HIV and AIDS.
However, the best way to do this is through
behaviour change. You should encourage
your pupils to be sexually responsible,
ideally postponing sexual activity until
they get married. is is a very sensitive
issue and you must tread carefully. You
may, however, use examples or case studies
to relate the suering that is oen caused
by HIV and AIDS.
Anti-corruption
Corruption is one of the greatest social
evils facing our country and society today.
Corruption cannot continue if the people
say NO to bribes or be refusing to accept or
pay bribes and by reporting culprits to the
relevant authorities. e content should
bring out these values and attitudes in the
26
copying notes from the writing board.
Some have itchy, watery eyes while others
complain of double vision.
Intervention measures
• Place them in an appropriate position
in the class where they are able to see
well.
• Arrange for them to make notes aer
the class.
• Give them more time to nish their
work.
• Give them extra tutorials on the work
covered.
Hearing impaired
Pupils who have trouble in hearing are
normally inattentive in class. ey also
seem to be confused by instructions and are
unwilling to participate in class activities.
Some complain of pain in the ears.
Intervention measures
• Allow them to sit in comfortable places
where they can hear well.
• Use teaching methods that involve
more reading and observation.
• Advice the parents to buy hearing aids
for them.
• Advise their parents to seek medical
treatment for them.
Physically handicapped
Physically handicapped pupils may
have one or more of the following
characteristics:
• Abnormal body postures in walking or
sitting, including limping and disuse of
some parts of the body, for example the
arm or hands.
Categories of groups with special
learning needs
Such groups of pupils may include:
- Mentally challenged
- Visually impaired
- Hearing impaired
- Physically impaired pupils
- Learners with speech problem.
- Academically slow learners
- Academically Gied/ talented learners
- Emotionally/ Psychologically disturbed
Mentally challenged
ese pupils take too long to learn a skill
that other pupils of the same age nd easy
to master. Sometimes, they do not learn at
all. Some pupils do not seem to be aware of
the objects and people around them. ey
do not initiate interaction.
Interventions measures
• Giving them plenty of time to do their
work.
• Rewarding them appropriately for their
input.
• Teaching them simple concept that will
not confuse them.
• Being friendly, kind, sympathetic,
trustworthy and reliable in order to win
and build their condence.
Special education experts may
recommend that a severely mentally
impaired pupil attend a school that caters
specially for his or her needs.
Visually impaired
Pupils who are visually impaired
experience diculty in reading and
27
• Encouraging their parents to seek
professional help from a speech
therapist.
Try to identify the nature of the pupils
special needs so that you can use the
appropriate methods to help him/her.
Academically slow learners
Slow pupils have the following problems:
• ey do not keep up with the rate of
learning in the class.
• ey have diculties in grasping
content.
• ey have problems in reading, writing
and expressing themselves verbally.
• ey tend to score lower than their
class members in achievement tests.
Intervention measures
• Giving them more time to do their
work.
• Varying your teaching methods,
including increased uses of group work,
teaching aids and demonstrations.
• Giving them remedial work or extra
attention.
• Providing them with a stimulating
environment by exposing them
to a variety of resources such as
photographs, drawing models and eld
visits.
• Giving positive feedback whenever
they show eort.
• Encouraging condence-building
activities through class participation.
e academically gied/talented learners
e academically talented pupils have the
following characteristics:
• Deformities like hunches.
• Diculties in using and controlling
parts of the body, for example in
control of the limbs.
Intervention measures
• Being kind and understanding
and arming them whenever the
opportunity arises.
• Giving them assignments that require
other skills like reading out loud so
that the class listens and appreciates
their ability.
• Making sure they are seated in
comfortable position near the front of
the class where they can move freely.
• Giving them more time in the
performance of some tasks like project
work, activities, etc.
• Giving individual attention in the
teaching of relevant topics and in
the assessment and performance of
activities.
• Giving helpful advice for treatment
and referring complicated cases to the
relevant health professionals.
Learners with speech problems
ese pupils nd it dicult to speak and
have problems reading. As a result, they
tend to be inactive and withdrawn.
Intervention measures
• Encouraging them to answer oral
questions.
• Not interrupting them when they are
talking.
• Using pictures and real objects to
illustrate words.
28
Various factors such as heredity, brain
disorder, diet, stress and family problems
have been suggested as possible causes
of emotional disturbance. Some of the
characteristics and behavior seen in pupils
who have emotional disturbances include:
• Hyperactivity (short attention span,
impulsiveness).
• Aggression/self-injurious behaviour
(acting out, ghting)
• Withdrawal (failure to initiate
interaction with others, retreat from
exchanges of social interaction,
excessive fear or anxiety)
• Immaturity (inappropriate crying,
temper tantrums, poor copying skills)
• Learning diculties (academically
performing below grade level).
Intervention measures
• You can refer cases to the relevant health
authorities.
• Help is available from psychiatrists,
psychologists or other mental health
professionals in public or private mental
health settings.
• Provide them with services based on
their individual needs, and all persons
who are involved with these pupils
should be aware of the care they are
receiving.
• It is important to co-ordinate all
services between home, school and
therapeutic community through open
communication.
Improvisation of teaching/
learning aids
Improvisation is the ability to make
something using any locally available
• ey possess superior intelligence,
making their academic performance
above average for their age.
• ey have a high degree of aptitude
for school subjects or specic learning
tasks.
• ey are highly interested in
schoolwork.
• ey usually get bored and restless
if they are not fully occupied and
stimulated.
Intervention measures
• Giving them more challenging work
than the other pupils to retain their
interest.
• Giving them research work involving
independent inquiry.
• Pairing them so that they can discuss
ideas at the same level.
• Giving them leadership roles to instill
concern for others.
Emotionally/Psychologically
disturbed
Pupils with emotional, behavioral or
mental disorders exhibit one or more of
the following characteristics to a marked
degree that adversely aects educational
performance:
• Inability to learn that cannot be
explained by intellectual, sensory or
health factors.
• Inability to build or maintain satisfactory
interpersonal relationships with peer
and teachers.
• Inappropriate types of behaviour or
feelings under normal circumstances.
29
made by commercial manufacturers are
usually expensive and majority of schools
cannot aord them. e teacher is therefore
advised to improvise using locally available
materials as much as possible.
Timing of topics and the local weather
pattern
e collection of mathematical data
in handling topics like probability and
statistics are done at particular specic
weather condition than at other times. For
example, when collecting data on dierent
makes of vehicles that pass through a
particular route, the weather and other
physical conditions must be put constant
and into consideration for accuracy and
to avoid biases. Certain insects appear
only during the dry weather while others
emerge with the onset of the rains. Nature
walks and visits are best done when the
weather is sunny and dry. e teacher
should therefore think ahead while making
the scheme of work so that the prevailing
weather pattern is considered. is will
ensure that suitable activities for learning
Mathematics are planned for with the
weather in mind.
However, a good scheme of work
should be suciently exible to cope with
unexpected situations and can be altered
or modied to suit certain circumstances.
Safety in the classroom
Pupils in Primary school are extremely
active and curious. As such, they are
inclined to getting harmed and injured.
ey should therefore be constantly
protected from sources of injury and harm.
materials which are found in our
environment, either at home or in school.
It involves use of low cost and locally
available resources. You can use them the
way it is, model it or come up with relevant
teaching aid like the commercial one.
Teachers should get out of the old believe
that all teaching and learning resources
must be commercially acquired.
Teachers and learners are expected to
be creative, inventive and critical thinkers
in coming up with improvised materials
from the surrounding environment. ese
materials whether collected, improvised
or bought should be well kept in the
mathematical corner in the classroom.
Improvisation helps where there are no
funds to acquire commercial ones or the
teaching aids are not readily available.
Tell learners to bring some of the
materials from home or market place.
Let the classroom be full of teaching and
learning materials. Always prepare and
improvise this material in advance before
the term begins or before the lesson activity
presentation.
e teacher should organise a place
within the school for the proper storage
of mathematical materials and in labelled
boxes.
Encourage learners to collect and bring
as many materials and apparatus to the
school as they can. is will continuously
replenish your materials and apparatus
collection.
If each learner is to have, a chance of
experimenting, cheap resources must be
made available. Expensive, complicated
apparatus may not always be available in
most schools. Such sophisticated equipment
30
• During nature walks and eld visits,
learners should avoid handling
poisonous plants and harmful animals,
etc.
Remember, the teacher is responsible
for the safety of the children during the
period he or she is handling them while in
school.
e teacher is therefore advised to take
strict safety precautions whenever learners
are in class or outside the classroom. Some
areas that need consideration as far as
safety is concerned include:
• When using tools and equipment
• During experiments or demonstrations
• When handling sharp or pointed
objects like a pair of scissors, razor
blade, etc.
31
Number concept
(Learner’s Book Pages 1 – 9)
Suggested number of lessons: 8 Lessons
Specic learning outcomes
By the end of the sub- strand the learner
should be able to use ordinal numbers to
identify positions 1 to 20.
Core competences
Communication and collaboration,
imagination and creativity, critical
thinking and problem solving, self-
ecacy
Key inquiry questions
In which position were you when you came
back to class from P.E lesson?
Link to PCIs
Life skills and values education:
Links to other subjects:
• Language activities
• Movement activity
Pre-requisite to the strand
Ordinal numbers is a new concept, being
introduced in Grade class three. Learners
may take time to understand it. is can
be achieved through thorough revision on
whole numbers.
Teaching/learning resources
• Marbles
• Bottletops
• Sticks
• Bottles
• Charts
Key words
• Groups
• Position
• Flat surface
• Distance
• Ordinal
Guidelines to teaching learning
experiences
Ordinal numbers up to 10
th
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to state a position using ordinal
numbers from one up to 10.
Activities 1 A and 1B
Preparation
• Make sure that the teaching and learning
resources are available in the Mathematics
corner. ese include bottles of dierent
sizes.
• Organise the learners in groups of
mixed abilities.
• Ensures that all the groups have bottles
of dierent sizes and heights.
1
32
ings arranged according to positions are
called ordinal numbers.
Assessment
• Ask questions about the position of
objects in the class.
• Give questions that entails stating the
position using ordinal numbers.
• Go round marking and guiding
learners with special needs.
• Let the learners do Exercise 1A as an
assignment.
Ordinal numbers up to 20
th
Speciﬁc learning outcome
By the end of the lesson learners should
be able to identify position and order of
objects from 11
th
up to 20
th
position.
Activity 1C
Preparation
• Ensure that the objects to be used for
Activity 1C are available.
• Get an open space outside the
classroom.
• Make sure that the eld is free from
harmful objects.
• Organise learner into convenient
groups.
Doing the activity
• Guide learners through the activity
which is to be held in the eld.
• Guide them on how to arrange bottle
tops in vertical columns on a at
ground starting from the easier to the
dicult ones.
Doing the Activity 1A
• Ask the learners to do Activity 1A and
1B while following the instructions
given in the Learner's book.
• Let them arrange the bottles from the
biggest to the smallest.
• Guide them as they state the number
in which each bottle is labelled.
• In groups of ten guide them to ll the
table in activity 1B involving dates of
birth.
Synthesis
• Explain to them that the bottle in
number one is in the 1st position,
number two is in the 2nd position and
so on.
• Ask them to name other situations in
real life where positions are used.
• Explain to them that in ordinal number
size or height do not matter.
• Explain to the learners that ordinal
numbers are used to show the position
of an object in a list of objects.
• Guide them through the table showing
the rst ten ordinal numbers and their
symbols.
• Use example 1 to reinforce the
importance of positions and ordinal
numbers from 1st to 10th in running
and nishing a race on a nishing
line.
• Guide them to ll in the table aer the
position of the pictures of the learners
as they reach the nishing line.
• Ask who was rst, second, third up
to the tenth position to reach the
nishing line.
Conclusion
Ordinal numbers give positions which
facilitate order of objects or animals from
number one up to last.
33
Assessment
• Give the learners time to answer the
questions in the Exercise 1B.
• Assist those with diculties in
carrying out the task and those with
special needs to answer questions.
• Revise the work together with the
learners. Observe learners as they do
the activities.
ANSWERS
Activity 1A
Observe the learners when they are picking
the bottles. at is who picked rst, second,
third, fourth and h bottle respectively.
Check their answers, mark them and guide
them appropriately.
Activity 1B
Ask the learners their dates of births in the
respective groups. Check how they ordered
the date of births, mark their answers and
guide them appropriately.
Exercise 1A
1.
Position 1
Position 4
Position 2
Position 3
Position 5
2
nd
5
th
3
rd
4
th
1
st
2.
(b) Sixth (c) Tenth
(d) First (e) ird
(f) Eighth (g) Fih
(h) Fourth (i) Seventh
(j) Ninth
• Let them start with a pile of one bottle
top, two bottle tops, and so on up
to 20 bottle tops piled vertically in a
column.
• Guide them to write the ordinal
numbers on the ground next to the
arranged bottle tops with a piece of
chalk.
• Ask them to count the number of
bottle tops from the easier ones to
arrange to the dicult ones as they
say their ordinal numbers.
Synthesis
• Discuss with the learners through the
table showing the rst twenty ordinal
numbers and their symbols.
• Explain to them that members of each
group arranged at dierent positions
forms an ordinal number.
• Each group can therefore be given
a position depending on their
arrangement from 1st to 20th.
• Guide them through the table to
understand the ordinal numbers in
words and in symbols from the 1
st
to
20
th
.
• Use Example 2 to reinforce the
concept of ordinal numbers using the
alphabetical letters.
• Guide them to do the activities
involved in Example 2 (a) and (b).
Conclusion
Summarise the lesson by emphasising
that position implies placing or arranging
(someone or something) in a particular
way.
Positions are represent by ordinal numbers.
34
3. Sunday – 1
st
Wednesday – 4
th
Tuesday – 3
rd
Saturday – 7
th
Monday – 2
nd
Friday – 6
th
4. (b) Fourth (c) Seventh
(d) ird (e) Second
(f) Sixth (g) Fih
Activity 1C
3. e rst (1
st
) column.
4. Column of 20 bottle tops
Twentieth (20
th
).
5. Column with 10 bottle tops
6. (i) 13
th
(ii) 16
th
(iii) 19
th
7. 14 bottle tops
Exercise 1B
2.
(b) January- 1
st
month
(c) June - 6
th
month
(d) July – 7
th
month
(e) October – 10
th
month
(f) September – 9
th
month
(g) November – 11
th
month
(h) April – 4
th
month
(i) August – 8
th
month
(j) February – 2
nd
month
(k) December – 12
th
month
(l) March – 3
rd
month
3.
Marks Position
Ordinal
number
Name
90 First 1 Olando
89 Second 2 Akwa
87 ird 3 Halima
85 Fourth 4 Kalekye
80 Fih 5 Mwazo
79 Sixth 6 Boke
78 Seventh 7 Mucheru
77 Eighth 8 Nyaga
75 Ninth 9 Cherono
74 Tent h 10 Oyaro
74 Eleventh 11 Nanok
73 Twelh 12 Sankale
72 irteenth 13 Wanjiru
71 Fourteenth 14 Barasa
70 Fieenth 15 Fatuma
69 Sixteenth 16 Mutua
60 Seventeenth 17 Solau
35
Whole numbers
(Learner’s Book Pages 10 – 32)
Suggested number of lessons: 20 Lessons
Specic learning outcomes
By the end of the sub-strand the learner
should be able to:
(a) Count numbers forwards and
backwards from 1 to 1000.
(b) Identify place value of digits in
numbers up to 1000.
(c) Read numbers 1 to 1000 in symbols.
(d) Read and write numbers 1 to 100 in
words.
(e) Identify missing numbers in number
patterns up to 1000.
(f) Appreciate number patterns as they
skip on the numberline.
Core competences
Communication and collaboration;
critical thinking and problem solving;
imagination and creativity; digital literacy
Key inquiry question(s)
How would you nd the total number of
people in a group?
Link to PCIs:
Life skills: Self- awareness -as learners
count their ngers and toes
Citizenship: social cohesion; as they work
in groups
Links to other subjects
• Environmental activities
• Language activities
Re-requisite to the strand
To achieve the specic outcomes the learners
ought to have learnt about whole number
in the previous class. is is because it is a
continuation of whole numbers taught in
their former class.
Teaching/learning resources
Bottle tops, marbles, sticks, stones, grains
and other readily available counters.
Key words
• Forward
• Backward
• Identify
• Placevalue
• Symbols
• Number patterns
• Appreciate
• Skip
• Numberline
2
36
Guidelines to teaching learning
experiences
Counting and reading
numbers
Counting in hundreds
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to count numbers in hundreds from
100 to 1000 by use of counters.
Activities 2A, 2B and 2C
Preparation
• Collect all the necessary materials that
is counters and others for this activity
and other activities in the sub-strand.
• Keep them at the Mathematics corner
in the class.
Doing the activity
• Ensure all the learning and teaching
resources are available before the lesson
begins i.e counters in bundles of ten.
• Guide learners to make bundles of ten
counters.
• Ask them to tie them as 1 ten.
• Guide them to discover that: 10 bundles
of 10 counters each make 100 counters.
• Guide them to tie 10 bundles together
to make 1 hundred.
• Guide them to count 2 bundles of
hundred counters, 3 bundles of hundred
counters, 4 bundles of hundred counters
and so on up to 10 bundles of hundred
counters to make a thousand counters.
Synthesis
• Guide learners to count and read from
100 to 500 using the bundles of hundred
counters.
• Repeat by starting from any hundreds
forward and backwards.
• Make sure that all the learners can read
numbers hundred from 100 to 1000
forward and backwards.
• Guide the learners to count in forward
starting from 100 to 1000 starting from
any hundreds orally.
• Display a chart of 100 to 1000.
• Encourage dierent learners to read
numbers loudly from 500 to 600 and
backwards 600 to 500.
Conclusion
• We count numbers in tens to make 1
hundred.
• We count numbers in hundreds to make
1 thousand. 10 tens equals 1 hundred
and 10 hundreds equals 1 thousands.
Assessment
• Pointing at numbers and on chart using
a pointer.
• Observation as they count the counters.
Counting in hundreds, tens
and ones
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to count numbers in
hundreds, tens and ones.
37
• Involve them in more practice starting
from 1 hundred to the next hundred up
to one thousand.
• Make sure they can count the counters
well as they read the numbers made
orally and aloud.
Conclusion
• 1 hundred put together with bundles of
ten and counters in ones give numbers
in between one hundred and the next
hundred up to 1000.
Counting in twos
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to count numbers from 1
to 1000 in twos and ves.
Activities 2D and 2E
Preparation
• Collect all the necessary materials such
as counters and others for this activity
and other activities in the sub-strand.
• Keep them at the Mathematics corner
in the class.
Doing the activity
• Arrange the learners into groups of
mixed ability.
• Display a number chart.
• Ask the learners to count in twos from
100 to 150 forward and backwards from
360 to 300.
• Ask them to count forward in twos from
450 to 500 and backwards from 1000 to
900.
Preparation
• Collect all the necessary materials
required for this activity and other
activities in the sub-strand.
• Keep them at the Mathematics corner
in the class.
Doing the activity
• Organise the learners into groups of
mixed abilities.
• Guide each group to count the counters
in bundles of hundreds, tens and ones.
• Guide them to learn and understand
that:
- 1 hundred bundle put together with
1 ones equals 101.
- 1 hundred bundle put together with
8 ones equals 108.
• Involve them in more counting of
bundles of hundreds and tens to learn
that 1 hundred bundles put together
with 1 ten bundles equals 110.
• Guide them to learn more and discover
that by putting together 1 hundred
bundle, 1 ten bundle and 4 ones bundle
equals 114.
• Guide them to do more activities as
they make other numbers in hundreds,
tens and ones as given in Activity 2B
and more.
Synthesis
• Guide learners to read a chart showing
dierent numbers written in hundreds,
tens and ones.
• Ensure all learners can read together
and each learner can also read aloud
any number in hundreds, tens and ones
38
Synthesis
• Guide the learners as they do their
activities to count forward and
backwards starting from any number
For example 580 to 800 and from 800
to 580.
• Guide them to practice further
activities by counting in twos
using both their ngers and toes as
instructed.
Conclusion
• Fingers and toes are counters in real
objects and can be used to count
numbers forward or backwards starting
from any number.
Assessment
• Ask the learners to do more activities
involving counting in twos forward or
backwards.
• Observation.
Counting in ﬁves and tens
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to count numbers forward
and backwards from 100 to 1000 in ves
and tens.
Activities 2G and 2H
Preparation
• Collect all the materials necessary for
this activity and other activities in the
sub-strand.
• Keep them at the Mathematical corner
in the class.
Synthesis
• Guide the learners to practice counting
numbers in twos forward using
number chart.
• Guide the learners to count in twos
backwards without using number
charts.
Conclusion
We can count numbers in twos forward
and backwards with or without using a
number chart.
Assessment
• Question and answer session.
• Ask the learners to do Activity 2E.
• Move round the class assisting learners
who have challenges.
• Give remedial work to the learners
Counting in twos using
ﬁngers and toes
Activity 2F
Preparation
• Organise Learners in pairs
Doing the activity
• Ask the learners to use their ngers to
count forwards in twos from 10 to20 as
in Activity 2F.
• Ask them to repeat counting backwards
from 20 to10.
• Ask them to use both their ngers and
toes to count forwards in twos from 1
to 40.
• Ask them to start counting backwards
in twos from 40 to1.
39
• Mark the work as you assist those who
may have a challenge in doing the
activity.
• Give a few questions for remedial work
from your own source.
