Longhorn
Mathematics
Grade 7
Teacher’s Guide
Scholastica Nyagechi
Leonard King’oo
Stephen Kamakia
Anne Olwande
Tonnia Mumo
Published by
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© S. Nyagechi • L. King’oo • S. Kamakia • A. Olwande • T. Mumo, 2020.
The moral rights of the authors have been asserted.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
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recording or otherwise without the prior written permission of the copyright owner.
First published 2022
ISBN: 978 9966 64 378 0
Printed by
iii
Contents
Introduction .......................................................................................................1
Background information on Competency-Based Curriculum.................................. 1
National goals of education ............................................................................................1
General learning outcomes for middle school .............................................................3
Essence statement for Mathematics...............................................................................3
General learning outcomes for Mathematics............................................................... 3
Interrelationship between the national goals of education, general
learning outcomes for middle school, general learning outcomes
for Mathematics and specic learning outcomes ........................................................4
Strengths of the Competency-Based Curriculum........................................................5
Structure of the Teacher’s Guide....................................................................................5
Core competences to be developed................................................................................7
Pertinent and Contemporary Issues (PCIs) .................................................................8
Teaching and Learning Resources .................................................................................9
e role of the teacher in learner-centred learning...................................................10
Grouping learners for learning experiences ...............................................................11
Suggestions on eective group activities..................................................................... 12
Facilitating dierentiated learning and learners with special needs .......................13
Integrating digital learning in Mathematics............................................................... 16
Guidelines on parental empowerment and engagement.......................................... 17
Competency-based assessment ....................................................................................18
Developing competency-based assessment tasks.......................................................21
Professional documents.................................................................................................22
Conclusion ......................................................................................................................25
1.0 Numbers ...................................................................................................26
1.1 Whole Numbers...................................................................................................26
1.2 Factors ...................................................................................................................43
1.3 Fractions ...............................................................................................................55
1.4 Decimals................................................................................................................69
1.5 Squares and square roots.....................................................................................79
iv
2.0 Algebra .....................................................................................................88
2.1 Algebraic expressions...........................................................................................88
2.2 Linear equations .................................................................................................. 95
2.3 Linear inequalities..............................................................................................102
3.0 Measurement..........................................................................................110
3.1 Pythagorean relationship...................................................................................110
3.2 Length..................................................................................................................117
3.3 Area .....................................................................................................................129
3.4 Volume and capacity..........................................................................................141
3.5 Time, Distance and Speed.................................................................................152
3.6 Temperature........................................................................................................159
3.7 Money ................................................................................................................166
4.0 Geometry................................................................................................181
4.1 Angles .................................................................................................................181
4.2 Geometrical constructions................................................................................ 191
5.0 Data handling and probability...............................................................202
5.1 Data handling .....................................................................................................202
Guidelines for Community Service Learning Project................................... 221
Appendix 1 .............................................................................................226
Appendix 2 .............................................................................................228
Appendix 3 .............................................................................................231
Appendix 4 .............................................................................................232
1
Introduction
Background information on Competency-Based Curriculum
e Competency-Based Curriculum (CBC) places the learner at the centre of learning
and emphasises on adapting to the changing needs of learners, teachers and the society in
general. Implementing this curriculum calls for you to focus on guiding each learner to
develop knowledge, skills and attitudes in accordance with the competency-based learning
guidelines. e vision of the basic education curriculum reforms is to enable every Kenyan
to become an engaged, empowered and ethical citizen. is will be achieved by providing
every Kenyan learner with the right standard of skills and knowledge in order to thrive in
the 21
st
century. is shall be accomplished through the provision of conducive teaching
and learning environment, resources and a sustainable visionary curriculum that provides
every learner with high quality learning experiences. In order to do this, you must engage
the learners in exciting activities that allow them to use and progressively demonstrate the
competencies outlined in the curriculum. is Teacher’s Guide has been designed to do just
that. It provides guidelines for identifying and nurturing the talents and interests of learners
to prepare them for the world of work, career progression and sustainability. In accordance to
the Competency-Based Curriculum, this Teacher’s Guide provides recommendations for
developing competencies, mainstreaming Pertinent and Contemporary Issues, promoting
national values and integrating national cohesion into the learning experiences. It is from
this background that the Mathematics curriculum for secondary school was reviewed, as a
paradigm shi from the traditional knowledge-based learning to competency-based learning.
National goals of education
e national goals of education in Kenya are:
1. Foster nationalism and patriotism and promote national unity: Kenyan people
belong to different communities, races and religions, but these differences need not
divide them. They must be able to live and interact as Kenyans. It is a paramount
duty of education to help young people acquire this sense of nationhood by doing
away with conflicts and promoting positive attitudes of mutual respect which enable
them to live together in harmony and foster patriotism in order to make a positive
contribution to the life of the nation.
2. Promote the social, economic, technological and industrial needs for national
development: Education should prepare the youth of the country to play an effective
and productive role in the life of the nation.
(a) Social Needs
Education in Kenya must prepare children for changes in attitudes and
relationships which are necessary for the smooth progress of a rapidly developing
2
modern economy. There is bound to be a silent social revolution following in
the wake of rapid modernization. Education should assist our youth to adapt
to this change.
(b) Economic Needs
Education in Kenya should produce citizens with the skills, knowledge, expertise
and personal qualities that are required to support a growing economy. Kenya is
building up a modern and independent economy which is in need of an adequate
and relevant domestic workforce.
(c) Technological and Industrial Needs
Education in Kenya should provide learners with the necessary skills and
attitudes for industrial development. Kenya recognizes the rapid industrial and
technological changes taking place, especially in the developed world. We can
only be part of this development if our education system is deliberately focused
on the knowledge, skills and attitudes that will prepare our young people for
these changing global trends.
4. Promote individual development and self-fulfilment: Education should provide
opportunities for the fullest development of individual talents and personality. It
should help children to develop their potential, interests and abilities. A vital aspect
of individual development is the building of character.
5. Promote sound moral and religious values: Education should provide for the
development of knowledge, skills and attitudes that will enhance the acquisition of
sound moral values and help children to grow up into self-disciplined, self-reliant
and integrated citizens.
6. Promote social equality and responsibility: Education should promote social
equality and foster a sense of social responsibility within an education system which
provides equal educational opportunities for all. It should give all children varied
and challenging opportunities for collective activities and corporate social service
irrespective of gender, ability or geographical environment.
7. Promote respect for and development of Kenya’s rich and varied cultures: Education
should instil in the youth of Kenya an understanding of past and present cultures and
their valid place in contemporary society. Children should be able to blend the best of
traditional values with the changing requirements that must follow rapid development
in order to build a stable and modern society.
8. Promote international consciousness and foster positive attitudes towards other
nations: Kenya is part of the international community. It is part of the complicated and
interdependent network of peoples and nations. Education should therefore lead the
youth of the country to accept membership of this international community with all
the obligations and responsibilities, rights and benefits that this membership entails.
3
General learning outcomes for middle school
By the end of Middle School, the learner should be able to:
(a) Apply literacy, numeracy and logical thinking skills for appropriate self-expression.
(b) Communicate eectively, verbally and non-verbally, in diverse contexts.
(c) Demonstrate social skills, spiritual and moral values for peaceful co-existence.
(d) Explore, manipulate, manage and conserve the environment eectively for learning
and sustainable development.
(e) Practise relevant hygiene, sanitation and nutrition skills to promote health.
(f) Demonstrate ethical behaviour and exhibit good citizenship as a civic responsibility.
(g) Appreciate the country’s rich and diverse cultural heritage for harmonious co-existence.
(h) Manage pertinent and contemporary issues in society eectively.
(i) Apply digital literacy skills for communication and learning.
Essence statement for Mathematics
We live in a world of Mathematics whereby we count, add, subtract, multiply or divide
quantities and substances throughout our daily interactions. Mathematics involves
understanding numbers and the numerical operations used to develop strategies for
mental mathematical problem-solving skills, estimation and computational uency.
We live in a world of space, shape and structures. It is impossible to think of a world
without Mathematics. It is applied in the economic activities, scientic, social, religious
and political worlds. It is therefore imperative that children are taught Mathematics from
early years.
In Junior Secondary, Mathematics builds on the competencies acquired by the learner
from primary school. It enhances the learner’s competencies in Mathematical skills as a
foundation for Science, Technology, Engineering and Mathematics (STEM) and other
pathways at Senior School. Mathematics also prepares the learner to have sucient skills
and competencies for application in solving problems in real life situations. is is in line
with vision 2030 and sessional paper number 1 of 2019 which emphasises on STEM areas.
General learning outcomes for Mathematics
By the end of the Junior Secondary School, the learner should be able to:
(a) Demonstrate mastery of number concepts by working out problems in day-to-day life.
(b) Represent and apply algebraic expressions in dierent ways.
(c) Apply measurement skills to nd solutions to problems in a variety of contexts.
(d) Use money and carry out nancial transactions in real life situations.
(e) Generate geometrical shapes and describe spatial relationships in dierent contexts.
(f) Collect and organize data to inform and solve problems in real life situations.
4
(g) Develop logical thinking, reasoning, communication and application skills through
a Mathematical approach to problem solving.
(h) Apply Mathematical ideas and concepts to other learning areas or subjects and in
real life contexts.
(i) Develop condence and interest in Mathematics for further training and enjoyment.
Interrelationship between the national goals of education, general learning
outcomes for middle school, general learning outcomes for Mathematics
and specic learning outcomes
e national goals of education are signicant in promoting political, social and economic
development of this country. e national goals reect on the needs of the Kenyan society
and gives direction on holistic development of learners to enable them play eective roles
in the society. As a result, all the learning outcomes, that is, the general learning outcomes
for middle school, the general learning outcomes for Mathematics and specic learning
outcomes are formulated towards the attainment of the national goals. e knowledge of
this interrelationship is very important for the teacher. It enables you to embed the goals
and establish the qualities that are most desirable among Kenyan citizens. An example of
this interrelationship is as follows:
National goal
Promote respect for and development of Kenya’s rich and varied cultures
General learning outcome for middle school
Appreciate the country’s rich and diverse cultural heritage for harmonious co-existence
General learning outcome for Mathematics
Demonstrate mastery of number concepts by working out problems in day-to-day life.
Specic learning outcomes
Recognise the use of money in day-to-day activities
5
Strengths of the Competency-Based Curriculum
1. Learner-focused: e focus is on the educational achievement of each individual
learner. e learner takes the centre stage in the learning experience with the teacher
as a facilitator.
2. Focus on competences: e focus is more on the development of competences and less
on content. It aims at the appropriate application of knowledge, and not necessarily
its acquisition.
3. Opportunities for local decision making and greater depth of study: It gives the
teacher great autonomy and exibility in implementing the curriculum as opposed
to a prescriptive curriculum where teaching or learning methods are prescribed to
the teacher. e competency-based curriculum focuses on programs that have more
learning outcomes.
4. Balance between formative and summative assessment: e curriculum avoids too
much focus on summative assessment. It adopts a range of assessment criteria that
focuses on the development of the learning outcomes, cross-curricular competencies,
literacy and numeracy.
5. Collaborative and co-development models: Teachers, learners, parents and all other
stakeholders are involved in the curriculum delivery.
6. Synchronous learning: An integrated and interactive approach is used to develop
competencies and encourage interdisciplinary learning.
Structure of the Teacher’s Guide
is Teacher’s Guide is organised into two main sections. Part 1 is the general introduction
section detailing pedagogical approaches and issues. Part 2 highlights the sub strands
just as outlined in the Learner’s Book. It gives in detail, the expected learning outcomes,
interesting teaching and learning experiences, tips on handling the special needs learners
and informative notes to the teachers. e strands have been structured as follows:
1.
Sub strand title: In Grade 7, the learner will build on the competencies acquired at
upper primary.
2.
Introduction: is section outlines the prerequisite knowledge, skills, attitudes and
values that learners need to have acquired in order to enhance their absorption of the
concepts in the sub strand.
3.
Specic learning outcomes: ese are the knowledge skills and attitudes that the
learner should be exposed to by the end of each sub strand. e specic learning
outcomes are accompanied with suggested learning experiences, which are a summary
of activities that should be carried out to meet the specic learning outcomes.
6
4.
Core competences to be developed
5.
Pertinent and Contemporary Issues (PCIs)
6.
Links to other subjects: is section highlights the other subjects that are related to
the concepts in the sub strands. e relationship is by way of the subjects applying the
skills being taught in the sub-strand and vice versa.
7.
Values: ese 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 of moulding ethical citizens. e core values emphasised
in this Teacher’s Guide are love, responsibility, respect, unity, peace, patriotism, social
justice and integrity.
8.
Key inquiry questions: is is an approach where the teacher uses questions to
stimulate learners’ thinking to allow them to generate information using their own
words and understanding. Key Inquiry Questions play the following functions:
• Help to focus the learning.
• Probe for deeper meaning and set the stage for further questioning.
• Foster the development of critical thinking skills and higher order capabilities
such as problem solving.
• Allow learners to explore ideas in a free, non- judgmental, meaningful and
purposeful way.
• Encourage collaboration amongst learners, teachers and the community thus
integrating technology to support the learning process.
Sample Key Inquiry Questions are given in this Guide. You are free to add your own
Key Inquiry Questions in each lesson. Consider the following when writing Key
Inquiry Questions:
• e focus of your learning outcome and the strand as given in the curriculum
design.
• Examine the concept in the curriculum design that must be addressed and
brainstorm on questions that would enable learners to think about the concept
without dictating the direction or outcome of their thinking.
• Utilise the six typical question words: Who? What? Where? When? Why? How?
9.
Suggestions on facilitating dierentiated learning and learners with special needs
10.
Suggested teaching and learning resources
11.
Teacher preparation for the lessons in this sub strand
12.
Suggested learning experiences: is section provides guidance to the teacher on
how to facilitate learning in each lesson.
7
13.
Suggested assessment methods: is section gives the teacher a range of suggested
methods they can use to assess the learner’s progress.
Core competences to be developed
A competency-based approach enables meaningful connections within and between
subjects. e seven core competences to be developed in every learner are:
1. Communication and collaboration
Communication is the act of transferring information from one place to another,
whether vocally, visually, or non-verbally. Collaboration on the other hand is the
process where two or more people or organisations work together to realise shared
goals. Strategies for eective communication enhance the attainment of greater
collaboration among learners. is ultimately increases their success as they engage in
collaborative problem solving.
2. Self-ecacy
Self-ecacy is a person’s belief in his or her capabilities to perform tasks or assignments
that can change and transform his or her life. It determines how a learner feels, thinks,
behaves and motivates himself or herself. Self- ecacy has the potential to determine
four major processes in a learner, namely: cognitive, motivational, aective and
selection processes.
3. Critical thinking and problem solving
An important outcome of quality education is teaching learners how to think critically.
It is possible for learners to reason in an uncritical way. When learners are empowered
with critical thinking competence, they avoid being subjective and use logic and
evidence to arrive at conclusions. Critical thinking further facilitates exploring new
ways of doing things and thus promotes learner autonomy. is gives learners ways of
solving problems in their lives and communities and will ultimately help them to full
their potential, which is the vision for the basic education curriculum.
4. Creativity and imagination
Creativity is the ability to imagine and create meaningful original ideas, forms, methods,
patterns and interpretations in the mind to produce something new. Imagination
only exists or happens in the mind and it remains in the mind. In educational terms,
creativity and imagination refers to the ability of learners and their teachers to form
images and ideas in their minds and turn them into real, visible creations. Learners
who are creative and imaginative are able to make life interesting for themselves and
others around them. ey use the knowledge, skills and values acquired in the learning
process to create new ideas that result in products that add value to their lives and to
the lives of others around them.
8
5. Citizenship
Human beings have always been known to form communities based on shared
identities. Such identities are formed in response to a variety of human needs, which
might be economic, political, religious or social. e individuals in these communities
identify themselves as citizens. Citizenship is the state of being vested with the rights,
privileges and duties of a citizen. A sense of citizenship helps to equip learners with
skills to deal with situations of conict and controversy knowledgeably and tolerantly.
It nurtures personal respect and respect for others, wherever they live.
6. Digital literacy
Digital literacy can be described as having the knowledge, skills and behaviour
necessary to eectively and safely use a wide range of digital content and devices. Such
devices include mobile phones, smart phones, tablets, laptops or desktops. Digital
literacy skills include being able to use computer communication networks, being able
to engage in online communication and social networks, being aware of and adhering
to ethical behaviour protocols, being aware of societal issues raised through digital
media and being able to search, evaluate and use information channelled through
digital platforms.
7. Learning to learn
Learning to learn is the ability to pursue and persist in learning, to organise one’s own
learning by the eective management of time and information, both individually and in
groups. It includes awareness of one’s learning process and needs, identifying available
opportunities and the ability to overcome obstacles in order to learn successfully.
Learning to learn helps learners to build on prior learning and life experiences in order
to use and apply knowledge and skills in a variety of contexts. ere are four pillars of
learning: learning to know, learning to do, learning to be and learning to live together.
ese core competences should be achieved once learners have met all the learning
outcomes in a strand.
Pertinent and Contemporary Issues (PCIs)
Learners, just like other people, are faced with a myriad of challenges owing to the legal,
technological, social, cultural and economic dynamics in society. ese challenges have
been captured in the Competency-Based Curriculum as Pertinent and Contemporary
Issues (PCIs). ere are six PCIs that have been addressed in this book. ese are:
1. Global citizenship: Peace education, integrity, ethnic and racial relations, social
cohesion, patriotism and good governance, human rights and responsibilities, child’s
rights, child care and protection, gender issues in education.
9
2. Health Education: HIV and AIDS Education, alcohol and drug abuse prevention, life
style diseases, and personal hygiene, and preventive health, common communicable
and chronic diseases.
3. Life skills and values education: Life skills, values, moral education and human
sexuality, etiquette.
4. Education for Sustainable Development (ESD): Environmental education, disaster
risk reduction, safety and security education (small arms, human tracking), nancial
literacy, poverty eradication, countering terrorism, extreme violence and radicalization,
gender issues and animal welfare.
5. Learner support programmes: Guidance services, career guidance, counselling
services, peer education, mentorship, learning to live together, clubs and societies,
sports and games.
6. Community service learning and parental engagement: Service learning and
community involvement, parental empowerment and engagement.
ese six PCIs have been captured in the learning activities.
Teaching and Learning Resources
ese refer to items that the teacher requires during the teaching and learning process.
ey include the classroom, textbooks, wall charts, cards, pictures, wall maps, classroom
objects, models, resource persons, social facilities, such as community halls, health centres
and other learning institutions.
1. Classroom as learning or teaching resource
Classroom generally refers to the place where learning takes place. Learners learn
from everything that happens around them such as the things that they hear, see,
touch, taste, smell or play with. It is therefore important for you to make the classroom
an attractive and stimulating environment. is can be done by:
• Carefully arranging the furniture and desks.
• Putting up teaching and learning resources on the walls. Examples are wall charts,
pictures or photographs.
• Displaying models
• Having a display corner in the classroom where learners display their work and
keep the materials they use in the activities. 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.
10
2. Safety in the classroom and during outdoor activities
Learners in secondary 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. You are 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 or
cutting tools.
• During nature walks and eld visits.
3. Improvisation
If each learner is to have a chance of experimenting, cheap resources must be made
available. Expensive equipment and materials may not always be available in most
schools. You are therefore advised to improvise using locally available materials as
much as possible. Improvisation should however not be regarded as a cheap substitute
for proper equipment.
e role of the teacher in learner-centred learning
e role of the teacher in Competency-Based Curriculum is that of a facilitator. He or
she facilitates discovery, acquisition and sharing of knowledge, skills, values and attitudes
through learning experiences. e teacher organises and coordinates these learning
experiences either in class or outside the classroom. Learning experiences comprise of
activities that the learner is engaged in during the lesson. e activities may be carried
out by an individual learner or as a group work activity. However, they should ultimately,
enable the learner to achieve the intended specic learning outcomes of the lesson.
Learning experiences enable the learner to:
• Acquire knowledge, skills and develop attitudes.
• Acquire the intended competences.
• Learn from one another.
• Self-evaluate and evaluate others.
• Engage deeply in the subject matter.
• Reect on the learning process.
• Interact with others during the learning process.
11
Grouping learners for learning experiences
e following are dierent ways of grouping learners:
1. Similar ability grouping
2. Mixed ability grouping
3. Similar interests grouping
4. Needs grouping
5. Gender grouping
Grouping learners has several advantages such as:
1. e individual learner’s progress and needs can easily be observed.
2. e teacher-learner relationship is enhanced.
3. A teacher can easily attend to the needs and challenges of a small group of learners.
4. Materials that were inadequate for individual work can be easily shared.
5. Learners can learn from one another.
6. Cooperation among learners can be easily developed.
7. Many learners accept correction from the teacher more readily and without feeling
humiliated when they are in a small group rather than individually.
8. Learner’s creativity, responsibility and leadership skills can easily be developed.
9. Learners can work at their pace.
e type of grouping that you may choose depends on:
1. e activity or task to be tackled.
2. e materials available.
3. Ability of learners in the class (gied or talented learners, average learners and the
time takers).
However, you must be exible enough to adjust or change the type of grouping to cope
with new situations. ere is no xed number of learners that a group must have. is will
be dictated by factors such as the task to be done, the materials available, characteristics
of learners in your class, size and the space available. However, groups should on average
have between four to seven learners. You can also resort to pair work depending on the
nature of the content being taught at the time.
ere is no one method or approach to teaching that is appropriate for all lessons.
erefore, as a teacher, choose wisely the method to use or a combination of methods
depending on the nature of the activity or task.
12
Suggestions on eective group activities
Most of the activities in the class will require learners to work in pairs or in groups. Group
activities expose learners to dierent opinions, problem-solving ideas and interactive
discussions that will help to broaden and deepen their understanding. Learners are
motivated by hearing the ideas and opinions of others, and by having the opportunity
to react to them. Collaborative learning helps facilitate a learner’s social and personal
development by allowing them to communicate and learn together. Pair and group
activities usually work best when every learner participates actively as they communicate
in order to discuss and evaluate ideas, and they may also produce shared answers or notes.
Creating eective groups in the classroom helps in developing core competencies and
values such as accountability, cooperation, integrity and life skills in the learners.
Below are suggestions on how you can make the activities more successful during
Mathematics lessons.
1. Co-create clearly dened expectations with the learners.
2. Come up with three to ve rules of group expectations with the learners. is helps in
developing ownership among learners.
3. Give job role cards to learners. Make the roles rotational. e following are some of the
suggested role cards:
Facilitator
• Ensures that everyone is on task.
• Encourages the group members to do their best.
• Ensures that the group work is completed.
Recorder
• Writes the names of the group members.
• Does all the writings and recordings for the group discussions.
Timekeeper
• Keeps track of time for group work.
Presenter
• Presents the group discussion and results to the class.
13
Facilitating dierentiated learning and learners with special needs
Inclusive education involves ensuring all learners are engaged in education and that they
are welcomed by other learners so that everyone can achieve their potential. Inclusive
practice embraces every individual regardless of gender or ability including those with
special needs. e focus of inclusive curriculum is on ensuring participation in education
of learners with dierent learning styles. To be successful, it entails a range of issues
including attitude, adapting the learning resources, a variety of teaching and learning
methods and working together. Overall, the benets of an inclusive curriculum extend to
all learners. Dierentiated learning may be conceptualized as a teacher’s response to the
diverse learning needs of individual learners. You are encouraged to know the learners,
understand their diverse learning styles and preferences and also tailor the concept
delivery process to meet the needs of each individual learner.
