Mathematics

Activities

Teacher’s Guide

Grade 3

T. Mukhuri

M. Okello

M. Mwimani

J. Mwaniki

S. Ndinwa

Published by

Longhorn Publishers Ltd.,

Funzi Road, Industrial Area,

P. O. Box 18033-00500,

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e moral rights of the authors have been asserted.

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

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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

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.

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

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

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

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

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

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

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.

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.

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

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.

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

• 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.

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

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.

(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.

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

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.

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.

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

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

(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.

(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.

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.

• 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.

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.

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

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

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

(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.

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

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

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

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

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

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.

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.

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

• 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.

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

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.

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

Speciﬁc learning outcome

By the end of the lesson learners should

be able to identify position and order of

objects from 11

up to 20

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.

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

Position 1

Position 4

Position 2

Position 3

Position 5

(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

• 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.

3. Sunday – 1

Wednesday – 4

Tuesday – 3

Saturday – 7

Monday – 2

Friday – 6

4. (b) Fourth (c) Seventh

(d) ird (e) Second

(f) Sixth (g) Fih

Activity 1C

3. e rst (1

) column.

4. Column of 20 bottle tops

Twentieth (20

5. Column with 10 bottle tops

6. (i) 13

(ii) 16

(iii) 19

7. 14 bottle tops

Exercise 1B

(b) January- 1

month

(d) July – 7

month

(e) October – 10

month

(f) September – 9

month

(g) November – 11

month

(h) April – 4

month

(i) August – 8

month

(j) February – 2

month

(k) December – 12

month

(l) March – 3

month

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

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.

(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

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.

• 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

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.

• 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.

• 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.

• 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.

• 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.

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

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

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

Activity 2N

1. (a) 2 bundles (b) 5 bundles

2. (a) hundreds (b) tens

Activity 2O

1. (a) (b)

(c)

2. (a) 415

4 – Hundreds

1 – Tens

5 – Ones

(b) 670

6 – Hundreds

7 – Tens

0 – Ones

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.

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

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

H T O

2 4 5

H T O

3 6 1

Exercise 2B

1. (a) (b)

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

(d) 5 hundreds, 0 tens, 0 ones

3. (a) 343 (b) 36

Activity 2P

Number ousands Hundreds Tens Ones

754 7 5 4

2. (a) 7 = hundreds (b) 5 = tens

Exercise 2C

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

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

3. (a) 7 hundreds, 3 tens, 2 ones

(b) 3 hundreds, 9 tens, 4 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

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

2. (a) 3-tens, 2- ones

(b) 9-tens, 4- 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

(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

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

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, ...

(a) 235 236 237 238 239 240 241 242 243 244

(b) 245 246 247 248 249 250 251 252 253 254

(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

6. (a) 334, 350, 366, 382, 398, …

(b) 81, 85, 89, 93, 97, 101, ...

Exercise 2G

1 95 13 172 106 14 183 117 15 194 128 16 20

30 3834 42 4631 3935 43 4732 4036 44 4833 4137 45 49 50

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

–

and

–

as part of a

whole.

(b) Identify

–

and

–

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

• 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 (

–

) 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.

• Give them more questions to practice

for the talented learners.

An eighth (

–

) 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

–

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

–

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

–

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.

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

–

(half) of the whole group.

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.

–

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

–

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.

10. 11. 12.

13. 14. 15.

Activity 3D

2. (a) 2 groups

(b) half (

)

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 (

)

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 (

)

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 (

)

Exercise 3C

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.

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:

• 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.

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.

• 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.

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 .

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.

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.

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

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

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

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

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

• 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.

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

0 84 12 161 95 13 172 106 14 183 117 15 19

9 5

3 + 9 + 5 = 17

0 84 121 95 132 1063 117

5 + 4 + 2 = 11

0 84 121 95 13 14 15 16 172 1063 117

6 + 3 + 7 = 16

0 84 121 95 132 1063 117

6 + 3 + 2 = 11

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

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

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

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

1. 4, 8, 12, 16,

2. 17, 22, 27, 32, 37

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.

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

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

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.

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.

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.

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.

• 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.

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.

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

H T O

3 5 3

H T O

3 1

H T O

3 2 2

–

H T O

4 9 3

H T O

7 2

H T O

4 2 1

–

H T O

5 4 7

H T O

1 6

H T O

5 3 1

–

H T O

1 7 6

H T O

1 7 1

–

H T O

3 4 6

H T O

3 4

H T O

3 1 2

–

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

H T O

3 5 4

H T O

1 7 2

H T O

1 8 2

–

H T O

3 6 4

H T O

2 7 2

H T O

9 2

–

H T O

1 2 7

H T O

9 2

H T O

3 5

–

H T O

2 3 8

H T O

1 9 3

H T O

4 5

–

H T O

4 1 9

H T O

3 2 5

H T O

9 4

–

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

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

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.

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.

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.

• 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

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.

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

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.

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.

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

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

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

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

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.

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.

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.

• 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.

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

• 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

(d) 6 × 3 = 18

Exercise 7C

× 6 = 18

2. 6 ×

= 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 =

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.

9 ÷ 3 =

8 ÷ 2 = 4

7. 5 ×

= 10 8. 1 ×

= 8

10 ÷ 5 =

8 ÷ 1 =

Activity 7 E

1. (a) 9

(b) 90 ÷ 10 = 9

2 (a) 6

(b) 60 ÷ 10 = 6

3. (a) 3

(b) 30 ÷ 10 = 3

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 =

4. 2 × 7 =

5. 14 ÷ 7 =

, 14 ÷ 2 =

6. 24 ÷ 8 =

, 24 ÷ 3 =

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

(e) 18 ÷ 6 = 3 (f) 15 ÷ 5 = 3

(g) 21 ÷ 3 = 7 (h) 16 ÷ 4 = 4

Exercise 7 D

1. 4 ×

= 24 2. 3 ×

= 12

24 ÷ 4 =

12 ÷

= 3

× 6 = 12 4. 3 × 7 =

12 ÷ 6 = 2

÷ 7 = 3

× 3 = 9 6.

× 2 = 8

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.

(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.

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

(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

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

(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.

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

• 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.

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

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.

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

(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

(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

(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

(a) 8 o’clock or 8:00

(b) 15 minutes past 10 or 10:15

Activity 11D

1. 8 O’clock

2. Half past 8

3. C. Half past 3

D. Half past 1

Exercise 11C

1. Half past 2

2. Half past 9

3. Half past 7

1. 2.

Half past 4 Half past 10

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

(a) 20 minutes past 12

(b) 20 minutes to 2

(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.

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.

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.

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.

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

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.

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

Triangle, rectangle and square-

straight lines.

Exercise 14 A

1. (a) (b)

Square Triangle

• 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

(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

(d) Straight lines

(e) Straight lines