Counting in ves and tens
using ngers and toes
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to count numbers 1 to 1000 in ves
and tens forward and backwards using
ngers and toes.
Activities 2I and 2J
Preparation
• Collect all the necessary materials that
are required for this activity and other
activities in the sub-strand.
• Keep them at the Mathematics corner
in the class.
Doing the activity
• Ask the learners to read through the
activity and follow the instructions as
they do the activity 2I and 2J.
• Ask learners to count forward in ves
starting from 150 to 350 and backwards
in ves from 600 to 500 using both
ngers and toes.
• Ask them to repeat the activity in pairs
starting from any other numbers in
tens moving forward and backwards as
instructed in Activity 2J.
Synthesis
• Guide the learners through further
practice from your own source.
Doing the activity
• Ask learners to count in ten’s starting
from 550 moving forward to 600 using
a number chart.
• Ask the learners to go through the same
activity and count backwards from 450
to 250.
• Ask them to repeat the activity in pairs
starting from any number as instructed
i.e 230 to 530 and 760 to 540.
Synthesis
• Guide the learners through more
practice to count numbers in ves and
tens using a table of 100 to 1000 as in
Activity 2H.
• Explain to them that counting forward
involves counting by adding 5 to each
number. Also explain that counting
backwards in ves is counting by
subtracting 5 from each number.
• Guide them to understand that
counting forward in tens is counting
by adding 10 to each number and
counting backwards in tens is counting
by subtracting 10 from each number to
reach the next number.
Conclusion
• We count numbers in ves and tens
by adding 5 or 10 respectively to the
previous number to get the next number.
• Counting forward involves addition
while counting backwards involves
subtraction.
Assessment
• Give learners more questions to answer
in their exercise books from your own
source.
40
• Prepare a chart showing ‘reading and
writing numbers in symbols’.
• Ensure that all the teaching and
learning resources required are
available before the lesson.
• Arrange the learners in mixed ability
groups
Doing the activity
• Display a chart showing numbers from
1 to 1000 in symbols.
• Encourage dierent learners to read the
numbers loudly as they point them on
the chart using a pointer.
• Guide the whole class to write the
numbers in their exercise books.
Synthesis
• Guide the learners through Exampels 1
and 2.
• Guide the learners to read and write
the numbers in their books.
Conclusion
We count, read and write number symbols
as they are from 1 to 1000.
Assessment
• Point at numbers randomly on the chart
using a stick as the learners read aloud.
• Read any number and ask a learner to
write the number.
• Ask them to write as you read the
number to them.
• Ask them to write the missing numbers
in Exercise 2A in their exercise books.
• Explain to them how to count in ves
and tens forward and backwards
starting from any number without using
their ngers and toes.
• Guide them to understand that
counting forward involves addition
while counting backward involves
subtraction.
Conclusion
• We count numbers forward and
backwards in ves and tens.
• Counting forward in ves involves
adding 5 and in tens involves adding 10.
• Counting backward in ves involves
subtracting 5 and in tens involves
subtracting 10.
Assessment
• Give learners more practice questions
to answer in their exercise books from
your own source.
• Go round supervising as they work
guiding the learners with challenges.
• Give few questions for remedial work.
Writing numbers 1 to 1000
in symbols
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to read and write numbers in
symbols.
Activities 2K and 2M
Preparation
• Before the lesson, ensure there
are enough number cards in the
Mathematics corner.
41
• Guide them to know that when writing
the place value of each digit it is always
written starting from ones, tens,
hundreds and thousands in that order.
• Guide them through further practice
from your own source.
Conclusion
• To determine place values, we separate
the digits of a number into thousands,
hundreds, tens and ones.
• We represent starting from ones, tens,
hundreds and thousands in that order
from right to le hand direction.
Assessment
• Question and answer session
• Observation
• Ask them to do Exercise 2B.
Activities 2P to 2Q
Preparation
• Collect all the necessary materials that
are necessary for this activity.
• Keep them at the Mathematics corner
in the class.
Doing the activities
• Arrange the learners into mixed ability
groups.
• Guide the learners to write the place
value and the value of digits in the
numbers 616 and 127.
Synthesis
• Guide the learners through Examples 5,
6, 7 and 8.
Place value
ousands (), hundreds
(H), tens (T) and ones (O)
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to identify the place value of digits
of numbers in thousands, hundreds, tens
and ones.
Activities 2N and 2O
Preparation
• Collect all the necessary materials that
are required for this activities.
• Keep them at the Mathematics corner
in the class.
Doing the activities
• Ensure all teaching and learning
resources are available.
• Organise the learners into mixed
ability groups.
• Ask them to read through Activity 2N
and do as instructed by counting bundles
of counters to represent number 256.
• Ask the learners to write the place value
of digits 2,3 and 4 in the number 234.
• Ask them to read through Activity and
do as instructed the abacus.
• Guide them to represent numbers 415,
670 and 809 using abacus and write the
place value of each digits.
Synthesis
• Guide the learners through Examples 3
and 4
• Explain to them that each digit in a
number has a place value for example
ones, tens, hundreds and thousands.
42
• Prepare a chart showing ‘writing
numbers in words’.
Doing the activity
• Make sure all the teaching and learning
resources required are available.
• Arrange the learners in mixed ability
groups.
• Ask the learners to read orally 1 up to 20
as in activity 2R.
• Count real objects like stones up to 100
as instructed in activity 2S.
• Ask the learners to read the numbers
loudly as they count in tens i.e 10, 20,
30, 40, 50, 60, 70, 80, 90, 100.
• Guide the learners through writing the
numbers words for tens up to 100 in
words on the chalkboard.
• Guide them to form numbers names
between the tens starting from 21 up to
100 in words. Let them work in pairs.
Synthesis
• Guide the learners to write numbers 21
to 100 in words.
• Emphasise the shaping of the letter
to form words and the shaping of the
symbols to form a digit.
• Use Examples 9, 10 and 11 to reinforce
the concepts of writing numbers in
words correctly up to 100.
• Ensure that the learners write numbers
in their correct spelling.
Conclusion
To write numbers in words, we must
learn their values in tens and in ones. e
number names in words are written down
in the way we read and say them orally.
• Draw a place value chart and guide
them to identify the place value of each
digit in the number 754.
• Emphasise that when writing place
value each digit has its own place value
starting from right hand side as ones,
tens, hundreds and thousands.
• Explain to them how to write the
short form of ones, tens, hundreds and
thousands.
Conclusion
We use abacus, spikes and place value charts
to tell place value of digits of a number.
ese are other ways of determining
place of digits in a number. ousands is
represented as (), hundreds as (H), tens
as (T) and ones as (O).
Assessment
• Question and answer
• Let them do Exercises session 2C and
2D in their exercise books under your
supervision.
• Mark their work and give remedial work
for practice.
Reading and writing
numbers in words
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to read and write numbers
in words up to 100.
Activities 2Q and 2T
Preparation
• Before the lesson, ensure there are enough
number cards in the Mathematics corner.
43
numbers aloud.
Synthesis
• Guide the learners to work out Example
12 in the Learner’s Book on lling in the
missing numbers. Help them to work
through to get rule of each pattern in
the example.
• Numbers form patterns when they either
increase by 10, 100, 200, 300, 400 or 500
up to 1000 or decrease by the same or
any other groups of denominations.
Conclusion
• Numbers form patterns when they
either increase by 10, 100, 200, 300,
400 or 500 up to 1000 or decrease
by the same or any other groups of
denominations less than 500.
• Next number in a pattern is found by
either adding or subtracting a xed
number of tens or hundreds.
Assessment
• Guide learners to do Exercise 2F in the
Learner’s Book.
• Ask them oral questions that are
related to forming number patterns of
10, 100, 200, and 300.
• Give them remedial work on missing
numbers in number patterns.
Appreciating number
patterns
Speciﬁc learning outcome
By the end of this lesson the learner
Assessment
• Ask the learners to write the numbers in
tens from 10 to 100 in symbols and in
words.
• Go round marking and guiding learners
with special needs.
• Ask them to do exercise 2E in their
exercise books.
• Give them remedial work for further
practice.
Identify missing numbers in
number patterns
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to identify and determine missing
numbers in number patterns..
Activity 2U and 2V
Preparation
• Before the lesson, ensure there
are enough number cards in the
Mathematics corner.
• Prepare a chart showing ‘writing
numbers in number patterns.’
Doing the activity
• Ask learners to look at the number
patterns in Activity 2U. Let them nd
the missing numbers.
• Guide them to nd the rule of the
pattern.
• Ask them to ll in the missing numbers
in Activity 2V. Let them read the
44
their home environment.
Digital games
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to count numbers forward
and backwards from 100 to 1000 in ves
and tens.
Activity 2X
Preparation
• Before the lesson, ensure that each
learner has access to a tablet.
Doing the activity
• Organize learners into mixed ability
groups.
• Guide them to read through Activity
2W and follow the instructions given
carefully.
• Guide learners to switch on their tablets.
• Let them identify the keyboard icon and
press on the buttons as instructed.
• Guide them to simply write the numbers
in symbols and in words from 21 up to
100 using their tablets.
• Initiate as many play games as possible
for the digital games involving number
patterns as you instruct them.
• Let learners play with numbers their
own choice.
Synthesis
• Let the learners understand that a tablet
or a computer is an advanced machine
which is used to solve number problems
and any other Mathematical issues
easily.
• Learners ought to appreciate the
should be able to create number patterns
by counting.
Activity 2W
Preparation
• Organise learners in groups of ve and
guide them through Activity 2X.
Doing the activity
• Ask learners to draw a number line on
the ground and use it to develop other
patterns. Ask them to practice skipping
10 steps forward and backwards between
200 to 340.
Synthesis
• Explain to the learners on how to make
patterns on numbers or use any other
examples.
• Guide them through other activities
involving skipping on a number line
starting from dierent numbers up to
1000.
Conclusion
• Increasing of a number by 100, 200,
300, and 400 up to 100 or decreasing
by the same or any other groups of
denominations forms number pattern.
• Number patterns are groups or series
or series of numbers following a certain
rule.
Assessment
• Ask learners to form patterns of 100,
200 and 300.
• Ask them to do exercise 2G
• Give them remedial work to identify
activities forming number patterns in
45
importance of digitisation in learning to
writing numbers and number patterns.
• Explain to them that in such machines
you don’t have to struggle much. It gives
solutions and answers automatically
once you follow the correct procedure.
Assessment
• Observe learners as they manipulate
and handle the digital equipment such
as the tablet or the computer.
• Ask oral questions to guide them do the
play game eectively.
Conclusion
• Guide learners to appreciate number
patterns by creating patterns during
play activities.
• Let them role play a cashier in a daily
life experience such as counting money
in sh 5 coins.
• Let them dramatise a short play as you
facilitate their play to be eective.
• Digital devices are used to reinforce
learning and make the work easier.
Assessment
• Observation as they play.
• Question and answer session.
ANSWERS
Activity 2K
1. 100, 101, 102, 103, 104, 105, 106, 107,
108, 109, 110 , 111, 112, 113, 114, 115,
116, 117, 118, 119 , 120, 121, 122, 123,
124, 125, 126, 127, 128, 129, 130, 131,
132, 133, 134, 135, 136, 137, 138, 139,
140, 141, 142, 143, 144, 145, 146, 147,
148, 149, 150
2. 251, 252, 253, 254, 255, 256, 257, 258,
259, 260, 261, 262, 263, 264, 265, 266,
267, 268, 269, 270, 271, 272, 273, 274,
275, 276, 277, 278, 279, 280, 281, 282,
283, 284, 285, 286, 287, 288, 289, 290,
291, 292, 293, 294, 295, 296, 297, 298,
299, 300
3. 428, 429, 430, 431, 432, 433, 434, 435,
436, 437, 438, 439, 440, 441, 442, 443,
444, 445, 446, 447, 448, 449, 450, 451,
452, 453, 454, 455, 456, 457, 458, 459,
460, 461, 462, 463, 464, 465, 466, 467,
468, 469, 470, 471, 472, 473, 474
Activity 2L
1. 535, 536, 537, 538, 539, 540, 541, 542,
543, 544, 545, 546, 547, 548, 549, 550,
551, 552, 553, 554, 555, 556, 557, 558,
559, 560, 561, 562, 563, 564, 565, 566,
567, 568
2. 789, 790, 791, 792, 793, 794, 795, 796,
797, 798, 799, 800, 801
3. 972, 973, 974, 975, 976, 977, 978, 979,
980, 981, 982, 983, 984, 985, 986, 987,
988, 989, 990, 991, 992, 993, 994, 995,
996, 997, 998, 999
Activity 2M
1. (a) 101, 102, 103, 104, 105, 106, 107,
108, 109, 110
2. (b) 273, 274, 275, 276, 277, 278, 279,
280, 281
3. (c) 488, 489, 490, 491, 492, 493, 494,
495, 496, 497
4. (d) 710, 711, 712, 713, 714, 715, 716,
717, 718, 719, 720
5. (e) 968, 969, 970, 971, 972, 973, 974,
975, 976, 977
46
Activity 2N
1. (a) 2 bundles (b) 5 bundles
(c) 6 sticks
2. (a) hundreds (b) tens
(c) ones
Activity 2O
1. (a) (b)
(c)
2. (a) 415
4 – Hundreds
1 – Tens
5 – Ones
(b) 670
6 – Hundreds
7 – Tens
0 – Ones
(c) 809
8 – Hundreds
0 – Tens
9 – Ones
Exercise 2A
1. (a) 180, 181, 182, 183, 184, 185, 186,
187, 188, 189,190, 191, 192, 193,
194, 195, 196, 197, 198, 199, 200.
(b) 312, 313, 314, 315, 316, 317, 318,
319, 320, 321, 322, 323, 324, 325,
326, 327, 328, 329, 330, 331, 332,
333, 334, 335, 336, 337, 338, 339,
340, 341, 342, 343, 344.
(c) 601, 602, 603, 604, 605, 606, 607,
608, 609, 610, 611, 612, 613, 614,
615, 616, 617, 618, 619, 620.
(d) 885, 886, 887, 888, 889, 890, 891,
892, 893, 894, 895, 896, 897, 898,
899, 900.
2. (a) 440, 441, 442, 443, 444, 445, 446,
447, 448
(b) 179, 180, 181, 182, 183, 184, 185,
186, 187
(c) 601, 602, 603, 604, 605, 606 , 607,
608, 609
(d) 854, 855, 856, 857, 858, 859, 860,
861, 862
(e) 495, 496, 497, 498, 499, 500, 501,
502 , 503
3. (a) 120, 122, 124, 126, 128, 130, 132,
134, 136, ...
(b) 784, 786, 788, 790, 792, 794, 796,
798, 800, ...
4. (a) 110, 120, 130, 140, 150, 160, 170,
180, 190, ...
(b) 590, 580, 570, 560, 550, 540, 530,
520, 510, ...
5. (a) 945, 950, 955, 960, 965, 970, 975,
980, 985, ...
(b) 475, 470, 465, 460, 455, 450, 445,
440, 435, ...
H T O
4 1 5
H T O
6 7 0
H T O
8 0 9
47
H T O
2 4 5
H T O
3 6 1
Exercise 2B
1. (a) (b)
(c) (d)
H T O
6 5 7
 H T O
1 0 0 0
2. (a) 9 hundreds, 0 tens, 4 ones
(b) 7 hundreds, 8 tens, 1 ones
(c) 3 hundreds, 9 tens, 2 ones
(d) 5 hundreds, 0 tens, 0 ones
3. (a) 343 (b) 36
(c) 573
Activity 2P
1.
Number ousands Hundreds Tens Ones
754 7 5 4
2. (a) 7 = hundreds (b) 5 = tens
(c) 4 = ones
Exercise 2C
1.
Number ousands Hundreds Ten s Ones
94 9 4
857 8 5 7
339 3 3 9
564 5 6 4
781 7 8 1
242 2 4 2
198 1 9 8
975 9 7 5
656 6 5 6
1000 1 0 0 0
2.
Number ousands Hundreds Tens Ones
432 4 3 2
891 8 9 1
1000 1 0 0 0
317 3 1 7
213 2 1 3
48
3. (a) 7 hundreds, 3 tens, 2 ones
(b) 3 hundreds, 9 tens, 4 ones
(c) 3 hundreds, 4 tens, 0 ones
(d) 7 hundreds, 0 tens, 1 ones
(e) 0 hundreds, 7 tens, 1 ones
(f) 8 hundreds, 4 tens, 5 ones
(g) 1 hundreds, 2 tens, 5 ones
(h) 8 hundreds, 4 tens, 3 ones
(i) 4 hundreds, 3 tens, 1 ones
(j) 6 hundreds, 3 tens, 4 ones
(k) 3 hundreds, 2 tens, 6 ones
(l) 1 hundreds, 3 tens, 6 ones
4. (a) 253 = 0, thousands , 2-hundreds,
5-tens, 3- ones
(b) 427 = 0, thousands , 4-hundreds,
2-tens, 7- ones
(c) 314 = 0, thousands , 3-hundreds,
1-tens, 4- ones
(d) 678 = 0, thousands , 6-hundreds,
7-tens, 8- ones
(e) 562 = 0, thousands , 5-hundreds,
6-tens, 2- ones
(f) 741 = 0, thousands , 7-hundreds,
4-tens, 1- ones
(g) 195 = 0, thousands , 1-hundreds,
9-tens, 5- ones
(h) 1000 = 1, thousand , 0-hundreds,
0-tens, 0- ones
Activity 2Q
(a) Value of 6 is 6 × 10 = 60,
Value of 9 is 9 × 1 = 9,
b) Value of 1 = 1 × 100 = 100,
Value of 0 is 0 × 10 = 0,
Value of 3 = 3 × 1 = 3
Exercise 2D
1. (a) 5-tens
(b) 9- ones
(c) 1-hundreds
2. (a) 3-tens, 2- ones
(b) 9-tens, 4- ones
(c) 1-hundreds, 0-tens, 0- ones
Activity 2S
1. 10 - ten
20 - twenty
30 - thirty
40 - forty
50 - y
60 - sixty
70 - seventy
80 - eighty
90 - ninety
100 - one hundred
Activity 2T
1. (a) 21 - twenty one
(b) 26 - twenty six
(c) 59 - y nine
(d) 73 - seventy three
(e) 98 - ninety eight
Exercise 2E
1. 17 - seventeen
2. 44 - forty four
3. 25 - twenty ve
4. 30 - thirty
5. 0 - zero
6. 50 - y
7. 8 - eight
8. 48 - forty eight
49
9. 9 -nine
10. 21-tenty one
11. 11-eleven
12. 55 - y ve
13. 20-twenty
14. 96 - ninety six
15. 1-one
16. 72-seventy two
17. 7-seven
18. 91-ninety one
19. 12-twelve
20. 63-sixty three
21. 19
22. 35
23. 40
24. 57
25. 68
26. 71
27. 83
28. 94
29. 99
30. 100
Activity 2U
1. 807, 817, 827, 837, 847, 857, 867, 877,
887, ...
(a) = 817
(b) = 857
(c) = 867
Activity 2V
801 802 803 804 805 806 807 808 809 810 811
821 822 823 824 825 826 827 828 829 830 831
841 842 843 844 845 846 847 848 849 850 851
861 862 863 864 865 866 867 868 869 870 871
871 872 873 874 875 876 877 878 879 880 881
891 892 893 894 895 896 897 898 899 900 901
Exercise 2F
1. 760, 761, 762, 763, 764, 765, 766, 767, 768, ...
2. 221, 222, 223, 224, 225, 226, 227, 228
3. 11, 12, 13, 14, 15, 16, 17, 18, 19, ...
4. 831, 851, 871, 891, 911, 931, 951, 971, 991, ...
5.
(a) 235 236 237 238 239 240 241 242 243 244
(b) 245 246 247 248 249 250 251 252 253 254
(c) 255 256 257 258 259 260 261 262 263 264
(d) 265 266 267 268 269 270 271 272 273 274
(e) 275 276 277 278 279 280 281 282 283 284
(f) 285 286 287 288 289 290 291 292 293 294
50
6. (a) 334, 350, 366, 382, 398, …
(b) 81, 85, 89, 93, 97, 101, ...
(c) 408, 420, 432, 444, 456, ...
Exercise 2G
1.
1 95 13 172 106 14 183 117 15 194 128 16 20
2.
30 3834 42 4631 3935 43 4732 4036 44 4833 4137 45 49 50
51
Fractions
(Learner’s Book Pages 33 -47)
Suggested number of lessons: 20 Lessons
Specic learning outcomes
By the end of the sub-strand, the learner
should be able to:
(a) Identify
1
–
,
1
–
and
1
–
as part of a
whole.
(b) Identify
1
–
,
1
–
and
1
–
as part of a
group.
Core competence
Imagination and creativity,
communication and collaboration, critical
thinking and problem solving.
Key inquiry questions
How can you represent a half, a quarter or
an eighth of a group?
Link to PCIs:
Life skills: Interpersonal relationships,
friendship formation and decision making
Citizenship: understanding integrity-
sharing; social cohesion as they work in
groups.
ESD: environmental awareness- objects
collection
Link to other subjects
• Nutrition and hygiene
• Environmental activities
• Language activities
Pre-requisite to strand
A fraction is part of a whole object.
Before teaching and learning, the learners
should have prior knowledge of the
following concepts.
• Reading and writing whole numbers
• Counting of whole numbers up to 100
• Addition
Teaching and learning this sub-strand can
be challenging to some learners. You are
encouraged to have individual assistance
to the learners. Make the teaching and
learning process as interesting as possible
to the learners by ensuring that they all
participate in lessons. Include regalia in
your activities.