Learners with special needs who may follow the regular curriculum include those with:
•
Physical impairment
•
Visual impairment
•
Hearing impairment
•
Mental diculties
•
Speech diculties
•
Gied and talented
•
Mild cerebral palsy
•
Emotional and behavioural diculties
Use the following strategies to facilitate dierentiated learning.
Type of learners Possible characteristics Suggested ways of facilitation
Gied and
talented learners
• ey learn easily and
have a high retention of
knowledge and skills.
• ey show interest in
several subjects and ask
challenging questions in
a critical and analytical
manner.
• ey are alert, curious,
observant and quick to
respond to issues.
• ey are restless when
given tasks that are less
challenging or do not
interest them.
• ese learners usually
exceed expectations.
• Gis and talents are innate
and you need to help the
learners to develop them.
• You can assist such
learners by providing
them with extra work in
terms of written tests and
other performances.
14
Time takers • ey learn slowly and have a
low retention of knowledge
and skills.
• Some may have better
physical development than
mental development.
• ey get distracted easily.
• ese learners may be
restless, aggressive and
disruptive resulting from
previous failure and
consequent dislike of the
subject.
• Encourage them to make
a study timetable and read
from a place that is free
from destructions.
• Give them small tasks that
can be done in a short
duration of time.
• Do not label the learner
and keep supporting them.
• Be patient with these
learners as they take time
to grasp the concepts.
Auditory learners • Prefer face-to-face
discussions, lectures,
podcasts and well narrated
videos.
• ey struggle with reading
and writing tasks.
• Revise by saying concepts
out loud.
• Prefer presentations or
discussions of assignments.
• Allow them to lead class
presentations and reward
participation.
• Allow auditory learners
who are having challenges
to take oral exams instead
of written ones.
• Encourage them to sing
songs and recite poems
about Mathematical
concepts.
Visual learners • Takes in new information
by looking at images,
videos, maps, diagrams, and
other graphic organizers.
• Make use of shapes, realia,
symbols, charts, diagrams,
typography among other
visual elements to appeal to
visual learners.
Kinaesthetic
learners
• Prefer hands-on activities
and learn best by doing.
• Encourage kinaesthetic
learners to participate in
experiments, projects and
other interactive activities
which engage their
psychomotor skills.
• Give them practical
assignments such as
making models.
15
Read/write
learners
• ey prefer learning
through reading articles,
textbooks, manuals, and so
on.
• ey like taking notes and
reading the notes back over
again.
• ese learners focus on
clarity of concepts that have
been written.
• Use lists to summarise
concepts and procedures.
• Allow them to rewrite
concepts and ideas in their
own words.
• Give these learners
hand-outs, manuals and
reading lists relevant to the
concepts being studied.
Use the following strategies to facilitate learners with special needs.
Special need Possible characteristics Suggested ways of facilitation
Visual
impairment
• Excessive blinking, rubbing of
the eyes, frowning, squinting or
sensitivity to light
• Double vision or sees
overlapping images of objects
• Fails to observe or notice details
in pictures, videos, shapes and
objects
• Views objects closely or too far
from the eyes
• Discharge from the eyes
• Frequent falling or stumbling
over objects
• Bad performance in games and
sports that demand eye-hand or
eye-foot coordination
• Over-reliance on other senses
such as touch and hearing
• Allow learners with short
sightedness to sit at the
front of the class.
• Write text on the
chalkboard and on charts
using large print.
• Give them materials to
handle instead of showing
them from a distance.
• Allow learners with long-
sightedness to sit at the
back of the class or at any
other appropriate distance
from the chalkboard.
• Encourage them to use
other senses such as
hearing.
16
Hearing
impairment
• Rarely responds when talked to
• Delayed response and requests
those speaking to repeat words
• Speaks too soly or too loudly
and fails to regulate the pitch of
their voice
• Directs their ears towards the
direction of the sound
• Discharge from the ears
• Stares blankly at you as you
speak
• Tilting of the head towards the
source of the sound
• Encourage them to learn
sign language
• Provide speech to text
captioning for videos.
• Encourage their parents or
guardian to buy hearing
aids for them.
• Use teaching and learning
resources that appeal to
their other senses such as
sight.
• Speak loudly for them
to hear as you explain
concepts.
Physical
impairment
• Stunted growth
• Hump development on the spine
• Weak bones that break easily
• Poor bladder or bowel control
• Poor balance and posture
• Crippled limbs
• Missing limbs
• Make use of their
functional body parts.
• Encourage their parents
to buy equipment that can
help them to do tasks.
Always remind learners that everyone is special and they need to assist those who are
dierent. Other suggestions on facilitating dierentiated learning and learners with special
needs have been outlined in the teaching guidelines for each sub strand. Treat all learners
fairly regardless of their challenges and encourage the learners to do the same. In extreme
cases, you can give recommendations for these learners to join special schools.
Integrating digital learning in Mathematics
e use of technology and digital devices in information delivery is the foundation
of digital learning. e purpose of integrating digital learning in Mathematics is to
improve the quality of the learning experiences and to equip learners with 21
st
century
skills. In the process of learning, you can use digital devices as tools for teaching,
assessment, introducing concepts or summarising what the learners have learnt. e
use of technology has the potential to enhance teaching and learning experiences by:
• Supplementing classroom instruction
• Stimulating and motivating the learner
17
• Enhancing concepts acquisition and retention
• Arousing the learner’s interest and promoting active participation during lessons
• Saving time used to explain concepts
• Enhancing digital literacy development
• Catering for individual learning dierences in the learners
• Reaching out to learners by multisensory presentation
During digital learning activities, always carry digital devices such as smartphones,
tablets, laptops and other resources to class. If possible, you can consider taking the
learners to the school’s computer room. Do not allow the learners to carry smartphones
or other digital devices to school.
Guidelines on parental empowerment and engagement
Parental empowerment and engagement underscores the critical role that parents
and guardians play towards the holistic growth and success of their children.
In the competency-based curriculum, parents or guardians need to be empowered and
given an opportunity to actively participate in their children’s learning experiences.
Parental engagement therefore will be enhanced through the following strategies:
1. Participatory decision making: Involve parents or guardians in the formulation of
decisions that aect the learner’s overall wellbeing within and outside the school.
Engage them in discussions concerning their children’s observed behaviour. is
allows parents or guardians to take part in the identication of their children’s natural
abilities, academic capabilities, career guidance and choices.
2. Communication and collaboration: Parents or guardians are key stakeholders in the
school community. Timely and eective communication enables them to collaborate
with the school towards the improvement of their children’s well-being. Update
parents and guardians regularly and provide them with opportunities to respond on
matters concerning their children’s learning and behaviour.
3. Learning and development process: Quality is at the heart of education and the
learning experiences that learners are exposed to is fundamentally important to their
future well-being. Quality learning should facilitate holistic growth and development
in the following aspects: physical, social, intellectual, emotional, moral and spiritual.
Involve parents in monitoring and providing support to their children as they grow
and learn.
4. Resourcing, volunteering and linkages: Schools require human, physical, nancial
and other types of resources to function eectively and eciently. Involve the parents
in supporting school activities and development through volunteerism, provision of
own resource and networking for the school.
18
5. Educate parents and guardians on their roles and responsibility in boosting the
achievement of desired learning outcomes during parents’ meeting and other
gatherings.
6. Encourage parents and guardians to engage with their children on school
assignments and projects.
Note: As you engage parents and guardians, exercise restraint and resist the
temptation of over engaging or overburdening them. Discourage them from
carrying out tasks, activities and assignments on behalf of their children.
e following are some of the characteristics of an empowered and responsible parent.
• Understands the child’s school calendar
• Visits school on certain occasions
• Is concerned with the child’s welfare
• Does follow-ups on the child’s learning
• Provides for the child’s needs
• Ensures safety and security of the child
• Is ethical and a good role model
• Provides career guidance to the child
• Disciplines the child
• Spends quality time with the child
• Supports education activities of the learning institution of his or her child
• Respects the child
• Identies and nurtures the child’s talents
Competency-based assessment
e main purpose of competency-based assessment is to:
• Inform teaching and learning decisions
• Establish the level of learner’s competence
• Ascertain progress against the learning outcomes
• Encourage learners to make judgments about their performance
• Enhance learner motivation
• Identify where intervention, focused support or referral is required
• Make decisions regarding choice of subject, course and careers pathways.
19
e following are the common forms of assessment in a Competency-Based Curriculum.
1. Formative Assessment or Assessment for learning (AFL)
is is an investigative tool to monitor the progress of an individual learner in
meeting the learning outcomes in a subject or learning area. It involves gathering data
during the learning process and providing feedback for you to rene the teaching and
learning strategies. is approach helps build an accurate and detailed understanding
of the learner and inform on suitable pedagogy so that you can provide appropriate
assistance to the learner.
2. Assessment as Learning
Assessment as learning occurs when a learner is assisted to develop a capacity to be
independent, self-directed to set individual goals, monitor own progress or carry out
a self-assessment and reect on his or her learning. A learner can assess himself or
herself when you provide them with a clear picture of the steps followed to reach
prociency or a set criterion that have a variety of examples and models of decent
work for comparison.
3. Assessment of learning
is is a summative assessment and is carried out at the end of a task, an activity, a
sub strand, a strand, a term, a year or level of learning. Summative assessment is a
comprehensive process used to summarise and communicate what a learner knows
and can do with respect to the learning outcomes and expectations aer a dened
instructional period of time. It summarises individual learner’s achievement. Since
summative assessment comes at the end of a sub stand, a strand or a term, the feedback
has less impact on learner’s learning compared to formative assessment. e evidence
is used to determine level of achievement. It is designed to provide information on the
achievement of a learner to parents, educators and learners themselves for appropriate
placement or further studies.
e assessment methods that could be used include the
following:
(a) Observation: involves monitoring the learner as he or she does an activity or a task
to see if he or she has the ability to perform it exquisitely.
(b) Written tests: involves answering questions by way of writing. Ensure that the test
is standardized to measure the ability of individual learners against the learning
outcomes.
(c) Oral questions: involves questioning the learners and using their answers to gauge
their mastery of knowledge, skills and attitude. Ensure that the language used in
asking the questions is at the level of the learner.
20
(d) Assignments: involves giving a learner activities or tasks to accomplish with the
purpose of exposing them to particular knowledge, skills and values.
e following assessment tools can be developed for use in assessing the learning
outcomes.
(a) Checklists: is an assessment tool that communicates goals and highlights the required
knowledge, skills and attitude to be assessed. It assists the teacher to determine areas
of focus to enable the learner to develop relevant knowledge and skills. A sample
checklist is provided on page 55 of this Teacher’s Guide.
(b) Rating scales: is an assessment tool that species the criteria and allows teachers
to gather information and make informed decisions about what learners can do in
relation to the outcomes. It uses descriptive words, such as always, usually, sometimes
and never. A sample rating scale is provided on page 116 of this Teacher’s Guide.
(c) Questionnaires: is self-assessment tool that allows a teacher to collect information
from a learner. It consists a list of questions on various aspects of the learner’s
experiences.
(d) Project: is a set of activities or tasks that are to be implemented within a set timeframe.
Learners identify a need in their community where they can provide services based
on what they have learned.
(e) Journals: the learner keeps a record of their personal feelings, thoughts and
experiences daily. It provides a window into the learner’s thinking and learning
experiences. A sample journal is provided on page 109 of this Teacher’s Guide.
(f) Portfolio: is a purposeful collection of work samples, self-assessments and goal
statements that reect a learner’s progress. A Portfolio is a le or binder, which
holds samples of individual learner’s work. At dierent points during the year, this
portfolio can be used to discuss with the learner, the learner’s parents, administrators
or other sta members regarding their progress as well as providing services for
learner. A sample portfolio is provided on page 200 of this Teacher’s Guide.
(g) Learner’s prole: is a summary of the teacher’s opinion on a learner’s mastery of
competencies. A sample learner’s prole is provided on page 87 of this Teacher’s
Guide.
(h) Anecdotal Records: are short reports, photographs and drawings that give detailed
descriptions of incidents, their contexts and what was said or done by the learner(s).
(i) Observation schedule: is an assessment tool that allows a teacher to record the
characteristics and behaviour that a learner displays as he or she performs learning
activities or tasks. A sample observation schedule is provided on page 42 of this
Teacher’s Guide.
21
Developing competency-based assessment tasks
Competency-based assessment tasks create opportunities for learners to apply the
competencies and skill they have acquired to solve real world problems and situations.
ese are real-life authentic tasks that enable the teacher to assess the learner’s ability
to synthesise, apply, analyse, evaluate and create solutions to challenges in their
immediate environment.
e following steps are used to develop the competency-based assessment tasks.
Step 1: Developing the competencies
e competencies are formulated from the specic learning outcomes. e
competencies determine what the learner knows and what they should be able to do.
For example:
• e learner can communicate and collaborate with other learners to collect data in
the immediate environment.
• e learner can curate collected data and develop tools for representing the data.
Step 2: Developing the authentic task
Develop a task from the competencies in step 1. e task should focus on the learning
experiences the learner should undertake.
For example:
• Instruct learners to carry out a research on dierent economic activities in the
community at their own free time and with the help of their friends. Let them collect
data and determine the most common economic activities in their community. ey
should represent their data using bar graphs, pie charts and line graphs.
Characteristic of a good authentic task
• It resembles real-life tasks, activities and experiences.
• It involves high order thinking (applying, analysing, evaluating and creating).
• It requires learners to communicate and collaborate with others.
• It involves application of knowledge already learnt in class.
Step 3: Developing the criteria
Create sample criteria to establish clarity with the learners about the concepts that are
applied while doing the authentic task.
For example:
• Ability to collect data from the immediate environment.
• Ability to represent the data using bar graphs, pie charts and line graphs.
22
Step 4: Developing a scoring guide for the authentic task
Use the criteria in step 3 to develop an appropriate assessment tool. Use the assessment
tool to calibrate the level performance of individual learners in the task.
Professional documents
ese are the documents used by the teacher in the preparation, implementation and
evaluation of teaching and learning. ey are vital documents that a teacher must
have to keep track of his or her work, that of the learners as well as to make teaching
and learning more eective. ey include:
1. Schemes of work
2. Lesson plans
3. Records of work covered
4. Progress records
1. Schemes of work
A scheme of work is a document that a teacher develops from the curriculum design.
A scheme of work shows how the planned curriculum content shall be distributed within
the time allocated for the subject.
A scheme of work helps the teacher to:
(a) Plan on what resources will be required
(b) Decide on the methodology to be used
(c) Plan for assessment
A sample scheme of work is provided in Appendix 1 on page 226 of this Teacher’s
Guide.
2. Lesson plan
A lesson plan is an essential document for eective teaching and learning. A well-
done lesson plan helps the teacher to:
•
Organise the content to be taught in advance focusing clearly on the content to be
covered and the way it should be taught hence avoiding vagueness and irrelevance.
•
Plan, prepare and assemble teaching or learning resources.
•
Present concepts and skills in a systematic manner, using appropriate strategies to
achieve the stated lesson outcomes.
•
Manage time well during the lesson.
•
Select and design appropriate assessment methods to evaluate the teaching and
learning process.
•
Make connections between components.
23
Components of the lesson plan
(a) Organisation of learning: shows where learning will be taking place. It could be in
the classroom, or outside the classroom or a visit to a nearby library or farm.
(b) Introduction: the lesson should be introduced in an interesting and stimulating
manner to arouse curiosity in the learners. Integrate the learner’s related past
experiences as much as possible, tapping into learner’s prior knowledge to prepare
them for additional content you are about to introduce.
(c) Lesson development: this is the actual teaching of the subject area content. e subject
matter is divided into steps. Each step should contain one main idea or experience.
Explicitly outline how you will present the lesson’s concepts to the learners and the
activities to be undertaken in each step-in order to achieve the stated outcomes. It
should indicate clearly how and what is to be taught and the learning experiences.
You as a teacher should vary the teaching or learning activities as the need arises.
(d) Conclusion: this step summarises the lesson by putting emphasis on important
points or concepts covered. During this time a wrap up of the lesson is given to help
learners organise the information into meaningful context in their minds.
is can be done by:
• Asking questions to establish whether the lesson outcomes have been achieved.
• Allowing learners to seek clarication.
• Summarising the main points in the lesson.
• Giving follow-up activity(ies) such as an assignment or a project.
• It is important to note that a lesson plan may not have all the details of the
content; therefore, the teacher should have lesson notes.
(e) Reection on the lesson: this is a critical analysis of the learning. e teacher is
called upon to make an honest assessment of his or her performance and that of the
learners during the lesson and give reasons for the success or failure of the lesson.
Suggestions or remedies should be highlighted in this section.
e lesson planning will require emphasis on embedding and infusing of the aspect
of the CBC such as core competences, PCIs, values, non-formal learning activities,
link to other learning areas, resources and assessment. A conscious eort must be
made during planning to include the types of questioning techniques that will be
used in the lesson.
A sample lesson plan is provided in Appendix 2 on page 228 of this Teacher’s
Guide.
24
3. Records of work
A Record of Work is a document kept by the teacher showing the work that has been
done at the end of every lesson, strand or sub strand. e individual teacher makes
the entries daily. It helps in:
• Accountability and transparency of work covered by the teacher.
• e continuity of teaching of a class.
• Giving a new teacher an idea of where to start teaching the class.
• Evaluation of schemes of work aer a period.
• Providing uniformity of content coverage in case of several streams.
e record tracks the achievement of learning outcomes and the competencies
acquired by the learner. e record can be used to show the teacher whether their
teaching has been eective in addressing the leaning needs of individual learners. It
therefore acts as a guide for the teacher to be able to give the required attention to
individual learners to ensure the desired outcomes as stated in the curriculum designs
are portrayed by all the learners. e progress record can also be used to give the
learner and the parents or caregiver information about the learner’s progress.
Components of records of work
(a) Time frame: ere should be an indication of the date and week when the work was
covered.
(b) Work done: Strand and sub strand as derived from the specic learning outcome(s).
(c) Reection: e remarks column should have statement(s) specifying the success
and or challenges of that lesson and recommendations.
(d) Details of the teacher: include the name, signature or initials of the implementing
teacher for accountability.
e school management should also regularly sign the record of work. A sample
records of work is provided in Appendix 3 on page 231 of this Teacher’s Guide.
4.
Assessment record book
An assessment record book is an elaborate arrangement of rubrics and any other
assessment tools that represent a learner’s performance against the learning outcomes
over a certain period of time. e assessment record book is handed over to the teacher
handling the learner in the next grade to ensure smooth transition of learners and
enable the new teacher to determine the characteristics, interests and entry behaviour
of individual learners.
25
It also helps to:
• Ensure the grading is fair and consistent for all learners.
• Compare a learner’s performance in dierent grades.
• Measure the product, process and learning progress of a learner
• Provide an opportunity for learners to evaluate their own strengths or weaknesses over
a period of time and to work collaboratively with their teachers in setting attainable
targets for the future.
A sample assessment record book is provided in Appendix 4 on page 232 of this
Teacher’s Guide.
Conclusion
is Teacher’s Guide has been written to help you guide learners to learn Mathematics
in the most enjoyable and captivating manner. You are reminded to always arouse the
curiosity of learners as you teach. Some things that you may do in preparation for a lesson
include:
• Go through the expected learning outcomes – this should help guide the manner of
teaching.
• Read through the lesson in advance to get an overview of the content to be covered.
• Form a mental picture of the learning activities and the ways in which you will interact
with learners when dealing with the suggested activities.
• Collect the materials that will be needed during the lesson in advance.
Remember: e suggested learning experiences in this book are just a guide.
You may not need to follow them to the letter. Feel free to incorporate other innovative
teaching methods that will help in delivering the intended content optimally.
26
1.1 Whole Numbers
Number of lessons: 20
Refer to Learner’s Book pages 1 to 17
Introduction
e learners have interacted with the concept of whole numbers from their early years of
education. In Grade 6, the learners explored place value, total value and writing numbers
in symbols up to millions. ey determined squares and square roots of whole numbers
and also read, ordered and rounded o numbers up to hundreds of thousands.
In this sub strand, the learners will build on the concepts learnt in the previous grades.
Even though the learners may have prior knowledge of some of the concepts in this sub
strand, it might be helpful to review what they learnt in upper primary. In this grade, the
learner will be introduced to prime numbers which plays a huge role in Mathematics,
ranging from nding square roots of whole numbers to calculating GCD and LCM.
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) Use place value and total value of digits up to hundreds of millions in real life.
(b) Read and write numbers in symbols up to hundreds of millions in real life situations.
(c) Read and write numbers in words up to millions for uency.
(d) Round o numbers up to the nearest hundreds of millions in real life situations.
(e) Classify natural numbers as even, odd and prime in dierent situations.
(f) Apply operations of whole numbers in real life situations.
(g) Identify number sequence in dierent situations.
(h) Create number sequence for playing number games.
(i) Use IT devices for learning more on whole numbers and for enjoyment.
(j) Appreciate use of whole numbers in real life situations.
1.0 Numbers
27
Core competencies to be developed
• Communication and collaboration: as learners speak and listen to each other while
working as a team to round o numbers using place value charts.
• Critical thinking and problem solving: as learners work together to identify, interpret
and create number patterns.
• Creativity and imagination: as learners play games, make observations and create
puzzles that involve number sequences.
Pertinent and contemporary issues (PCIs)
• Financial literacy: as learners practice writing dummy cheques for dierent sums of
money.
• Self-esteem: as learners create puzzles that involve number sequences.
Links to other subjects
• Business studies: writing numbers in words and in symbols as the learners practice
writing dummy cheques at home.
• Computer studies: as learners use digital devices to play number games.
• Language: as learners write numbers in words and as they use new vocabulary such
as prime numbers.
Values
• Respect: as learners appreciate each other’s contribution while playing number games
in pairs and in groups.
• Unity: as learners work together as a team towards achieving the set goals of making
puzzles involving number patterns.
• Peace: as learners work in groups and share dierent roles while playing games
involving whole numbers.
Key inquiry questions
1. Why do we write numbers in words and in symbols?
2. Where do we write numbers in words and in symbols?
3. Why do we round o numbers in real life situations?
28
Suggestions on facilitating dierentiated learning and learners with special
needs
Facilitating dierentiated learning Facilitating learners with special needs
• Give both the time takers and the gied
learner’s equal chances to participate
in class activities. Ensure that they
accommodate one another and work
together despite their dierences.
• Encourage the time takers to
participate in class activities such as
discussions, role play, reading number
stories or drawing number lines.
• Give gied learners extra activities to
keep them busy and avoid boredom or
idling.
• Ensure that the learners are positioned
evenly in the class.
• Identify each learner’s needs and
characteristics and adjust the content
delivery process accordingly. is will
help learners with dierent abilities to
learn and acquire information in their
own way.
• Rene learning strategies and
experiences according to the learning
needs of the learner, resources and
assigned time.
• Ensure the short-sighted learners
sit at the front of the class and the
long-sighted ones sit at the back to
ensure appropriate distance from the
chalkboard during lessons.
• In Activity 6 and Activity 9, learners
are required to make number cards.
Encourage learners to make number
cards in large print to assist visually
impaired learners.
• Encourage learners to speak clearly
and audibly during the group
activities. e learners can also
use gestures and sign language if
possible, to assist learners with
hearing impairment. During the
digital learning activities, provide
speech to text captioning for
the videos or you may also avail
headphones with amplied sound for
learners with hearing impairment.
• In Activity 1 and Activity 2, give
more time to learners with missing
limbs so that they can participate
in drawing place value charts and
manipulating the abacus.
Suggested teaching and learning resources
• Number cards
• Place value charts
• Abacus
• Place value tins
• Place value pockets
• Counters
• Dummy cheques
• Number games
• Number puzzles
29
Teacher preparation for the lessons in this sub strand
Ensure that there is enough place value apparatus, number cards, dummy cheques and
other required teaching and learning resources. For Activity 1 and Activity 2, ensure that
all learners have enough place value apparatus. e place value apparatus can include place
value charts, abaci, place value tins and place value pockets. You can involve learners in
making the place value apparatus prior to the lesson. is will give them an opportunity to
showcase their creativity and imagination as they make improvised place value apparatus
using locally available materials. For Activity 4, make sure that all learners have enough
pieces of paper to make dummy cheques. Allow them to exercise autonomy in their
creativity and imagination while making the cheques. You may consider guiding them to
make blank cheques prior to the lesson, so that the learners can concentrate on writing
numbers in words and in symbols during the activity.
Suggested learning experiences
Place value of digits in a number
Refer to Learner’s Book page 1
Activity 1: In pairs
1. Given that this is the rst lesson, introduce yourself and welcome the learners to
Junior Secondary. Assure the learners that the concepts they are going to learn will
build on their learning experiences from upper primary. is will help calm down the
learners and allay any anxieties that may hinder the learning process.
2. Guide learners to draw a place value chart. Let them write the number 416 928 305
in the place value chart. Give them an opportunity to discuss and determine how to
write the number in the place value chart. is will help you gauge the learners’ entry
behaviour. It will also develop communication and collaboration as they discuss.
3. Encourage the learners to discuss and nd the place value for each digit in the number
416 928 305. Let them give priority to nding the place value of digit 4 because its
place value is hundreds of millions and that is the scope for this sub strand. As learners
take their roles in pairs to achieve common solutions, the value of responsibility is
enhanced.
4. Let the learners discuss and identify the digit that is in the place value of tens of
millions in the number 416 928 305. Write the number 9 999 999 on the chalkboard.
Ask the learners to count forward and mention the whole number that follows 9 999
999. is will help the learners to make a transition from the place value of millions
which they are familiar with to the place value of tens of millions which is part of what
they are going to learn. is enhances critical thinking and problem solving.
30
5. Emphasise that the place values of the digits in a number increases from right towards
the le. Randomly choose a few learners to present the group’s ndings to the rest of
the class; this will help promote self-ecacy and peer education.
6. Harmonise the concepts the learners have learnt using Example 1 on page 1 of the
Learner’s Book. Let them write numbers of their own choice then discuss and write
their place values. is will encourage learning to learn.
7. Tell individual learners to do Practice exercise 1 in the Learner’s Book.
Practice exercise 1: Expected answers (Pages 1 and 2)
1. (a) e place value of digit 1 is hundreds of thousands.
e place value of digit 2 is tens of thousands.
e place value of digit 7 is thousands.
e place value of digit 6 is hundreds.
e place value of digit 3 is tens.
e place value of digit 5 is ones.
(b) e place value of digit 3 is tens of millions.
e place value of digit 2 is millions.
e place value of digit 5 is hundreds of thousands.
e place value of digit 6 is tens of thousands.
e place value of digit 1 is thousands.
e place value of digit 3 is hundreds.
e place value of digit 7 is tens.
e place value of digit 4 is ones.
(c) e place value of digit 9 is hundreds of millions.
e place value of digit 3 is tens of millions.
e place value of digit 5 is millions.
e place value of digit 7 is hundreds of thousands.
e place value of digit 2 is tens of thousands.
e place value of digit 9 is thousands.
e place value of digit 4 is hundreds.
e place value of digit 6 is tens.
e place value of digit 1 is ones.
31
2. (a) Millions (b) Tens of millions
(c) Tens of thousands (d) Tens of millions
(e) Hundreds of thousands (f) Hundreds of millions
3. Hundreds of millions
4. e place value of digit 1 is tens of millions.
e place value of digit 2 is millions.
e place value of digit 8 is hundreds of thousands.
e place value of digit 5 is tens of thousands.
e place value of digit 7 is thousands.
e place value of digit 1 is hundreds.
e place value of digit 0 is tens.
e place value of digit 0 is ones.
5. Tens of millions
Total value of digits in a number
Refer to Learner’s Book page 2
Activity 2: In groups
1. Let learners put objects on an abacus as shown in the Learner’s Book. Let them discuss
and identify the number shown on the abacus. ey should be able to identify the
number shown on the abacus as 673 521 341.
2. Guide the learners to relate the number of objects and the place value of each digit.
Guide them to work out the total value of each digit in the number 673 521 341. Critical
thinking and problem-solving is enhanced as learners establish the relationship
between the place value of a digit and its total value. ey should recognise that the
total value of a digit in a number is the product of that digit and its place value.
3. Ask the learners to come up with other numbers of their choice. Let them use place
value charts and other place value apparatus to calculate the total values of the digits
in the numbers. Randomly choose a few learners to present their ndings to the rest
of the class. is will help promote self-ecacy and peer education. Harmonise
their ndings by guiding them through Example 2 on page 2 of the Learner’s Book.
Emphasise the fact that to get the total value of the digit, they have to multiply the
digit by its place value.
4. Tell individual learners to do Practice exercise 2 in the Learner’s Book.
32
Practice exercise 2: Expected answers (Page 3)
1. (a) e total value of digit 3 is 300 000.
e total value of digit 2 is 20 000.
e total value of digit 9 is 9 000.
e total value of digit 5 is 500.
e total value of digit 5 is 50.
e total value of digit 9 is 9.
(b) e total value of digit 6 is 60 000 000.
e total value of digit 0 is 0.
e total value of digit 3 is 300 000.
e total value of digit 3 is 30 000.
e total value of digit 4 is 4 000.
e total value of digit 9 is 900.
e total value of digit 7 is 70.
e total value of digit 7 is 7.
(c) e total value of digit 3 is 300 000 000.
e total value of digit 6 is 60 000 000.
e total value of digit 5 is 5 000 000.
e total value of digit 4 is 400 000.
e total value of digit 7 is 70 000.
e total value of digit 8 is 8 000.
e total value of digit 6 is 600.
e total value of digit 0 is 0.
e total value of digit 2 is 2.
(d) e total value of digit 2 is 2 000 000.
e total value of digit 0 is 0.
e total value of digit 0 is 0.
e total value of digit 8 is 8 000.
e total value of digit 5 is 500.
e total value of digit 6 is 60.
e total value of digit 4 is 4.
(e) e total value of digit 1 is 10 000 000
e total value of digit 4 is 4 000 000.
e total value of digit 8 is 800 000.
e total value of digit 6 is 60 000.
e total value of digit 5 is 5 000.
e total value of digit 6 is 600.
e total value of digit 3 is 30.
e total value of digit 2 is 2.
(f) e total value of digit 7 is 700 000 000.
e total value of digit 3 is 30 000 000.
e total value of digit 0 is 0.
e total value of digit 2 is 200 000.
e total value of digit 6 is 60 000.
e total value of digit 9 is 9 000.
e total place value of digit 4 is 400.
e total place value of digit 1 is 10.
e total place value of digit 8 is 8.
2. (a) 70 (b) 7 000 000 (c) 700 000 000
(d) 70 000 000 (e) 700 000 (f) 700 000
33
3. e total value of digit 5 is 500 000 000.
e total value of digit 3 is 30 000 000.
e total value of digit 1 is 1 000 000.
e total value of digit 3 is 300 000.
e total value of digit 9 is 90 000.
e total value of digit 8 is 8 000.
e total value of digit 0 is 0.
e total value of digit 7 is 70.
e total value of digit 9 is 9.
4. 900 000 000 5. 60 000
Reading and writing numbers in symbols
Refer to Learner’s Book page 3
Activity 3: In pairs
1. Guide learners to read aloud the numbers in the Learner’s Book. Walk around the
classroom and listen to them as they read the numbers and oer guidance to those
who may have challenges. Ensure that the learners are able to read the numbers
clearly, accurately and uently. Communication and collaboration is developed as
learners read the numbers for uency.
2. Instruct the learners to discuss and write the numbers in symbols using any strategy
of their choice. Creativity and imagination is enhanced as learners explore various
ways of writing the numbers in symbols.
3. Randomly choose a few learners to present their group work to the rest of the class.
is will help promote self-ecacy and peer education.
4. Guide the learners through Example 3 on page 3 of the Learner’s Book. For them to
internalise the concept, ask them to construct and state sentences involving numbers
up to hundreds of millions. Self-awareness is enhanced as learners use and write
down numbers.
5. Tell the learners to do Practice exercise 3 in the Learner’s Book with the help of their
parents or guardian. is will promote parental empowerment and engagement.
Practice exercise 3: Expected answers (Page 4)
1. (a) 6 001 018 (b) 94 731 232
(c) 173 841 526 (d) 435 052 690
2. 47 564 296 3. 149 600 000 km
4. 30 370 000 km
2
5. 315 360 000 seconds
34
Reading and writing numbers in words
Refer to Learner’s Book page 4
Activity 4: In groups
1. Using a piece of paper, guide learners to make a dummy cheque like the one in the
Learner’s Book. is enhances unity and integrity as they work together in groups. It
also develops communication and collaboration among the learners.
2. Let the learners read the amount of money written in symbols on the cheque. Task
them to brainstorm and write the amount of money in words. is enhances critical
thinking and problem solving.
3. Instruct the learners to make other dummy cheques. Let them write any amount of
money in symbols. Tell them to read the amount of money written on the cheques
they have made. is inspires career guidance in the learners as they understand
the dierent jobs that require the use of numbers in real life such as accounting. is
also develops nancial literacy as the learners practice writing dummy cheques for
dierent amounts of money.
4. Let the learners write the amount of money on each cheque in words. Take them
through Example 4 on page 5 of the Learner’s Book in order to harmonise what they
have learnt. is will help them to grasp the concept and internalise how total value
can be used to write numbers in words.
5. Tell individual learners to do Practice ex ercise 4 in the Learner’s Book. is will
promote self-ecacy and self-esteem.
Practice exercise 4: Expected answers (Page 5)
1. (a) Eight million, seventy eight thousand, nine hundred and eighty nine.
(b) Six hundred and forty thousand, ve hundred and seven.
(c) Twenty ve million, six hundred and twelve thousand, seven hundred and twenty
eight.
(d) Ninety seven million, eight hundred and ninety seven thousand and thirteen.
(e) Two hundred and fourteen million, eighty seven thousand, six hundred and
twenty three.
(f) ree hundred and twenty two million, six hundred and ninety eight thousand,
one hundred and one.
2. Five hundred and thirty ve thousand, three hundred and forty two.
3. Nineteen million, six hundred and eleven thousand, four hundred and twenty three.
4. Two hundred and thirty seven million, seven hundred and seventy seven thousand,
three hundred and y one.
5. Five hundred and twenty four million, three hundred and eight thousand, six
hundred and seventy one.
35
Rounding o numbers
Refer to Learner’s Book page 6
Activity 5: In groups
1. Let learners read about the dams that are to be built by the national government so as
to provide water for the people as mentioned in the Learner’s Book. Let them discuss
the estimated cost of building four dams. is develops citizenship and nancial
literacy in the learners.
2. Guide the learners to draw a number line and mark the midpoint of Ksh 800 000 000
and Ksh 900 000 000 as Ksh 850 000 000. Let them mark the position of the cost of
each dam on the number line.
3. Instruct the learners to identify the costs that are closer to Ksh 800 000 000 than to
Ksh 900 000 000 and also identify the costs that are closer to Ksh 900 000 000 than to
Ksh 800 000 000. e learners should be able to use the number line to round o the
costs of the dams to the nearest hundreds of millions, they can consider which side
of Ksh 850 000 000 on the number line the cost falls in. If the cost is to the le of Ksh
850 000 000, then it can be rounded o to Ksh 800 000 000, but if the cost is to the
right of Ksh 850 000 000, then it can be rounded o to Ksh 900 000 000. is enhances
critical thinking and problem solving.
4. Instruct the learners to draw a place value chart and ll in the cost of each dam. Let
them discuss and determine how to round o the numbers to the nearest hundreds
of millions. is develops the values of unity, peace and responsibility among the
learners. Communication and collaboration is also enhanced as learners come up
with the guidelines of rounding o numbers to the nearest hundreds of millions.
5. Randomly choose a few learners to present their ndings to the rest of the class. is
will encourage peer education as they learn from each other.
6. Harmonise their ndings by guiding the learners through Example 5 and Example 6
on pages 6 and 7 of the Learner’s Book.
7. Tell individual learners to do Practice exercise 5 in the Learner’s Book. is promotes
honesty, responsibility and integrity.
Practice exercise 5: Expected answers (Page 7)
1. (a) 600 000 000 (b) 700 000 000 (c) 100 000 000
(d) 700 000 000 (e) 100 000 000 (f) 900 000 000
2. 100 000 000 trees 3. 200 000 000 people
4. Ksh 300 000 000 5. 500 000 000 litres
36
Natural numbers
Refer to Learner’s Book page 7
Even and odd numbers (page 7)
Activity 6: In pairs
1. Guide learners to make number cards like the ones in the Learner’s Book.
2. Instruct the learners to draw a sorting chart involving numbers that are divisible by
2 and those that are not divisible by 2 as shown in the Learner’s Book. Let them sort
and stick the number cards on the sorting chart. is encourages the values of social
cohesion, unity and respect as they work together to sort the cards.
3. Let the learners brainstorm and mention the name given to numbers that are divisible
by 2. ey should also mention the name given to numbers that are not divisible
by 2. Emphasise the fact that the digit in the ones place value of an even number is
0, 2, 4, 6 or 8 and the digit on the ones place value of an odd number is 1, 3, 5, 7 or
9. Classifying the numbers on their own develops self-ecacy as the learners get a
sense of achievement.
4. Randomly select a few learners to present their ndings to the class. Harmonise
their ndings through probing and demonstration. Guide them through Example 7
and Example 8 on page 8 of the Learner’s Book. In order to assess the skills that the
learners have learnt, ask them at random to pick out even and odd numbers from a
group of numbers.
5. Ask individual learners to do Practice exercise 6 in the Learner’s Book.
Practice exercise 6: Expected answers (Pages 8 and 9)
1. 5 086, 4 160, 4 894, 2 952, 2 960
2. 97 657, 4 925, 5 083, 326 455
3. 102, 104, 106, 108, 110, 112,114,116,118
4. 251, 253, 255, 257, 259, 261, 263, 265, 267, 269
5. 400, 402, 404, 406, 408, 410, 412, 414, 416, 418
Digital learning
Guide learners to use a computer, a tablet or a smartphone to search for a game involving
odd and even numbers.
ey may use this link: https://www.iknowit.com/lesson/a-odd-and-even-numbers.html.
37
Prime numbers (page 9)
Activity 7A: In pairs
1. Ask learners to write down numbers from 1 to 10. Guide them to list all the factors of
each of the numbers from 1 to 10. Walk around the classroom assessing the learners’
ability to determine the factors of dierent numbers and giving guidance to those
who may have challenges.
2. Let the learners identify the numbers with only two factors (one and itself). Lead
them in a discussion to name numbers that have only two factors (one and itself).
ey should be able to discover that these numbers are called prime numbers.
Activity 7B: In groups
1. Instruct learners to copy the number chart in the Learner’s Book and cross out number 1.
ey can copy the chart on a manila paper.
2. Let them leave 2 but cross out all multiples of 2. Tell them to leave 3 but cross out
all multiples of 3. Let them repeat the process for numbers 5 and 7. is develops
learning to learn.
3. Instruct the learners to list down all the numbers in the table that are not crossed out.
Let them determine the factors of each number in the table that is not crossed out.
ey should be able to deduce that each of the numbers has only two factors (one and
itself) and therefore they are prime numbers. is promotes self-ecacy. Emphasise
the fact that 1 is not a prime number and 2 is the only even number that is a prime
number.
Additional information
is method is called the sieve of Eratosthenes. e sieve of Eratosthenes method
can be used to identify all prime numbers that are less than 100. ey are 2, 3, 5, 7,
11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. ese
are the numbers that should remain aer the learners have crossed out all the other
numbers in the table. For this concept, factorisation and division methods can also
be used in identifying prime numbers and composite numbers. By using the sieve
of Eratosthenes method, the learner can easily list down prime numbers among a
set of numbers in a quick way.
4. Harmonise the learners’ ndings by guiding them through Example 9 on page 10 of
the Learner’s Book. Emphasise that a prime number has only two factors (one and
itself). In order to assess the skills that the learners have learnt, ask them at random to
pick out prime numbers from a group of numbers.
5. Ask individual learners to do Practice exercise 7 in the Learner’s Book.
38
Practice exercise 7: Expected answers (Page 10)
1. (a) 2, 11, 13 (b) 23, 29
2. 61, 67, 71, 73, 79
3. 5, 7
4. 7 387
Operations on whole numbers
Refer to Learner’s Book page 10
Addition and subtraction (page 10)
Activity 8: In groups
1. Guide learners to make number cards like the ones in the Learner’s Book. Let them
use the number cards to form the largest possible number and the smallest possible
number. e learners should discover that the numbers on the cards should be
arranged in descending order to get the largest possible number and in ascending
order to get smallest possible number. is develops critical thinking and problem
solving. It also promotes the value of social justice as the learners give each other
equal opportunity to contribute towards the group’s intended goals.
2. Instruct the learners to work out the sum of the largest and the smallest numbers
formed. Let them subtract 329 100 from the largest number formed by the digits using
a place value chart. Let them discuss and identify the digits that require regrouping.
is enhances communication and collaboration.
3. Let the learners form dierent numbers using the number cards and carry out addition
and subtraction of the numbers formed.
4. Randomly select a few learners to present their ndings to the class. Consolidate their
ndings by guiding them through Example 10 and Example 11 on page 11 of the
Learner’s Book.
5. Ask individual learners to do Practice exercise 8 in the Learner’s Book.
Practice exercise 8: Expected answers (Page 12)
1. (a) 912 567 (b) 8 490 048 (c) 69 553 048
(d) 106 098 (e) 1 526 195 (f) 82 131 513
2. 36 358 895 learners 3. Ksh 8 900 000 4. 1 244 400 litres
5. 748 306 tourists
39
Multiplication and division (page 12)
Activity 9: In groups
1. Guide learners to make number families like the ones in the Learner’s Book. Let them
write multiplication and division sentences from the number families.
2. Instruct the learners to create other number families involving multiplication and
division. is develops creativity and imagination. Lead them into a discussion to
ascertain the relationship between multiplication and division.
3. Guide the learners through Example 12 and Example 13 on page 13 of the Learner’s
Book. For learners to internalise the concept, let them explain to each other the steps
followed when multiplying and dividing numbers. As they work in groups, encourage
the learners to respect each other’s opinions regardless of whether they agree with
them or not.
4. Ask individual learners to do Practice exercise 9 in the Learner’s Book.
Practice exercise 9: Expected answers (Pages 13 and 14)
1. (a) 265 896 (b) 376 040 (c) 4 813 233
(d) 1 359 (e) 89 (f) 2 265 remainder 18
2. 720 packets 3. 3 597 440 bags 4. Ksh 2 244 000
5. 50 kg 6. 1 066 cartons 7. 302 250 loaves of bread
8. Ksh 5 300 9. Ksh 3 906 250 10. Ksh 1 118 000
Combined operations
Refer to Learner’s Book page 14
Activity 10: In pairs
1. Let learners discuss the order of calculating the combined operations in the Learner’s
Book. is develops critical thinking and problem solving. It also promotes the
value of unity as they agree on the correct order.
2. Let the learners use a calculator or other digital devices to work out the questions
involving combined operations. Let them work out the same combined operations
without using a digital device and compare the answers. Emphasise that when four or
more operations are in the same expression, they should start with Brackets (B), work
out ‘Of ‘(O), perform Division (D), then Multiplication (M), followed by Addition
(A) and nally Subtraction(S) in that order. Let them observe that in short, this order
is referred to as BODMAS.
3. Guide the learners through Example 14 on page 15 of the Learner’s Book. Clearly
explain to them the steps followed when carrying out combined operations using
BODMAS.
40
4. Tell the learners to do Practice exercise 10 in the Learner’s Book with the help of their
parents or guardian. is will promote parental empowerment and engagement.
Practice exercise 10: Expected answers (Page 15)
1. (a) 52 (b) 19 (c) 12 (d) 6
(e) 43 (f) 48 (g) 5 (h) 70
2. (a) 5 310 eggs (b) 177 trays (c) Ksh 61 950
3. (a) Ksh 150 [2 400 – (975 + 554)] (b) Ksh 130 650
Number sequences
Refer to Learner’s Book page 15
Activity 11A: In pairs
1. Guide learners to identify the rule that has been used to form each of the sequences
in the Learner’s Book. is enhances critical thinking and problem-solving as they
use consecutive numbers in a sequence to derive the rule.
2. Instruct the learners to write the next number in each sequence. is encourages
learners to reason and apply dierent strategies to solve sequences. Emphasise that a
sequence is a list of numbers that follow a certain rule.
Activity 11B: In groups
1. Guide learners to use sequences to estimate the population of Kenya from the year
2019 to the year 2025 using the data information in the Learner’s Book. is inspires
citizenship and career guidance in the learners as they understand the dierent jobs
such as statisticians who use data to make educated predictions and estimations in
real life.
2. Instruct the learners to create sequences using the rules in the Learner’s Book. Walk
around the classroom and observe them as they create sequences and oer guidance
to those who may have challenges.
3. Randomly select a few learners to present their sequences to the class. Consolidate
their ndings through probing and demonstration. Guide them through Example 15
and Example 16 on page 16 of the Learner’s Book. Reinforce the concepts that the
learners have learnt by asking them at random to identify a sequence and work out
the next number.
4. Ask individual learners to do Practice exercise 11 in the Learner’s Book.
41
Practice exercise 11: Expected answers (Page 17)
1. (a) 23, 32 (b) 19, 9 (c) 93, 142 (d) 33, 15
(e) 130, 176 (f) 96, 192 (g) 59, 73 (h) 36, 49
2. (a) 8, 9, 11, 14, 18, 23, 29, 36 (b) 44, 53
3. (a) 652, 637, 622, 607, 592, 577 (b) 2, 8, 32, 128, 512, 2 048
Digital learning
1. Guide learners to use a computer, a tablet or a smartphone to search for a game
involving number sequences.
ey may use this link: https://www.mathgames.com/skill/4.108-patterns-involving-
addition-and-multiplication.
2. Walk around and encourage the learners to use the digital devices for their intended
purpose. Ensure that the learners are kept safe from insecure or indecent sites and
materials. is promotes cyber security and digital literacy.
Extended activity
Instruct learners to play games that involve creating number puzzles using sequences.
Allow them to do this activity at their own free time and with the help of their friends.
is will enhance learning to learn.
Suggested assessment task
e Extended activity in the Learner’s Book is an authentic task that the learner is required
to perform. It gives an opportunity for the learners to demonstrate that they have the
understanding and the ability to apply their learning in relevant and meaningful ways.
Aer learners have played games that involve creating number puzzles using sequences,
use their results to assess their understanding by letting them:
1. Explain the rule they used to create each pattern.
2. Demonstrate how to calculate the next number in each of the patterns.
Assessment methods
(a) Written questions: Ask learners to do the practice exercises in the Learner’s Book.
(b) Observation: Walk around the classroom and monitor the learners’ practical skills
as they carrying out the activities.