Teaching/learning resources
• Circular and rectangular cut-outs
• Marbles
• Bottle tops
• Sticks
• Grains
• Stones
• Fruits like oranges
Key words
• Fraction
• Cut-out
• Group
3
52
• Emphasise to the learners that, when
a whole object is cut into two equal
parts, each part is called half.
Conclusion
Emphasise that half means two equal
or corresponding parts into which
something is or can be divided.
Assessment
• Ask the learners to do Exercise 3A
Questions 1, 2, 3, 4, 5 in their books.
Check their work and help those who
may have challenges identifying half
shaded parts and those that may be
colour blind.
• Aer checking and marking their
books, encourage them to do
Questions 5, 6, 7, 8, 9 and 10 as an
assignment.
A quarter (
1
4
–
) of a whole
Speciﬁc learning outcomes
By the end of this lesson the learners
should be able to represent a quarter of a
whole.
Activity 3B
Preparation
• Ensure that there is enough manilla
papers and pairs of scissors in the
Mathematics corner to be used in this
activity.
• You may make cuttings of some shapes
that will guide the learners.
• Fold
• Equal parts
• A whole
Guidelines to the teaching/
learning experiences
Part of a whole
Half of a whole
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to represent half of a
whole.
Activity 3A
Preparation
• Organise to have enough manila
papers and pairs of scissors in the
Mathematics corner.
• Ensure that all the learners have all the
materials required for this activity.
Doing the activity
• Put the learners in groups of ve.
Ask them to carry out Activity 3A by
following the instructions given.
• Caution them against hurting each
other when using the pair of scissors.
Synthesis
• Discuss with the learners Example 1.
• Explain to them why the shaded parts
and the unshaded in the example are
equal.
53
• Give them more questions to practice
for the talented learners.
An eighth (
1
8
–
) of a whole
Speciﬁc learning outcome
By the end of the lesson the learners
should be able to represent numbers as an
eighth of a whole.
Activity 3C
Preparation
Ensure that the learners can be able to
obtain the shapes they cut and named as
quarter in Activity 3B.
Doing the activity
• Guide the learners in groups to carry
out Activity 3C while following the
instructions given.
• Advise them to be careful with the
cutting tools.
• Ensure that they are cutting the shapes
in the right way to get eight.
• ey should also take back all the
materials used and clean the working
area.
Synthesis
• Use Example 4 in the Learner’s Book
to explain that an eighth
1
8
–
is one
part of eight equal parts of a whole.
• Emphasise to them that; when a whole
object is divided into eight equal parts,
one of the parts is an eighth.
Doing the activity
• Organise the learners to carry out
Activity 3B. Advise them to follow the
instructions given.
• Learners should also be careful not to
hurt themselves when using the pairs
of scissors.
• Encourage them to share their ndings
amongst themselves in class. is will
enhance their communication skills as
well as enhance cohesion among them.
• Advise them to clean up their working
areas aer doing the activity.
Synthesis
• Take the learners through Example 2.
Let them appreciate that a circle can
be cut into 4 equal parts and in turn
embrace the idea of sharing an orange
amongst 4 friends.
• Explain to them that the shaded part
of the circle is
1
4
–
part of the whole
circle.
• Allow them to discuss Example 3
further as you go around checking
their work.
Conclusion
In conclusion, explain to the learners that
when one whole object is divided into
four equal parts, each part is referred to as
a quarter, and is written as
1
4
–
.
Assessment
• Ask the learners to do Questions 1-4
in Exercise 3B in class. Ensure that
the learners have grasped the concept.
• Let them work out Questions 5-10 as
an assignment.
54
Synthesis
• Use Example 5 in the Learner’s Book
to demonstrate to them that if a group
had 2 objects and was divided into 2,
the result is 1. is means half of 2 is 1.
• Similarly, explain to them that in
order to get the half of a group, always
divide the objects in the group into
two groups, for example:
• Guide the learners to understand that
half of 6 tomatoes is 3 tomatoes as
shown in Example 6.
Conclusion
Emphasise that when you divide a group
of members into two equal small groups,
each of the groups is referred to as half of
the group.
Assessment
• Use the question – answer method to
test the learner’s level of understanding
of the concept of a half.
• Ensure that they appreciate that in both
cases the answer is the same i.e. half
of a whole object and half of a group
mean the same.
• Take them to Exercise 3D. Discuss
Questions 1 and 4. Ask them to do
Questions 2, 3 and 5 as you mark their
books in class. Let the learners attempt
Questions 6, 7, 8 and 9 in their books
as further exercise.
Quarter of a group
Speciﬁc learning outcomes
By the end of this lesson, the learners
should be able to represent quarter of a
group.
Conclusion
Conclude the class by emphasising that an
eighth is each of the eight equal parts into
which something is or may be divided.
Assessment
• Take the learners through a Question
– answer session.
• Ask them to do Questions 1 to 9
in Exercise 3C. Give individual
attention to challenged learners. Let
them attempt Questions 10 to 15 as
homework.
Part of a group
Half of a group
Speciﬁc learning outcome
By the end of this lesson, learners should
be able to illustrate half of a group.
Preparation
Arrange enough containers in the
Mathematics corner that should be
enough for Activity 3D.
Doing the activity
• Organise the learners in pairs to
carry out Activity 3D by following the
instructions given.
• Ask them to discuss their ndings
amongst themselves. Engage the whole
class in discussing the same.
• Explain to them how the two groups
are formed and how each one of them
becomes
1
2
–
(half) of the whole group.
55
An eighth of a group
Speciﬁc learning outcome
By the end of this lesson the learners
should be able to represent an eighth of a
group.
Activity 3F
Preparation
Organise enough containers to be used
in Activity 3F in the Mathematics corner.
e containers should be of same size or
approximately of the same size.
Doing the activity
• Organise the learners to carry out
Activity 3F. Ensure that they follow all
the steps given.
• Encourage all the learners to participate
in the activity so as to sharpen their
skills.
• Advise them to take the counters back
to the Mathematics corner.
Synthesis
• Use Example 8 in the Learner’s Book
to explain to the learners the concept
of an eighth of a group.
1
8
–
is read as an eighth.
Conclusion
Assessment
• Ask the learners to do Questions 1 to
5 in Exercise 3F in order to gauge their
understanding of the concept. Let
them work out as you mark in class.
• Give a further exercise as an assignment.
Activity 3E
Preparation
Arrange the materials to be used by learners
to do Activity 3E.
Doing the activity
• Review the concept on
1
4
–
that was
previously taught.
• Organise the learners in pairs to carry
out Activity 3E. Introduce a quarter of
a group and compare their response.
• Encourage the learners to give answers
to the questions in the activity.
• Ask them to keep the counters for
future use. ey should also leave the
demonstration table clean as a way of
caring for their environment.
Synthesis
• Use Example 7 in the learner’s book to
demonstrate further the concept of a
quarter of a group.
Conclusion
In conclusion explain to them that a group
of objects divided into four gives a quarter.
Assessment
• Carry out an oral assessment on the
concept.
• Ask the learners, to do questions of
your own choice from Exercise 3E.
Supervise their work and mark in class.
• Give further exercise to the talented
learners as you attend to the ones
having diculties in understanding.
56
4.
1
8
5.
1
8
6.
1
8
7.
1
8
8.
1
4
9.
1
8
10. 11. 12.
13. 14. 15.
Activity 3D
2. (a) 2 groups
(b) half (
1
2
)
(c) 2
Exercise 3D
1. 4 2. 5 3. 6
4. 8 5. 10 6. 9
7. 7 8. 13 9. 17
Activity 3E
2. (a) 1 counter
(b) quarter (
1
4
)
(c) 1
Exercise 3E
1. 3 2. 2 3. 4
4. 5 5. 6 6. 8
7. 3 8. 10 9. 12
Activity 3F
2. (a) 2 groups
(b) an eight (
1
8
)
(c) 2
Exercise 3F
1. 1 2. 2 3. 3
4. 4 5. 5 6. 6
ANSWERS
Activity 3A
9. Half an orange
Exercise 3A
1. 2.
3. 4.
Shape 5, 6, 9, 10, 11, 12, 13 14, and 16 are
half shaded.
Activity 3B
3. (a) 2 pieces
(b) Yes. ey are equal. Compare their
sizes.
Exercise 3B
1. 2.
3. 4.
Shape 5, 8, 9, 12, 14, and 16 are half shaded.
Activity 3C
3. (a) 4 pieces
(b) Yes. ey are equal. Compare their
sizes.
4. 8 pieces. One-eight (
1
8
)
Exercise 3C
1.
1
8
2.
1
4
3.
1
8
57
Addition
(Learner’s Book Pages 48-66)
Suggested number of lessons: 20 Lessons
Specic learning outcomes
By the end of the sub-strand, the learner
should be able to:
(a) Add a 3- digit number to up to a
2 - digit number without regrouping
with sum not exceeding 1000.
(b) Add a 3- digit number to up to a
2- digit number with single
regrouping with sum not exceeding
1000.
(c) Add three single digit numbers with
sum up to 27.
(d) Add two 3- digit numbers without
regrouping.
(e) Add two 3- digit numbers with single
regrouping with sum not exceeding
1000.
(f) Work out missing numbers in
patterns involving addition up to 1000
(g) Create number pattern involving
addition up to 1000.
Core competences
Communication and collaboration,
Critical thinking and problem solving;
digital literacy, imagination and creativity
Key inquiry question(s)
1. How do you arrange numbers when
adding vertically?
2. How do you identify the rst two
numbers to add when adding three
single digit numbers?
3. How can you get the next number in a
given pattern?
Link to PCIs
ESD: DRR; Safety and Environmental
awareness, animal welfare- feeding
animals Life skills: Self- awareness-as they
use body parts in counting.
Link to other subjects:
Link to other subjects:
• Environmental activities
• Language activities
• Religious activities
Pre-requisite to the strand
Skills, knowledge, attitudes and values.
For the learners to understand addition
easily, they are expected to have learnt the
following:
• Basic addition facts
• Reading and writing whole numbers
• Identifying place value of numbers
• Knowledge of addition of up to 2-digit
numbers with and without regrouping
with sum not exceeding 100.
• Whole numbers, counting on,
forward and backwards
• Number concept – order numbers by
positions
• Addition of 3-single digit numbers up
to sum of 20.
4
58
Doing the activity
• Write the following mathematical
problem on the chalkboard: 356 + 32 =
• Discuss the addition process together
with the learners.
• Work with the learners through
Activity 4A.
• Guide them to add the numbers using
counters.
• Encourage them to start by adding
ones, then tens and nally the
hundreds.
Synthesis
rough class discussion;
• Guide the Learners to do Examples 1
and 2 in the Learner’s Book.
• Write the addition sentence below on
the chalkboard.
Work out: 413+6 =
• Guide them on how to work out the
problem.
413 + 6 = 419
add ones: 3+6 = 9,
add tens: 1+0 = 1,
add hundreds: 4 + 0 = 4
• Tell them to rst add ones then tens
and lastly hundreds.
Conclusion
Addition of numbers is easy without
regrouping.
Assessment
• Let the learners do Exercise 4A in the
Learner’s ’s Book.
• Ask them some oral questions as they
perform the activity.
Teaching/learning resources
• Counters
• Pictures in the Learner’s Book,
• Number cards
Key words or points
• Addition
• Sum
• With regrouping
• Without regrouping
• Vertical
• Horizontal
• Counting on forward and backwards
• Number patterns
• Column
• Ones, tens, hundreds
• Place value chart.
Guideline to teaching/learning
experiences
Addition of a 3-digit
number to a 2-digit number
Horizontal addition without
regrouping
Speciﬁc learning outcome
By the end of this lesson, the learner should
be able to add a 3-digit number to a 2-digit
number.
Activity 4A
Preparation
• Ensure that the learners have collected all
the necessary materials for this activity.
• Keep them at the Mathematics corner.
59
• Make sure you guide them on where to
write the answers they get according to
their place values.
• Guide them through Example 3 on the
chalkboard.
Add ones: 6 + 1 = 7,
Add tens: 1 + 6 = 7,
Add hundreds: 2 + 0 = 2
• Emphasise to the learners about where
to write the answers and how to write
them correctly.
Conclusion
Vertical addition is made easier by
drawing place value charts.
Assessment
• Ask the learners to do the rst 2
questions in Exercise 4B as you move
round guiding the weaker ones and
marking their work.
• Allow them to do Questions 3 to 5
from Exercise 4B as homework.
Horizontal addition with
regrouping
Speciﬁc learning outcome
By the end of this lesson, the learner
should be able to do horizontal addition
without regrouping.
Activity 4C
Preparation
• Ensure that the learners, have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
• Observation
Vertical addition without
regrouping
Speciﬁc learning outcome
By the end of this lesson, the learner should
be able to do vertical addition without
regrouping.
Activity 4B
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
Doing the activity
• Explain to the learners the meaning of
vertical addition and other key words
they might not be familiar with.
• Guide them how to solve problems
related to addition in a vertical
alignment.
• Let them use counters to do the addition.
• Allow them to share their ndings with
the whole class.
• Assist those with diculties in solving
the additional sentences.
Add ones: 5 + 1 = 6
Add tens: 4 + 3 = 7
Add hundreds: 1 + 0 = 1
Synthesis
rough class discussion;
• Emphasise to the learners that in order
to work out any addition sentence, one
must follow the given steps strictly.
60
Vertical addition with
regrouping
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to do vertical addition with
regrouping.
Activity 4D
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
Doing the activity
• Instruct learners to collect all the
materials which will be required in the
activity.
• Write the addition question on the
chalkboard from Activity 4D.
• Guide the learners to work out the
question using place value concept of
First add ones: 4 + 2 = 6
Add tens: 9 + 6 = 5
Take 1 hundred to the hundreds
Add hundreds: 1 + 6 = 7
• Explain and guide them through
Activity 4D.
Synthesis
• Let the learners do Example 5 on the
chalkboard as you guide them to get
the right answer.
rough class discussion;
• Write a similar example on the
chalkboard.
Doing the activity
• Write on the chalk board the addition
sentence:438 + 47 =
• Instruct them to follow the steps as you
explain.
• Guide them to realise that regrouping
replaced carrying. Tell them there is no
more use of carrying.
• Emphasise on the use of the word
regrouping. Summarise your activity by
letting them know the meaning of the
new key words.
Synthesis
rough a class discussion;
• Explain to the learners that addition
sentences can be with and without
regrouping.
• Lead and guide the learners to do
Example 4 in the Learner’s Book.
• Emphasise that they should always
start adding numbers in ones.
• Conclude your activity by ensuring
that the learners work together and
assist one another in their activity.
• Ask the learners to copy the example
done in their exercise books.
Conclusion
• Let them realise that regrouping was
replaced by carrying. Tell them there is
no more use of carrying.
Assessment
• Ask learners to do Exercise 4C in the
Learners Book .
61
Doing the activity
• Ask the learners to collect all the
necessary materials to be used in the
activity.
• Guide them to work out 6 + 8 + 9
using “counting on” strategy.
• Make sure they follow and understand
the steps involved in counting on.
• Guide the learners to work out
problems involving 3–single digit
numbers by use of a number line.
Synthesis
• Guide the learners to do Example 6 in
the Learner’s Book by counting on.
8 + 7 + 6 =
Steps:
- Count and have 8 in the head.
- Add 7 counters by counting on to 15.
- Have 15 in the head then count on 6
counters to 21.
Conclusion
• Fingers are quite instrumental when
counting on.
Assessment
• Ask learners to do Exercise 4E in the
Learners Book.
– Oral questions
– Observation as they work out the
questions.
erefore 8 + 7 + 6 = 21.
Addition by using the
numberline
Speciﬁc learning outcome:
By the end of this lesson, the learner
should be able to use the number line to
add 3-single digit numbers.
• Guide them on how to do the question
as discussed earlier.
• Summarise by making sure that the
learners understand how to work out
addition vertically with regrouping.
Conclusion
• Summarise by emphasising the key
word ‘regrouping’.
Assessment
• Ask learners to do Exercise 4D in
Learner’s Book.
• Ask them oral questions and let them
answer.
• Observe them as they work on the
exercise.
\
Addition of 3- single digit
numbers
Addition by counting on
Speciﬁc learning outcome
By the end of this lesson, the learner
should be able to do addition of 3-single
digit numbers.
Activity 4E
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
62
Speciﬁc learning outcome
By the end of this lesson, the learner
should be able to do addition of 3-single
digit numbers without regrouping.
Activity 4G
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
Doing the activity
• Guide the learners through Activity 4G
in the Learner’s Book.
• Guide them on how to use place value
charts.
• Emphasise the key words to the
learners.
• Assist those with learning diculties.
Synthesis
• Work out with learners the addition:
142 + 130 = ___
• Use the place value chart to work out
the question in Example 8.
H T O
4 5 2
H T O
3 1 6
H T O
7 6 8
+
=
Emphasise that they should add ones,
tens then hundreds in that order.
• Ask them to do Question 1 in Exercise
4G on the chalkboard.
Add: 334 – 125 =
• Ask them to use the same procedure
and steps as in Example 8 above.
Activity 4F
Preparation
• Ask the learners to be in pairs.
Learning experience
• Use the numberline to add: 4 + 3 + 2 =
• Guide the learners to add using the
number line by following the steps in
the Learner’s Book.
Steps
1. From 0 count 4 steps forward.
0 + 4 = 4.
2. From 4 count on 3 steps forward
4 + 3 = 7.
3. Now from 7 count 2 steps forward
7 + 2 = 9.
0
4
3
2
1 2 3 4 5 6 7 8 9 10
4. erefore 4 + 3 + 2 =9.
5. Take them through Example 7.
Conclusion
• e number line is a good and easy
way of doing additions of 3-single digit
numbers.
Assessment
• Ask learners to do Exercise 4F in the
Learner’s Book.
Addition of two 3-digit
numbers without
regrouping
Horizontal addition without
regrouping
63
steps of working out the question.
Discuss with the learners Example 9.
Add ones: 1 + 4 = 5,
Add tens: 2 + 3 = 5,
Add hundreds: 3 + 2 - 5
H T O
3
2
2
3
1
4
5 5 5
+
Conclusion
• Addition without grouping is very
straight forward because addition
begins with ones, then tens and nally
hundreds.
Assessment
• Ask the learners to do Exercise 4H in
the Learner's book.
• Ask oral questions
• Make observations as they do the
activity and the exercise.
Addition of two 3-digit
numbers with single
regrouping
Horizontal addition with
single regrouping
Speciﬁc learning outcome
By the end of this lesson, the learner
Assessment
• Ask learners to do Exercise 4G in the
Learner’s Book.
Vertical addition without
regrouping
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to do vertical addition
without regrouping.
Activity 4H
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
Doing the activity
• Guide learners though Activity 4H.
• Write the sentence on the chalkboard.
• Ask them to do the activity in their
books.
• Encourage them to use the place value
chart to add.
Add ones: 8+1=____
Add tens: 1+3=____
Add hundreds: 4+1=____
• Continue reminding learners that they
must add starting from ones, tens and
then hundreds.
Synthesis
rough a class discussion;
• Work out Example 9 on Learner’s
Book.
• Guide the learners as you explain the
64
the chalkboard.
(a) 124 + 383 =
(b) 436 + 183 =
• Use the place value charts to work out
each question.
• As usual learners should start adding
from the ones column.
Conclusion
• Remind them of the key words such as
column.
Assessment
• Let the learners do Exercise 4I in the
Learner’s Book Questions 1 to 5.
• Oral Questions can also be used to
assess the learners’ understanding.
• Observation.
Vertical addition with
single regrouping
Speciﬁc learning outcome
By the end of this lesson, the learner
should be able to do vertical addition with
single regrouping.
Activity 4J
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
Doing the activity
• Guide the learners through Activity 4J
in Learner’s Book.
should be able to do horizontal addition
with single regrouping.
Activity 4I
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
Doing the activity
• Guide learners through Activity 4I in
Learner’s Book.
• Invite one learner to come and work
out the sum on the chalkboard
465 + 173 =
• Guide the learners to draw the correct
place value chart.
Ask them to rst add ones: 5 + 3 = 8.
Emphasize that they write 8 in the
ones place.
en Add tens: 6 + 7 = 13. Regroup.
Help them to regroup 13 into 1
hundreds and 3 tens.
• Let them write 3 tens under the tens
column.
• Tell them to take 1 hundred to the
hundreds column and add to 4 before
adding to 1. 1 + 4 + 1= 6.
erefore, 465 + 173 = 638.
• Encourage the learners to always
participate in class activity.
Synthesis
• Guide the learners to work out the
questions correctly.
• Copy the questions in Example 10 on
65
By the end of this lesson the learner
should be able to do addition with a
digital device.
Activity 4K
Preparation
• Ensure that the learners have their
tablets for this activity.
Doing the activity
• Provide the digital tablets and other
materials to enhance the activity.
• Guide the learners to switch on their
tablets.
• Guide them to follow instructions on
the digital game you have selected
involving addition.
• Ensure all the learners participate
fully and are almost at at par with each
other.
Synthesis
rough class discussion;
• Guide learners to work out addition by
using the key board.
• As you guide them, ensure you keep
on emphasising on major key words
like icons, keyboard, control bulletin
‘+’, button, ‘=’ sign button and many
others.
Let them add:
3 + 4 =
15 + 7 =
76 + 22 =
232 + 46 =
567 + 121 =
478 + 51 =
• Invite one learner to come and work
out the sum on the chalkboard.