(c) Oral questions: Ask questions to probe a learner’s understanding of the concepts.
42
Suggested assessment tool
Observation schedule
An observation schedule is an assessment tool that carefully species beforehand the
categories of behaviour or concepts under scrutiny. is category of behaviour may be
structured to include a wide range of knowledge, skills, attitude and values to provide an
insight into the holistic learning process of the learner.
A sample observation schedule is given below.
(a) Administrative information
School: Neema Junior Secondary School Date: 16/01/2022
Learner’s name: Teresa Amani Teacher’s name: Maxwell Nyongesa
Class: Grade 7 Red Subject: Mathematics
Strand: Numbers Sub strand: Whole numbers
(b) Learning activities/tasks
• In groups, learners to identify number sequences.
• In groups, learners to create number sequences.
(c) Competency assessed (knowledge, skills, attitude,
values) Tick appropriately
Yes No Comments
• e learner completes the activity within the assigned
time.
√ Diligent and
focused
• e learner assists others to ensure the group targets are
realized.
√ Shows
leadership
skills
(d) Feedback on the learner’s ability to relate activities to
identify number sequences.
Good work, keep it up.
(e) Feedback on the learner’s ability to relate activities to
create number sequences.
e learner needs more
practice.
Learner’s signature:_____________________
Teacher’s signature: _____________________
43
1.2 Factors
Number of lessons: 7
Refer to Learner’s Book pages 17 to 34
Introduction
At this level, the learner is already conversant with the concept of factors and multiples
of numbers. In this sub strand, the focus will be on divisibility of numbers and using
factors to calculate the GCD and the LCM of numbers. e learner will test the divisibility
of dierent numbers and determine whether the number is divisible by another number
without actually carrying out the division.
One way in which the prime numbers are useful in Mathematics is in prime factorisation.
In exploring prime factorisation, learners will investigate how to nd the greatest common
factor and the least common multiple of two or more numbers. is will be of great use
when they explore how to add and subtract fractions with dierent denominators. e
knowledge of divisibility, GCD and LCM is oen applied in planning our day to day
activities, so be sure to mention the rationale of the concept at the onset.
Specic Learning Outcomes
By the end of the sub strand, the learner should be able to:
(a) Test divisibility of numbers by 2, 3, 4, 5, 6, 8, 9, 10 and 11 in dierent situations.
(b) Express composite numbers as a product of prime factors in dierent situations.
(c) Work out the Greatest Common Divisor (GCD) and the Least Common Multiples
(LCM) of numbers by factor method in dierent situations.
(d) Apply the Greatest Common Divisor (GCD) and the Least Common Multiples
(LCM) in real life situations.
(e) Use IT devices for learning more on factors and for enjoyment.
(f) Appreciate use of factors in real life situations.
Core Competencies to be developed
• Creativity and imagination: as learners work in groups to determine whether a
number is divisible by another number without actually carrying out the division.
• Critical thinking and problem solving: as learners apply GCD and LCM in solving
real life problems.
Pertinent and contemporary issues (PCIs)
• Self-awareness: as learners work in groups to test for divisibility of numbers.
• Education for Sustainable Development (ESD): as learners use locally available
materials for making number cards and charts.
Links to other subjects
• Performing Arts: as learners work in groups to create and sing songs and poems on
divisibility tests.
44
• Home Science: Learners apply LCM or GCD as they plan for smallest or largest
containers for measuring dierent substances.
Values
• Unity: as learners work together to solve puzzles on factors trees and factor rainbows.
• Respect for self and others: as learners work in groups to write factors of composite
numbers using factor trees.
Key inquiry questions
1. Where do we use factors in day to day activities?
2. How do we use factors in day to day activities?
3. How do we apply the GCD and the LCM on day to day activities?
Suggestions on facilitating dierentiated learning and learners with special
needs
Facilitating dierentiated learning Facilitating learners with special
needs
• Kinaesthetic learners acquire information best
when they are actively involved in manipulating
the teaching and learning resources. Activity 11,
Activity 12 and Activity 14 are specically
designed to engage kinaesthetic learners in
hands on activities because this is how they
learn best.
• Visual learners absorb concepts best by seeing.
Factor trees and factor rainbows have been used
to illustrate prime factorisation in a manner that
will appeal to the visual learners.
• Ensure that the sitting arrangement of learners
suits the activity being carried out. Do this
before starting the activity to ensure proper
time management.
• Regardless of the variation in the types of learners
you have, see to it that no learner is passive or idle
especially when carrying out the activities.
• Pay attention to individual learners’ dierences
and adjust your pedagogy accordingly if
required. For example, you may need to
demonstrate the concept of prime factorisation
to the time takers. Probe them to be sure they
have understood the concept and reinforce
accordingly.
• In Activity 10B, learners
are required to draw factor
trees. is can be challenging
to learners with physical
impairment on their hands.
Allow them some extra time to
draw the factor trees. Ensure
that they are grouped with
other learners so that their
contribution in the entire
learning process is enhanced.
• Use your discretion to see
to it that visually impaired
learners are facilitated. You can
encourage other learners to
assist them to visualise the factor
trees, factor rainbows and factor
tables.
• During the digital learning
activities, provide speech to text
captioning for the videos or you
may also avail headphones with
amplied sound for learners
with hearing impairment.
45
Suggested teaching and learning resources
Use locally available materials to make counters. ese may include the following:
• Buttons
• Beads
• Stone pebbles
• Grain seeds
• Bottle tops
• Strings
• Sticks
• Charts on factor trees and factor rainbows
Teacher preparation for the lessons in this sub strand
Assemble the learning materials prior to the lesson. Be sure to organise the sitting
arrangement of the learners according to the type of activities. Group together learners of
mixed abilities and encourage each one of them to participate actively.
Suggested learning experiences
Divisibility tests of numbers
Refer to Learner’s Book page 17
Divisibility test of 2 (page 17)
Activity 1: In pairs
1. Ask learners to write down the multiples of 2 between 1 and 21.
2. Guide the learners to check the ones place value digits of the multiples. Allow them to
discuss what they notice. is enhances communication and collaboration.
3. Guide the learners to determine the divisibility test of 2. Randomly select a few
learners to present their ndings to other learners in the class. Harmonise their
ndings through probing and demonstration. Guide them through Example 1 on
page 18 of the Learner’s Book.
Divisibility test of 3 (page 18)
Activity 2: In pairs
1. Guide learners to make number cards like the ones in the Learner’s Book using locally
available materials. is promotes Education for Sustainable Development (ESD).
2. Instruct them to divide the number on each card by 3. Let them mention the numbers
that are divisible by 3.
3. Ask the learners to add the digits of the number on each card. Let them investigate
and nd out numbers from the cards whose digits add up to multiples of 3 and those
that do not. Encourage them to identify which of the two groups of numbers are
divisible by 3.
46
4. To enhance critical thinking and problem solving, ask the learners to come up
with the divisibility test of 3. Enhance their understanding by guiding them through
Example 2 on page 18 of the Learner’s Book.
Divisibility test of 4 (page 19)
Activity 3: In groups
1. Ask learners to read the story given in the Learner’s Book. Let them identify the
books that were arranged in the shelves without a remainder? is will develop the
competency of learning to learn.
2. Ask the learners to divide the last two digits of each number of books by 4. Let them
interpret their ndings and infer that a number is divisible by 4 if the number formed
by the digits in the tens and ones place value is a multiple of 4. e learners will
develop social cohesion and the values of unity and respect as they work together to
test for the divisibility of 4.
3. Allow a few learners to present their ndings in class. Enhance their understanding
by guiding them through Example 3 on page 19 of the Learner’s Book.
4. Tell individual learners to do Practice exercise 1 in the Learner’s Book. is will
promote self-ecacy and self-esteem.
Practice exercise 1: Expected answers (Page 19)
1. 346, 348, 350, 352, 354, 356, 358 and 360
2. (a) 84, 82 260, 201 579 (b) 84, 82 260
3. 5 832, 2 400, 7 316
4. (a) Ksh 3 750 (b) Yes
5. (a) Rice (b) Maize
Divisibility test of 5 (page 20)
Activity 4: In groups
1. Ask learners to list the multiples of 5 that are less than 41. Guide them to observe the
multiples and probe them to conclude that a number is divisible by 5 if the digit in the
ones place value is either 0 or 5. is encourages learning to learn.
2. Allow a few learners to present their ndings in class. For learners to internalise the
concept, allow them to ask and respond to questions from their peers. is enhances
communication and collaboration.
3. Guide the learners through Example 4 on page 20 of the Learner’s Book.
47
Divisibility test of 6 (page 20)
Activity 5: In pairs
1. Ask learners to draw a table like the one in the Learner’s Book. Let them divide each
number in the table by 2 and by 3. Ask them to complete the table.
Number Is the number
divisible by 2?
Is the number
divisible by 3?
Is the number
divisible by 6?
200 Yes No No
702 Yes Yes Yes
1 389 No Yes No
1 764 Yes Yes Yes
47 298 Yes Yes Yes
2. Let the learners study the table and conclude that a number is divisible by 6 if it is
divisible by both 2 and 3. is fosters critical thinking and problem solving as they
discover that numbers divisible by 6 are also divisible by 2 and 3.
3. Enhance the learners understanding by guiding them through Example 5 on page 21
of the Learner’s Book.
Divisibility test of 8 (page 21)
Activity 6: In pairs
1. Ask learner to create a pattern of ve numbers by adding 8, starting with 1 624.
Instruct them to divide the number formed by the digits in the hundreds, tens and
ones place value of each number by 8. Responsibility is enhanced as learners check
whether or not the last 3 digits in each of the numbers is divisible by 8.
2. Let the learners discuss how they can test for the divisibility of 8.
3. Allow a few learners to present their ndings in class. For learners to internalise the
concept, guide them through Example 6 on page 21 of the Learner’s Book.
4. Tell the learners to do Practice exercise 2 in the Learner’s Book with the help of their
parents or guardian. is will promote parental empowerment and engagement.
48
Practice exercise 2: Expected answers (Page 22)
1.
Number
Divisible by
5 6 8
785 Yes No No
6 112 No No Yes
15 024 No Yes Yes
13 400 Yes No Yes
30 144 No Yes Yes
2. 1 740, 2 250, 23 370
3. 2 376, 22 608, 24 600
4. (a) Oranges and mangoes (b) 3 avocados
Divisibility test of 9 (page 22)
Activity 7: In groups
1. e numbers given in the Learner’s Book have missing digits. Tell the learners to copy
the numbers as they are, in their notebooks.
2. Instruct the learners to work out the missing digit in each number given that the sum
of all the digits in the number is divisible by 9. is will enhance critical thinking
and problem solving as learners use arbitrary methods to nd the missing digit in
the numbers.
3. Let the learners divide each number by 9 to ascertain their divisibility. Guide them to
deduce the divisibility test of 9.
4. Guide them through Example 7 on page 23 of the Learner’s Book. Ask them to share
what they have learnt with their peers. is encourages peer education.
Divisibility test of 10 (page 23)
Activity 8: In pairs
1. Ask learners to make number cards like the ones in the Learner’s Book.
2. Let them divide the number on each card by 10 and identify the numbers that are
divisible by 10?
3. Ask the learners to identify the numbers that are divisible by 2. Ask them to identify
the numbers that are divisible by 5.
4. Instruct the learners to list the numbers that are divisible by both 2 and 5. ey should
be able to infer that a number that is divisible by 10, is also divisible by both 2 and 5.
is develops responsibility and unity as they work together.
5. Harmonise the learners’ ndings by guiding them through Example 8 on page 23 of
the Learner’s Book.
49
Divisibility test of 11 (page 24)
Activity 9: In groups
1. Ask learners to copy and complete the multiplication table in the Learner’s Book to
get multiples of 11. e learners are given an opportunity to use their skills in the
concept of multiplication. is develops self-ecacy.
2. Guide the learners to work out the sum of the digits in the hundreds and ones place values.
Ask them to also calculate the sum of the digits in the thousands and tens place values.
3. Ask the learners to work out the dierence of the sums. Let them discuss their ndings
and determine the divisibility test of 11. is cultivates the competence of critical
thinking and problem solving.
4. Guide the learners through Example 9 on page 24 of the Learner’s Book.
5. Tell individual learners to do Practice exercise 3 in the Learner’s Book to assess their
understanding. Walk around the classroom checking the learners work and giving
guidance to those who may have challenges.
Practice exercise 3: Expected answers (Page 25)
1. 6 210, 100 000, 7 190
2. 5 346, 495, 11 880, 2 376, 9 702
3. (a) 5 (b) 7 (c) 2 (d) 0
4. (a) Yes (b) Yes; (1 + 6) − 7 = 0
Additional information
⇒ Divisibility tests of numbers can be summarised as follows:
• A number is divisible by 2 if the digit in the ones place value is 0, 2, 4, 6 or 8.
• A number is divisible by 3 if the sum of its digits is divisible by 3.
• A number is divisible by 4 if the digits in the tens and ones place value form a
number that is divisible by 4.
• A number is divisible by 5 if the digit in the ones place value is either 0 or 5.
• A number is divisible by 6 if it is divisible by both 2 and 3.
• A number is divisible by 8 if the digits in the hundreds, tens and ones place value
form a number that is divisible by 8.
• A number is divisible by 9 if the sum of its digits is divisible by 9.
• A number is divisible by 10 if the digit in the ones place value is 0.
• A number is divisible by 11 if the dierence of the sums of the digits in alternate
positions is 0, 11 or a multiple of 11.
⇒ Randomly pick a few learners and ask them to explain the divisibility test of a number
of their choice. is will help you establish their level of mastery. You may wish to use
a checklist to assess the learner during this lesson.
50
⇒ You may consider guiding your learners to create a song or poem on divisibility tests
of numbers from this summary. is will not only be a chance for them to showcase
their creativity and imagination but also will be handy to help them recall the
divisibility tests that they have learnt.
⇒ Moving forward encourage learners to practice using the divisibility tests to
determine the divisibility of numbers rather than using long division.
Expressing a number as a product of its prime factors
Refer to Learner’s Book page 26
Activity 10A: In groups
1. Instruct learners to use the digits 4, 6, and 8 to form a 2-digit number. Ask them to
divide the number they have formed by the smallest prime number that leaves no
remainder.
2. Again, let the learners divide the quotient by the smallest prime number without
a remainder. Ask them to repeat the process, until the quotient becomes 1. Let
them multiply all the prime factors and make an inference. Critical thinking and
problem solving is enhanced as they brainstorm on how this concept can be applied
in simplication of fractions.
3. Ask the learners to use digits 4, 6, and 8 to form dierent 2-digit numbers. Let them
repeat the process for each of the numbers.
4. Allow a few learners to present their ndings in class. Harmonise their understanding
by probing and demonstration using other composite numbers.
Activity 10B: In pairs
1. Guide learners to draw factor trees. Let them complete each factor tree by writing
down pairs of factors in the branches of the tree. Critical thinking and problem
solving is enhanced as they decide where to place the prime factor and where to
place the composite numbers. Ensure that the learners understand why the composite
number is placed in the box while the smallest prime number is placed in the circle.
2. Ask the learners to express each of the given composite numbers as a product of its
prime factors.
3. For learners to internalise the concept, guide them through Example 10 and Example 11
on page 27 of the Learner’s Book. Probe them to gauge their level of understanding.
4. Tell individual learners to do Practice exercise 4 in the Learner’s Book. is will
promote responsibility and integrity.
5. Wind up the activity by clarifying the dierence between a composite number and a
prime number so that the concept of prime factorisation is well reinforced.
51
Practice exercise 4: Expected answers (Pages 27 and 28)
1.
1 2
4
5
10
20
1 3
5
9
15
45
2. (a) 2 × 2 × 2 × 3 × 3 (b) 2 × 2 × 2 × 2 × 2 × 3 (c) 2 × 2 × 3 × 3 × 3
(d) 2 × 2 × 31 (e) 5 × 5 × 5 × 5 (f) 3 × 67
(g) 2 × 2 × 3 × 5 × 5 (h) 3 × 3 × 3 × 3 × 3 (i) 3 × 5 × 107
(j) 2 × 2 × 3 × 3 × 7 × 7
3. (a)
36
2
3
18
9
2
3
(b)
210
2
3
5
7
35
105
(c)
60
10
6
2
3 2 5
Digital learning
1. Guide learners to use a computer, a tablet or a smartphone to search for a video
involving expressing a number as a product of its prime factors.
ey may use this link: https://tinyurl.com/primefactorsG7.
2. To ensure safety of your learners as they interact with digital devices, you may consider
downloading the video beforehand so that pop up advertisements don’t interrupt the
learning sessions and in the process distract your learners.
Greatest Common Divisor (GCD)
Refer to Learner’s Book page 28
Activity 11: In groups
1. Guide learners to divide 24 beads and 32 marbles into dierent number of groups
without leaving a remainder. ey can improvise and use other locally available
52
materials such as grains, sticks or stone pebbles. This promotes Education for
Sustainable Development (ESD).
2. Let the learners write down the number of groups for each item. Guide them to
interpret this in terms of factors or divisors of the numbers. Instruct them to list the
common divisors of 24 and 32.
3. Guide them to nd the greatest common divisor of 24 and 32. Enhance the learners’
understanding by guiding them through Example 12 and Example 13 on pages 28 and
29 of the Learner’s Book. Probe them to gauge their level of understanding. Reinforce
their responses accordingly.
4. Tell individual learners to do Practice exercise 5 in the Learner’s Book. is will
promote honesty and responsibility as they attempt the task individually.
Practice exercise 5: Expected answers (Page 29)
1. (a) 4 (b) 4 (c) 6 (d) 30 (e) 12 (f) 17
2. (a) 20 (b) 3 (c) 120 (d) 16 (e) 14 (f) 15
Applying the Greatest Common Divisor (GCD)
Refer to Learner’s Book page 29
Activity 12: In groups
1. Guide learners to measure three strings of length 24 cm, 32 cm and 36 cm. Instruct
them to brainstorm and determine the length of the longest equal pieces that can be
cut out from each of the strings without a remainder. e concept of GCD can become
challenging to learners especially in situations where word problems and real-life
situations are involved. For this reason, this hands-on activity is very vital as it helps
the learners to use the knowledge they have acquired in class to solve problems in
real-life situations. In addition, it also facilitates dierentiated learning by varying
the stimulus.
2. Allow a few learners to present their ndings in class. Enhance their understanding
by guiding them through Example 14 on page 30 of the Learner’s Book. Encourage
them to practise using prime factorisation to work out the GCD of numbers.
3. Ask individual learners to do Practice exercise 6 in the Learner’s Book. is will
promote self-ecacy and self-esteem.
Practice exercise 6: Expected answers (Page 30)
1. 5 kg 2. 30 litres 3. 9 learners 4. 18 m 5. 5 kg
53
Least Common Multiples (LCM)
Refer to Learner’s Book page 31
Activity 13: In pairs
1. Ask learners to use factor trees to express 12 and 18 as products of their prime factors.
2. Let them match similar prime factors vertically. Ask them to drop down the prime
factors in each column. is develops creativity and imagination.
3. Instruct the learners to multiply the prime factors to get the LCM of 12 and 18. Let
them repeat the steps to nd the LCM of the numbers in the Learner’s Book. Walk
around the classroom observing the learners as they work out the LCM and give
guidance to those who may have challenges. is enhances respect for self and others
as they work in groups to calculate the LCM of numbers using prime factors.
4. Ask a few learners to present their ndings in class. Enhance their understanding by
guiding them through Example 15 and Example 16 on pages 31 and 32 of the Learner’s
Book. Task them to use dierent methods of working out the LCM of numbers using
prime factorisation.
5. Instruct individual learners to do Practice exercise 7 in the Learner’s Book.
Practice exercise 7: Expected answers (Page 32)
1. (a) 144 (b) 60 (c) 96 (d) 105 (e) 567
(f) 84 (g) 45 (h) 60 (i) 400
2. 150 3. 93 4. 95
Applying the Least Common Multiples (LCM)
Refer to Learner’s Book page 32
Activity 14: In groups
1. Ask the learners to get three bottles with capacities of 200 ml, 250 ml and 500 ml. In
case you have challenges nding a 200 ml bottle, you could consider working with
bottles of capacities 500 ml, 1 litre and 2 litres.
2. Instruct the learners to determine the capacity of the smallest container that can be
lled using any of the bottles without a remainder. Let them get a container with the
capacity they have calculated and use any of the bottles to ll the container.
3. For learners to internalise the concept, guide them through Example 17 on page 33 of
the Learner’s Book.
4. Instruct the learners to do Practice exercise 8 in the Learner’s Book with the help of their
parents or guardian. is will promote parental empowerment and engagement.
54
Practice exercise 8: Expected answers (Page 33)
1. 240 tree seedlings 2. 360 cm 3. 60 pieces of sugarcane 4. 8.00 p.m.
5. (a) Ksh 600
(b) Peter would have sold 5 books. Paul would have sold 4 books.
Digital learning
1. Guide learners to use a computer, a tablet or a smartphone to search for a game
involving expressing a number as a product of its prime factors.
ey may use this link: https://www.mathgames.com/skill/6.54-gcf-and-lcm.
2. Walk around and encourage the learners to use the digital devices for their intended
purpose. Ensure that the learners are kept safe from insecure or indecent sites and
materials. is promotes cyber security and digital literacy.
Extended activity
Instruct the learners to research and determine the application of factors, GCD and LCM
in their day to day activities. Allow them to do this activity with the help of friends, parents
or guardian. is will foster learning to learn.
Suggested assessment task
Making connections between factors, LCM and GCD and their real life applications is a
very important part of understanding the concept. e Extended activity in the Learner’s
Book gives learners an opportunity to research and determine this connection. Giving and
receiving change is a common activity that relies on the knowledge of factors. For example,
ve 200 shilling notes make Ksh 1 000. Looking at this in terms of factors, two factors of
1 000 are 5 and 200. Similarly, Ksh 1 000 can be changed for ten 100 shilling notes (factors
10 and 100), twenty 50 shilling notes (factors 20 and 50) and so on. Use the learners results
to assess their understanding by letting them explain in details each application of factors,
LCM and GCD.
Assessment methods
(a) Written questions: Ask learners to do the Practice exercises in the Learner’s Book.
(b) Observation: Walk around the classroom and monitor the learners’ practical skills
as they manipulate objects while carrying out the activities.
(c) Oral questions: Ask questions to probe the learner’s understanding of the concepts.
55
Adaptation of assessment tools for learners with special needs
Use your discretion to make modications on the assessment methods and tools when
dealing with learners with special needs. is may be in terms scheduling, presentation of
assessment tasks, duration of tackling the task and ways of responding to the task. However,
ensure that armative action is taken to treat all learners as equals and encourage them
to do the same.
Suggested assessment tool
Checklist
A checklist is a good way to evaluate your learners’ competency on a given wide subject
area. Use a checklist to record the learners’ ability to apply divisibility tests of numbers in
solving questions in Practice exercises 1 to 3. Below is a sample checklist that you could use.
School: Kadiri Secondary School
Period of assessment: February 2022 Teacher’s name: Wangari Wangui
Class: Grade 7 White Subject: Mathematics
Strand: Numbers Sub strand: Factors
Name
Competence (knowledge, skills, attitude, values) Tick appropriately
Apply divisibility test of number:
2 3 4 5 6 7 8 9 10
Yes No Ye s No Yes No Ye s No Ye s No Ye s No Yes No Ye s No Ye s No
Kimei
√ √ √ √ √ √ √ √ √
Wahome
√ √ √ √ √ √ √ √ √
Akinyi
√ √ √ √ √ √ √ √ √
Patel
√ √ √ √ √ √ √ √ √
Faiza
√ √ √ √ √ √ √ √ √
1.3 Fractions
Number of lessons: 9
Refer to Learner’s Book pages 34 to 50
Introduction
In upper primary, learners explored the concept of GCD (greatest common divisor), LCM
(least common multiple), adding and subtracting fractions. In this sub strand, learners
will build on these concepts by using LCM to compare, add and subtract fractions.
e learners will also be introduced to multiplication, division and number sequences
involving fractions.
56
In the process of learning the concepts in this sub strand, some learners may oen result to
memorization of the concepts rather than understanding the underlying principles. is
sometimes leads to a lack of appreciation of the use of fractions in real life situations.
e learning activities have therefore been adapted to focus on the mathematical thinking
processes involved in adding, subtracting, multiplying and dividing fractions. is will
enable learners to not only understand the procedure, but also analyse and describe their
own methods.
Specic Learning Outcomes
By the end of the sub strand, the learner should be able to:
(a) Compare fractions in dierent situations
(b) Add fractions in dierent situations
(c) Subtract fractions in dierent situations
(d) Multiply fractions by a whole number, fraction and a mixed number in real life
situations
(e) Identify the reciprocals of fractions in dierent situations
(f) Divide fractions by a whole number, fraction and a mixed fraction in real life situations
(g) Divide a whole number by fractions in dierent situations
(h) Identify number sequence involving fractions in dierent situations
(i) Create number sequence involving fractions for playing number games
(j) Use IT devices for learning more on fractions and for enjoyment
(k) Appreciate the use of fractions in real life situations.
Core Competencies to be developed
• Creativity and imagination: as learners observe and create puzzles involving fractions.
• Critical thinking and problem solving: as learners apply fractions in evaluation and
decision-making using cut outs, cards, charts and models from local resources.
Pertinent and Contemporary Issues (PCIs)
• Citizenship: as learners carry out division of fractions in real life situations which
implies sharing.
• Social cohesion: as learners share items at home and outside school using fractions.
• Health education: as learners read about mental health awareness sensitization
campaigns.
Links to other subjects
• Music: as learners use fractions in types of musical notes like semi-quavers (
1
16
) and
quavers.
• Agriculture: as learners give fractional portions of animal feeds.
57
Values
• Social justice: as learners share items and resources fairly among themselves.
• Responsibility: as learners perform multiplication and division of fractions when
sharing or allocating resources.
Key inquiry question
1. Where do we use fractions in daily activities?
2. How do we use fractions in daily activities?
Suggested teaching learning resources
• Multiplication tables
• Circular and rectangular cut-outs
• Manila papers
Teacher preparation for the lesson
Organise for the availability of adequate learning resources prior to the lessons. Organise
the learners in various groups depending on the activity to be carried out and the resources
available.
Suggestions on facilitating dierentiated learning and learners with special needs
Facilitating dierentiated learning Facilitating learners with special needs
• Before doing the activities with the
learners, it would be a good idea to
complete all (or at least part) of the
activities yourself. It would be even
better if you could try out the activities
with a colleague. Trying out the
activities yourself prior to the lesson
will enable you to get insights into a
learner’s experiences and acknowledge
the challenges they are facing. is can
in turn assist you to rene the learning
experiences to suit the learners’ needs
and locality.
• Aer each activity, think about the
experiences and the learning that
occurred. is will help you to develop
a more learner-centred teaching
environment and address the needs of
the time takers.
• In Activity 1B learners are required
to make a practice card. Encourage
learners to make a practice card with
fractions that are written in large print
to assist visually impaired learners.
• In Activity 2A, Activity 4, Activity 5 and
Activity 9, give more time to learners
with physical impairment on their
hands so that they can participate in
making and shading paper cut outs.
Encourage the other learners support
them through armative action for
example allowing them to take the rst
turn when doing tasks that require
taking turns.
58
Comparing fractions
Refer to Learner’s Book page 34
Activity 1A: In pairs
1. Ask learners to mention the number of hours in a day. Let them mention some of the
activities they do during the day and say the number of hours they spend on each
activity. In case some of the activities take less than an hour use your discretion to
guide the learners accordingly, otherwise it would be good to emphasise on them
using whole numbers greater than 1 hour.
2. Challenge the learners to use the time taken by each activity to make fractions. Let
them compare the fractions and arrange them in an increasing order.
Activity 1B: In groups
1. Instruct learners to make a practice card like the one in the Learner’s Book. Tell them
to write the denominator of each fraction on the card.
2. Give the learners an opportunity to apply the skills they learnt in previous
sub strands by letting them calculate the LCM of the denominators. Communication
and collaboration is developed as learners work together towards achieving a
common goal while Critical thinking and problem solving is enhanced as they
apply the concept of LCM.
3. Guide the learners to rename all the fractions to have the LCM as the denominator.
Let them shade rectangular strips of paper to represent the equivalent fractions. is
enhances cooperation, safety and responsibility as the learners use cutting tools and
share resources to accomplish the task. You may consider preparing these strips prior
to the lesson and marking the boxes in groups of ten. Tell them to compare the shaded
parts and then arrange the fractions in descending or decreasing order.
4. Guide the learners through Example 1 and Example 2 on page 35 and lay emphasis on
the methods illustrated in the Learner’s Book. ese methods involve using LCM and
percentages to compare and order fractions.
5. Wrap up the activity by emphasising the concept and instructing the learners to do
the questions on Practice exercise 1 individually. is will promote self-ecacy.
Practice exercise 1: Expected answers (Page 36)
1. (a)
1
7
,
2
7
,
3
7
,
4
7
,
6
7
(b)
5
12
,
5
11
,
5
9
,
5
8
,
5
6
(c)
1
4
,
4
15
,
3
5
,
2
3
,
5
6
(d)
1
2
,
9
16
,
3
4
,
7
8
, (e)
2
9
,
1
3
,
7
12
,
11
18
,
3
4
(f)
1
2
,
4
5
,
9
11
,
9
10
59
2. (a)
1
2
,
1
3
,
1
5
,
1
7
,
1
9
(b)
9
12
,
17
24
,
3
8
(c)
7
12
,
19
36
,
4
9
,
1
6
(d)
3
7
,
5
14
,
1
4
,
1
10
(e)
3
4
,
11
15
,
13
20
,
3
10
,
1
5
(f)
8
9
,
2
3
,
14
30
,
5
18
3.
27
50
,
19
25
,
4
5
4.
3
8
,
5
18
,
1
6
Adding fractions
Refer to Learner’s Book page 36
Activity 2A: In pairs
1. Guide learners as they draw a rectangular grid with three columns. Let them shade
the grid to represent the fraction
2
3
. Direct them to note that the number of columns
is equal to the denominator of the fraction.
2. Instruct the learners to draw four rows on the same grid and then shade the remaining
unshaded part to represent
1
4
of the whole grid. Direct them to note that the number
of rows is equal to the denominator of the fraction. ey should also be able to
recognise and identify the sum as
11
12
.
3. Challenge the learners to write the equivalent fractions of
2
3
and
1
4
from the grid.
ey should be able to identify the equivalent fractions as
8
12
and
3
12
respectively. e
two fractions add up to
11
12
as shown on the grid. is promotes the core competence
of critical thinking and problem solving in the learners. Let them use a grid and
follow the same procedure to add
1
3
to
1
2
to get a sum of
5
6
.
Activity 2B: In groups
1. Let learners brainstorm and come up with 2 mixed fractions. Let them add the whole
numbers and the proper fractions separately to nd the sum of the mixed fractions.
2. Let the learners convert the mixed fractions into improper fractions and work out
the sum. Allow the learners to compare the sum of their mixed fractions by adding
the whole numbers and the proper fractions separately and by converting the mixed
fractions into improper fractions.
3. Let the learners discuss the outcome in their groups and randomly choose a group
representative to elaborate their ndings to the rest of the class. is enhances
communication and collaboration. It also promotes self-ecacy and peer education.
60
4. Consolidate their ndings by guiding the learners through Example 3 and Example 4 on
page 37 of the Learner’s Book. Emphasise on the dierent methods that can be used
to do the sums.
5. Instruct learners to work on Practice exercise 2 individually as this builds up their
self-ecacy and self-esteem.
Practice exercise 2: Expected answers (Page 38)
1. (a)
9
16
(b)
41
63
(c) 5
13
24
(d) 2
1
10
(e) 14 (f) 20
7
12
2. 1
7
12
m 3.
7
16
3. 66
3
4
metres
Subtracting fractions
Refer to Learner’s Book page 38
Activity 3: In groups
1. Direct learners to observe the denominators provided in the Learner’s Book. Let them
ll in numerators of their choice to complete the fractions. Guide them to ensure
the numbers chosen won’t lead to formation of whole numbers. However, improper
fractions and unsimplied fractions are permissible.
2. Guide the learners to arrange the fraction in an increasing order. Instruct them to
work out the dierence between the largest and smallest fractions.
3. Give an opportunity to dierent learners to explain to the class about how they worked
out the dierence. is promotes peer learning and builds up their self-esteem.
4. Guide the learners through Example 5 and Example 6 on pages 38 and 39 of the
Learner’s Book. Emphasise on renaming of fractions and using LCM to get common
denominators before working out the subtraction. For mixed fractions emphasise on
working out the whole numbers and the proper fractions separately or converting the
mixed fractions into improper fractions before renaming.
5. Harmonise the concepts that the learners have learnt by instructing them to solve the
questions in Practice exercise 3 individually. This promotes self-efficacy and
independence.
Practice exercise 3: Expected answers (Page 39)
1. (a)
3
10
(b)
17
60
(c) 1
9
26
(d) 4
7
9
(e) 4
1
10
(f) 1
1
4
2. 31
2
3
kg 3. 9
7
12
years 4. 4
11
42
litres 5. 4
5
36
m
61
Multiplying fractions
Refer to Learner’s Book page 40
Multiplying a fraction by a whole number (page 40)
Activity 4: In groups
1. Guide the learners to make ve circular cut-outs. Let them divide and shade a quarter
of each cut out as shown in the Learner’s Book. Let them count and write down the
total number of quarters. Ask them to discuss and come up with a multiplication
sentence as,
1
4
× 5 =
5
4
= 1
1
4
. Creativity and imagination competence is developed
as learners come up with the multiplication sentence involving a fraction and a whole
number.
2. Encourage the learners to make more dierent fractions and write multiplication
sentences from them and share their work with other groups. is promotes the core
competence of communication and collaboration.
3. Guide the learners through Example 7 on page 40 of the Learner’s Book. Assist them
to recognise that mixed fractions should be converted into improper fractions prior
to carrying out the multiplication. Sensitise them on the importance of writing the
whole number as a fraction by giving it a constant denominator; digit 1. is makes
their work easier and helps them overcome the temptation of multiplying both the
numerator and denominator of the fraction by the whole number.
Additional information
A common error made by learners when multiplying a fraction by a whole
number is that they multiply both the numerator and the denominator by the
whole number. To remedy this error, emphasise that only the numerator is
multiplied by the whole number.
4. Harmonise the concepts learnt by asking probing oral questions and nally allowing
learners to individually attempt the questions in Practice exercise 4. is will promote
and build the learners self-esteem and self-ecacy as they solve the questions
successfully.
Practice exercise 4: Expected answers (Pages 40 and 41)
1. (a) 28 (b) 16 (c) 18
3
4
(d) 168 (e) 136 (f) 31
1
2
2. 4
1
8
m
2
3. 12 litres 4. 445
1
3
m 5. 56 m
62
Multiplying a fraction by a fraction (page 41)
Activity 5: In pairs
1. Guide learners to make a rectangular cut-out. Let them divide the cut-out into 6 parts
and shade it as shown in the Learner’s Book. is promotes unity and cooperation.
2. Instruct the learners to determine the fractions represented by the part shaded with
red lines, part shaded green and the double shaded part. Challenge them to write a
multiplication sentence representing the set up. ey should note that:
1
3
×
1
2
=
1
6
.
3. Give a chance for the learners to volunteer to describe how to multiply fractions. is
develops the core competencies of self-ecacy.
4. Harmonise their ndings by guiding them through Example 8 and Example 9 on
pages 41 and 42 of the Learner’s Book. Emphasise on the importance of multiplying
the numerators and the denominators separately and giving answers in their simplest
form.
5. Tell the learners to do Practice exercise 5 in the Learner’s Book.
Practice exercise 5: Expected answers (Page 42)
1. (a)
2
13
(b)
7
24
(c)
17
32
(d) 24 (e) 29
4
11
(f) 65
13
32
2. 2
1
8
m
2
Digital learning
1. Guide learners to use laptop, a computer, a tablet or a smartphone to search for a
game involving multiplying fractions.
They may use this link: https://www.iknowit.com/lessons/e-multiplying-two-
fractions.html.
2. Encourage learners not to open random and inappropriate sights. Ensure they are
kept safe from insecure and indecent sites and materials. Walk around the class to
observe them as they use digital devices for fun and enjoyment. is promotes cyber
security.
Reciprocal of a fraction
Refer to Learner’s Book page 42
Activity 6: In pairs
1. Let learners make a number card like the one in the Learner’s Book. Let them use the
numbers on the card to form a proper fraction and an improper fraction. ey should
63
be able to come up with the proper fraction
2
11
and the improper fraction
11
2
.
2. Guide the learners to compare the numerator and the denominators of the two
fractions. Direct them to notice that when they ip the numerator and the denominator
of a fraction, they get the reciprocal.
3. Instruct the learners to multiply the proper and improper fractions. Let them discuss
their ndings in pairs, this promotes the value of respect and cooperation as learners
work together and learn to support each other.
4. Allow two or three learners to volunteer to present their ndings to the rest of the
class. is encourages peer education and enhances the learner’s self-esteem. At
this point, learners should be able to recognise that the product of a fraction and its
reciprocal is 1. Team work and unity is inspired in the learners as they work in pairs
to prove that the product of a fraction and its reciprocal is 1.
5. Guide some learners to demonstrate Example 10 and Example 11 on page 43 of the
Learner’s Book to the rest of the class. Let the learners focus on recognizing that the
numerator of a given fraction becomes the denominator in the reciprocal fraction
and vice-versa.
6. Instruct individual learners to work out questions in Practice exercise 6.
Practice exercise 6: Expected answers (Page 43)
1. (a) 2 (b)
5
2
(c)
19
6
(d) 7 (e)
11
3
(f)
4
11
(g)
9
14
(h)
13
69
(i)
12
85
(j)
15
152
2.
15
8
Dividing fractions
Refer to Learner’s Book page 44
Dividing fractions by a whole number (page 44)
Activity 7: In groups
1. Guide learners to make a rectangular strip of paper. Let them fold and divide the
strips into ten equal parts. Tell them to shade 9 parts of each of the strips.
2. Instruct the learners to divide the 9 shaded parts into 3 equal groups. Let them write
the fraction for each group as part of the whole. Challenge the learners to calculate the
quotient of
9
10
divided by 3. ey should be able to infer that
9
10
divided by 3 is equal
to
1
3
. Let the learners indulge in more similar activities in groups. is promotes
social cohesion and unity as learners work together, sharing resources and helping
one another.
64
3. Demonstrate the use of reciprocals in division of fractions by whole numbers, through
Example 12 and Example 13 on page 44 of the Learner’s Book. Lay emphasis on the
relationship between division and multiplication by changing the division sign to a
multiplication sign. Also insist on writing the reciprocal of the second fraction and
following the same procedure learnt in multiplication of fractions to get the answer.
4. Reinforce the concept by involving learners in working out the questions in Practice
exercise 7. is will sharpen their critical thinking and problem-solving competence.
Practice exercise 7: Expected answers (Page 45)
1. (a)
1
4
(b)
1
12
(c)
7
32
(d)
11
20
(e) 2
17
18
(f) 2
23
40
2. 3
1
14
tonnes
3.
7
30
metres
4.
1
4
litres 5.
1
8
of the bar of soap
Dividing a fraction by a fraction (page 45)
Activity 8: In groups
1. Instruct learners to copy the divisions in the Learner’s Book. For each division, let
them keep the rst fraction, change the sign to multiplication and write the reciprocal
of the second fraction.
2. Guide the learners to m ultiply the rst fraction by the reciprocal of the second fraction.
Ask them to give the answers in their simplest form. ey should be able to refer to
the division concept learnt previously and gure out the quotients. is enhances
critical thinking and problem-solving competence. It also promotes respect, unity
and social cohesion as they discuss, brainstorm and conclude on the methods to use
in their groups.
3. Guide the learners through Example 14, Example 15 and Example 16 on page 46 of the
Learner’s Book. Emphasise on the procedures followed when working out division of
fractions.
Additional information
Some common errors made by learners when dividing a fraction by a fraction
is that they may multiply the dividend by the divisor instead of the reciprocal
of the divisor. Some learners may also make the error of changing both the
dividend and the divisor into their reciprocals and then multiplying them. To
remedy these errors, stress on the signicance of expressing only the divisor as
a reciprocal. Emphasise on multiplying the dividend by the reciprocal of the
divisor.
4. Encourage learners to work individually on the Practice exercise 8. is will enhance
self-ecacy as they engage in more practice. Move round to observe learners as they
work.
65
Practice exercise 8: Expected answers (Page 47)
1. (a)
9
10
(b)
22
23
(c) 2 (d) 3
13
24
(e) 5 (f) 35
7
13
(g) 3
1
81
(h) 2
43
175
(i) 4
38
715
2. 6 pieces 3. 8 lessons 4. 54 animals 5. 4 kettles
Dividing a whole number by a fraction (page 47)
Activity 9: In groups
1. Guide learners make four circular cut-outs. Let them divide and shade halves in
each of the cut-outs as shown in the Learner’s Book. ey should be able to divide
each of the cut-outs into halves and end up with 8 halves. e values of cooperation,
unity and humility are demonstrated as learners work together in groups and share
teaching and learning resources.
2. Instruct the learners to count the number of halves in 4 wholes. Let them discuss and
gure out the value of 4 divided by
1
2
. is develops critical thinking and problem
solving. Encourage the learners to explain to one another how to divide a whole
number by a fraction. is promotes peer education and builds up self-esteem of the
learners involved.
3. Harmonise their ndings by taking them through Example 17 and Example 18 on
pages 47 and 48 of the Learner’s Book. Let them apply the procedure of multiplication
and division of fractions to get the answer.
4. Let the learners put in practice the concepts learnt through working out Practice
exercise 9 in the Learner’s Book. is will enhance self-ecacy and problem-solving.
Practice exercise 9: Expected answers (Page 48)
1. (a) 18 (b) 30 (c) 5
1
3
(d) 8
4
7
(e) 2
1
17
(f) 3
3
59
2. 24 half litre containers 3. 6 sessions 4. 16 days 5. 600 bottles
Digital learning
Guide learners to use a computer, a tablet or a smartphone to search for a game
involving dividing fractions.
ey may use this link: https://www.iknowit.com/lessons/e-dividing-whole-numbers-and-
fractions.html.
66
Number sequence involving fractions
Refer to Learner’s Book page 49
Activity 10A: In pairs
1. Let learners draw and mark number lines like the ones in the Learner’s Book.
2. Instruct the learners to use their own strategies to deduce the missing numbers and
the rule used to arrive at the numbers. Let them also conclude whether or not the
fractions form a sequence. is will enhance critical thinking and problem solving.
It will also promote communication and collaboration as they reason together to
come up with logical conclusions.
Activity 10B: In groups
1. Guide learners to arrange the given fractions in a decreasing order. Encourage them
to use their own means to infer the rule used and work out the next two fractions in
the sequence. As they discuss and reason together, learners will be mandated to think
critically to solve the problems at hand.
2. Let the learners create a sequence of 5 numbers using the rule given in the Learner’s
Book. is will give learners more practice thus enhancing their self-ecacy and
problem solving skills.
3. Randomly select two learners to guide the class through Example 19 and Example 20
on pages 49 and 50 of the Learner’s Book. is promotes peer education.
4. Let the learners do Practice exercise 10 to sharpen their understanding of the concepts
learnt.
Practice exercise 10: Expected answers (Page 50)
1. (a) 2
1
6
, 2
1
2
(b)
8
9
, 1 (c) 2
5
6
, 2
17
24
(d)
30
37
,
15
37
2. (a)
1
4
,
5
8
, 1, 1
3
8
, 1
3
4
(b) 30
18
19
, 15
9
19
, 7
14
19
, 33
33
38
, 1
71
76
3. (a)
+
1
2
1
3
1
4
1
5
1
4
3
4
7
12
1
2
9
20
1
5
7
10
8
15
9
20
2
5
1
6
2
3
1
2
5
12
11
30
1
7
9
14
10
21
11
28
12
35
(b) Check for correctness of the learner’s sequences.
67
Extended activity
Extended activity
1. Instruct the learners to make a list of musical notes that they have learnt in Music.
Let them use the value of the musical notes to form fractions and work them out. For
example, the sum of a quiver and a crotchet.
2. Encourage learners to work with their parents, guardians or friends. is will promote
parental empowerment and engagement.
Suggested assessment task
e Extended activity in the Learner’s Book is an authentic task that the learner is required
to perform. It gives an opportunity for the learners to demonstrate that they have the
understanding and the ability to apply their learning in relevant and meaningful ways.
Aer learners have used the values of musical notes to form fraction and work them out,
use their results to assess their understanding by letting them:
1. Explain the value of each musical note.
2. Demonstrate how to calculate the sums or the dierences.
Assessment methods
(a) Class activities: Learners are involved in learning activities in class where they work
in pairs or in groups to accomplish tasks given.
(b) Written questions: Learners work on written tests individually for more practice on
learnt concepts and gauging their understanding of concepts.
(c) Assignments: Learners carry out home assignments for more practice and involve
friends, parents or guardians in their learning activities. is helps to promote, build
and nurture their relationships.
Suggested assessment tool
Assessment rubric
At the end of each learning outcome in this sub strand you can consider using an assessment
rubric to evaluate the learner accordingly. is will give you a holistic assessment of a
learner’s abilities based on the specied learning outcomes. You may want to use the
assessment rubric shown below.
Indicators Exceeds
expectations
Meets
expectations
Approaches
expectations
Below
expectations
Ability to
compare
fractions
e learner
correctly
compares
fractions
using various
methods.
e learner
correctly
compares
fractions.
e learner
partially
compares
fractions.
e learner
shows
diculty in
comparing
fractions.
68
Ability
to add
fractions
e learner
correctly adds
fractions using
various methods.
e learner
correctly
adds
fractions.
e learner
correctly adds
some fractions.
e learner
shows
diculties
in adding
fractions.
Ability to
subtract
fractions
e learner
precisely subtracts
fractions.
e learner
correctly
subtracts
fractions.
e learner
correctly
subtracts some
fractions.
e learner
shows
diculties in
subtracting
fractions.
Ability to
multiply
fractions
by a whole
number,
fraction
and a
mixed
number
e learner
correctly and
consistently
multiplies
fractions by a
whole number,
a fraction and a
mixed number
using various
methods.
e
learner
correctly
multiplies
fractions
by a whole
number,
fraction
and a
mixed
number.
e learner
inconsistently
multiplies
fractions
by a whole
number,
a fraction
and a mixed
number
correctly.
e learner
shows
diculties
in
multiplying
fractions
by a whole
number,
a fraction
and a mixed
number.
Ability
to nd
reciprocals
of fractions
e learner
systematically
nds reciprocals
of fractions.
e learner
correctly
nds
reciprocals of
fractions.
e learner
correctly nds
reciprocals of
some fractions.
e learner
shows
diculties
in nding
the
reciprocals
of fractions.