582 + 356 =
• Guide the learners to draw a correct
place value chart.
• Ask them to rst add ones: 2 + 6 = 8
• Add tens and emphasise that 8 + 5 = 13.
Regroup 13 into hundreds and 3 tens.
• Let them write 3 tens under the tens
column.
• Guide them to take 1 hundred to
hundreds column and add to 5 before
adding to 3. 1 + 5 + 3 = 9
erefore, 582 + 356 = 938.
Synthesis
• Guide the learners to discuss Example
11 in class.
• Let them follow the above steps and
perform addition.
Conclusion
• Remind them of the key words such
as column place value, tens, ones and
hundred.
Assessment
• Let the learners do Exercise 4J in the
Learner’s Book.
• Supervise them to individually to do
Questions 1 to 3.
• Let them have questions 4 to 6 as home
work.
Digital game
Speciﬁc learning outcome
66
• Let them nd the missing numbers
using the addition rule.
What is 293 – 289?
• Let them know that the answer is the
addition rule for the pattern.
Guide them to add 4 to 281 to get 285?
is is the second number in the
pattern.
Add 4 to 297 =? is is the sixth number
in the pattern.
Add 4 to ___ =? is is the seventh
number in the pattern.
• Ask them to write their answers.
Synthesis
Guide them through Example 12.
326, 351, 356, ____, 371.
Guide them through Example 13 on
solving word problems on addition.
Conclusion
• Summarise by highlighting that we use
the addition rule to get values of the
next number in a pattern.
Assessment
• Let them do question in Exercise 4K in
their exercise books.
• Ask them to do Questions 2 to 6 of word
problems in Exercise 4L as a further
exercise.
ANSWERS
Activity 4A
1. 3 + 5 = 8
2. 4 + 2 = 6
3. 2 +0 = 2
359 + 24 =
• Guide those with diculties to move at
the same pace with others.
Conclusion
Tablets help in performing quick addition.
Assessment
• Let the learners do addition using their
tablets.
• Let them repeat the questions you
worked with them a, b, c, d, e, f and g
on their own.
• Move around and observe what the
learners are doing.
Number patterns involving
addition
Speciﬁc learning outcome
By the end of this lesson, the learner
should be able to identify missing
numbers in a pattern.
Activity 4L
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
Doing the activity
• Guide the learners to work out the
missing numbers by lling the gaps in
the addition patterns.
281,____ 289, 293, 297, ___, ___, 303.
67
438 + 47 = 484
Exercise 4C
1. 591 2. 685 3. 790
4. 436 5. 840 6. 335
Activity 4D
694 + 62 = 756
Exercise 4D
1. 261 2. 862 3. 206
4. 959 5. 351 6. 441
7. 585 8. 495 9. 790
Activity 4E
6 + 8 + 9 = 23
Exercise 4E
243 + 25 = 268
Exercise 4A
1. 498 2. 318 3. 449
4. 299 5. 186 6. 878
7. 878 8. 699 9. 198
10. 187 11. 239 12. 325
Activity 4B
1. 5 + 1 = 6
2. 4 + 3 = 7
3. 145 + 31 = 176
Exercise 4B
1. 346 2. 477 3. 288
4. 459 5. 879 6. 199
Activity 4C
1. 19 2. 19 3. 18
4. 14 5. 27 6. 20
Activity 4F
8 + 3 +4 = 15
Exercise 4F
1.
0 84 12 161 95 13 172 106 14 183 117 15 19
3
9 5
3 + 9 + 5 = 17
2.
0 84 121 95 132 1063 117
5
4
2
5 + 4 + 2 = 11
68
3.
0 84 121 95 13 14 15 16 172 1063 117
6
3
7
6 + 3 + 7 = 16
4.
0 84 121 95 132 1063 117
6
3
2
6 + 3 + 2 = 11
5.
0 5 10 15 204 9 14 19 24 251 6 11 16 212 7 12 17 223 8 13 18 23
8 8 8
8 + 8 + 8 = 24
Activity 4G
142 + 130 = 272
Exercise 4G
1. 334 + 125 =
H T O
3 3 4
+
H T O
1 2 5
=
H T O
4 5 9
2. 143 + 341 =
H T O
1 4 3
+
H T O
3 4 1
=
H T O
4 8 4
3. 207 + 121 =
H T O
2 0 7
+
H T O
1 2 1
=
H T O
3 2 8
4. 635 + 122 =
H T O
6 3 5
+
H T O
1 2 2
=
H T O
7 5 7
5. 205 + 113 =
H T O
2 0 5
+
H T O
1 1 3
=
H T O
3 1 8
69
6. 734 + 245 =
H T O
7 3 4
+
H T O
2 4 5
=
H T O
9 7 9
7. 214 + 163 =
H T O
2 1 4
+
H T O
1 6 3
=
H T O
3 7 7
8. 364 + 431 =
H T O
3 6 4
+
H T O
4 3 1
=
H T O
7 9 5
Activity 4H
418 + 131 = 549
Exercise 4H
1. 588 2. 939 3. 949
4. 897 5. 656 6. 699
Activity 4I
465 + 173 =
H T O
4 6 5
+
H T O
1 7 3
=
H T O
6 3 8
Exercise 4I
1. 157 + 661 =
H T O
1 5 7
+
H T O
6 6 1
=
H T O
8 1 8
2. 643 + 162 =
H T O
6 4 3
+
H T O
1 6 2
=
H T O
8 0 5
3. 284 + 271 =
H T O
2 8 4
+
H T O
3 7 1
=
H T O
6 5 5
4. 314 + 294 =
H T O
3 1 4
+
H T O
2 9 4
=
H T O
6 0 8
5. 754 + 164 =
H T O
7 5 4
+
H T O
1 6 4
=
H T O
9 1 8
70
6. 419 + 390 =
H T O
4 1 9
+
H T O
3 9 0
=
H T O
8 0 9
7. 438 + 181 =
H T O
4 3 8
+
H T O
1 8 1
=
H T O
6 1 9
8. 841 + 73 =
H T O
8 4 1
+
H T O
7 3
=
H T O
9 1 4
Activity 4J
582
+ 356
938
Exercise 4J
1. 790 2. 940 3. 562
4. 361 5. 890 6. 509
Activity 4L
281, 285, 289, 293, 297, 301, 305, 309
Exercise 4K
A
1. 510, 520, 530, 540, 550, 560, 570, 580,
590, 600
2. 115, 116, 117, 118, 119, 120, 121, 122,
123, 124
3. 675, 680, 685, 690, 695, 700, 705, 710,
715, 720
4. 100, 200, 300, 400, 500, 600, 700, 800,
900, 1000
5. 322, 323, 324, 325, 326, 327, 328, 329,
330, 331, 332, 333
B
1. 4, 8, 12, 16,
2. 17, 22, 27, 32, 37
71
Subtraction
(Learner’s Book Pages 67–85)
Suggested number of lessons: 20 Lessons
Specic learning outcomes
By the end of the sub-strand, the learner
should be able to:
(a) Subtract up to 3- digit numbers with
single regrouping.
(b) Subtract up to 3- digit numbers
involving missing numbers without
regrouping.
(c) Work out missing numbers in number
patterns involving subtraction up to
1000.
Core Competences to be
developed
Communication and collaboration,
critical thinking and problem solving,
digital literacy
Key inquiry question(s)
• When do you regroup during
subtraction?
• How do you identify the missing
number in a number pattern ?
Link to PCIs
ESD: environmental awareness as learners
work out subtraction
Link to other subjects
• Languages
• Nutrition and Hygiene
• Environmental activities
Pre-requisites to the strand
Subtraction is a sub-strand under
numbers. is is not a new concept to the
learners as it has been taught in Grades 1
and 2 so the basic subtraction facts have
been covered.
For the teaching and learning process
to proceed with less diculties, learners
ought to be reminded:
• Reading and writing numbers in
symbols
• Counting
• Subtraction of up to 2-digit numbers
• Number patterns involving subtraction
Teaching learning resources
• Counters
• Place value chart
Key words
• Subtraction
• Regrouping
• Subtraction
• Sentences
5
72
numbers from 3-digit numbers without
regrouping.
• Emphasise to the learners that when
subtracting they have to start with ones
followed by tens and nally hundreds.
• Give them another example to discuss
the same. Let the ve groups work it
out together on the board. Encourage
them to participate as this helps
develop their problem solving skills,
critical thinking, communication and
collaboration.
• Use Example 2 to show that subtraction
can be done without displaying the
place value letters, H, T, O.
Conclusion
• e abacus makes subtraction of
numbers easier and workable.
Assessment
• Start by working out Exercise 5A
together with the learners.
• Ask them to work out, questions from
Exercise 5A. Supervise their working
and mark the books.
• Revise the questions in class.
• Let them attempt questions in Exercise
5B. Revise with them aer marking.
Vertical subtraction without
regrouping
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to do vertical subtraction
without regrouping.
Guidelines to the teaching/
learning experiences
Subtraction of 2-digit
numbers from 3-digit
numbers
Horizontal subtraction without
regrouping
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to do horizontal
subtractions without regrouping.
Activity 5A
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Organize the learners into groups of 5.
Doing the activity
• Guide the learners to using the abacus
to do this activity.
• Guide them to remove the beads on
the abacus from the ones rod and from
the tens rod. Let them write down the
result of the subtraction.
• Make them understand that in
subtraction we start with ones, tens
then nally subtract the hundreds.
Synthesis
rough a class discussion:
• Use Example 1 to discuss with the
learners on subtraction of 2-digit
73
Assessment
• Ask the learners to attempt Exercise 5C
Questions 2-12.
• Mark their books to assess their level of
understanding.
Horizontal subtraction with
regrouping
Speciﬁc learning outcome
By the end of this lesson, the learner
should be able to do horizontal
subtraction with regrouping.
Activity 5C
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
Doing the activity
• Review subtraction with regrouping.
• Guide the learners through all the
steps involved in working out 456 – 29.
• Make the lesson as interactive as
possible by ensuring that all the
learners answer your questions.
• Encourage the learners to ask questions
aer which you involve other learners
in answering. is inculcates the
competitive spirit.
Synthesis
• Discuss Example 4 with the learners
• Explain to them how regrouping in the
ones is done.
Activity 5B
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
• Organise the learners into groups of 5.
Doing the activity
• Review vertical subtraction of up to
2-digits without regrouping.
• Guide the learners through Activity 5B.
• Ensure that they understand each and
every step in the activity.
• Emphasise on starting with ones, then
tens and nally hundreds.
Synthesis
rough a class discussion;
• Guide with the learners through
Example 3.
• Explain to them that subtraction is only
possible if the smaller number is being
taken away from the bigger number.
• Use Question 1 of Exercise 5C as a
further example.
• Ask ve learners to work it out on the
chalkboard with the contribution of
others in the class. Find out who is
correct.
• Review the question together.
Conclusion
• Subtraction of numbers is possible if
the number being taken away is smaller
than the other number.
74
Activity 5D
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
Doing the activity
• Guide the learners through the steps of
Activity 5D.
• Demonstrate to the learners the
concept of regrouping using counters.
Synthesis
• Use Example 5 to reinforce the concept
of subtraction with regrouping.
Examples 5
Subtract ones by regrouping 94
into 9 tens and 4 ones.
Take away 1 ten from 9 tens to
make 10 ones.
10 ones plus 4 ones gives 14 ones.
Subtract 5 from 14 to get 9. Write 9
in the ones place.
Subtract tens: 8 – 7 = 1
Subtract hundreds. 2 – 0 = 2
Explain to the learners how
regrouping 4 makes it possible to
subtract 5.
• Guide the learners to carry out
subtraction with regrouping. Encourage
them to participate by choosing 3
learners to work it out on the board.
• Ensure that the learners understand
when to regroup.
• Emphasise that regrouping can only
be done when a bigger number is to be
subtracted from a smaller number i.e
2-7 is not possible.
erefore, 2 is regrouped to 12 ones
aer taking away 1 tens from 8 tens.
1 ten = 10 ones added to 2 to give 12.
Conclusion
• Emphasise that regrouping can only
be done when a bigger number is to be
subtracted from a smaller numbers.
Assessment
• Guide the learners in working out
questions of Exercise 5D.
• Ask them to attempt Questions 2, 3, 4,
5 in their books, supervise the working
and mark the books in class.
• Give more work to the gied learners
while oering individual attention to
the ones having diculties.
• Ask them to complete the exercise as
homework for further practice.
Vertical subtraction with
regrouping
Speciﬁc learning outcome
By the end of this lesson, the learner
should be able to do vertical subtraction
with regrouping.
75
Synthesis
rough a class discussion:
• Discuss with the learners the working
out of Example 6.
• rough question/answer method,
reinforce this concept.
Conclusion
• Placing the numbers in a place value
chart makes it easier to subtract..
Assessment
• Let the learners do Questions 1-5 of
Exercise 5F in class mark and correct
the work with them.
• Ask them to do 5 more questions as
homework.
• At this point the learners could be
tested on the concept.
• Carry out remedial lessons for those
with challenges.
Vertical subtraction without
regrouping
Speciﬁc learning outcome
By the end of this lesson, the learner
should be able to do vertical subtraction
without regrouping.
Activity 5F
Preparation
• Ensure that the learners have collected
all the necessary concepts for this
activity.
• Keep them at the Mathematics corner.
Conclusion
It is only through regrouping that we are
able to subtract bigger numbers from
smaller numbers.
Assessment
• Let the learners do the questions in
Exercise 5E.
• Give more questions for practice so as
to master the concept.
Subtraction of two 3-digit
numbers
Horizontal subtraction
without regrouping
Speciﬁc learning outcome
By the end of this lesson, the learner should
be able to do horizontal subtraction without
regrouping.
Activity 5E
Preparation
• Ensure that the learners have collected all
the necessary materials for this activity.
• Keep them at the Mathematics corner.
Doing the activity
• Guide the learners through all the steps
in this Activity 5E.
• Let them work out the answers at every step.
Are they able to see how the nal answer
develops from the steps?
• is should be an interactive lesson
where you guide the learner to discover
by himself/herself.
76
Activity 5G
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
Doing the activity
• Review the previous lesson through
a question and answer session and an
example and correct previous work.
• Organise the learners to carry out
Activity 5E involving subtraction of
172 from 854.
• Ensure that the learners have grasped
the steps and particularly regrouping
the tens before subtracting.
Synthesis
rough a class discussion;
• Use Example 8 to explain to the
learners the concept of subtraction
with regrouping the tens.
• Guide them on how to regroup the tens
and hundreds.
Conclusion
• Emphasise on regrouping to the
learners.
Assessment
• Ask the learners to do Questions 1 to 3
from Exercise 5H.
• Observe what they are doing. Mark
their work and revise with them.
• Let them do other questions for further
practice.
Doing the activity
• Review with the learners the lesson
on horizontal subtraction without
regrouping.
• Also organise to revise the test
previously done.
• Take the learners through Activity 5F.
• Guide them through all the steps
leading to the answer.
• Advise them to make use of the place
value chart for consistency wherever
necessary.
Synthesis
• rough question and answer.
• Guide the learners through Example 7.
• Give a similar example on the chalkboard
for three learners to workout.
Conclusion
Subtraction of 3-digit numbers without
regrouping is made easier by using place
value charts.
Assessment
• Ask them work out 4 questions in
Exercise 5G.
• Ask them to do Questions 6 to 12 in
their exercise books as further practice.
Horizontal subtraction with
regrouping
Speciﬁc learning outcome
By the end of this lesson, the learner
should be able to do subtraction of
two 3-digit numbers horizontally with
regrouping.
77
• Discuss an example involving word
problems.
Conclusion
• Conclude by briey reviewing the
concept of regrouping.
•
Assessment
• Ask the learners to do Exercises 5I
and 5J in class and as homework
respectively.
Finding missing numbers
in subtraction sentences
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to do missing numbers in
subtraction sentence.
Activities 5J and 5K
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity. ese include stones, number
cards, ash card etc.
• Keep them at the Mathematics corner.
Doing the activities
• Guide the learners through Activity 5J.
• Let them write their answers in exercise
books.
• Ask them to do Activity 5K in pairs.
Synthesis
• rough brainstorming.
Vertical subtraction with
regrouping
Speciﬁc learning outcome
By the end of this lesson, the learner
should be able to do vertical subtraction
with regrouping.
Activities 5H and 5I
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
Doing the activity
• Review the lesson on vertical
subtraction of up to 2 – digits with
regrouping.
• Ask them probing questions to test how
much they have grasped the idea of
regrouping.
• Take them through Activity 5H, guiding
them in every step.
• Prepare them for Activity 5I. Let them
carry out the activity in pairs.
Synthesis
rough a class discussion:
• Discuss with the learners the working
of Example 9. Explain how possible it
is to subtract 7 from 6.
6 – 7 = not possible
• It is only possible by regrouping 76.
• rough a question/answer method,
reinforce this consent of regrouping.
• Use more examples like Examples 10
and 11 and take time to listen and attend
to challenged learners.
78
Doing the Activity
• Guide the learner through the Activity.
• Prompt them to identify the rule of
the pattern by subtracting consecutive
numbers.
• Ask them to complete the pattern using
the rule.
Synthesis
• Use Example 13 to discuss with the
learners the rules involved in nding
the missing numbers.
Conclusion
• is is done by nding a subtraction
rule.
• Emphasize to the learners that use of
subtraction rules helps in getting the
next number in the pattern.
Assessment
• Let them work out Exercise 5L
questions 1 to 5 in the Learners Book.
• Test the learner’s understanding of the
concepts learnt in this strand.
Digital game
Speciﬁc learning outcome
By the end of this lesson, the learner
should be able to do subtraction using a
tablet.
Activity 5K
Preparation
• Ensure that the learners have tablets for
this activity.
• Guide the learners through Example
12.
• Let them understand how the missing
numbers are obtained by use of
number families.
• Use another example, and let them
discuss it on chalkboard.
• is will help build their condence.
Conclusion
• Explain to them that in number
families, the numbers are inter-related.
For example,
294 – 113 = 181 and
294 – 181 = 113.
Assessment
• Let the learners do Questions 1 to 5 of
Exercise 5K.
• Mark and return the books.
• Give them the remaining questions to
do as homework.
Number patterns
Finding missing numbers
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to nd missing numbers
in number patterns.
Activity 5L
Preparation
• Ensure the learners have picked necessary
materials from the mathematical corner.
79
Activity 5A
2. 114
(d) 4
(e) 1
3. 146 – 32 = 114
H T O
1 4 6
H T O
3 2
H T O
1 1 4
–
=
Exercise 5B
1. 271 2. 311 3. 511
4. 321 5. 820 6. 301
7. 425 8. 323 9. 921
10. 305
Activity 5B
1. 8 – 2 =6
2. 6 – 4 = 2
3. 5 – 0 = 5
568 – 42 = 526
Exercise 5C
1. 536 2. 647 3. 422
4. 310 5. 162 6. 112
7. 120 8. 255 9. 160
10. 714 11. 316 12. 472
Activity 5C
Step 2: 16 ones – 9 ones = 7 ones
Step 3: 4 tens – 2 tens = 2 tens
Step 4: 4 hundreds – 0 hundreds = 4
hundreds
456 – 29 = 427
Exercise 5D
1. 326 2. 237 3. 455
4. 508 5. 609 6. 125
7. 356 8. 305 9. 146
10. 256
Doing the activity
• Guide them on how to use the tablets
using the steps given in Activity 5M
• Ensure that they are able to play games
involving subtraction using the tablets.
Synthesis
rough observation;
• Give the learners more questions and
observe as they do.
• Assist those with challenges.
Conclusion
• Tablets are able to perform subtraction
with or without grouping very fast.
Assessment
• Give the learners an exercise which
they can solve while playing the games.
ANSWERS
Activity 5A
114
Exercise 5A
1.
H T O
3 5 3
H T O
3 1
H T O
3 2 2
–
=
2.
H T O
4 9 3
H T O
7 2
H T O
4 2 1
–
=
3.
H T O
5 4 7
H T O
1 6
H T O
5 3 1
–
=
4.
H T O
1 7 6
H T O
5
H T O
1 7 1
–
=
5.
H T O
3 4 6
H T O
3 4
H T O
3 1 2
–
=
80
4. 411 5. 121 6. 45
7. 20 8. 5 9. 122
10. 343 11. 251 12. 223
Activity 5G
Step 1:
H T O
8 5 4
H T O
1 7 2
H T O
6 8 2
–
=
Step 2: 4 ones – 2 ones = 2 ones
Step 3: 15 tens – 7 tens = 8 tens
Step 4: 7 hundreds – 1 hundreds = 6
hundreds
854 – 172 = 682
Exercise 5H
1.
H T O
3 5 4
H T O
1 7 2
H T O
1 8 2
–
=
2.
H T O
3 6 4
H T O
2 7 2
H T O
9 2
–
=
3.
H T O
1 2 7
H T O
9 2
H T O
3 5
–
=
4.
H T O
2 3 8
H T O
1 9 3
H T O
4 5
–
=
5.
H T O
4 1 9
H T O
3 2 5
H T O
9 4
–
=
6.
H T O
5 3 9
H T O
4 6 3
H T O
7 6
–
=
7. 238
8. 128
9. 216
Activity 5D
Step 1: 12 ones – 8 ones = 4 ones
Step 2: 5 tens – 3 tens = 2 tens
Step 3: 5 hundreds – 0 hundreds =
5 hundreds
562 – 38 = 524
Exercise 5E
1. 328 2. 437 3. 549
4. 627 5. 128 6. 216
Activity 5E
Step 1:
H T O
4 6 8
H T O
2 4 3
H T O
2 2 5
–
=
Step 2: 8 ones – 3 ones = 5 ones
Step 3: 6 tens – 4 tens = 2 tens
Step 4: 4 hundreds – 2 hundreds =
2 hundreds
448 – 243 = 225
Exercise 5F
1. 122 2. 103 3. 214
4. 204 5. 110 6. 206
7. 111 8. 124 9. 502
10. 44
Activity 5F
Step 1: 9 ones – 2 ones = 7 ones
Step 2: 8 tens – 7 tens = 1 ten
Step 3: 4 hundreds – 3 hundreds =
1 hundreds
489 - 372 = 117
Exercise 5G
1. 512 2. 122 3. 227
81
10. 118
11. 151
12. 351
Activity 5H
Step 2: 14 tens – 6 tens = 8 tens
Step 4: 4 hundreds – 3 hundreds = 1
hundreds
546 – 362 = 184
Exercise 5I
1. 163 2. 162 3. 250
4. 130 5. 328 6. 143
7. 246 8. 216
Activity 5I
1. 83
2. 207
Exercise 5J
1. 28 2. 230 3. 305
4. 456 5. 277 6. 486
7. 207
Activity 5J
1 (a) 349 – = 296
(b) 53
2 (a) – 24 = 109
3. 133
Activity 5K
225 + 10 = 235
235 – 225 = 10
Exercise 5K
1. 442,564 2. 13,163 3. 39,685
4. 363,379 5. 466 6. 374
7. 53 8. 108 9. 458
10. 400 11. 0 12. 267
13. 547 14. 729
Activity 5L
1. 94 – 90 = 4 and 90 – 86 = 4
2. 82, 78, 70
Exercise 5L
1. 90, 85, 80, 60, 55
2. 100, 80
3. 180, 60, 30, 0
4. 350, 250, 200
5. 64, 60, 56, 52
6. 300, 100
82
Multiplication
(Learner’s Book Pages 86–102)
Suggested number of lessons: 10 Lessons
Specic learning outcomes
By the end of the sub-strand, the learner
should be able to:
• Multiply single-digit numbers by numbers
from 1 to 10 in dierent contexts.
Core competences
Communication and collaboration,
Imagination and creativity, Self-ecacy
Key inquiry question(s)
What is 5 × 6?
What is 7 × 10?
Link to PCIs
Life skills: Self –awareness- use of body
parts
ESD: DRR; Environmental conservation
-learners re-use materials and objects;
animal welfare-feeding animals
Link to other subjects
• Language activities
• Environmental activities
• Movement and creative activities
Pre-requisite to the sub-strand
For the learners to acquire the knowledge,
skils and values visualised in this sub-
strand with ease, they ought to have learnt
addition, subtraction and counting of
numbers 1 to 100. e knowledge acquired
in the previous classes will facilitate the
teaching and learning process while
tackling this sub-stand. For example, the
meaning of multiplication, multiplication as
repeated addition, and the number line and
multiplication sentences.
Teaching /learning resources
• Counters
• Chart showing multiplication of
numbers
• Realia
Key words
• Multiplication
• Digit
• Group
• Repeated addition
• Multiplication table
Multiplication by 1
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to multiply single-digit numbers
by 1.
6
83
Assessment
• Go through question 1 of Exercise 6A
together with the learners.
• Select some 4 questions for the learners
to do in class. Ensure that all the
learners receive individual attention
when necessary.
• Ask the learners to do 2 more questions
as homework.
Multiplication by 2
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to multiply single-digit numbers
by 2.
Activity 6B
Preparation
• Ensure there are enough counters, and
other required materials for this activity
in the Mathematics corner.
Doing the activity
• Review the previous lesson by taking
the learners through a question and
answer session. is is meant to gauge
their level of understanding as well as
how much they can still remember.
• Ask the learners to be in groups. Let
them carry out Activity 6B.
• Advise them to pay attention to the
instructions given.
• Encourage the learners to discuss among
themselves aer which they can answer
the questions in the activity. Note that
this will promote teamwork and help
boost their self-esteem.
Activity 6A
Preparation
• Ensure that there are enough counters,
and other required materials for this
activity in the Mathematics corner.
Doing the activity
• Organise the learners into convenient
groups.
• Ask them to do Activity 6A.
• Guide the learners to answer the
questions asked in the activity.
• Let learners appreciate the basic multiplication
facts; as a group of objects and as repeated
addition as well.
• Ask them to take back the counters for future
use. ey should also leave the working area
clean and neat.
Synthesis
• Multiplication of single-digit numbers will
involve numbers 1 to 10. Multiplication
shall be taught as:
(i) A group of objects.
(ii) Repeated addition.
(iii) Using a multiplication table
• Discuss with the learners through
Example 1 in the learner’s Book
• Learners to understand that; 1 group of
2 objects is written as 1 × 2 which is the
same as 1 + 1 = 2.
• Ask the learners some oral questions
related to the lesson so as to test their
understanding.
Conclusion
We use repeated addition to correctly
multiply numbers by 1.
84
Activity 6C
Preparation
• Ensure that there are enough counters,
and other required materials for this
activity in the Mathematics corner.
Doing the activity
• Organise the learners into groups of 3.
• Let them pick 6 counters from the
Mathematics corner.
• Guide the learners to read through
Activity 6C in their various groups.
• Encourage the learners to share their
ndings with the rest of the class.
• Ask the learners to take counters back
to the Mathematics corner aer the
activity.
Synthesis
• Discuss with the learners Example 3.
• Ask them some oral questions related
to the example.
• Ask the learners to explain or discuss
why 3 groups of 2 baskets is
3 × 2 = 6 and 2 + 2 + 2 = 6
• Go through Question 1 of Exercise 6C
so as to facilitate their understanding.
Ask them to do numbers 2 and 3 in
their books as you supervise.
• Correct on the board where necessary.
Conclusion
We use repeated addition or tablets or
calculators to correctly multiply numbers
by 3.
Assessment
• Discuss with the learners Question 1 of
Exercise 6C in the Learner’s Book.
• Ask the learners what they understand
by multiplication by 2. Advise them to
leave the working area clean aer taking
back the counters.
Synthesis
• Discuss with the learners through
Example 2 in the Learner’s Book.
• Ask the learners some oral questions
related to the Example above. is helps
their imagination and thinking.
• Guide the learners to learn that 2 groups
of 2 cups can be written as
2 × 2 = 4. is is also true. 2 +2 = 4
Conclusion
We use repeated addition or tablets or
calculators to correctly multiply numbers
by 2.
Assessment
• Discuss with the learners Question 1 of
Exercise 6B in the Learner’s Book.
• Encourage them to ask you as many
questions as possible.
• Ask the learners to do Questions 2 and
3 of Exercise 6B as you move around
the classroom marking their books.
• Carry out the recapitulation session so
that the less talented learners can catch
up with the rest of the class.
Multiplication by 3
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to multiply single-digit
numbers by 3.
85
• Ask them to identify the number of
groups of the objects per group.
• Guide the learners to appreciate the
basic multiplication and addition facts.
• Allow the learners to copy the example
in their books. Ask them to explain the
working of Question 1 of Exercise 6D.
Conclusion
We use repeated addition or tablets or
calculators to correctly multiply numbers
by 4.
Assessment
• Ask the learners to do Questions 2 and
3 in Exercise 6D. Supervise and mark
the learners work in class.
• Do corrections and give related
questions to the learners as homework.
• Ask them to do the rest of the questions
in Exercise 6D.
Multiplying by 5
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to multiply single-digit numbers by
5.
Activity 6E
Preparation
• Ensure there are enough counters, and
other required materials for this activity
in the Mathematics corner.
• Organise them in groups.
Doing the activity
• Ask the learners to do Activity 6E
following the given instructions.
• Encourage them to ask as many
questions as possible.
• Ask the learners to do some other
questions as home work.
Multiplication by 4
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to multiply single-digit numbers
by 4.
Activity 6D
Preparation
• Ensure that there are enough counters,
and other required materials for this
activity in the Mathematics corner.
Doing the activity
• Ask the learners some probing questions
related to multiplication. Find out from
them what repeated addition is and ask
them to relate multiplication to repeated
addition.
• Conveniently group the learners.
• Let the learners pick the teaching and
learning materials from the Mathematics
corner.
• Ask the learners to carry out Activity
6D. Advise them to read and to follow
the instructions.
• Encourage them to share their ndings
with other members of the class.
• Ask them to return the counters in their
right box.
Synthesis
• Discuss with the learners Example 4.
86
to discover that the addition statements
are related to the multiplication ones.
• Discuss and share with the learners the
ndings of the activity.
Synthesis
• Discuss with the learners Example 6.
• Guide the learners to make a conclusion
that:
2 + 2 + 2 + 2 + 2 + 2 = 6 × 2 = 12
• Give more related examples to the learners
so as to help them to practice.
• Display a chart showing multiplication
of single-digit numbers up to 12.
Conclusion
We use repeated addition, tablets or calculators
to correctly multiply numbers by 6.
Assessment
• Let the learners work out Questions 2
and 3 of Exercise 6F. Mark their work
while correcting them where necessary.
• Give more related questions to the
learners as homework.
Multiplication by 7
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to multiply single-digit numbers
by 7.
Activity 6G
Preparation
• Ensure that there are enough counters,
and materials required for this activity
in the Mathematics corner.
Synthesis
• Discuss with the learners Example 5.
• Guide them to make a conclusion that:
2 + 2 + 2 + 2 + 2 = 5 × 2 = 10
• Give more related examples to the
learners so as to help them to practice.
• Display a chart showing multiplication
of single-digit numbers up to 10.
Conclusion
We use repeated addition or tablets or
calculators to correctly multiply numbers
by 5.
Assessment
• Let the learners work out Exercise
6E. Mark their work correcting them
where necessary.
• Give more related questions to the
learners as homework.
Multiplying by 6
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to multiply single-digit numbers
by 6.
Activity 6E
Preparation
• Ensure that there are enough counters,
and other required materials for this
activity are in the Mathematics corner.
Doing the activity
• Organise the learners in groups. Let them
follow the instructions of Activity 6E in
the Learner’s Book. Guide the learners
87
Multiplying by 8
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to multiply single digit numbers
by 8.
Activity 6H
Preparation
• Ensure that there are enough counters,
at the Mathematics corner to carry out
the activity.
• Let the learners be in groups of mixed
abilities.
Doing the activity
• Guide the learners to do Activity 6H
and discover that the addition and
multiplication are related.
• Discuss and share with the learners the
ndings of the activity.
Synthesis
• Discuss with learners Example 8.
• Guide them to make a conclusion that:
2 + 2 + 2 + 2 + 2 + 2 + 2+ 2 = 8 × 2 = 16
• Give more examples to the learners to
practice.
• Display a chart showing multiplication
of single-digit numbers up to 16.
Conclusion
We use repeated addition, tablets or calculators
to correctly multiply numbers by 8.
Assessment
• Let the learners work out Exercise 6H.
Mark their work correcting them where
necessary.
• Give more related questions to the learners
as homework.
Doing the activity
• Ask the learners some probing questions
related to multiplication. Find out from
them what repeated addition is and ask
them to relate multiplication to repeated
addition.
• Conveniently group the learners.
• Let the learners pick the teaching and
learning materials from the Mathematics
corner.
• Ask them to carry out Activity 6G.
Encourage them to share their ndings
with other members of the class in a
class discussion.
• Ask them to return the counters in their
right box.
Synthesis
• Discuss with the learners Example 7.
• Ask them to identify the number of
groups of the objects per group.
• Guide the learners to appreciate the
basic multiplication and addition facts.
• Allow them to copy the example in their
books. Explain to them the working of
the example.
Conclusion
We use repeated addition or tablets or
calculators to correctly multiply numbers by 7.
Assessment
• Ask the learners to do Exercise 6G.
Supervise and mark the learners work
in class.
• Do corrections and give related
questions to the learners as homework.
88
Mark their work correcting them where
necessary.
• Give more related Questions to the
learners as homework.
Multiplying by 10
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to multiply single-digit numbers
by 10.
Activity 6J
Preparation
• Organise the learners in groups.
• Ask them to assemble all the counters.
Doing the activity
• Ask the learners to carry out the activity
as per the instructions given in the
Learners Book. Discuss and share with
them the ndings of the activity.
Synthesis
• Discuss with the learners Example 10.
• Guide the learners to make a conclusion
that:
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 =
10 × 2 = 20
• Give more related examples to the
learners to practice.
• Display a chart showing multiplication
of single-digit numbers up to 20.
Conclusion
Multiplying by 9
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to multiply single-digit numbers
by 9.
Activity 6I
Preparation
• Organise the learners in groups.
• Ask them to assemble all the counters.
Doing the activity
• Ask the learners to carry out the
activity as per the instructions given.
• Discuss and share with them the
ndings of the activity.
Synthesis
• Discuss with the learners Example 9.
• Guide them to make a conclusion that:
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2
= 9 × 2 = 18
• Give more related examples to the
learners to practice.
• Display a chart showing multiplication
of single-digit numbers up to 18.
Conclusion
We use repeated addition, tablets or
calculators to correctly multiply numbers
by 9.
Assessment
• Let the learners work out Exercise 6I.
89
is 4.
2 × 2 = 4,
two groups of 2 objects give 4.
• Also, 2 +2 = 4. is is the repeated
addition which is true.
• Ask the learners questions related to
multiplication of single-digit numbers.
Let them use the multiplication table to
get the answers.
Synthesis
• Discuss the Example 11 with the
learners.
• Guide them to understand the use of
the multiplication table.
• Organise the learners to play with
the numbers i.e. one learner asks a
question, and another one gives the
answers, for instance, what is 3 × 2? –
work out: 4 × 3 =
Conclusion
We use multiplication tables to correctly
multiply numbers.
Assessment
• Ask the learners to do Questions 1 to 5
in Exercise 6K. Supervise their working
and mark their books if possible.
• Discuss the exercise for those who may
have been disadvantaged.
• You may ask the learners to use their
laptops to practice multiplying numbers.
• At the end of this sub-strand, ask the
learners to do questions from the
revision papers and revision books.
We use repeated addition or tablets or
calculators to correctly multiply numbers
by 10.
Assessment
• Let the learners work out Exercise 6J in
their exercise books. Mark their work
correcting them where necessary.
• Give more related questions to the
learners as homework.
Multiplication table
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to multiply single-digit numbers
from 1 to 10.
Activity 6K
Preparation
• Ensure that there are enough counters,
and other required materials for this
activity are in the Mathematics corner.
Doing the activity
• Having guided the learners through
the process of multiplying numbers by
single-digit numbers, the products in
each stage of the multiplication sentence
can be obtained from a table. is table
is again formed from the multiplication
sentences.
1 × 1 = 1, 2 × 2 = 2, 3 × 2 = 6, 4 × 2 = 8
etc
• When 2 is multiplied by 2, the answer
90
Exercise 6D
1. 3 × 4 = 12 2. 4 × 4 = 16
3. 4 × 5 = 20 4. 4 × 6 = 24
5. 4 × 7 = 28 6. 4 × 9 = 36
7. 4 × 10 = 40
Activity 6E
4 + 4 + 4 + 4 + 4 = 20
5 × 4 = 20
Exercise 6E
1. 5 × 3 = 15 2. 5 × 4 = 20
3. 5 × 5 = 25 4. 5 × 6 = 30
5. 5 × 7 = 35 6. 5 × 8 = 40
7. 5 × 9 = 45 8. 5 × 10 = 50
Activity 6F
6 + 6 + 6 = 18
6 × 3 = 18
Exercise 6E
1. 6 × 3 = 18 2. 6 × 4 = 24
3. 6 × 5 = 30 4. 6 × 4 = 24
5. 6 × 7 = 42 6. 6 × 8 = 48
7. 6 × 9 = 54 8. 6 ×10 = 60
Activity 6G
7 + 7 + 7 + 7 + 7 + 7 = 42
7 × 6 = 42
Exercise 6G
1. 7 × 3 = 21 2. 7 × 4 = 28
3. 7 × 5 = 35 4. 7 × 6 = 42
5. 7 × 7 = 49 6. 7 × 8 = 56
7. 7 × 9 = 63 8. 7 × 10 = 70
ANSWERS
Activity 6A
1. 1
2. 1 × 3 = 3
Exercise 6A
1. 1 × 3 = 3 2. 1 × 4 = 4
3. 1 × 5 = 5 4. 1 × 6 = 6
5. 1 × 10 = 10 6. 1 × 5 = 5
7. 1 × 8 =8 8. 1 × 9 = 9
9. 1 × 10 = 10
Activity 6B
a) 2 + 2 = 4
b) 2 × 2 = 4
Exercise 6B
1. 2 × 3 =6 2. 2 × 4 = 8
3. 2 × 5 = 10 4. 2 × 6 = 12
5. 2 × 7 = 14 6. 2 × 8 =16
7. 2 × 9 = 18 8. 2 × 10 = 20
Activity 6C
3. (a) 3 + 3 + 3 + 3 = 12
(b) 3 × 4 = 12
Exercise 6C
1. 9 2. 12
3. 15 4. 18
5. 21 6. 24
7. 27 8. 30
Activity 6D
(a) 4 + 4 + 4 = 12
(b) 4 × 3 = 12
(c) 12
91
Activity 6J
10 + 10 +10 + 10 + 10 + 10 + 10 = 70
10 × 7 = 70
Exercise 6J
1. 10 × 3 = 30 2. 10 × 4 = 40
3. 10 × 5 = 50 4. 10 × 6 = 60
5. 10 × 7 = 70 6. 10 × 8 = 80
7. 10 × 9 = 90 8. 10 × 10 = 100
Activity 6 K
(a) 6 × 4 = 24
(b) 7 × 6 = 42
(c) 8 × 9 = 72
Exercise 6 K
1. 7 × 7 = 49 2. 2 × 8 = 16
3. 7 × 5 = 35 4. 6 × 9 = 42
5. 4 × 8 = 32 6. 3 × 9 = 27
7. 5 × 3 = 15 8. 6 × 9 = 42
9. 5 × 6 = 30 10. 3 × 4 = 12
11.2 × 7 = 14 12. 9 × 9 = 81
Activity 6H
8 + 8 + 8 + 8 + 8 + 8 + 8 = 56
8 × 7 = 56
Exercise 6H
1. 8 × 3 = 24 2. 8 × 4 = 32
3. 8 × 5 = 40 4. 8 × 6 = 48
5. 8 × 7 = 56 6. 8 × 8 = 64
7. 8 × 9 = 72 8. 8 × 10 = 80
Activity 6I
9 + 9 + 9 + 9 + 9 + 9 = 54
9 × 6 = 54
Exercise 6I
1. 9 × 3 = 27
2. 9 × 4 = 36
3. 9 × 5 = 45
92
Division
(Learner’s Book Pages 103–112)
Suggested number of lessons: 8 Lessons
Specic learning out comes
By the end of the sub-strand the learner
should be able to:
(a) Represent division as equal sharing.
(b) Represent division as equal grouping.
(c) Use ‘÷’ sign in writing division
sentences.
(d) Divide numbers up to 25 by 2, 3, 4
and 5 without a remainder in real life
situations.
Core competences
• Communication and collaboration,
critical thinking and problem solving,
digital literacy.
Key inquiry questions
How can you share objects equally?
Link to PCI’s
• Citizenship: Social cohesion- group
work
• ESD:DRR; safety of materials
Link to other subjects
• Languages activities
• Environmental activities
Pre-requisite to the sub-strand
For learners to learn division with ease
they should have learnt the following
concepts:
• Addition of whole numbers
• Subtraction of whole numbers
• Multiplication of whole numbers
• Place value of whole numbers
• Reading and writing numbers up to 20
in symbols and in words
Teaching/learning resources
• Counters
• Pictures in the Learner’s Books
• Multiplication table
• Bottle tops
• Concrete objects e.g. bucket
Key word
• Division
• Repeated Subtraction
• Equal sharing
• How many times?
Guidelines to teaching/learning
experiences
Ensure that all concrete objects and
materials required for the activities are
available at the Mathematics corner.
7
93
Assessment
• Let learners do Exercise 7A.
• Guide them through the exercise
especially the slow learners.
• Give more exercise to the learners as
an assignment.
Division as repeated
subtraction
Speciﬁc learning outcome
By the end of this lesson this learner
should be able to do division as repeated
subtraction.
Activity 7B
Preparation
• Collect enough small stones or maize
seeds for all the groups that will be
formed by the learners.
• Organise the Learners in convenient
groups.
Doing the activity
• Let learners carry out the Activity 7B.
• Let them count 15 objects and place
them on the table or desk.
• Guide them to pick 5 objects one at a
time until none is le on the table.
• Let learners present their ndings
to the whole class in form of a
discussion.
Division as equal sharing
Speciﬁc learning outcome
By the end of the lesson the learners
should be able to represent division as
equal sharing.
Activity 7A
Preparation
Before the beginning of the class ensure
that you have enough concrete objects for
the activity.
Doing the activity
• Put the learner in convenient groups
to carryout Activity 7A.
• Ensure all the learners follow the steps
listed in Activity 7A in the Learner’s
Book.
• Guide the learners to understand that
division is equal sharing.
• Ask the learners to share their ndings
with other groups. is enhances
communication and collaboration
among the learners.
Synthesis
• Guide learners to understand that 6
mangoes or any other concrete object
can be shared equally.