Ability
to divide
fractions
by a whole
number,
fraction
and a
mixed
number
e learner cor-
rectly and pro-
ciently divides
fractions by a
whole number,
fraction and a
mixed number.
e learner
correctly
divides
fractions
by a whole
number,
fraction and
a mixed
number.
e learner
inconsistently
divides fractions
by a whole
number, a
fraction and a
mixed number.
e
learner
shows
diculties
in dividing
fractions
by a whole
number,
a fraction
and a
mixed
number.
69
1.4 Decimals
Number of lessons: 6
Refer to Learner’s Book pages 51 to 60
Introduction
In upper primary, the learners were introduced to decimals. Particularly in Grade 6,
learners identied decimals up to ten thousandths, rounded them o, converted decimals
to fractions and percentages, added and subtracted decimals in various situations. In
Grade 7, the learners will build on the concepts of place value of digits in decimals. ey
will also be introduced to the concept total value of digits in decimals. e main focus of
this sub strand will be on multiplication and division of decimals with whole numbers and
with other decimals as well.
Multiplication, division, fractions and decimals are not new concepts to the learners, but
since they have been studied at dierent times, dierent sub strands and in dierent grades,
the learners may have challenges seeing the connections between the dierent concepts.
As a result, their knowledge can become fragmented. To address this fragmentation, the
learning experiences in this sub strand, task the learners to make connections between
these concepts, for instance when solving multiplication of decimals, they will rst convert
the decimals into fractions or work with whole numbers and incorporate the total number
of decimal places involved into the answer. e activities require learners to work in pairs
or in groups and exchange their ideas with other learners.
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) Identify the place value and total value of digits in decimals in real life
(b) Multiply decimals by a whole number and by a decimal in real life situations.
(c) Divide decimals by a whole number and by a decimal in real life situations.
(d) Use IT devices for learning more on decimals and for enjoyment.
(e) Appreciate the use of decimals in real life situations.
Core competences to be developed
• Critical thinking and problem solving: as learners identify and obtain the place value
and the total value of decimals using place value apparatus and work sheets.
• Digital literacy: as learners use digital devices to interacting with technology and
learn more on decimals.
Pertinent and contemporary issues (PCIs)
Safety: as learners make paper cut-outs or other materials and models.
70
Links to other subjects
• Integrated science: as learners express quantities in decimal forms and notations in
measurement.
• Home science: as learners measure the masses of ingredients in decimals.
Values
• Unity: as learners work in groups to multiply and divide decimals using cut-outs,
cards charts and models.
• Responsibility: as learners perform multiplication and division of decimals.
Key inquiry question
1. Where are decimals applicable in real life situations?
2. How do you use decimals in daily activities?
Suggestions on facilitating dierentiated learning and learners with special needs
Facilitating dierentiated learning Facilitating learners with special needs
• Auditory learners acquire
information by listening. In Activity 1
and Activity 5 engage auditory learners
in face-to-face discussions and
classroom presentations because this
is how they learn best.
• Give both the time takers and fast
learners equal chances to participate
in class activities. Ensure that they
accommodate one another and work
together despite their individual
dierences.
• Give gied learners extra activities to
keep them busy and avoid boredom
or idling.
• Ensure that the learners are
positioned evenly in the class based
on their abilities.
• Identify each learner’s needs and
characteristics and adjust the content
delivery process accordingly. is will
help learners with dierent abilities to
learn and acquire information in their
own way.
• Ensure short-sighted learners sit
at the front of the class and the
long-sighted ones sit at the back to
ensure appropriate distance from the
chalkboard during lessons.
• In Activity 4 and Activity 5, learners
are required to make grids. Encourage
the learners to make large grids to
assist visually impaired learners.
• Encourage learners to speak clearly and
audibly during the group activities. e
learners can also use gestures and sign
language if possible, to assist learners
with hearing impairment.
• During the digital learning activities,
provide speech to text captioning
for the videos or you may also avail
headphones with amplied sound for
learners with hearing impairment.
• In Activity 1, give more time to
learners with physical impairment
so that they can participate in the
drawing of place value charts.
71
Suggested teaching and learning resources
• Rectangular cut-outs
• Place value charts
• Abacus
• Counters
• Square grids
• Multiplication tables
• Digital devices
Teacher preparation for the lessons in this sub strand
Ensure that the teaching and learning resources are available and are enough for all the
learners. In Activity 4 and Activity 5, make sure that learners have sucient square grids.
You can decide to involve learners in drawing the square grids prior to the lesson.
Suggested learning experiences
Place value of digits in a decimal
Refer to Learner’s Book page 52
Activity 1: In groups
1. Let learners read the story in the Learner’s Book. Ask them probing questions to
enhance their comprehension of the information in the story. Critical thinking and
problem-solving is developed as they make out what the game is all about, having
seen the number cards.
2. Let the learners identify the decimals written on the number cards from the story.
Instruct them to draw a place value chart. Guide the learners to write the decimals in
the place value chart.
3. Walk around the classroom and observe the learners as they write the decimals in
the place value chart. Positively reinforce correct working and give guidance to those
learners who are having challenges.
4. Let the learners write down the place value of digit 2 in each of the numbers. Encourage
them to make other number cards with decimals up to ten thousandths. Let them use
a place value chart to nd the place value of each digit in the numbers. Instruct the
learners to identify the digits in ten thousandths place value and write them down.
is enhances self-ecacy and learning to learn.
72
5. Allow a few learners to present their ndings to the class. Consolidate their ndings
by guiding them through Example 1 on page 51 of the Learner’s Book. ey should
note that a decimal point separates the whole number and the decimal parts.
6. Ask individual learners to do Practice exercise 1 in the Learner’s Book.
Practice exercise 1: Expected answers (Page 52)
1.
Place value
Numbers Ones Decimal
point
Tenths Hundredths ousandths Ten
thousandths
0.67 0 . 6 7
2.579 2 . 5 7 9
5.8703 5 . 8 7 0 3
9.7234 9 . 7 2 3 4
2. (a) Hundredths (b) ousandths
(c) Tenths (d) Ten thousandths
3. (a) e place value of digit 2 is tens.
e place value of digit 3 is ones.
e place value of digit 1 is tenths.
e place value of digit 5 is hundredths.
e place value of digit 8 is thousandths.
(b) e place value of digit 2 is ones.
e place value of digit 0 is tenths.
e place value of digit 5 is hundredths.
e place value of digit 4 is thousandths.
e place value of digit 3 is ten
thousandths.
(c) e place value of digit 1 is tens.
e place value of digit 2 is ones.
e place value of digit 0 is tenths.
e place value of digit 9 is hundredths.
e place value of digit 6 is thousandths.
e place value of digit 4 is ten
thousandths..
(d) e place value of digit 3 is hundreds.
e place value of digit 5 is tens.
e place value of digit 6 is ones.
e place value of digit 1 is tenths.
e place value of digit 4 is
hundredths.
The place value of digit 9 is thousandths.
4. e place value of digit 1 is tens.
e place value of digit 0 is ones.
e place value of digit 9 is tenths.
e place value of digit 8 is hundredths.
The place value of digit 7 is thousandths.
e place value of digit 1 is ten
thousandths.
5. ousandths
73
Total value of digits in a decimal
Refer to Learner’s Book page 52
Activity 2: In groups
1. Introduce this activity by involving learners in a simple discussion on total value.
As learners mention what they know about total value, correct any misconceptions,
inconsistencies or factual issues. is fosters communication and collaboration as
learners share information on the subject matter.
2. Let the learners identify the time taken by four athletes to nish a marathon as
mentioned in the Learner’s Book.
3. Guide the learners to nd the total value of digit 3 in the time taken by each athlete.
Let them draw a table like the one in the Learner’s Book and ll it in. Emphasise the
importance of nding the place value of a digit rst, since total value is the product of
the digit and its place value.
4. Guide learners through Example 2 on page 53 of the Learner’s Book. Reinforce the
concepts they have learned by instructing them to attempt questions in Practice
exercise 2 individually.
Practice exercise 2: Expected answers (Page 53)
1. (a) e total value of digit 6 is 6.
e total value of digit 7 is 0.7.
(b) e total value of digit 7 is 7.
e total value of digit 8 is 0.8.
e total value of digit 1 is 0.01.
(c) e total value of digit 2 is 20.
e total value of digit 5 is 5.
e total value of digit 6 is 0.6.
e total value of digit 2 is 0.02.
e total value of digit 4 is 0.004.
(d) e total value of digit 1 is 100.
e total value of digit 0 is 0.
e total value of digit 9 is 9.
e total value of digit 7 is 0.7.
e total value of digit 6 is 0.06.
e total value of digit 4 is 0.004.
e total value of digit 1 is 0.0001.
2. (a) 0.007 (b) 0.7 (c) 0.07
(d) 0.0007
3. e total value of digit 2 is 20 000.
e total value of digit 1 is 1 000.
e total value of digit 1 is 100.
e total value of digit 7 is 70.
e total value of digit 8 is 8.
e total value of digit 5 is 0.5.
e total value of digit 6 is 0.06.
4. 0.005 5. 0
74
Extended activity
1. Guide learners in a discussion on ‘how to make an abacus’. Let them mention the
materials required and procedure to be followed.
2. Let learners involve their friends, parents or guardians in the activity if circumstances
allow. is promotes parental empowerment and engagement.
3. Encourage learners to use the abacus to practice what they have learnt in their free
time.
Multiplying a decimal by a whole number
Refer to Learner’s Book page 54
Activity 3: In pairs
1. Let learners draw a table like the one in the Learner’s Book. Instruct them to ignore
the decimal points and multiply the factors like whole numbers.
2. Let the learners count the number of decimal places in the factors and move the
decimal point in the product, one place to the le for each decimal place they count.
Allow them to ll the table.
3. Guide the learners to compare the number of decimal places in the factors and in the
products. ey should be able to infer that the sum of the number of decimal places
in the factors is equal to the number of decimal places in the product. is enhances
critical thinking as they read and comprehend the instructions given to solve the
multiplications.
4. Guide the learners through Example 3 on page 54 of the Learner’s Book. Emphasise
on multiplying the decimals like whole numbers rst and then placing the decimal
point in the product according to the total number of decimal places in the factors.
5. Encourage the learners to form their own multiplication sentences involving decimals
and whole numbers. Tell them to work the multiplication sentences in pairs for more
practice. Instruct the learners to embark on doing Practice exercise 3 individually. is
enhances self-ecacy and promotes self-esteem as the learners get correct answers
to the questions.
Practice exercise 3: Expected answers (Pages 54 and 55)
1. (a) 1.2 (b) 31.14 (c) 30.144 (d) 162.58 (e) 197.75 (f) 27.36
2. 16.56 m
2
3. 15.6 minutes
4. Ksh 1 485.60
5. 4.82 km
75
Digital learning
1. Guide learners to use a computer, a tablet or a smartphone to search for a game
involving multiplication of a decimal by a whole number.
ey may use this link: https://www.iknowit.com/lessons/e-multiplying-decimals-by-
whole-numbers.html.
2. Walk around and encourage the learners to use the digital devices for their intended
purpose. Ensure that the learners are kept safe from insecure or indecent sites and
materials. is promotes cyber security and digital literacy.
Multiplying a decimal by a decimal
Refer to Learner’s Book page 55
Activity 4: In groups
1. Instruct learners to draw a grid with 100 squares. You may consider having the grids
drawn prior to the lesson. Guide them to shade the grid vertically to represent 0.3.
2. Let them use a dierent colour to shade the grid horizontally to represent 0.5 as shown
in the Learner’s book.
3. Direct the learners’ attention to the overlapping area (double shaded). Let them know
that this represents the product of the two decimals. Tell them to count the number
of decimal places in the product.
4. Instruct the learners to use grids to work out the product of dierent decimals that
have one decimal place. You may even ask them to think of how to use the grid to
work out the product of decimals with 2 decimal places. is way Creativity and
imagination is invoked in the learner as they gure out how to go about it. As you
look at their responses, reinforce the concepts.
5. Randomly select a few learners to present their ndings to the class. Consolidate
their ndings by guiding them through Example 4 and Example 5 on page 56 of the
Learner’s Book. In order to assess the skills that the learners have learnt, randomly ask
them to multiply a pair of decimals.
6. Instruct individual learners to do Practice exercise 4 in the Learner’s Book.
Practice exercise 4: Expected answers (Pages 56 and 57)
1. (a) 1.52 (b) 17.023 (c) 147.3432 (d) 359.9485 (e) 8.1666 (f) 86.9913
2. 35.9784 3. 395.59 km 4. 253.076 m
2
5. (a) 30.25 cm
2
(b) 46.305 cm
2
(c) 44.53 cm
2
(d) 97.5375 cm
2
76
Digital learning
1. Guide learners to use a computer, a tablet or a smartphone to search for a game
involving multiplication of a decimal by a whole number.
ey may use this link: https://www.iknowit.com/lessons/e-multiplying-decimals.html.
2. Encourage learners to use digital devices for learning and enjoyment.
Dividing a decimal by a whole number
Refer to Learner’s Book page 57
Activity 5: In groups
1. Let learners draw grids like the ones in the learner’s book. Guide them to write the
shaded part in each grid as a decimal.
2. Guide the learners to divide the shaded part in grid (a) into 3 equal groups and use
the set up to complete the division sentence in the Learner’s Book. ey should also
divide the shaded part in grid (b) into 4 equal groups and use the set up to complete
the division sentence in the Learner’s Book.
3. Allow a few learners to explain to other learners in the class how to divide decimals by
whole numbers. is promotes peer education. Harmonise their ndings through
probing and demonstration. Guide them through Example 6 and Example 7 on page
58 of the Learner’s Book.
4. Ask individual learners to do Practice exercise 5 in the Learner’s Book. Dividing
decimals by whole numbers on their own makes a learner believe in his or her own
ability and this develops self-ecacy.
Practice exercise 5: Expected answers (Page 58 and 59)
1. (a) 1.43 (b) 1.4 (c) 0.609 (d) 4.4 (e) 0.173 (f) 0.012
2. 20.6 cm 3. 0.4 km 4. 0.465 kg 5. 0.0813 ha
Digital learning
Guide learners to use a computer, a tablet or a smartphone to search for a game involving
division of a decimal by a whole number.
ey may use this link: https://www.iknowit.com/lessons/e-dividing-decimals-by-a-whole-
number.html.
77
Dividing a decimal by a decimal
Refer to Learner’s Book page 59
Activity 6: In groups
1. Guide learners to make practice cards like the ones in the Learner’s Book. Lead them
in a discussion to determine how they can work out the divisions. Critical thinking
and problem solving is developed as learners brainstorm and devise strategies of
dividing decimals by decimals. At the same time communication and collaboration
is portrayed as they express their ideas.
2. Allow the learners to share and compare their answers with other groups. As they
review the answers and strategies used by their peers, they are intuitively encouraged
to build and nurture relationships through fairness and open mindedness.
3. Consolidate their ndings through probing and demonstrations. Take them through
Example 8 and Example 9 on pages 59 and 60 of the Learner’s Book.
4. Wrap up the whole activity by instructing the learners to do Practice exercise 5.
Encourage them to use the methods they have learnt in dividing a decimal by a
decimal.
Additional information
Reinforce the concept of converting decimals into fractions before working out. When
dividing the fractions, remind them to multiply the rst fraction by the reciprocal of the
second fraction and express their answers as decimals. e learners can also remove the
decimal points in the dividend and the divisor by multiplying them by a power of ten,
depending on the decimal with the highest number of decimal places, followed by long
division to get the answer.
Practice exercise 6: Expected answers (Page 60)
1. (a) 16 (b) 105 (c) 7.8 (d) 1.1 (e) 12.3 (f) 0.89
2. 11.3 cm 3. 75.4 km 4. 36 pieces 5. 14 containers
Digital learning
Instruct learners to use a computer, a tablet or a smartphone to search for a game involving
division of decimals by decimals. is promotes digital literacy as the learners search for
the game online and also enhances critical thinking and problem-solving as they carry
out mental arithmetic when working out the questions.
Encourage them to use this link: https://www.iknowit.com/lessons/e-dividing-a-decimal-
by-a-decimal.html.
78
Extended activity
Encourage learner to solicit the help of parents, guardians and peers in discussing how
decimals are used in daily activities. ey should also to identify dierent jobs that require
the use of decimals and gather basic information about them. is inspires career guidance
in the learners as they understand the dierent jobs in the community.
Assessment methods
(a) Written tasks: Ask learners to do the practice exercises in the Learner’s Book.
(b) Observation: Observe and check the work of the learners as they discuss the activities
and practice exercises provided.
(c) Oral questions: Ask oral questions as learners discuss and make class presentations
of the concepts that they have learnt.
(d) Take away assignment: Make worksheets with questions on the concepts they have
studied. Give the worksheets to learners as take away assignments which can be done
with the help of their parents or guardians.
Suggestions on developing competency based assessment tasks
Develop authentic assessment tasks that will enable learners to apply the knowledge
and skills that they have studied in class. Let learners engage in games that involve
decimals. Challenge them to write and recite poems that will give them an insight on
multiplication of decimals.
Suggested assessment tool
Checklist
School: Weyma Secondary School
Period of assessment: March 2022 Teacher’s name: James Ole Tunai
Class: Grade 7 West Subject: Mathematics
Strand: Numbers Sub strand: Decimals
Competency assessed (knowledge, skills, attitude, values) Tick appropriately
Name of
learner
Identies
place value
and total
value of
decimals
Multiplies
decimals
by a whole
number and
by a decimal
Divides
decimals
by a whole
number
and by a
decimal
Uses digital
devices for
learning
and for
enjoyment
Recognises use
of decimals
in real life
situations
Teacher’s
comments
Yes No Yes No Yes No Yes No Yes No
Mary √ √ √ √ √
Diligent and
focused
Ali
Ruth
Teacher’s signature: _________________ Date: _________________
79
1.5 Squares and square roots
Number of lessons 5
Refer to Learner’s Book pages 61 to 68
Introduction
Squares and square roots is a new sub strand to the learner though it is not entirely a
new concept. e learners were introduced to the concept of squares and square roots in
Grade 6. ey also possess the prerequisite knowledge of multiplication involving whole
numbers, fractions and decimals. In this sub strand, the learners will extend their prior
knowledge of squares and square roots of perfect squares. e learning activities in this
sub strand have been tailored to give learners a hands-on approach to working out squares
and square roots of whole numbers, fractions and decimals. e knowledge of factors
and prime factorisation will also be signicant when nding square roots of numbers.
e learners will nd it easy and enjoyable to calculate the squares and square roots of
numbers in their day-to-day activities.
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) Determine the squares of whole numbers, fractions and decimals by multiplication
in dierent situations.
(b) Determine the square roots of whole numbers, fractions and decimals of perfect
squares in dierent situations.
(c) Use IT devices for learning more on squares and square roots and for enjoyment.
(d) Appreciate the use of squares and square roots in real life situations.
Core Competencies to be developed
• Critical thinking and problem solving: as learners use grid squares and charts to
nd squares and square roots.
• Digital literacy: as learners use digital devices and interact with technology to work
out the squares and square roots of numbers.
Pertinent and Contemporary Issues (PCIs)
Environmental education: as learners consider shapes of dierent objects in the school
compound especially the ones that are squares.
Links to other subjects
Pre-career and pre-technical: as learners relate square and square roots to areas such as
carpentry and technical drawing.
Agriculture: as learners determine the number of seedlings that would t in a square
portion of land.
80
Values
• Respect: as learners appreciate each other’s contribution in groups while using grids
and charts to nd squares and square roots of whole numbers, fractions and decimals.
• Unity: as learners work in groups to calculate the factors of numbers to get the square
roots.
Key inquiry question
1. Where do we apply squares and square roots in daily activities?
2. How do we apply squares and square roots in daily activities?
Suggested teaching and learning resources
• Cards
• Square grids
• Charts
• Manila papers
• A pair of scissors
Suggestions to facilitating dierentiated learning and learners with special
needs
Facilitating differentiated learning Facilitating learners with special needs
• Identify each learner’s needs and
characteristics and adjust the
content delivery process accordingly.
is will help learners with dierent
abilities to learn and acquire
information in their own way.
• Rene learning strategies and
experiences according to the
learning needs of the learner,
resources and assigned time.
• In Activity 3 and Activity 4, encourage
learners to make number cards in
large print to assist visually impaired
learners.
• In Activity 1, give more time to
physically impaired learners so that
they can participate in the shading of
square grids.
Teacher preparation for the lessons in this sub strand
Ensure availability of required teaching and learning resources prior to the lesson. For
Activity 1, ensure that all learners have pieces of paper with square grids. ey can use a
square ruled exercise book. In Activity 5, ensure that learners have rulers, papers, pencils
and crayons to draw and use dierent colours to shade square grids.
81
Suggested learning experiences
Squares of whole numbers
Refer to Learner’s Book page 61
Activity 1: In pairs
1. Ensure that all learners have a piece of paper with square grids. Instruct them to shade
one square of the grid.
2. Guide the learners to shade the next group of squares by adding 3 to the rst one. Tell
them to keep shading the next group of squares by adding the next odd number to the
squares that they have already shaded. Let them make a pattern like the one shown
in the Learner’s Book. Creativity and imagination is exhibited as learners create a
pattern involving perfect squares and as they shade squares on the grid to represent
the pattern. You may want to probe them to brainstorm on how the pattern can be
used to determine a sequence of squares of whole numbers. is will enhance critical
thinking and problem solving.
3. Guide the learners to multiply the number rows by the number of columns for each
group of squares that they have shaded.
4. Lead the learners in a discussion for them to deduce that a square is obtained by
multiplying a number by itself. Involve the learners in making more squares.
Encourage them to write multiplication sentences from the columns and the rows
involved in getting a perfect square.
5. Guide the learners through Example 1 on page 61 of the Learner’s Book.
6. Allow individual learners to do Practice exercise 1 in the Learner’s Book. is enhances
the values of honesty, responsibility and self-ecacy.
Additional information
Challenge learners to demonstrate how to calculate squares of whole numbers and
explain its relationship with the concepts they learnt in previous grades and also in
other sub strands in this grade. Explain to the learners that a good understanding of
multiplication of whole numbers, fractions and decimals will come in handy as they
explore the concept of squares. Encourage them to practice expressing numbers as
products of their prime factors, since this is prerequisite skill in calculating square roots
of numbers using factor’s method.
82
Practice Exercise 1: Expected answers (Pages 61 and 62)
1. (a) 81 (b) 1 089 (c) 1 681 (d) 4 489 (e) 9 025
2. (a) 225 (b) 676 (c) 3 364 (d) 5 329 (e) 7 569
(f) 10 000 (g) 14 400 (h) 22 500 (i) 34 225 (j) 43 264
3. 900 eggs
Squares of fractions
Refer to Learner’s Book page 62
Activity 2: In pairs
1. Guide learners to draw a table like the one in the Learner’s Book. Guide them to
multiply each fraction by itself.
2. Lead the learners in a discussion to deduce that when multiplying a fraction by itself
the numerator and the denominator should be multiplied separately to get the square.
3. Let the learners compare their answers with those of other groups. is enhances
cooperation and learning to learn as the learners discuss and compare their answers
with those of other groups.
4. Guide the learners through the Example 2 and Example 3 on pages 62 and 63 of the
Learner’s Book. Emphasise that for a mixed fraction, they should convert it into an
improper fraction rst and then multiply the improper fraction by itself.