• Explain that when 6 mangoes are
shared equally among 3 learners each
one will get 2 mangoes.
• Give examples related to the concept
besides Example 1.
94
• Organise learners in groups.
Doing the activity
• In groups convenient to you, let
learners collect and count 18 sticks.
• Instruct them to put the sticks on the
table.
• Guide them to follow instructions
given the activity carefully.
• Tell them to put the sticks into
separate groups of 3 sticks each.
• Ask them oral questions to guide them
to get the correct answers for Activity
7C.
Synthesis
• Division is the opposite of
multiplication. Guide the learners to
embrace this concept.
• Write Examples 3 and 4 on the
chalkboard and guide them through.
Conclusion
Let the learners understand that division
is the reverse of multiplication.
Assessment
• Guide the learners through Questions
1 and 2 in Exercise 7C in the Learner’s
Book.
• Let them attempt the rest of the
questions as you go round the class
marking and guiding them.
• Give more related questions as an
assignment.
e multiplication Table
Speciﬁc learning outcome
By the end of this lesson learners should
be able to use the multiplication table to
Synthesis
• Division questions can be solved by
subtracting the same number severally.
• Use Example 2 provided in the
Learner’s Book to explain this concept
further.
• rough question and answer session
you can discuss with the learners more
examples on division by repeated
subtraction.
Assessment
• Ask the learners to do Exercise 7B in
the Learner’s Book.
• Observe them as they do the activity.
• Ask them oral questions as they
proceed with the activity.
• Move around as you mark their work.
Conclusion
Conclude the class by letting learners
understand that division questions can be
solved by repeatedly subtracting the same
number (divisor).
Relationship between
Division and multiplication
Speciﬁc learning outcome
By the end of the lesson the learner should
be able to tell the relationship between
division and multiplication.
Activity 7C
Preparation
• Collect enough sticks to be used
Activity 7C.
95
product and multiply.
Conclusion
Let learners understand that
multiplication tables are used to simplify
multiplication and division questions
drastically without necessarily computing.
Assessment
• Let the learners do Exercise 7D in the
Learner’s Book.
• Let them do Questions 1 and 2 rst and
nd out if they are progressing well.
• Allow them to do the other Questions
3 to 8 in their books.
Multiplication and division
by 10
Speciﬁc learning outcome
By the end of this lesson the learners
should be able to multiply and divide
numbers by 10.
Activity 7E
Preparation
• Ensure that there are enough counters
in the Mathematics corner.
• Organise the learners in groups.
Doing the activity
• Instruct the learners to carry out
Activity 7E.
• Let them follow the instructions given
to them correctly.
• Ask the learners to count 100 counters.
do simple operations.
Activity 7 D
Preparation
• Ensure availability of a chart with
a multiplication table is in the
Mathematics corner.
• Ask the Learners to make Mathematics
tables like the one in Activity 7D.
Doing the activity
• Ask learners to collect the
multiplication table drawn on a chart
from the Mathematics corner.
• Guide them to display the charts on
the walls.
• Guide them to read all the numbers in
the table.
• Ensure that you instruct them
to understand that when using a
multiplication table start with numbers in
the rows as the rst number the numbers
in the columns as the second number.
Where the two meet is the product.
• Ask them to read and work out
questions on multiplication table in
this activity.
Synthesis
• Mathematical tables are lists of
numbers showing the results of
multiplication of given numbers.
• Write Examples 5 and 6 on the
chalkboard and guide them on how to
work them out from the mathematical
table.
• Explain some key words such as
96
• Move around the class to assist those
experiencing diculties.
ANSWERS
Activity 7A
3. 2
4. 8 ÷ 4 = 2
Exercise 7 A
1. 4 ÷ 2 = 2 2. 6 ÷ 2 = 3
3. 8 ÷ 4 =4 4. 9 ÷ 3 = 3
Activity 7 B
2 (a) 3 times each
(b) 3 seeds
3. 15 ÷ 3 = 5
Exercise 7B
1. 14 ÷ 2 = 7 2. 8 ÷ 4 = 2
3. 6 ÷ 3 = 2 4. 9 ÷ 3 = 3
5. 18 ÷ 3 = 6 6. 15 ÷ 3 = 5
7. 21 ÷ 3 = 7 8. 12 ÷ 4 = 3
9. 20 ÷ 2 = 10 10. 16 ÷ 4 = 4
11. 8 ÷ 2 = 4 12. 24 ÷ 4 = 6
Activity 7 C
2. (a) 3 sticks
(b) 6 groups
(c) 18 ÷ 3 = 6
(d) 6 × 3 = 18
Exercise 7C
1.
6
× 6 = 18
2. 6 ×
4
= 24
• Guide them to pick 10 counters at a
time until the 100 counters get nished.
• Ask the whole class oral questions to
guide them in getting the answer.
• Let the learners give their feedback.
Synthesis
• When any number 1 to 10 is multiplied
by 10, it gives ten times of that
number.
• Give them more examples related to
multiplication of numbers up to 25.
• Tell them that 9 × 10 means 9 groups
of 10 counters.
Explain to them how 9 × 10 = 90.
• Tell them that this is also read as 9 times
10. Take them through Example 7.
• Allow them time to work out other
questions given here:
(a) 2 × 10 = (e) 10 ÷ 2 =
(b) 4 ×10 = (f) 40 ÷ 10 =
(c) 3 × 10 = (g) 30 ÷ 10 =
Conclusion
Make a summary of the key works and
content by telling them that if any number
between 1 and 10 is multiplied by 10, the
product gives a ten of the number.
Assessment
• Ask the learners to do Exercise 7E in
the Learner’s Book.
• Ask them some oral questions as you
involve them in the activities.
97
9 ÷ 3 =
3
8 ÷ 2 = 4
7. 5 ×
2
= 10 8. 1 ×
8
= 8
10 ÷ 5 =
2
8 ÷ 1 =
8
Activity 7 E
1. (a) 9
(b) 90 ÷ 10 = 9
(c) 10 × 9 = 90
2 (a) 6
(b) 60 ÷ 10 = 6
(c) 10 × 6 = 60
3. (a) 3
(b) 30 ÷ 10 = 3
(c) 10 × 3 = 30
4. Mark the learner’s answer and guide
them accordingly.
5. Mark the learner’s answer and guide
them accordingly.
Exercise 7 E
1. 9 × 10 = 90 2. 6 × 10 = 60
90 ÷ 10 = 9 60 ÷ 10 = 6
3. 4 × 10 = 40 4. 5 × 10 = 50
40 ÷ 10 = 4 50 ÷ 10 = 5
3. 7 × 3 =
21
4. 2 × 7 =
14
5. 14 ÷ 7 =
2
, 14 ÷ 2 =
7
6. 24 ÷ 8 =
3
, 24 ÷ 3 =
8
7. 2 × 4 = 8
8. 5 × 3 = 15
9. 4 × 3 = 12
10. 5 × 2 = 10
11. 20 ÷ 2 = 10, 20 ÷ 10 = 2
12. 27 ÷ 3 = 9, 27 ÷ 9 = 3
Activity 7D
(a) 3 × 5 = 15 (b) 4 × 6 = 24
(c) 3 × 7 = 21 (d) 9 × 2 = 18
(e) 18 ÷ 6 = 3 (f) 15 ÷ 5 = 3
(g) 21 ÷ 3 = 7 (h) 16 ÷ 4 = 4
Exercise 7 D
1. 4 ×
6
= 24 2. 3 ×
6
= 12
24 ÷ 4 =
6
12 ÷
4
= 3
3.
2
× 6 = 12 4. 3 × 7 =
21
12 ÷ 6 = 2
21
÷ 7 = 3
5.
3
× 3 = 9 6.
4
× 2 = 8
98
Length
(Learner’s Book Pages 113–123)
Suggested number of lessons: 6 Lessons
Specic learning outcomes
By the end of the sub-strand the learner
should be able to:
(a) Measure length in metres.
(b) Add length in metres.
(c) Subtract length in metres.
(d) Estimate length up to 20 metres.
Core competences
Communication and collaboration,
Imagination and creativity Critical
thinking and problem solving Self-ecacy
Key inquiry question(s)
1. How do you measure the chalkboard
using a metre stick?
2. How do you get the total length in
metres of the 4 classroom walls?
3. How do you measure the distance
between the ag post and the
staroom using 5 metre long string?
Link to PCIs
ESD:DRR; – reuse of materials ,safe
materials
Links to other subjects
• Environmental activities
• Language activities
Pre-requisite to the strand
For learners to understand the concept
they ought to have learnt.
1. Basic addition facts
2. Subtraction
3. Metre stick as a standard measure
Teaching/learning resources
• Metre
• Stick
• 5-metre long strings
Key words
• Estimate
• Metre
• Knots
• Intervals
• Distance
Guidelines to teaching and
learning experiences
Measuring length in metres
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to measure length of
dierent objects in metres.
8
99
Assessment
• Assist the learners to do Exercise 8A
questions (a) to (h).
Activity 8D
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
• Organise the learners into four groups
A,B,C and D.
Doing the activity
• Guide each group to measure and tie
knots that are 1m apart and 5m string.
• Guide each group to measure the
football and netball pitches.
• Let them record the results in their
books.
• Let them share their ndings with the
other measurements with the other
groups.
• Compare the results from the groups
and record the nal answer in the table.
• Advise them to clear the strings of their
working areas.
• Let them indicate which length is
longer and which one is shorter.
Synthesis
rough a class discussion:
• Encourage them to use the word
metres.
• Guide them to ll in the tables.
Activities 8A to 8C
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
• Organise the learners into groups of
three considering their abilities.
Doing the activity
• Guide the learners to do Activity 8A.
• Observe them as they measure the
lengths.
• Let them answer question asked in
Activity 8A.
• Let them record the number of sticks
they have counted per distance in
Activity 8B.
• Guide them to make a 5- metre long
string.
• Guide them to measure the places
highlighted in the activities.
• Let them record their answers in the
books as shown in the table.
Synthesis
rough brain storming;
• Guide the learners to do Exercise 8A
and record their answers in their books.
• Go round marking and assisting the
learners with special needs.
• Let them share their ndings.
Conclusion
• Ropes and sticks can be used to
measure length but the rope may give
more accurate results.
100
• Let them record their answers in the
exercise books.
Conclusion
ere is no dierence between the
distance measured using a metre rule and
the distance between the knots.
Assessment
• Let learners do Exercise 8B Questions 1
to 6 as you go round marking for them.
• Let them have Questions 7 to 12 as
homework.
Word problems involving
addition of length
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to solve word problems
involving addition of lengths.
Preparation
• Prepare the learners for word problems
by asking probing questions.
Learning experiences
• Ask them oral question about adding
metres.
Synthesis
• Let the learners to understand that in
order to solve word problems involving
addition of lengths all measurement
must have similar units.
Conclusion
• When solving word problems, it is
important to read and understand the
question rst.
Conclusion
Strings can be used for measuring length.
Assessment
• Let all the groups, discuss their ndings
and complete the table in Activity 8D.
Addition of length in metres
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to perform addition of
lengths in metres.
Activity 8E
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
Doing the activity
• Ask them to read the activity and
follow the instructions through your
guidance. Let them ll in the table in
Activity 8E with the ndings.
• Guide learners to perform addition
using counters.
• Add the ones rst, followed by tens.
• Let them write the answers in their
exercise books.
Synthesis
rough group discussions;
• Guide the learners through Examples 1
to 3 of the Learner’s Book.
• Emphasise on adding the ones rst
then followed by tens.
101
• Emphasise on subtracting ones
followed by tens and lastly hundreds.
Note that regrouping may be necessary.
• Let them record their answers in their
Books.
• Guide learners through Example 5 in
Learner's Book.
Conclusion
• When subtracting the concept of place
value is still key.
Assessment
• Let the learners do some questions in
Exercise 8D as you go round marking
for them.
• Let them have Questions 7 to 11 in
Exercise 8E as homework.
Word problems involving
subtraction of length
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to solve word problems
involving subtraction of length in metres.
Activity 8H
Preparation
• Organise the learners in pairs.
• Ask the learners familiar questions.
Learning experiences
• Ask them oral question related to
subtracting metres.
Synthesis
• Explain to the learners that, in order
to solve word problems involving
subtraction of metres, read the
Assessment
Let the learners attempt questions in
Exercise 8C.
Subtraction of length in
metres
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to subtract length in
metres.
Activity 8F
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
• Organise the learners into four groups.
Doing the activity
• Ask them to read the activity and
follow the instructions through your
guidance.
• Guide them to perform subtraction
using counters.
• First subtract ones.
• Guide them to subtract the tens.
• Lastly let them subtract the hundreds.
• Ask them to write the answers in their
books.
Synthesis
rough group discussion;
• Guide the learners through Example 5.
102
• Let them repeat the same activity with
dierent lengths.
• Observe them as they perform the
activity and help the ones with
challenges.
Synthesis
• Explain to the learners that a metre
stick or metre-rule can be used to
measure almost the same length.
Conclusion
• Estimated length is usually almost the
same value as the real length.
Assessment
• Let the learners attempt Exercise 8G.
ANSWERS
Activity 8A
Learners' own answers
While measuring
Exercise 8A
Learners' own measurement
Activity 8B
Learners' own answers while measuring
Activity 8C
Learners' own measurement
Activity 8D
Learners' own measurement
question, determine what is required
then subtract the metres.
• Take the learners through Example 6.
Conclusion
• When solving word problems, it is
important to read and understand the
question rst.
Assessment
Let the learners attempt Example 8F.
Estimating Length
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to estimate lengths.
Activity 8I
Preparation
• Ensure that the learners have
collected all the necessary materials
for this activity and Keep them at the
Mathematics corner.
• Organise them in groups of 5 Learners.
Doing the activity
• Guide the learners to collect the
1-metre rule and 5-metre string from
the Mathematics corner.
• Let them move out of the classroom.
• Guide them to follow the instructions
in the activity.
Synthesis
• Guide the learners to do Activity 8G
following the steps indicated.
103
Exercise 8 E
1. 2 m 2. 12 m
3. 45 m 4. 1 m
5. 63 m 6. 28 m
7. 625 m 8. 329 m
9. 202 m 10. 182 m
11. 82 m
Exercise 8 F
1. 61 m 2. 1 m
3. 13 m 4. 2 m
Exercise 8 G
Mark the learner’s work and guide them
accordingly.
Exercise 8 A
Mark the learner’s work appropriately
Exercise 8 B
1. 9 m 2. 50 m
3. 3.78 m 4. 29 m
5. 48 m 6. 69 m
7. 847 m 8. 588 m
9. 994 m 10. 637 m
11. 90 m 12. 467 m
Exercise 8 C
1. 5 m 2. 30 m
3. 500 m 4. 17 m
Exercise 8 D
Mark the learner’s work and guide the
accordingly.
104
Mass
(Learner’s Book Pages 124-131)
Suggested number of lessons: 6 Lessons
Specic learning outcomes
By the end of the sub-strand the learner
should be able to:
(a) Measure mass in kilogrammes
(b) Add mass in kilogrammes
(c) Subtract mass in kilogrammes
(d) Estimate mass up to 5 kilogrammes
Core competences
Communication and collaboration,
imagination and creativity, critical
thinking and problem solving, self-
ecacy
Key inquiry question(s)
How can you make a 1 kilogram mass
using a beam balance?
Link to PCIs
Life skills: self- awareness- as they
measure own mass Citizenship: social
cohesion- working in group ESD:DRR-
Safety in selecting appropriate materials
and security, safe materials/items
Link to other subjects
• Environmental activities
• Language activities
• Movement and creative activities
Pre-requisite to the strand
Mass may not be a new concept to most
learners as it has been taught/learnt in the
previous classes. erefore learners have
been equipped with the required skills and
knowledge to tackle this sub-strand. A
review of the basis may be necessary at the
introductory stage.
However, for this sub-strand to be taught/
learnt with ease, the learners should be
equipped with basic skills in
• Counting
• Addition
• Place value
Prepare the learners to use their
imagination and creativity.
Teaching/learning resources
• Learner’s Book
• Concrete objects
• Pictures in the Learner’s Book.
Key words
• Mass
• Beam balance
• Weighing stone
9
105
Synthesis
• Use your own examples to discuss with
the learners the concepts of lighter and
heavier.
• Explain to them why the brush is lied
up and not the ball.
• Let them know that the brush is lighter
than the ball while the ball is heavier
than the brush.
• Emphasise that when two objects have
the same mass, there is balance on
either side of the beam balance.
Conclusion
• ere are objects which are lighter than
others, heavier than others or they have
the same mass.
Assessment
• Give further exercise for practice.
• Questions-answer session.
• Observation.
Making 1-kilogram masses
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to make 1 kilogramme masses.
Activity 9B
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
• Organise the learners to form groups of
four Learner’s which should be of mixed
abilities.
Guidelines to teaching/learning
experiences
Measuring mass in
kilogrammes
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to weigh mass of objects in
kilograms.
Activity 9A
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
Doing the activity
• Pick a beam balance and other
materials needed for a demonstration.
• Introduce the sub-strand through
probing questions.
• Guide the learners to carry out the
activity under your supervision.
• Allow them to ask as many questions
as possible. Make the lesson more
interesting by asking them some
probing questions, for example, have
you ever carried a 1-kilogram mass?
• Explain to them that in this case an
item is only 1 kg if the two sides of the
beam balance balances.
• Ask the learners to measure the
mass of their Mathematics textbook.
Encourage them to add books until it
balances.
106
Addition of mass in real-life
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to add mass in kilogrammes.
Activity 9C
Preparation
• Ensure that the learners have collected
all the necessary materials as per
Activity 9C.
• Keep them at the Mathematics corner.
• Organise the learners into groups of
ve.
Doing the activity
• Ask the learners to imagine that
each mass of sand previously made
is equivalent to 1 kg of sugar. is is
meant to invoke their imaginative and
creative thinking.
• Introduce the topic of addition by
asking them some probing questions.
• Let them carry out Activity 9C as
instructed.
Synthesis
rough group discussion;
• Use Examples 3 and 4 to explain the
concept of addition in mass.
• Emphasise that addition of mass
involves numbers. ese numbers
should be added in the same way as
in addition while paying attention to
place values, for example, in Example 3
digits 6 and 5 are in the ones. ey are
added rst and separately.
• en add 9 and 1 as the tens with
regrouping.
Doing the activity
• Organise the learners to make four
1-kg masses as instructed in Activity
9B.
• Let them collect the 1-kilogramme
mass containers.
• Put the stone on one side of the beam
balance and the 1 kg mass container on
the other side.
• Add sand to the container until the two
sides balance.
• Emphasise that when the beam
balances then the 1 kg mass and the
mass of the sand are the same.
• Repeat the activity again to make four
such masses from sand and keep them
for future use.
• Always insist on the learners cleaning
their working area and washing their
hands aer such an activity as a way of
caring for the environment as well as
maintaining their own hygiene.
Synthesis
rough question and answer;
• Let the learners discuss Examples 1 and
2 by stating the mass of rice.
• When using a weighing stone, the exact
mass of the object is known.
Conclusion
Emphasise to the learners in a conclusive
manner that, when comparing masses
using a beam balance, the lighter mass is
always raised.
Assessment
• Ask the learners to do Exercise 9A.
• Guide them to perfect their skills in
measuring mass using a standard unit.
107
• Organise the learners into convenient
groups.
Doing the activity
• Make the session as interactive as
possible by asking the learners some
probing questions.
• Ask the learners to imagine that they
have 3kg of rice with them.
• Ask them how many kilogrammes
remain if one kilogramme is taken
away.
I have 3 kg of rice. I take away 1 kg,
how many kilogrammes are le?
• is will facilitate the introduction of
subtraction in mass.
• Ask them to do Activity 9D.
Synthesis
rough a class discussion;
• Explain to the learners that subtraction
of mass is not dierent from subtraction
of numbers.
• Use Example 5 to emphasise to them
that subtraction involves taking away
from the group.
• Remind them about subtraction that
involves regrouping.
• D
iscuss
with the learners Example 6
so as to improve their reading and
communication skills.
Conclusion
• Remind them about subtraction that
involves regrouping.
Assessment
• Ask the learners to do Exercise 9C
questions 1 to 3 and mark for them.
• Add 1 and 1 as hundreds.
• Write down the answers.
• Ask them to attempt question 4 using
the above steps.
Conclusion
• Addition of mass in kilogrammes
is done the same way as addition of
numbers.
Assessment
rough a class discussion;
• Discuss with the learners Question 1
in Exercise 9B. Work out the question
together with the learners.
• Ask them to do Questions 2 and 3 in
class as you supervise and mark their
work.
• Give them Questions 4 to 6 as further
exercises for homework.
• Introduce to the learners word problems
by discussing a word Question 7.
• Let them attempt word Questions as an
assignment.
Subtraction of masses in
real-life
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to subtract mass in kilogrammes.
Activity 9D
Preparation
• Ensure that the learners have collected all
the necessary materials for this activity
and keep them at the Mathematics corner.
108
Synthesis
• Discuss the concept of estimating mass
using as many examples as possible.
Use Example 7 to discuss estimation of
masses with the learners.
Conclusion
• e dierence between estimated mass
and the actual mass is very small.
Assessment
• Ask the learners to copy and complete
the table in Exercise 9E.
• Review the table together with them.
ANSWERS
Activity 9A
5. 1 kg
Exercise 9A
1. 1 kg 2. 2 kg
3. 1 kg 4. 3 kg
5. 2 kg 6. 2 kg
7. 2 kg 8. 3 kg
Activity 9C
3. (a) 7 kilogrammes of soil
(b) adding the two masses
Exercise 9B
1. 830 kg
2. 879 kg
3. 505 kg
4. 417 kg
5. 850 kg
6. 535 kg
• Let them do Questions 7 to 10 and mark
for them..
• Give further exercise in Questions 4 to
6 for practice in Exercise 9C.
Estimating mass
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to estimate mass of an
object.
Activity 9E
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Organise the learners into groups.
Doing the activity
• Organise the learners to pick dierent
objects like stones, pieces of wood, sand/
soil and beans from the Mathematics
corner. Guide them through Activity 9E.
• Estimate the mass of each by comparing
how heavy the objects are. Make the lesson
as interactive as possible by ensuring that
every learner participates in the discussion.
• ey should be able to tell the one that
is heavier than the other.
• Let them use the same masses on a beam
balance. With weighing stones of up to
5kg, ask them to get the exact values in
terms of mass.
• Caution the learners against dropping
the weighing stones as they can get hurt.
109
3. 633 kg
4. 129 kg
5. 331 kg
6. 191 kg
7. 27 kg of beans
8. 3 kg of rice
9. 49 kg of maize
10. 68 kg of rice
Exercise 9D
Amina’s estimate of 7 kg was the closest.
7. 140 kg of maize
8. 728 kg of sand
9. 217 kg of beans
10. 402 kg of mass
Activity 9D
54 kilogrammes of rice
Exercise 9C
1. 860 kg
2. 629 kg
110
Capacity
(Learner’s Book Pages 132-140)
Suggested number of lessons: 8 Lessons
Specic learning outcomes
By the end of the sub-strand the learner
should be able to:
(a) Measure capacity in litres
(b) Add capacity in litres
(c) Subtract capacity in litres
(d) Estimate capacity up to 5 litres
Core competences
• Communication and collaboration,
critical thinking and problem solving,
digital literacy.
• Imagination and creativity, citizenship,
self- ecacy
Key inquiry questions
What is the unit of measuring capacity?
Link to PCIs
ESD-Animal welfare.
Links to other subjects
• Language activities
• Nutrition and Hygiene
• Environmental activities
• Movement and creative activities
Pre-requisite to the strand
For learners to be able to understand
the new concept in this strand they are
expected to have learnt the following:-
• Measuring capacity using xed units
• Measuring capacity in litres
• Identing a litre as a unit of measuring
capacity
• Measuring capacity using arbitrary
units
• Conservation of capacity through
manipulation
• Addition of numbers
• Subtraction of numbers
Teaching/learning resources
Containers of dierent sizes (1 litre,
10 litres, 20 litres and 5 litres)
• Jugs • Bucket
• Sufurias • Drums
• Cups • Pots
• Kettle • Glasses
• Water.
Key words
• Compare • Capacity
• Litres • Container
• Measure.
Guideline to teaching/learning
experiences
Measuring capacity in litres
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to measure capacity in litres.
10
111
Addition of capacity in litres
Speciﬁc learning objective
By the end of this lesson the learners
should be able to add capacity in litres.
Activity 10B
Preparation
Ensure that containers of dierent sizes
are available in the Mathematics corners.
Doing the activity
• Organise the learners in groups.
• Guide them through the steps in
Activity 10B in the Learner’s Book.
• Let them follow the instructions
carefully and nd out how many 5-litre
containers ll a 20-litre container.
Synthesis
• Guide them by asking them guiding
questions to make them count the
number of 5-litre containers.
• Show them on the chalkboard that;
5L + 5L + 5L + 5L = 20 L
• Guide them through the addition
of capacity in litres by working out
Examples 1 and 2 in the Learner’s
Book.
• Let them do another Example of your
choice on the chalkboard as you guide
them.
Conclusion
Summarise by telling them that four
5-litre containers hold 20 litres.
Activity 10A
Preparation
• Ensure that you guide the learners to
collect all the teaching and learning
resources to be used in the sub-strand
early enough and be kept at the
Mathematics corner. Instruct them to
always take care of their Mathematics
corner.
• Organise learners in groups.
Doing the activity
• Guide them through Activity 10A.
• Guide them to have 1-litre containers
with them.
• Let them ll the containers with water.
• Instruct them to use the 1-litre
container to ll the bucket.
• Ask them questions to nd out how
many 1-litre containers lled the bucket,
jerrican and 20-litre containers.
• Ask them guiding questions to list their
ndings if they are really doing the
right thing.
Synthesis
• Let the learners understand that smaller
containers can be used to ll the larger
container.
Conclusion
• Summarise the lesson by reminding
the learners that capacity is measured
in units called litre.
Assessment
• Ask the learners to do Exercise 10A in
the Learner’s Book.
• Ask oral questions while they are in the
learning activities.
112
Activity 10C
Preparation
• Prepare the learners to do Activity
10C in the Learner’s Book.
Doing the activity
• Guide the learners to work out Activity
10C given in the Learner’s Book.
• Guide them through the steps of
subtracting.
• Discuss with them how to work out the
litres that remain.
24L – 13L = 11L
4 – 3= 1
2 – 1 = 1
Synthesis
• Ask the learners to volunteer and come
to the blackboard to work out Example
4 in the Learner’s Book.
• Guide them through to get the right
answer.
Conclusion
Remind them to always apply the basic
subtraction facts. Appreciate their work
and encourage them to have condence
in working out the problem on the
chalkboard.
Assessment
• Ask the learners to do Exercise 10D in
the Learner’s Book
• Ask them oral questions to test whether
they are following the right steps.
Assessment
• Ask them to do Exercise 10B in the
Learner’s Book.
• Involve the learners in oral questions
on addition of capacity. is improves
their communication skills and self-
esteem.
Word problems involving
addition of capacity
Learning experience
• Take the learners through the Example
3 in the Learner’s Book.
• Read the example and guide them on
how to read the sentences.
• Guide them on how to write and then
add horizontally and vertically.
Synthesis
• Let the learners on thenselves nd
out the answer as you guide and help
them where necessary.
•
Let them copy the example in their
exercise book and give them more practice
questions to do at their own free time
.
Assessment
• Ask the learners to do Exercise 10C in
the Learner’s Book.
• Observe their participation in working
out the problem on the chalkboard and
appreciate their eort.
Subtraction of capacity in
litres
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to work out subtraction involving
capacity in litres.
113
Activity 10D
Preparation
Collect containers of dierent capacities
and put them in the Mathematics corner.
Ensure that there are also containers with
specic capacity up to 5 litres.
Doing the activity
• Ask learners to collect containers
of dierent capacities from the
Mathematics corner.
• Use the 1-litre container to guide the
learners to ll the other containers.
• Ask them guiding questions as they do
the measuring using water lled in the
one-litre containers.
• Let them ll the table in the Learner’s
Book.
Synthesis
• Guide them to ll the table correctly.
Ensure that they write the capacity in
litres.
• Explain to the learners that estimating
capacity of a container involves use of a
container with known capacity.
Summarise by advising them to
always:
(a) Water owers and trees in the
school compound.
(b)Help the community at home to
water owers.
Ask learners to do Exercise 10F in the
Learners Book.
ANSWERS
For the activities in this unit, Check
the learner’s answers and guide them
accordingly.
Word problems involving
addition of capacity
Preparation
Prepare the learners for word problems by
asking them probing questions.
Learning experiences
• Read the sentence with the learners.
Let the learners read alone.
• Repeat reading for them twice. en
let them read for themselves together.
• Ask them what to deduce from
sentences.
Synthesis
• Guide them through Example 5.
• Emphasise that they should always
start with ones: 5 – 0 = 5,
then tens: 6 – 2 = 4
65 Litres
– 20 Litres
45
• Help them to get the answer correct
them where necessary.
Assessment
1. Ask them to do Exercise 10E in the
Learner’s Book.
2. Ask them oral questions as they work
out an example similar to Example 5 on
the chalkboard.
Estimating Capacity
Speciﬁc learning outcome
By the end of this lesson the learners
should be able to estimate capacity in litres
up to 5 litres.
114
Exercise 10 C
1. 45 litres 2. 75 litres
3. 45 litres 4. 79 litres
Exercise 10 D
1. 24 litres 2. 47 litres
3. 114 litres 4. 328 litres
5. 348 litres 6. 421litres
7. 696 litres 8. 124 litres
9. 100 litres
Exercise 11 E
1. 60 litres 2. 5 litres
3. 13 litres 4. 30 litres
Exercise 10 G
John
Exercise 10 A
Mark the learner’s answers.
Exercise 10 B
1. 18 litres 2. 38 litres
3. 68 litres 4. 22 litres
5. 71 litres 6. 117 litres
7. 397 litres 8. 503 litres
9. 531 litres 10. 860 litres
11. 997 litres 12. 942 litres
115
Time
(Learner’s Book Pages 141–161)
Suggested number of lessons: 10 Lessons
Specic learning outcomes
By the end of the sub-strand the learner
should be able to:
(a) Identify the minute as a unit of
measuring time.
(b) Read and tell time using the digital
clock.
(c) Read and tell time using ‘past’ and ‘to’
the hour using the clock face.
(d) Write time using ‘past’ and ‘to’ the
hour.
(e) Estimate time in hours.
(f) Add time involving hours and
minutes without conversion.
(g) Subtract time involving hours and
minutes without conversion.
Core competences
Communication and collaboration,
critical thinking and problem solving,
digital literacy. Learning to learn.
Key inquiry question(s)
How do we convert hours to minutes?
Link to PCIs
Health education: HIV and AIDS- drugs
time adherence citizenship: governance-
law and order in school in keeping time
Link to other subjects:
• Language activities
• Nutrition and Hygiene
• Environmental activities
• Nutrition and hygiene
Pre-requisite to the sub-strand
For learners to be able to learn and
acquire the new concept in the sub-strand
they are expected to have learnt the
following:
• Relating daily activities to time.
• Relating days of the week with various
activities.
• Saying months of the year in order.
• Relate months of the year with various
activities.
• Measure time using arbitrary units.
• Measure time using xed unit.
• Identify and read the clock face by xed
colours called O’clock.
• Read and write time on the clock face
by the hour hand.
Teaching/learning resources
• Clock face/wallclock
• Wristwatch
• Stop watch
• Calendar
• Mobile phone
11
116
• Guide the learners to move the minute
hand clockwise from 12 to 1 – 2 – 3 – 4
round to 12 again.
• Ensure that they understand how much
time has past when the minute hand
moves from 12.
• Guide them through Activity 11B as
they answer in this activity.
Synthesis
• Guide them to count the number of
small markings between the two big
numbers. Lead them to nd that on the
clock face from one large number to the
next large number is 5 minutes.
• Emphasise that from 12 to 1, 1 to 2, 2 to
3, 3 to 4, 4 – 5, 5 -6, 6 -7, 7- 8, 8 – 9, 9 –
10, 10 – 11, 11 back to 12 is 5 minutes
each. Which means a complete rotation
is 60 minutes.
Conclusion
Summarise by telling them that one
complete clockwise rotation by the minute
hand counts or makes 60 minutes.
Assessment
• Let the learners do Exercise 11A in the
Learner’s Book.
• Ask them oral questions to guide them
do the activities well.
Reading and telling time
using a clock face
Quarter past
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to tell that 15 minutes is a quarter
Key words
• Minute hand
• Hour hand
• Clock face
Guide to teaching/learning
experience
Minute as a unit of time
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to tell minutes as a unit of time.
Activities 11A and 11B
Preparation
Ensure that the Mathematics corner has
all the teaching and learning resources
required for this activity. Involve the
learners to collect them in advance and be
kept. Instruct them to always take care of
the resources in the Mathematics corner.
Doing the activities
• Provide the learners with enough wall
clocks or otherwise called clock faces
for the groups.
• Organise them in groups and let them
discuss the divisions on the clock face.
• Take them through the features of the
clock face such as the minute hand, hour
hand, the big marked numbers and the
small markings in between them.
• Let them know how the hands move
and in which direction (clockwise or
anticlockwise).
• Ask them to do Activity 11A.
117
Assessment
• Ask the learners to tell the time in the
Exercise 11B in the Learner’s Book.
• Oral question to guide them read the
time.
• Observation by looking at how to
manipulate, handle and move the
hands of the clock face.
Half past
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to tell time as half past the
hour.
Activity 11D
Preparation
Ensure that there are enough improvised
wall clocks in the Mathematics corner to
be used in the activity.
Doing the activity
Group the learners. e groups should
comprise of learners with varied abilities.
ey should also have gender balance in
case it is a mixed class.
• Guide the learners through Activity
11D in the Learner’s Book.
• Ask them to state the time shown on the
clock face.
• Give each group a clock face.
• Ask them to move the minute hand
clockwise to point at 6. Ask them to
read and tell the time.
way round the clock face in the clockwise
direction.
Activity 11C
Preparation
• Provide the learners with the wall clock
or ensure that they are available in the
Mathematics corner.
• Organise them in groups.
Doing the Activity
• Lead them to read the clock face and tell
the time when the minute hand is at 12
and the hour hand is directly pointing
at 7 as shown in clock face A.
• Guide them to move the minute hand
to point at 3. Ask them what they see on
the hour hand.
Synthesis
• Guide them to learn and understand
that when the minute hand moves from
12 to point at 3 then the hour hand also
moves slightly past 7.
• Let them realise that this is then read as
a quarter past 7.
• Let them understand that when it
points at 3 that means 15 minutes past 7
O’clock.
• Ask one learner to lead and show the
rest of the class how to read and tell
time using. Examples 1 discuss with the
learners
Conclusion
Emphasise and summarise by telling them
that 15 minutes is a quarter way round the
clock face in the clockwise direction.
118
Quarter to
Speciﬁc learning outcome
By the end of this lesson the learners should
be able to tell that a quarter to means the
minute hand is pointing at 9.
Activity 11E
Preparation
• Ensure that there are enough improvised
wall clocks in the Mathematics corner
to be used in the activity.
Doing the activity
• Guide the learners to read the time on
clock face A and clock face B.
• Ask one of the learners to come to
the front and lead others to move the
minute hand. Let him/her lead others
to move the minute hand from 12
O’clock clockwise to point at 9.
• Ask them what happens to the hour
hand.
• Let them nd out that the minute hand
has moved 45 minutes clockwise and
the hour hand is slightly moving next to
3 from 2.
Synthesis
• Guide the learners to read the time as
shown on the clock face. Let them read
the time as 15 minutes to 3. Emphasise
that this is properly read as quarter to 3.
• Organise them in groups and let
them tell the time on the clock face in
Example 3.
• Emphasise that when the minute hand
points at 9 it means that is 15 minutes to
reach O’clock or to the next hour time.
Conclusion
• Guide the groups to do the same thing
as you instruct them. Let them nd
out how many minutes past when the
minute is at point 6.
Synthesis
• Guide them to discover that when a
minute hand points at 6 then that is 30
minutes past the hour or 30 minutes to
the next hour hand.
• Let them understand that when the
minute hand points at 6 the hour hand
is in between half way the two hours
and this is read as half past.
• Guide them through Example 2 in the
Learner’s Book as you facilitate and help
the weaker and slow learners. Let them
read and tell the time.
Conclusion
Let them understand that when the minute
hand points at 6 the hour hand is in
between half way the two hours and this is
read as half past.
I2
II
I0
9
8
7
6
5
4
3
2
I
Assessment
• Ask learners to do Exercise 11C in the
Learner’s Book.
• Observe the learners while handling
moving of the hands of the clock faces.
119
• Guide the learners through Example 4.
• Introduce them to digital watches and
show them how to tell time.
Assessment
• rough a question and answer session
let the learners master the concept of
writing time using minutes past or to
an hour.
• Guide the learners as they do Exercises
11 E and 11F in the Learner’s Book.
Estimating time in hours
Speciﬁc learning outcome
By the end of this lesson the learners
should be able to estimate time in hours.
Activity 11G
Preparation
Provide the learners with the clock faces
in the Mathematics corner.
Doing the activity
• Organise them in groups to carry out
Activity 11G.
• Ask them to look at the sky outside and
estimate time at dierent times of the
day.
• Guide them as they do the activity.
• Ask them to tell the actual time by
reading.
• Let them ll in a table such as the one
in this activity.
• What is the time. Let them nd out the
dierence in the estimated and actual
times. Ask them which group had
closer estimates.
Synthesis
Summarise by telling them that a quarter
to means the minute hand is pointing at 45
minutes or at number 9.
Assessment
• Ask learners to do Exercise 11D in the
Learner’s Book.
• Observe them as they move and read
the hands of the clock faces. Let them
read and tell the time.
Telling time in minutes
past or to an hour
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to write time in terms of minutes to
and minutes past.
Activity 11F
Preparation
Ensure learners are in groups and their
clock faces are available.
Doing the activity
• Learners have already covered how to
read time in quarter to and quarter past.
Use this section to guide them on how
we can write time in a similar way.
• Ask the learners to carry out Activity
11F.
• Encourage them to be keen on where
the minute hand is pointing.
• Emphasise that there are 5 sub-divisions
any two between any two major divisions.
Synthesis
120
• Guide the learners to work out addition
involving time without conversion.
• Guide them to do simple addition of
time for example 2 hours 35 minutes
and 3 hours 20 minutes.
• Let them use the place value chart they
used when in learning addition.
• Let them know that the short form of
hours is ‘h’ and minutes is min’.
Synthesis
• Guide them to add by re-arranging the
time vertically.
Hours minutes
2 35 First add minutes
35 + 20 = 55
+ 3 20 Add hours.
2 + 3 = 5
5 55
• Ask the learners to come to the
chalkboard and work out Examples
7 and 8 for the rest of the class. Guide
them where necessary.
Assessment
• Ask the learners to do Exercise 11H in
the Learner’s Book.
• Guide them to complete the exercise
that involves addition of word problems.
Subtraction involving time
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to work out subtraction
questions involving time.
Activity 11 I
• Set the clock face that the short hand
points at 8 and the long hand at 12.
• Now ask them to say to which numbers
the minute hand and the hour hand are
pointing at. Ask them to tell the time.
• Ask one learner to come at the front and
guide her through Example 6.
• Let her ask the rest of the class to tell
and estimate the time.
Conclusion
Let them know that they can estimate time
in hours when the short hand points at any
number.
Assessment
• Ask the learners to do Exercise 11 G.
• Ask them oral questions to guide them
through estimated time using the short
hand and the long hand.
• Observation by looking at their work
and appreciating their eorts and skills
of manipulation.
Addition involving time
Speciﬁc learning activities
By the end of this lesson the learner
should be able to do addition involving
time.
Activity 11 H
Preparation
Review vertical additional with and
without regrouping.
Doing the activity
121
• Oral questions by asking and guiding
questions to test them if they are
really following the instructions and if
they understand the concept they are
learning.
• Guide them on how to solve word
problems.
ANSWERS
Activity 11A
1. 7 O’clock 2. 7:05
3. 5 marks 4. 60 minutes
Activity 11B
3. (a) 60 minutes
(b) 1
(c) 1 hour
(d) 1 hour = 60 minutes
Exercise 11A
2. 50 minutes 3. 20 minutes
4. 10 minutes 5. 55 minutes
6. 35 minutes 7. 20 minutes
8. 55 minutes 9. 35 minutes
Activity 11C
1. 7 O’clock
2. 7: 15
3. C. Quarter past 6
D. Quarter past 5
E. Quarter past 10
Exercise 11B
1. Quarter past 8 2. Quarter past 1
3. Quarter past 9 4. Quarter past 5
5. Quarter past 4 6. Quarter past 11
Doing the activity
• Guide the learners by working out:
Subtract 5 hours 10 minutes from 6
hours 40 minutes
• Write on the chalkboard for them.
• Help them to write properly by making
sure the time with smaller number in
the hours is put below the other when
arranged vertically.
H Min
6 40
5 30
__
Synthesis
•
Guide the learners to work out the subtraction.
Let them write down this way:
H Min
6 40 Subtract the
minutes rst
5 10 en hours 6 – 5 = 1
1 30
• Guide the learners to work out the
following questions in Examples 9
and 10 in the Learners Book on the
chalkboard.
• Guide them through Examples 9 and 10
in the Learner’s Book.
• Observe if they followed the steps or the
instructions you gave. Reward them by
appreciating them with a clap.
Assessment
• Ask the learners to do Exercise 11I in
the Learner’s Book.
• Observation as they do the example
on the chalk board and Exercise 11 I in
their books.
122
Exercise 11D
1. Quarter to 4 2. Quarter to 2
3. Quarter to 11 4. Quarter to 1
5. Quarter to 6 6. Quarter to 8
Activity 11F
1. (b) A - 10 minutes
(c) B - 10 minutes
(d) A - 10 minutes past 10, B- 20
minutes to 2
Exercise 11E
(a) 5 minutes past 5 or 5:05
(b) 26 minutes past 11 or 11:26
(c) 16 minutes past 4 or 4:16
(d) 7 minutes past 10 or 10:07
(e) 34 minutes past 1 or 1:34
(f) 5 minutes past 5 or 5:05
(g) 14 minutes to 6 or 5:46
(h) 38 minutes past 2 or 2:38
(i) 13 minutes to 12 or 11:47
(j) 16 minutes past 7 or 7:16
(k) 19 minutes to 9 or 8:41
(l) 12 minutes to 10 or 9:48
Exercise 11F
1. 10:08
2. 12:27
3. 12:34
4. 3:38
5.