5. Write proper and mixed fractions on the chalkboard. Allow learners to volunteer and
work out the example you have written on the chalkboard. Encourage them to explain
the procedure they have used to calculate the squares. is enhances peer education
as the learners volunteer to guide other learners through the examples.
6. In order to assess each individual learner’s level of understanding, ask him or her to
do Practice exercise 2 in the Learner’s Book.
Practice exercise 2: Expected answers (Page 63)
1. (a)
1
4
(b)
9
16
(c)
16
49
(d)
4
25
(e)
49
225
(f) 1
7
9
(g) 17
67
81
(h) 109
36
121
(i) 37
329
400
(j) 248
152
289
2.
289
625
m
2
3. 4 017
3
32
cm
2
4. 90.25 m
2
83
Squares of decimals
Refer to Learner’s Book page 64
Activity 3: In groups
1. Guide learners to make number cards like the ones in the Learner’s Book. Let them
work out the squares of the decimals on each card by converting the decimals into a
fraction, working out the square of the fraction and expressing the square as a decimal.
Walk around the classroom and observe them as they work out squares of decimals by
rst converting the decimal into a fraction. Oer guidance to those learners who may
have challenges in doing the conversions. is will enhance respect as they work out
the squares of decimals in groups.
2. Guide learners to discuss other methods they can use to calculate the squares of decimals.
Creativity and imagination is developed as learners come up with dierent strategies
and methods of working out squares of decimals. In this, they should be able to deduce
that squares of decimals can be calculated using direct multiplication of the decimals.
3. Let the learners multiply the decimals on the cards using direct multiplication of the
decimals. Encourage the learners who are having challenges using this method of
direct multiplication to review the concept of multiplying decimals as learnt in the
previous sub stand.
4. Let the learners work out the squares of the decimals using other methods, compare
their answers and then discuss their ndings.
5. Consolidate their ndings by guiding the learners through Example 4 on page 64 of the
Learner’s Book.
6. Instruct individual learners to do Practice exercise 3 in the Learner’s Book.
Practice exercise 3: Expected answers (Page 64)
1. (a) 1.44 (b) 7.84 (c) 0.25 (d) 29.16 (e) 0.49
(f) 1.2321 (g) 45.2929 (h) 9.3636 (i) 0.0144 (j) 0.9604
2. 342.25 m
2
3. 306.25 cm
2
4. 105.0625 m
2
Digital learning
1. Instruct learners to use calculators to work out squares of the numbers in the Learner’s
Book. is promotes digital literacy among the learners.
84
2. Instruct the learners to work out the squares of the same numbers without using a
calculator. Encourage them to show the method they used to get the answer. For each
number, they should compare the square they have calculated with and without the
calculator. Let them discuss the accuracy of their answers, the time taken to get the
answer and the ease of getting the answer.
Digital learning: Expected answers (Page 65)
(a) 196 (b) 1 444 (c) 2 500 (d) 4 225 (e) 7 056
(f)
1
16
(g)
25
144
(h) 5
229
324
(i) 87
82
121
(j) 13
897
4624
(k) 39.69 (l) 114.49 (m) 53.1441 (n) 0.7225 (o) 0.0016
Square roots of whole numbers
Refer to Learner’s Book page 65
Activity 4: In pairs
1. Begin this concept by giving a brief recap of expressing a number as a product of its
prime factors as learnt earlier in the sub strand of factors. is supports a learner’s
understanding to progress from known to unknown.
2. Let learners brainstorm and think of a 2-digit number. Tell them to multiply the
number by itself and write down the answer on a card. Learning to learn is enhanced
as they organise their thoughts to form a 2-digit number which is multiplied by itself
to get a perfect square.
3. Instruct the learners to express the number as a product of its prime factors. Guide
them to pair up factors that are the same. Let them choose one factor from each pair and
then multiply them. is procedure enhances a learner’s ability to follow instructions
and thus promoting peace and social cohesion which are very important values in his
or her day-to-day life.
4. Lead the learners in a discussion to ascertain that the result they got aer multiplying
the factors is the number that they had thought about at the beginning. ey should be
able to discover that this number represents the square root of the number written on
the card. Use the discussion to introduce the square root symbol. ey should be able
to recognise that the symbol √ means square root.
5. Take the learners through Example 5 and Example 6 on pages 65 and 66 of the
Learner’s Book. Support their understanding by allowing them to ask questions and
seek clarication on factors method and division method of working out square roots.
6. Encourage the learners to continue working out square roots using division method
and any other methods in groups for more practice. Let them do Practice exercise 4
in the Learner’s Book with the help of their parents or guardian. is will promote
parental empowerment and engagement.
85
Practice Exercise 4: Expected answers (Page 66)
1. (a) 7 (b) 18 (c) 29 (d) 35
2. (a) 15 (b) 30 (c) 63 (d) 92
3. 76 4. 28 cm 5. 24 chairs
Square roots of fractions
Refer to Learner’s Book page 66
Activity 5: in pairs
1. Instruct learners to draw a square grid with 4 columns and 4 rows and shade it as
shown in the Learner’s Book. Let them write a fraction to represent the parts shaded
green and red.
2. Tell the learners to write a fraction to represent the double shaded part of the grid. Let
them discuss and determine the relationship between the single shaded and double
shaded parts. ey should be able to recognise that the single shaded parts represents
the square root while the double shaded part represents the square of the fraction.
3. Let the learners use square grids to nd the square root of other fractions that are
perfect squares. is encourages critical thinking and problem solving.
4. Guide the learners through Example 7 and Example 8 on page 67 of the Learner’s Book.
Emphasise on working out the square roots of the numerators and the denominators
separately through mental reasoning, factors method or division method. Remind
them to always change mixed fractions into improper fractions before working out
the square roots as explained in the Learner’s Book.
5. Instruct the learners to make worksheets that involve working out square roots of
perfect squares. Allow the dierent groups of learners to exchange the worksheets
and work out them out. is enhances creativity and imagination as learners choose
numbers that make perfect squares to form their fractions.
Practice exercise 5: Expected answers (Page 67)
1. (a)
1
3
(b)
1
2
(c)
5
8
(d)
9
10
(e)
6
11
(f) 1
1
3
(g) 1
3
4
(h) 6
2
3
(i) 2
1
5
(j) 2
7
8
2. 9
7
10
cm 3. 11
2
5
m 4. 410 m
86
Square roots of decimals
Refer to Learner’s Book page 68
Activity 6: in pairs
1. Let learners read aloud the information in the Learner’s Book. Give them a minute to
read silently and comprehend the information. is develops communication and
collaboration. It also promotes self-ecacy as learners read, comprehend and follow
instructions to solve mathematical sentences.
2. Challenge the learners to devise strategies of working out square roots of decimals.
Let them implement those strategies to calculate the square root of the number 67.24.
Critical thinking and problem solving is enhanced as learners come up with the
strategies. Some of the strategies could include converting the decimal into a fraction
and then using factors method or division method to calculate the square root.
Practice exercise 6: Expected answers (Page 68)
1. (a) 0.2 (b) 0.4 (c) 1.3 (d) 1.9 (e) 2.6 (f) 3.5
2. 8.4 m 3. 13 tiles 4. 6.4 m
Digital learning
1. Talk to the learners about the square root sign and let them identify it on a calculator.
Let them use trial and error method to determine how to use a calculator to compute
the square roots of numbers. is enhances the learner’s digital literacy and self-
ecacy competencies.
2. Instruct learners to use calculators to work out square roots of the numbers in the
Learner’s Book. Encourage the gied learners to help their counterparts in using the
calculators, this encourages responsibility and unity as learners assist one another.
3. Randomly select learners from dierent groups to present their work to the class. is
promotes peer education. Remind the learners to handle the digital devices with care.
Digital Learning: Expected answers
1. (a) 25 (b) 32 (c)
1
5
(d) 1
5
6
(e) 0.7 (f) 2.4
Extended activity
Instruct learners to explain to one another the concepts that they have learnt in this sub
strand. Allow them to do this activity at their own free time and with the help of their
friends. is will enhance peer education.
87
Suggested assessment task
Competency based assessment tasks aim at testing and building the knowledge and skills
of the learner. In this sub strand, encourage the learner to carry out a case study and write
about the uses of squares and square roots in their day to day activities.
Assessment methods
(a) Written questions: Ask learners to individually work on the practice exercises
(b) Observation: go round the class observing learners at work, advice and help where
need be.
(c) Oral questions: Ask oral questions to summarize or prompt learners throughout the
lesson where need be.
Suggested assessment tool
Learner’s prole
Learner’s Name: Majore Waswa Teacher’s name: Sarah Atieno
Subject: Mathematics Period of assessment: 21
st
to 28
th
March 2022
Strand: Numbers Sub strand: Decimals
Learning outcome: Determine the square roots of whole numbers, fractions and
decimals of perfect squares in dierent situations.
Criteria Learner’s strengths Learner’s
weaknesses
Learner’s interests
Determining the
square roots of
whole numbers
He has excellent
knowledge in using
division method to get
squares roots of whole
numbers.
He has challenges
in sharing
information about
squares roots with
peers.
He loves drawing grids and charts
to obtain squares roots of whole
numbers.
Determining the
square roots of
fractions
He prociently
demonstrates the
procedure of working out
square roots of fractions.
He has challenges
presenting the
group’s ndings to
the class.
He is talented in drawing factor
trees to get square roots using
factors method.
Determining the
square roots of
decimals
He has exceptional skills
in using a calculator to
work out square roots of
decimals.
He has challenges
converting
decimals to
fractions before
working out
square roots.
He loves expressing himself using
drawings.
Appreciating use
of squares roots in
real life
He is very condent in
applying square roots
to work out the side of
square objects in the
environment.
None observed He loves manipulating square
objects in the environment and
working out square roots.
Teacher’s signature: _________________
88
2.1 Algebraic expressions
Number of lessons: 5
Refer to Learner’s Book pages 69 to 74
Introduction
Concepts involving algebra have been studied by the learners long before they had heard
about the word, let alone fathom its meaning. As early as in Early Years Education, the
concept of collecting like terms had been introduced through sorting and grouping of
similar items as they counted them. Algebra is a branch of Mathematics that deals with
operations on expressions involving numbers and letters which represent unknowns.
Algebraic expressions are formed or simplied by carrying out operations such as addition,
subtraction, multiplication and division. In Grade 4, the learners were introduced to
forming and simplifying algebraic expressions. ey learnt that algebraic expressions are
simplied by grouping like terms. is sub strand will enrich learners’ prior experiences.
e concept of forming and simplifying algebraic expressions helps to boost the learners’
logical reasoning ability and aptitude in decision making.
e learning activities in this sub strand will encourage learners to explore open tasks
that have various solutions or strategies that focus on developing core competencies and
algebraic skills. When forming and simplifying algebraic expressions, the learners will
be provoked to compare, contrast and classify objects in their immediate environment
according to given attributes.
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) Form algebraic expressions from real life situations.
(b) Form algebraic expressions from simple algebraic statements in real life situations.
(c) Simplify algebraic expressions in real life situations.
(d) Use IT devices for more learning on algebraic expressions and for enjoyment.
(e) Appreciate the use of algebraic expressions in real life.
Core competencies to be developed
• Communication and collaboration: as the learners speak, listen and discuss in groups
and teams on formation of algebraic expressions.
• Critical thinking and problem solving: as the learners interpret statements to form
and simplify algebraic expressions.
2.0 Algebra
89
Pertinent and contemporary issues (PCIs)
• Environmental education: as learners classify objects from the immediate environment
according to given attributes.
• Friendship formation: as learners works and discuss in groups on formation of
algebraic expressions.
Links to other subjects
• Language: as learners interpret statements to form algebraic expressions.
• Integrated Science: as learners classify living and non-living things in their immediate
environment.
Values
• Unity: as learners classify similar objects in groups to form algebraic expressions.
• Respect: as learners appreciate each other’s contribution while discussing and forming
algebraic expressions.
Key inquiry questions
1. How do we use algebraic expressions in daily activities?
2. How do we form algebraic expressions from classied objects?
3. How do we simplify algebraic expressions from classied objects?
Suggestions on facilitating dierentiated learning and learners with special needs
Facilitating dierentiated learning Facilitating learners with special needs
• Make your concept delivery process
varied to cater for learners with dierent
needs and characteristics. Combine
reading and writing tasks with group
discussions, pictures, verbal explanations
and practical activities.
• Social learners acquire information
by working in pairs or in groups with
others. Solitary learners prefer to use
self-study and work alone. Cater for
social and solitary learners by using
the think-pair and share strategy. Start
by asking learners to individually
think about an algebraic statement,
then pair learners together to discuss
their results and ndings and nally
allow each pair to share their ideas
with the rest of the class.
• In Activity 1, give more time to the
physically challenged learners so that
they can participate in the observations
and classication of objects outside the
classroom. Encourage the other learners to
support them example helping in pushing
a wheel chair for them
• All activities involve using letters and
numbers to represent the numbers of
different living and non-living things.
Encourage the learners to write the
letters and numbers in large print during
activities so that the visually impaired
learners can also see. Ensure the short-
sighted learners sit at the front of the class
and the long-sighted ones sit at the back
to ensure appropriate distance from the
chalkboard during lessons.
90
Suggested teaching and learning resources
• Manila papers
• Pens
• Pencils
• Rulers
• Pairs of scissors
• Pictures
Teacher preparation for the lessons in this sub strand
In Activity 1, plan to have an area in the school compound, such as the playground, where
learners can go to and observe their immediate environment. In Activity 2, ensure that the
learners have enough pencils, pens and rulers.
Suggested learning experiences
Forming of algebraic expressions
Refer to Learner’s Book page 69
Activity 1: As a class
1. Direct learners’ attention to the classication chart in the Learner’s Book. Let them
discuss the information in the classication chart. e learners are expected to give their
responses as they are familiar with the information in the chart from their experiences
in Integrated Science. is chart drives the learners into thinking intuitively about
classication and grouping of items. It will help them build up on the idea of putting
together similar items.
2. Take learners to observe their immediate school environment. Use your discretion to
nd a conducive location within the school compound where a variety of the classied
things can be found. Encourage them to use letters to represent the number of dierent
living and non-living things. ey could for example, use w to represent plants, x to
represent animals, y to represent natural non-living things and z to represent man-
made non-living things. Let them form an expression for all the living and non-living
things put together. is promotes environmental education as the learners become
aware of their immediate environment.
3. Let the learners form an expression for the dierence between the number of plants
and animals. Ask them to sort and group the man-made non-living things according
to colour and then form an algebraic expression for twice the number of green
man-made things.
91
Forming algebraic expressions involving addition and subtraction
Refer to Learner’s Book page 69
Activity 2: In groups
1. Let learners collect a number of pencils, pens and rulers. Guide them to use letters to
represent the numbers of each item they have collected. Instruct them to discuss and
form expressions for the total number of pens and pencils that they have collected. Tell
them to form an expression for the number of rulers that remain if they take away 1
ruler. is will enhance the aspect of communication and collaboration. By speaking
listening and contributing to the discussion it enhances team work.
2. Encourage the learners to share their answers with other learners in class. Let
them discuss and form algebraic expressions from other statements of their choice.
Randomly allow some learners to present their results to the rest of the class. In so
doing, it promotes self-ecacy and peer education.
3. Consolidate their ndings by guiding them through Example 1 on page 70 of the
Learner’s Book.
4. Instruct individual learners do Practice exercise 1 in the Learner’s Book.
Practice exercise 1: Expected answers (Page 70)
1. y + 6 2. 2y – 3 3. 3p – 4 – 2x 4. 4b + y + 5 5. 3r + 12q – 5
Forming algebraic expressions involving multiplication and division
Refer to Learner’s Book page 70
Activity 3: In groups
1. Let learners read the story in the Learner’s Book. Using the knowledge obtained from
previous grades, let them form an expression to represent the area of the farm that was
occupied by the maize.
2. Guide the learners to form an expression for the perimeter of the farm. Remind them
to work out the area and perimeter of the farm using 7 n metres as length and the width
as 50 metres.
3. Take the learners through Example 2 and Example 3 on page 71 of the Learner’s
Book and let them form algebraic expressions involving multiplication and division.
4. Ask individual learners to do Practice exercise 2 in the Learner’s Book with the help of
their parents or guardians. is will promote parental empowerment and engagement.
92
Practice exercise 2: Expected answers (Page 71)
1. (a) 40j (b) 7.5p – 5 (c) 16r
2
2.
1
3
g 3. 10h 4. 4x + 5 5.
1
2
x
Simplifying algebraic expressions involving addition and subtraction
Refer to Learner’s Book page 72
Activity 4: In groups
1. Let learners form an expression for the sum of three consecutive whole numbers.
In so doing, their critical thinking and problem-solving competence is enhanced.
Emphasise to them that consecutive numbers follow each other in order from the
smallest to the largest. To obtain the next consecutive whole number, they should add
one to the previous whole number. Instruct them to simplify the expression for the
sum of three consecutive whole numbers.
2. Let the learners write down an expression for the sum of three consecutive odd
numbers. ey should be able to determine that to obtain the next consecutive odd
numbers, they should add 2 to the previous odd number. Instruct them to simplify the
expression for the sum of three consecutive odd numbers.
3. Instruct learners to use a letter to represent a number. Let them add 12 to the number
and subtract 5 from the sum to obtain the required expression then simplify it.
4. Randomly allow a few learners to present their group’s ndings to the rest of the class.
is promotes the values of self-esteem and respect as they compare their answers.
Harmonise their ndings through probing and demonstration.
5. Guide the learners through Example 4 in the Learner’s Book. Empha sise that they
s h o u ld co l le c t li k e t er m s t o sim p lif y a n exp r es sio n.
6. T e l l in di v id u a l le a r n er s t o do P r a c t i c e ex er ci s e 3 in t h e L e a r n er’s b o o k.
Practice exercise 3: Expected answers (Pages 72 and 73)
1. (a) r + 7 (b) 3a + 6b (c) 3x + 2y (d) 5c +17
(e)
7
9
s + 9 (f) t + 6 (g)
1
10
n +
3
20
(h) 0.75p + 3
2. 18n + 1 3. p – 70 4. 2x + 21 5. 2z + 5
Simplifying algebraic expressions involving multiplication
Refer to Learner’s Book page 73
Activity 5: In groups
1. Let learners discuss and brainstorm on how to calculate the area of rectangle A,
rectangle B and the triangle. Walk around the classroom and observe as the learners
form algebraic expressions involving multiplication and give guidance to those who
may have challenges. Critical thinking and problem solving is developed as learners
form expressions for the areas of the dierent shapes.
93
2. Challenge the learners to form an expression for the area and another expression for the
perimeter of the shape. To nd the area of the shape, they should add the expressions
they have obtained for the area of rectangle A, rectangle B and the triangle. To work
out an expression for the perimeter, they should add the distance all round the shape.
Communication and collaboration is developed as learners work together in groups
to form algebraic expressions.
3. Harmonise their ndings by guiding them to simplify the expressions in Example 5
on page 73 of the Learner’s Book. Demonstrate to them how to open the brackets by
multiplying the term on the outside of the bracket with each term inside the brackets. Let
them open the brackets and collect the like terms to simplify the algebraic expressions.
4. Allow individual learners to do Practice exercise 4 in the Learner’s Book while at home
and with the help of their parents or guardians. is promotes parental empowerment
and engagement.
Practice exercise 4: Expected answers (Page 74)
1. (a) 8 + 4a (b) 6y (c) 11a + 12 (d) 28x + 9y + 11 (e) 5 + 6m (f) 28x + 10
2. 4x + 6 3. 4p + 8 4. 5w 5. 8x + 81
Digital learning
1. Guide learners to use a computer, a tablet, or a smartphone to search for a game
involving simplifying algebraic expressions.
ey may use this link: https://www.mathgames.com/skill/7.108-simplify-variable-
expressions-using properties.
2. Walk around the classroom and encourage the learners to use the digital devices as
intended. To promote cyber security and digital literacy, ensure that the learners are
kept safe from insecure or indecent cites and materials.
Extended activity
Instruct the learners to discuss how to form and simplify algebraic expressions from their
day to day activities.
Suggested assessment task
Authentic tasks are tailor made to evaluate a learner’s competency in practical and hands-
on vocational skills. In this substrand, encourage the learner to form and simplify algebraic
expressions that involve statements from their real-life experiences.
94
Assessment methods
(a) Written tasks: Ask the learners to do the practice exercises in the Learner’s Book.
(b) Observation: Observe and monitor the learners as they discuss and carry out
activities.
(c) Oral questions: Ask probing questions to gauge each learner’s level of understanding.
(d) Take away assignment: Make worksheets with questions on the concepts they have
studied. Give the worksheets to learners as take away assignments which can be done
with the help of their parents or guardians.
Suggested assessment tool
Assessment rubric
Indicators Exceeds
expectations
Meets
expectations
Approaches
expectations
Below expectations
Ability
to form
algebraic
expressions
e learner
correctly and
systematically
forms algebraic
expressions.
e learner
correctly
forms
algebraic
expressions.
e learner
partially forms
algebraic
expressions.
e learner shows
diculties in forming
algebraic expressions.
Ability
to form
algebraic
expressions
from simple
algebraic
statements
e learner
correctly and
systematically
forms algebraic
expressions
from simple
algebraic
statements.
e learner
correctly
forms
algebraic
expressions
from simple
algebraic
statements.
e learner
partially forms
algebraic
expressions
from simple
algebraic
statements.
e learner shows
diculties in forming
algebraic expressions
from simple algebraic
statements.
Ability to
simplify
algebraic
expressions
e learner
correctly and
prociently
simplies
algebraic
expressions.
e learner
correctly
simplies
algebraic
expressions.
e learner
partially
simplies
algebraic
expressions.
e learner shows
diculties in
simplifying algebraic
expressions.
95
2.2 Linear equations
Number of lessons: 6
Refer to Learner’s Book pages 74 to 80
Introduction
In Grade 5, the learners were introduced to forming and solving simple equations in one
unknown. In this sub strand, the learners will build on their learning experiences on
forming and solving linear equations in one unknown. ey will also learn how to apply
linear equations in real life situations for example in balancing of weighing scales and
working out bills in shopping activities.
e learning activities in this sub strand will increase the learners’ awareness that linear
equations are useful in real life situations. It is therefore important for you as the teacher,
to motivate and encourage the learners to actively participate in the activities.
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) Form linear equations in one unknown in dierent situations.
(b) Solve linear equations in one unknown in dierent situations.
(c) Apply linear equations in one unknown in dierent situations.
(d) Use IT devices for more learning on linear equations and for enjoyment.
(e) Appreciate use of linear equations in real life situations.
Core competencies to be developed
• Communication and collaboration: as learners speak, listen and work as a team
during role play activities involving equations with one unknown.
• Self-ecacy: as learners enhance their self-awareness skills when carrying out role
playing activities.
• Learning to learn: as learners organise their own learning when applying linear
equations in real life.
Pertinent and Contemporary Issues (PCIs)
• Social cohesion: as learners work in groups to role play shopping activities.
• Self-esteem: as learners participate in role play activities like shopping that will lead
to equations with one unknown.
Links to other subjects
Computer studies: as learners use digital devices in forming and solving equations.
96
Values
• Integrity: as learners share resources as per the given equation or conditions.
• Responsibility: as the learners use a given letter in the equation to represent an item.
Key inquiry questions
1. How do we use linear equations in real life?
2. Why do we use linear equations in real life?
Suggestions on facilitating dierentiated learning and learners with special
needs
Facilitating dierentiated learning Facilitating learners with special needs
• Give both the time takers and
gied learners equal chances
to participate in class activities.