(a) 8 o’clock or 8:00
(b) 15 minutes past 10 or 10:15
(c) Half past 1 or 1:30
Activity 11D
1. 8 O’clock
2. Half past 8
3. C. Half past 3
D. Half past 1
Exercise 11C
A
1. Half past 2
2. Half past 9
3. Half past 7
B.
1. 2.
I2
II
I0
9
8
7
6
5
4
3
2
I
I2
II
I0
9
8
7
6
5
4
3
2
I
Half past 4 Half past 10
3.
I2
II
I0
9
8
7
6
5
4
3
2
I
Half past 1
Activity 11E
1. 2 O’clock
2. Quarter to 3
123
Activity 11I
2 hours 41 minutes
Exercise 11H
1. 6 h 35 min 2. 9 h 50 min
3. 6 h 35 min 4. 4 h 49 min
5. 5 h 55 min 6. 5 h 38 min
7. 4 hours 8. 5 h 55 min
9. 3 h 45 min
Activity 11J
1. She spent 1 hour 23 minutes
watching the television
Exercise 11I
1. 2 h 20 min
2. 2 h 20 min
3. 10 min
4. 2 h 10 min
5. 3 hours
6. 4 h 5 min
7. 2 hours
8. 2 hours 30 minutes
9. 35 minutes
(d) A quarter to 5 or 4:45
(e) 20 minutes past 8 or 8: 20
(f) 10 minutes past 3 or 3:10
(g) 25 minutes to 11 or 10:35
(h) 20 minutes to 10 or 9:40
6.
(a) 20 minutes past 12
(b) 20 minutes to 2
(c) A quarter to seven
(d) 5 minutes past seven
(e) A quarter past 9
(f) A half past 7
(g) 25 minutes past 10
(h) 25 minutes to 3
(i) 10 minutes to 2
7. Mark correct answers according to
their local languages.
Exercise 11G
Mary 2:00
124
Money
(Learner’s Book Pages 162-176)
Suggested number of lessons: 10 Lessons
Specic learning outcomes
By the end of the sub-strand the learner
should be able to:
(a) Identify Kenyan currency notes up to
ksh.1000.
(b) Count money in dierent
denominations up to ksh.1000.
(c) Add and subtract money involving
gures up to ksh.1000.
(d) Carry out shopping activities
involving change and balance.
(e) Relate money to goods and services
up to ksh.1000.
(f) Dierentiate between needs and
wants.
(g) Appreciate spending and saving of
money in real-life situations.
Key inquiry question(s)
What are needs and wants?
Pre-requisite to the sub-strand
For the learners to understand the
concept they ought to have learnt the
following:-
• Addition of whole numbers
• Counting of numbers up to 100
• Number concept.
Teaching/learning resources
• Notes of dierent denominations
• Classroom shop
• Pictures of dierent items
Key words
• Currency
• Coins
• Notes
• Denominations
• Value
• Money
• Saving
• Spending
Guidelines to teaching and
learning experiences
Kenyan currency
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to identify the Kenyan currency.
Activity 12A
Preparation
Ensure all teaching and learning resources
are available. For the notes you can make
a full colour photocopy of the notes to be
used by the learners.
Doing the activity
• Arrange the learners into convenient
groups.
• Let them collect coins and notes of
dierent values from the Mathematics
corner.
12
125
Activity 12B
Preparation
• Ensure that the notes in the
Mathematics corner comprises of
dierent denominations of the Kenyan
currency.
Doing the activity
• Organise learners into convenient
groups of mixed ability.
• Ask the learners to sort out the notes
starting with the one they think is the
smallest in terms of value.
• Guide them through Activity 12 B in
the Learner’s Book.
• Ask the learners to carry out the
activity using dierent denominations.
Synthesis
• Guide the learners through Example 1
in the Learner’s Book.
• Put more emphasis on the fact when
a specic number of coins or notes
are put together they form a certain
denomination.
Conclusion
• Guide them also to realise that dierent
coins and notes have dierent values.
• Emphasise that dierent coins or notes
of same denomination can be used to
show a certain value.
Assessment
• Ask the learners to do Exercise 12A in
the Learner’s Book.
• Mark their books giving special
attention to the learners who have
diculties.
• Ask them to sort the currency notes
they have picked according to the
features and the value of the notes.
• Lead them to complete Activity 12 A.
Synthesis
• Ask the learners to look at the pictures
in the Learner’s Book.
• Ask the learners to identify the features
on the coins and notes.
• Guide them to realise that dierent
coins have dierent features.
Conclusion
Summarise the lesson by explaining to the
learners that the Kenyan currency is made
up of dierent valid denominations. Each
note or currency of dierent value has
dierent features.
Assessment
• Engage all learners in questions and
answer sessions to help them master
the dierent concepts from the activity.
• Attend to those who are unable to work
out as they continue working.
• Mark the work and give remedial
questions.
Counting money in
dierent denominations
Speciﬁc learning outcome
By the end of lesson the learners should
be able to count money dierent
denominations of the Kenyan currency.
126
be having diculty in adding.
• Give them more work on addition of
money to do as an assignment.
Note: Money includes shillings and
cents. However, currently cents (cts)
are not so much in circulation.
Subtraction of money
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to work out subtraction of
money.
Activity 12D
Doing the activity
• Arrange the learners in groups. e
groups should comprise learners of
varied abilities. If the class is mixed the
groups should have gender balance.
• Guide the learners through Activity
12D.
• Ensure that they are following the right
procedure when subtracting.
Synthesis
• Ensure that learners are subtracting
correctly.
• Take them through Examples 4 and 5
in the Learner’s Book.
Conclusion
e concept of place value is still valid.
Assessment
• rough question and answer session
guide the learners on how to subtract
money.
• Give the learners remedial work.
Addition of money
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to work out addition of
money.
Activity 12 C
Doing the activity
• Arrange the learners in pairs. e
groups should comprise learners of
varied learning capabilities. If the class
is mixed the groups should have gender
balance.
• Guide the learners through Activity
12C.
• Ensure that they are following the right
procedure when adding.
Synthesis
• Ensure that when the learners are
adding they don’t mix the value of
shillings given in digit form.
• Guide them through Examples 2 and 3
in the Learner’s Book.
Conclusion
Remind the learners that when adding
money the concept of place value is
important.
Assessment
• rough question and answer session
guide the learners on how to add
money.
• Let the learners do Exercise 12B in the
Learner’s Book. Guide those who may
127
Conclusion
Summarise the lesson by reminding them
that money is used for buying and selling
goods and services.
Assessment
• Give the learners time to work out
Exercise 12D.
• Move round marking the books giving
individual attention.
• Give more questions as an assignment.
Balance and change
Speciﬁc learning outcome
By the end of this lesson learners should
be able to understand how to do shopping.
Activity 12F
Preparation
is is an outdoor activity. It is important
that you look for time to take the learners
to the nearest shop for them to take part
in shopping.
Doing the activity
• Arrange the learners into groups of ve.
e groups should be of mixed ability.
• Let all the learners participate in doing
Activity 12F in the Learner’s Book.
• Guide those who have never gone for
shopping understand what takes place
during shopping.
Synthesis
• Guide the learners as they discuss
about the experiences they had during
shopping.
• Let the learners do Exercise 12C in the
Learner’s Book. Guide those who may
be having diculties in subtracting.
• Give them more work on subtracting
money to do as an assignment.
Shopping activities
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to explain how buying and selling
takes place.
Activity 12E
Preparation
• Ensure that all teaching/learning
resources are available.
• Prepare an area that will be used by the
learners as a shop. e arrangement
should be done in such a way that it
depicts a real shop.
• Arrange some items to be used in this
activity in the class shop that you have
arranged.
Doing the activity
• Arrange learners into groups of mixed
abilities.
• Guide the learners to read through
Activity 12E as they do it following
instructions.
Synthesis
• Discuss with the learners the picture of
a shop in the Learner’s Book.
• Guide the learners through Example 6
and work it out on the chalkboard.
How much money did she spend?
128
• Let them look at the pictures in Activity
12 G. Guide them as they sort the items
from the picture that they must have
and the ones that they can live without.
• Ask the learners to talk about needs
and wants.
Synthesis
• Needs are the items that they must have
while wants are those that they don’t
necessarily need.
• Guide the learners through Example 8
in the Learner’s Book. Use the example
to emphasise the dierence between
needs and wants.
Conclusion
Emphasise to the learners that needs are
the things we cannot live without while
wants are the things we can live without.
Assessment
• Learners to discuss orally on dierent
wants and needs.
• Give the learners time to do Exercise
12F.
• Give them remedial work to go and
write more needs and wants in the
home environment.
Appreciating spending and
saving money
Speciﬁc learning outcomes
By the end of this lesson the learner should
be able to appreciate the essence of saving
and spending money.
• Let them understand that during
shopping money is used in the process.
• Guide the learners through Example 7
in the Learner’s Book.
Conclusion
Conclude by reminding the learners the
dierent activities that take place during
shopping. is includes; picking the items,
paying for them and being given the
balance in case you pay with more money
than the actual amount for the items.
You can also ask for change if you have
a note of higher value and need notes of
smaller values.
Assessment
• Learners to discuss orally
• Give learners time to do Exercise 12E
• Give them more work to do as an
assignment.
Needs and Wants
Speciﬁc learning outcome
By the end of this lesson learners should
be able to dierentiate between needs and
wants.
Activity 12G
Preparation
Ensure all teaching and learning resources
are available.
Doing the activity
• Arrange the learners into groups of
mixed abilities.
129
Activity 12 C
Mark the learner’s work and guide them
accordingly.
Exercise 12 B
1. sh 480 2. sh 129
3. sh 955 4. sh 240
5. sh 990 6. sh 847
7. sh 595 8. sh 142
9. sh 947 10. sh 749
11. sh 1000 12. sh 794
Activity 12 D
1. sh 200
3 sh 200 – sh 50 = _____
4. sh 150
Exercise 12 C
1. sh 492 2. sh 693
3. sh 176 4. sh 231
5. sh 580 6. sh 74
7. sh350 8. sh 55
9. sh 190 10. sh 800
Exercise 12 D
1. sh 400 2. sh 800
3. sh 40 4. sh 190
5. sh 40 6. sh 510
7. sh 30
Exercise 12 E
1. 5 2. 5
3. 2 4. 2
5. 4 6. 10
7. 10 8. 2
Activity 12H
Preparation
• Arrange learners into groups of mixed
ability groups.
• Ask the learners to discuss about
money and what they know about
saving.
Synthesis
• Guide the learners in the discussion
about why people save.
• Guide the learners in discussion on
where people save money.
Conclusion
Conclude the lesson by encouraging the
learners to save the pocket money that
they are given, in case they are not using it
at the moment.
Assessment
• Oral question and answers.
• Ask learners to do Exercise 12G on
savings. Mark their work and guide
them appropriately.
ANSWERS
Activity 12A
Listen to the answers the learners give and
guide them accordingly.
Exercise 12 A
1. sh 600 2. sh 250
3. sh 850 4. sh 350
5. sh 300 6. sh 800
7. sh 200 8. sh 900
9. sh 550 10. sh 850
130
Exercise 12 F
Mark the learner’s answers and guide
them accordingly.
Exercise 12 G
1. Savings
2. Bank (mark the learner’s answer
appropriately)
3. Home
131
Position and Direction
(Learner’s Book Pages 177-181)
Suggested number of lessons: 6 Lessons
Specic learning outcomes
By the end of the sub-strand the learner
should be able to:
(a) Move along a straight line from a
point.
(b) Turn to the right from a point.
(c) Turn to the le from a point.
Core competences
• Communication and collaboration,
critical thinking and problem solving,
digital literacy, imagination and
creativity
Key inquiry question(s)
What do you do when you get to a road
junction?
Link to PCIs:
Life skills: Self – awareness - as they use
their body parts in movement citizenship;
social cohesion- as they work in groups
Links to other subjects
• Language activities
• Movement and creative activities
• Environmental activities
Pre-requisites to the strand
Introduce this sub-strand by reviewing
the concept of straight lines learnt in
Grade 1. Other sub-strands that may make
background information include;
1. Length 1 and 2
2. Geometry 2
Since this is a new concept, the learners
are likely to have challenges. More time
may be taken at the introductory stage to
enable them grasp the content. is sub-
strand is important as it could be used to
promote road safety.
Teaching/learning resources
• Stick
• Rope
• Text book
• Tablets
Key words
• Position
• Line
• Direction
• Straight
• Point
• Junction
Guidelines to the teaching/
learning experiences
Position and direction
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to draw straight lines.
13
132
• Ask the learners to mention any two
points within the school which are on a
straight line.
• Ask them to name any two directions
in which people turn.
Moving and turning
Speciﬁc learning outcome:
By the end of this lesson the learner should
be able to draw straight lines.
Activities 13C and 13D
Preparation
• Organise the learners into groups of 5.
Doing the activities
• Guide the learners outside the
classroom.
• Guide them through Activity 13C and
13D using the lines drew earlier.
• Let them walk in a straight line on the
class verandah.
• Guide them to answer the questions
asked in the activity.
Synthesis
rough brain storming;
• Discuss with the learners the ndings
of the activity.
• Ensure that all of them have
participated in the activity.
• Explain why a junction is important in
position and direction.
• Encourage them to participate in the
discussion.
Activities 13A and 13B
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Keep them at the Mathematics corner.
• Organise the learners into groups of 5.
Doing the activities
• Guide them to draw straight lines on
the ground.
• Guide them to do Activity 13A in their
books.
• Guide learners to do Activity 13B in
their books.
• Dene the key words for the learners to
understand.
Synthesis
rough a class discussion;
• Discuss with the learners the concept
of position and direction. Engage
them in questions as they answer. is
should form the introductory part of
the lesson.
• Explain to the learners the meaning of
position and direction.
• Emphasise on all the key words related
to this sub strand.
• Be sure that they have drawn straight
lines.
Conclusion
Lines can start from dierent points and
meet at one point.
Assessment
rough question and answer;
133
Assessment
• Observation as they walk.
• Oral questions.
• Let them attempt exercise 13A
Digital game
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to draw straight lines using
a tablet.
Activity 13F
Preparation
• Ensure that the learner’s tablets are
available for this activity.
Doing the activity
• Guide them to open their tablets and
draw lines.
• Guide them to play games involving
shapes and colour.
• Let them share with the others what
they have drawn.
• Advise them to record their ndings as
they answer the questions given.
Synthesis
rough brainstorming;
• Discuss with the learners the ndings
of the activity.
• Ensure that they can dierentiate
between le and right when they reach
a junction.
Conclusion
Junctions are important points in lines
because they enable change of direction.
Assessment
• Let them draw 3 points with a junction
outside the classroom.
• Allow the learners to practice turning
le or right in a junction.
• Observe as they turn and help those
with challenges.
Activity 13E
Speciﬁc learning outcome
By the end of the lesson the learner should
be able to practice concepts learnt outside
the classroom.
Preparation
Organise the learners in groups of mixed
abilities.
Doing the activity
• Ensure that all the learners are
participating in the walk.
• Observe as they walk and make turns
to the le and right of the classroom
block.
Synthesis
Explain and dene new words like turn. Use
demonstrations for case of understanding.
Conclusion
Turns to the le or right facilitate
movement.
134
Assessment
• Ask the learners to draw a line with a
junction and colour it.
• Carry out oral assessments.
• Observations as they draw.
ANSWERS
Activity 13A
1. (a) B, right (b) B, le
2. (a) P, right (b) Q, le
(c) P, le (d) Q, right
135
Shapes
(Learner’s Book Pages 182–190)
Suggested number of lessons: 5 Lessons
Specic learning outcomes
By the end of the sub- strand the learner
should be able to:
(a) Make patterns involving rectangles,
circles, triangles, ovals and squares.
(b) Appreciate making patterns involving
rectangles, circles, triangles, ovals and
squares.
Core competences
Communication and collaboration,
creativity and imagination, critical
thinking and problem solving, digital
literacy.
Key inquiry question(s)
What shapes can you identify in your
school?
Link to PCIs
Citizenship: leadership development,
Social cohesion- as they work in groups
Life skills: Self- esteem and awareness
Link to other subjects
• Language activities
• Movement and creative activities
• Environmental activities
Pre-requisite to the sub-strand
Introduce this sub-strand by reviewing
the concept of straight lines learnt in
Grade 2. Other sub-strands that may make
background information include:
1. Length 1 and 2
2. Shapes 2
Since this is a new concept, the learners
are likely to have challenges. More time
may be spent at the introductory stage to
enable them grasp the content. is
sub-strand is important as it could be used
to promote road safety.
Teaching learning resources
• Stick • Rope
• Tablets
Key words
• Position • Line
• curved • Direction
• Straight • Point
• Junction
Guidelines to the teaching/
learning experiences
Conrm that the materials necessary for
the activities in this sub-strand are readily
available at the Mathematics corner.
Sorting and grouping shapes
Speciﬁc learning outcome
By the end of this lesson the learner should
be able to sort and group shapes.
14
136
and others.
Assessment
• Ask learners to do Exercise 14A in the
Learner’s Book.
• Ask them oral questions to sort and
group the shapes properly.
• Observe them and appreciate their
eort in sorting and grouping
according to the colour.
Shapes found in the
environment
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to sort and group shapes in
the surroundings.
Activity 14B
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity such as cut-outs of dierent
shapes.
• Let the learners keep them at the
Mathematics corner.
Doing the activity
• Organise for every learner to have access
to Mathematics Activities Grade 3.
• Ask them to critically look at page 184
of the Learners Book and note what
they can see. is exercise should help
them to improve their critical thinking,
imagination and the power to observe
things.
• Encourage them to answer the
Activity 14A
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity such as cut-outs of dierent
shapes.
• Keep them at the Mathematics corner.
• Organise learners in pairs.
Doing the activity
• Ask them to pick 20 cut-outs of
dierent shapes with dierent colours.
• Guide them to place the cut-outs on
the table.
• Help them to sort out the cut-outs
according to their colour.
• Ask them guiding questions to help
them ll the table in the Learner’s
Book.
Shape Colour How Many
Rectangle Red 3
Synthesis
• Guide the learners to understand that
shapes can be grouped into dierent
colours and sizes.
• Discuss the name and the features of
the shapes such as rectangles, circles,
triangles, ovals and squares.
• Let the learners nd out which type of
lines form the edges of the shape.
• Let them draw the shapes in their
exercise books.
Conclusion
Dierent objects have dierent shapes
such rectangular, circular, square, round
137
• Ensure that the learners follow the
instructions given in the Learner’s
Book. Supervise and correct where
necessary.
• Take them outside. Ask them to use a
rope and a stick to make a circle on the
ground.
• Ask them to share their results.
Synthesis
• Discuss the results obtained in Activity
14C.
• Encourage them to draw more shapes
on the ground.
Conclusion
Round objects are circular in shape.
Assessment
Ask the learners to attempt Exercise 14C.
Making Patterns
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to make patterns using
shapes.
Activity 14D
Preparation
• Ensure that the learners have collected
all the necessary materials for this
activity.
• Organise learners in groups.
Doing the activity
questions asked. If possible ask them
to write the answers in their books.
Synthesis
Discuss the learner’s answers. Oer individual
attention to those who may have challenges.
Conclusion
Dierent objects have dierent shapes
such rectangular, circular, square, round
and others.
Assessment
• Gauge the learner’s understanding
using the question and answer method.
• Ask them to do Exercise 14B under
your supervision.
• Review the exercise for better
understanding.
Drawing and making shapes
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to make a circle.
Activity 14C
Preparation
• Ensure that all the necessary materials
for this activity are available at the
mathematics corner.
Doing the activity
• Organise for the learners to carry out
Activity 14C. Let them make simple
tracings around sh. 20 coins and
rectangular cut-outs.
138
• Let them collect materials to be used
in Activity 14E from the mathematical
corner.
Doing the activity
• Organise for the learners to have access
to the tablets.
• Ask them to carry out Activity 14E using
their tablets. Supervise the activity.
• Let them share and discuss their results
with others.
Assessment
• Oral assessment of the learners. Ask
them oral questions to determine
whether they have understood.
ANSWERS
NB For the activities in this unit check
the learner’s answers and guide them
accordingly.
Activity 14A
3. (a) Circle, rectangle, square, triangle,
oval.
(b) 5
(c) Circle and oval-curved lines.
Triangle, rectangle and square-
straight lines.
Exercise 14 A
1. (a) (b)
Square Triangle
(c) (d)
• is activity requires cut-outs
previously made. Facilitate for the
learners to carry out Activity 14D.
• Give guidance where necessary.
• Let them make dierent patterns and
colour them.
• Ask them to share results amongst
groups.
Synthesis
• Discuss with the learners about their
ndings.
• Discuss the various patterns formed by
joining dierent shapes.
• Emphasise to them that shapes are
wrongly joined to make patterns.
Conclusion
• We can beautify the environment by
using patterns from shapes.
Assessment
• Observation
• Oral questions
• Let them do Exercise 14D in their
Exercise books.
Digital Games
Speciﬁc learning outcome
By the end of this lesson the learner
should be able to make a circle using a
tablet or computers.
Activity 14F
Preparation
• Ask the learners to be in pairs.
139
3. (a) Triangle (b) Triangle
(c) Circle (d) Circle
(e) Triangle (f) Rectangle
(g) Triangle (h) Triangle
Exercise 14 B
1. Oval
2. Circle
3. Rectangle
4. Rectangle
5. Triangle
Exercise 14 C and 14 D
Mark the learner’s answers and guide them
accordingly
Circle Rectangle
(e)
Oval
2. (a) Curved lines
(b) Straight lines
(c) Curved lines
(d) Straight lines
(e) Straight lines