Ensure that they accommodate
one another and work together
despite their dierences.
• Identify each learner’s needs
and characteristics and adjust
the content delivery process
accordingly. is will help
learners with dierent abilities to
learn and acquire information in
their own way.
• Encourage learners to use large print
when making bar models in Activity 3 to
assist visually impaired learners.
• Encourage learners to speak clearly and
audibly during the group activities. e
learners can also use gestures and sign
language if possible, to assist learners
with hearing impairment.
Suggested teaching and learning resources
• Strings
• Drinking straws
• Paper money
• Pencils
Teacher preparation for the lessons in this sub strand
Make sure the required teaching and learning resources are available prior to the lesson. In
Activity 1, ensure that you have enough drinking straws and strings. In Activity 2, ensure
that you have enough pencils and paper money for all the groups. You can involve the
learners in making paper money, bar models and other teaching and learning resources
from locally available materials. is promotes Education for Sustainable Development.
97
Suggested learning experiences
Forming linear equations involving addition and subtraction
Refer to Learner’s Book page 74
Activity 1: In groups
1. Guide learners to measure a string or a drinking straw of length 16 cm and cut it
out. Guide them to discuss and bend the string to form a rectangular shape whose
length is 2 cm longer than the width. is will develop critical thinking and problem
solving.
2. Instruct the learners to use a letter to represent the width of the rectangle. Let them
form an expression for the length of the rectangle.
3. Guide the learners to form an equation for the distance all around the rectangle.
Allow a few learners to present their ndings to the rest of the class. is enhances
communication and collaboration and promotes self-ecacy and peer education.
Consolidate their ndings by guiding the learners through Example 1 and Example 2
on page 75 of the Learner’s Book.
4. Instruct learners to do Practice exercise 1 in the Learner’s Book.
Practice exercise 1: Expected answers (Page 75)
1. c + 12 = 16
2. 2b + 6 = 60 (Accept: b + b + 6 = 60)
3. x – 3 = 8
4. 2b + 7 = 45 (Accept: b + b + 7 = 45)
5. 4y + 50° = 180 (Accept: y + y + 30° + y + y + 30° – 10° = 180°)
Forming linear equations involving multiplication and division
Refer to Learner’s Book page 76
Activity 2: In groups
1. Guide learners to make paper money worth Ksh 300. It is advisable to have the learners
make the paper money prior to the lesson so that they can exercise their creativity and
imagination in so doing. Besides, this will save you some reasonable time that can be
used constructively in the role play activity. Let them take turns to role play buying t
pencils using the paper money. e learners can make a classroom shop and use it for
this activity. One learner should pretend to be the shopkeeper while another learner
pretends to be a customer. Tell the learners to switch roles aer every turn such that
98
every one of them gets an opportunity to be both a customer and a shopkeeper.
is develops communication and collaboration. Instruct the learners to change the
price of each pencil aer every turn.
2. For each price they choose, guide the learners to write an equation that can be used
to solve for t.
3. Let the learners form an equation assuming they have Ksh d and want to buy 12 pens
at Ksh 30 each.
4. Guide the learners through Example 3 and Example 4 on page 76 of the Learner’s
Book to enhance the concept of forming the equations.
5. Tell individual learners to do Practice exercise 2 in the Learner’s Book.
Practice exercise 2: Expected answers (Pages 76 and 77)
1. 3g = 2 400 2. 5p + 72 = 97 3. 60y = 780
4. m =
6
3
5. 4f + 6 000 = 18 000
Solving linear equations
Refer to Learner’s Book page 77
Activity 3: In pairs
1. Guide learners to make bar models like the ones in the Learner’s Book. Emphasise
that in each bar model the sum of the unknown and the numbers in the bottom row
(shaded blue) is equal to the number in the top row (shaded green).
2. Instruct the learners to solve for the unknown in each bar model. Guide them to make
other bar models and solve for the unknowns. is enhances their critical thinking
and problem solving skills.
3. Allow the learners to compare their bar models and discuss their answers with other
learners in class. For the learners to internalise the concept, guide them through
Example 5, Example 6, Example 7 and Example 8 on pages 77 and 78 of the Learner’s
Book.
4. Instruct individual learners to do Practice exercise 3 in the Learner’s Book. is
enhances the values of honesty, responsibility and integrity as they heed to the
instruction.
Practice exercise 3: Expected answers (Page 78)
1. (a) r = 8 (b) s = 1 (c) x = 10 (d) m = 2 (e) y = 0
(f) z = 6 (g) p = 12 (h) t = 24
2. Ksh 50 3. 2
1
2
litres 4. 15 years
99
Digital learning
1. Guide learners to use a computer, a tablet or a smartphone to search for a game on
solving equations.
e learners may use this link: https://www.iknowit.com/lessons/d-basic-equations-
four-operations.html.
2. Let the learners play the games involving linear equations for fun and enjoyment.
Applying linear equations
Refer to Learner’s Book page 79
Activity 4: In pairs
1. Ask learners to read the story in the Learner’s Book and answer the questions that
follow. Let them discuss the information in the story. This develops communication
and collaboration in the learners.
2. Let learners use letter c to represent the number of parents. Guide them to form an
equation for the total number of people at the event. This enhances critical thinking
and problem solving.
3. Guide the learners to solve for c in the equation they have formed. Let them determine
the number of teachers at the event?
4. Instruct the learners to calculate the total number of people at the event.
5. Guide the learners through Example 9 on page 79 of the Learner’s Book as a way of
reinforcing the concept.
6. Tell individual learners to do Practice exercise 4 in the Learner’s Book.
Practice exercise 4: Expected answers (Page 80)
1. Ksh 60 2. (a) 140 m (b) 9 800 m
2
3. 9 bags 4. 98 men
5. 1 200 people 6. 12 tables
7. (a) 360p + 30 000 = 66 000
(b) Ksh 600 8. Ksh 84 000
9. 24 cows 10. 12 cm
100
Extended activity
Instruct learners to visit a nearby butchery or cereals shop. Allow them to do this activity
at their own free time and with the help of their friends.
ey should observe the way a beam balance is used and record the measurements being
taken at the shop or butchery. Tell them to use the measurements they have recorded to
form simple linear equations.
Suggested assessment task
1. Organise learners in groups of not more than ve members. Instruct them to make an
improvised beam balance using local available materials.
2. Let the learners collect materials of dierent masses and put them on the improvised
beam balance until it balances. Instruct them to form simple linear equations with
one unknown.
3. Discuss with the learners and agree on the timelines for this task.
Assessment methods
• Written questions: Ask learners to do the Practice exercises in the Learner’s Book.
• Observation: Move around the classroom guiding learners in the dierent activities as
well as assisting those who may have diculties in forming and solving linear equations.
• Oral questions: Ask probing questions to reinforce the learner’s understanding of the
concepts as well as assess process of learning.
Suggested assessment tools
1. Learner’s prole
A learner’s prole is a useful assessment tool that encourages personalised and
dierentiated learning. A teacher can use a learner’s prole to develop an inclusive
classroom and make the required adaptations to cater for individual learners.
101
A sample learner’s prole is given below.
School: Karibu Junior Secondary School Class: Grade 7 Green
Learner’s name: Isaac Kamau Teacher’s name: Joice Awuor
Subject: Mathematics Strand: Algebra
Sub strand: Linear Equations Learning outcome: Form and solve linear
equations in one unknown.
Criteria Learner’s strengths Learner’s
weaknesses
Learner’s interests
Forming linear
equations.
Excellent knowledge in
forming linear equations.
Challenges in
completing
activities on time.
Talented in role
playing shopping
activities involving
equations.
Solving linear
equations.
Good skills in solving
linear equations.
None observed Loves expressing
himself through
role playing.
Reect on
use of linear
equations.
Very condent in forming
and solving linear
equations in real life.
None observed Enjoys using digital
devices for learning
linear equations.
2. Diagnostic assessment
Use this assessment tool to assist learners who are having challenges with dierent
concepts. is tool can help you in designing individualised instruction and make
intervention for learners who do not meet expectations. A sample is given below.
Learner’s name: Omar Nuidin
Specic learning outcome: Apply linear equations in one unknown
Areas of strengths Areas that need improvement Next steps
Omar has improved in
applying linear equations in
one unknown.
Omar has challenges applying
linear equations involving
multiplication.
Additional tasks
and support to be
provided.
102
2.3 Linear inequalities
Number of lessons: 8
Refer to Learner’s Book pages 81 to 87
Introduction
In Grade 6, the learners were introduced to the meaning and use of dierent inequality
symbols in inequality statements. In this sub strand, learners will enrich their knowledge
on inequalities by forming simple linear inequalities and compound linear inequalities.
ey will also learn how to illustrate simple and compound linear inequalities on a number
line.
ere are several prerequisite skills that will bolster the learners’ condence as they embark
on the concepts in this sub strand. Some of these prerequisite skills include addition,
subtraction, multiplication, division, meaning of inequality symbols and drawing number
lines among others. e activities in this sub strand provide opportunities for learners to
use their prior knowledge and skills to advance their learning of the concepts in this sub
strand.
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) Apply inequality symbols to inequality statements in learning situations.
(b) Form simple linear inequalities in one unknown in dierent situations.
(c) Illustrate simple inequalities on a number line.
(d) Form compound inequality statements in one unknown in dierent situations.
(e) Illustrate compound inequalities in one unknown on a number line.
(f) Use IT devices for more learning on linear inequalities and for enjoyment.
(g) Appreciate use of linear inequalities in real life.
Core competencies to be developed
• Communication and collaboration: as learners discuss about how to form the linear
inequalities.
• Creativity and imagination: as learners draw and represent inequality statements on
a number line.
Pertinent and contemporary issues (PCIs)
• Health education: as learner observe correct dosage in drugs or limits on drug
consumption.
• Gender equality: as learners work in varied groups that promote gender representation
for inclusivity.
103
Link to other subjects
• Language: as learners form linear inequalities from dierent statements and situations.
• Pre-career and pre-technical: as learners measure dierent quantities of items to form
linear inequalities.
Values
• Social justice: as learners apply linear inequalities and as they share resources equally
in groups.
• Integrity: as learners observe the conditions of the given inequalities.
Key inquiry questions
1. How do we use linear inequalities in real life?
2. Why do we use linear inequalities in real life?
Suggestions on facilitating dierentiated learning and learners with special
needs
Facilitating dierentiated learning Facilitating learners with special needs
• Encourage gied learners to be patient
with those who take time to carry out
the group activities.
• Guide the learners through activities in
a manner that encourages all of them
to participate actively.
• Identify each learner’s needs and
characteristics and adjust the content
delivery process accordingly. is will
help learners with dierent abilities to
learn and acquire information in their
own way.
• Encourage learners to use large print
when making cards in Activity 1A and
Activity 5 to assist visually impaired
learners.
• Encourage learners to speak clearly and
audibly during the group activities. e
learners can also use gestures and sign
language if possible, to assist learners
with hearing impairment.
Suggested teaching and learning resources
• Number cards
• Inequality sign cards
Teacher preparation for the lessons in this sub strand
Make sure that the required teaching and learning resources are available prior to the
lesson. In Activity 1 and Activity 5, ensure that you have enough number cards and
inequality cards for each pair of learners. You can involve learners in making of the cards.
104
Suggested learning experiences
Inequality symbols
Refer to Learner’s Book page 81
Activity 1A: In pairs
1. Guide learners to make cards like the ones in the Learner’s Book. Allow them to discuss
the meaning of each inequality symbol.
2. Let the learners take turns to pick any two number cards and place an inequality card
between them to form an inequality statement. This extends their critical thinking
and problem solving competence as they decide the applicable inequality symbol
to be used. Let them have a discussion on the meaning of the inequality statements
they have formed. Let them realise that the ≤ and ≥ symbols are applicable in relating
unknowns to numbers and therefore cannot be put between any two known numbers.
3. Select a few learners to present their inequality statements to the class. Harmonise
their findings by probing and demonstration.
Activity 1B: In groups
1. Ask learners to estimate the heights of different people and items in the environment
2. Let the learners compare the heights using inequality symbols. This promotes the value
of integrity as the learners use the right inequality symbols to relate the two items.
3. Allow the learners to discuss their answers with other learners in their class.
4. Guide the learners through Example 1 and Example 2 on page 82 of the Learner’s Book
to enhance their understanding of the concept.
5. Ask the learners to do Practice exercise 1 in the Learner’s Book.
Practice exercise 1: Expected answers (Page 82)
1.(a) 645 > 89 (b) 4 × 2 > 4 + 3 (c)
2
5
>
3
8
(d) 90 minutes < 5 hours
2. (a) x < 10 (b) y > 1 (c) t ≥ 5 (d) r ≤ 17
3. 87 < 93 (Accept: 93 > 87)
4. w ≤ 1 000
105
Forming simple inequalities in one unknown
Refer to Learner’s Book page 83
Activity 2: In groups
1. Let learners discuss and form an inequality for each of the statements provided in the
Learner’s Book: Select a few learners to present their inequalities to the class.
2. Guide the learners through Example 3 and Example 4 on page 83 of the Learner’s Book
to reinforce the concept of forming simple inequalities in one unknown.
3. Ask individual learners to do Practice exercise 2 in the Learner’s Book.
Practice exercise 2: Expected answers (Pages 83 and 84)
1. g ≤ 33 2. 23 – p > 9 3. 2m + 5 ≥ 21 4. c – 5 < 10
5. q – 6 < 2 6.
1
2
y ≤ 3 7. 10p > 50 8.
1
5
d < 120
Showing simple inequalities on a number line
Refer to Learner’s Book page 84
Activity 3: In groups
1. Guide learners to draw a number line like the one shown in the Learner’s Book. Let
them write down this simple linear inequality; c > 3.
2. Let the learners identify the number 3 on the number line. Guide them to draw an
unshaded circle (○) over number 3 position. Ask them to identify numbers on either
side of the circle that satisfy the inequality c > 3.
3. Let the learners draw an arrow from the circle in the direction of the numbers that
make the inequality true.
4. Let the learners repeat the procedure above to show other inequalities on a number line.
5. Guide the learners to infer that an unshaded circle (○) is used for < or > and a shaded
circle (●) is used for ≥ or ≤.
6. For the learners to internalise the concept, guide them through Example 5 on pages
84 and 85 of the Learner’s Book.
7. Ask individual learners to do Practice exercise 3 in the Learner’s Book.
106
Practice exercise 3: Expected answers (Page 85)
1. (a)
6 7543210
(b)
5 643210
(c)
543210
(d)
543210
(e)
131211 15141098
(f)
765 1098432
2. (a) x < 9 (b) x > 1 (c) x ≥ 36 (d) x ≤ 54
<
Forming compound inequalities
Refer to Learner’s Book page 85
Activity 4: In pairs
1. Guide learners to make cards like the ones in the Learner’s Book.
2. Instruct the learners to read the statement provided in the Learner’s Book. Let them
arrange the cards to represent the statement they have read. Encourage the learners
to use all the cards provided in the arrangement. This develops critical thinking and
problem solving.
3. Ask the learners to compare their arrangement with those of other learners in their
class. Lead them in a discussion to investigate how two simple inequalities can be
combined to form a compound inequality.
4. Consolidate their findings by guiding the learners through Example 6 on page 86 of
the Learner’s Book
5. Instruct individual learners to do Practice exercise 4 in the Learner’s Book.
107
P r ac t i c e e x e r cis e 3: E xp e c t e d a ns w e rs (P a ge 85)
1. (a)
6 7 5 4 3 2 1 0
(b)
5 6 4 3 2 1 0
(c)
5 4 3 2 1 0
(d)
5 4 3 2 1 0
(e)
13 12 11 15 14 10 9 8
(f)
7 6 5 10 9 8 4 3 2
2. (a) x < 9 (b) x > 1 (c) x ≥ 36 (d) x ≤ 54
<
F o rmin g c o m p o und ine q u a li t i es
R ef er t o L e a r n er’s B o o k p a ge 85
A c t iv i t y 4: I n p a irs
1. G uide le a r n er s t o m a k e c a r d s li k e t h e o n es in t h e L e a r n er’s B o o k.
2. I n s t r uc t t h e le a r n er s t o r e ad t h e s t a t em en t p r o v ide d in t h e L e a r n er’s B o o k. L et t h em
a r ra n g e t h e c a r d s t o r ep r es en t t h e s t a t em en t t h e y h a v e r e ad. En co ura g e t h e le a r n er s
t o u s e a l l t h e c a r d s p r o v ide d in t h e a r ra n g em en t. Thi s de v e lo ps cri t i c a l thin k in g a nd
p r o b l e m s o lv in g.
3. A s k t h e le a r n er s t o co m p a r e t h eir a r ra n g em en t w i t h t h os e o f o t h er le a r n er s in t h eir
c l a s s. L e ad t h em in a di s c u s sio n t o in v es t iga t e h o w t w o sim p le in e q u a li t ies c a n b e
co m b in e d t o f o r m a co m p o un d in e q u a li t y.
4. C o n s o lid a t e t h eir f in din gs b y guidin g t h e le a r n er s t hr o ug h E x amp l e 6 o n p a g e 86 o f
t h e L e a r n er’s B o o k
5. I n s t r uc t in di v id u a l le a r n er s t o do P r a c t i c e ex er ci s e 4 in t h e L e a r n er’s B o o k.
Practice exercise 4: Expected answers (Page 86)
1. (a) 4 < x < 10 (b) 15 < y < 15 (c) 2 ≤ q ≤ 6 (d) 11 ≤ f < 16
2. 36 < g < 37 (Accept any letter of the alphabet)
3. 65 < p < 90 (Accept any letter of the alphabet)
4. 9 < x < 13 (Accept any letter of the alphabet)
5. 5 < y < 8 (Accept any letter of the alphabet)
Showing compound inequalities on a number line
Refer to Learner’s Book page 86
Activity 5: In groups
1. Ask learners to read the statement in the Learner’s Book.
2. Let them form a pair of simple inequalities from the statement.
3. Guide the learners to illustrate the simple inequalities on the same number line.
4. Let them join the simple inequalities to form a compound inequality. This enhances
critical thinking and problem solving as they figure out how to illustrate the
compound inequality.
5. Choose a few learners to present their findings to the class. Harmonise their findings
through probing and demonstration.
6. To enhance the learner’s understanding of the concept, take them through Example 7
on page 87 of the Learner’s Book.
7. Ask the learners to do practice exercise 5 in the Learner’s Book.
Practice exercise 5: Expected answers (Page 87)
1. (a)
765 1098432
(b)
2921
22
23
24 25 26 27 28
(c)
16
17
18
19 20 21 22 23
(d)
654 7321
0
108
(e)
10
11
12
13 14 15 16 17 16 17
(f)
32
33
34
35 36 37 38 39 40 41 42
2. (a) Let the initial number of eggs in the tray be x; 21 < x ≤ 30
(b)
20
21
22
23 24 25 26 27 28 29 30 31
Digital learning
Guide learners in using a computer, a tablet or a smartphone to search for a video showing
inequalities on a number line.
ey may use this link: https://tinyurl.com/inequalitiesG7.
Extended activity
1. Give learners the guidelines for the activity. Ask them to count the number of spoons,
plates, cups and other utensils in your kitchen at home. Ask them to use inequality
symbols to compare the numbers.
2. Allow learners to carry out the activity at their own time but give a timeline for
completion. Plan for the presentation of their ndings to other learners, parents or
guardians.
Assessment methods
(a) Written questions: Ask learners to do the Practice exercises in the Learner’s Book.
(b) Observation: Move around the classroom guiding learners in the dierent activities
as well as assisting those who may have diculties.
(c) Oral questions: Ask probing questions to reinforce the learner’s understanding of
the concepts as well as assess the process of learning.
109
Suggested assessment tool
Learner journals or diaries
Guide a learner to create a journal in which he or she can reect, self-assess and review
his or her learning. It could include activities, tasks, projects, target setting, charts and
learning outcomes.
Some of the sentence starters in a Mathematics journal include:
• e rst thing I did was… • I decided…
• I gured out… • I can show this by…
• I noticed… • I compared…
• I thought… • I can use this in my real life when…
A sample learner’s journal in Mathematics is given below.
Learning outcome: Apply inequality symbols in learning situations
What I know: ‘>’ means greater than and ‘<’ means less than.
What I have learnt: ‘≥’ means greater than or equal to and ‘≤’ means less than or equal to.
Proof: If x ≥ 24 then 24 ≤ x.
Reection:
Today evening, as I was walking home from school, I bought x sweets at 2 shillings
each. I spent less than 20 shillings. at is: 2x < 20.
110
3.1 Pythagorean relationship
Number of lessons: 4
Refer to Learner’s Book pages 88 to 96
Introduction
Learners were introduced to squares of whole numbers and fractions in Grade 6. ey
have also learnt about squares and square roots of whole numbers, fractions and decimals
in strand 1 of this grade. ese learning experiences form part of the prerequisite skills
that will be useful in investigating the concept of Pythagorean relationship. In Grade 5 and
Grade 6, the learners studied 2-D shapes, 3-D shapes and angles. Prior knowledge in these
concepts will be helpful as the learners observe and recognise the sides of right-angled
triangles. In this sub strand, the learners will be introduced to Pythagorean relationship.
Pythagorean relationship explains the relation between the sides of aright-angled triangle.
It is also called the Pythagoras eorem. Pythagorean relationship is fundamentally used
to calculate the length of an unknown side of a right-angled triangle.
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) Recognise the sides of a right-angled triangle in dierent situations.
(b) Identify Pythagorean relationship in dierent situations.
(c) Apply Pythagorean relationship to real life situations.
(d) Use IT devices for more learning on Pythagoras eorem and for enjoyment.
(e) Appreciate the use of Pythagoras eorem in real life situations.
Core competencies to be developed
• Critical thinking and problem solving: as learners identify Pythagorean relationship
in dierent situations and make interpretations and inferences.
• Creativity and imagination: as learners create Pythagorean relationship puzzles of
their choice, they develop open mindedness and creativity.
• Learning to learn: as learners apply Pythagorean relationship in real life situations
and as they share learnt knowledge through presentation.
Pertinent and contemporary issues (PCIs)
• Peer education: as learners work in groups to establish the Pythagorean relationship.
• Safety: as learners take care when using the ladder to do various activities on Pythagorean
relationship.
3.0 Measurement
111
Link to other subjects
Pre-career and pre-technical: as learners relate Pythagorean relationship to technical
drawing, building construction and surveying.
Values
• Unity: as learners carry out various activities together, such as drawing triangles,
squares and counting.
• Respect: as learners appreciate each other’s opinions when identifying and applying
Pythagorean relationship in real life situations.
Suggestions on facilitating dierentiated learning and learners with special
needs
Facilitating dierentiated learning Facilitating learners with special needs
• Encourage the time takers to participate
in class activities such as discussions
and role play.
• Identify each learner’s needs and
characteristics and adjust the content
delivery process accordingly. is will
help learners with dierent abilities to
learn and acquire information in their
own way.
• Choose learning strategies and
experiences according to the learning
needs of the learner, resources and
assigned time.
• Encourage learners to use big squares
in Activity 2A to ensure visually
impaired learners can count the unit
squares with ease.
• Encourage learners to speak clearly and
audibly during the group activities. e
learners can also use gestures and sign
language if possible, to assist learners
with hearing impairment.
Key inquiry question
How do we use Pythagorean relationship in real life situations?
Suggested teaching and learning resources
• Rulers
• Papers
• Pair of scissors
Teacher preparation for the lessons in this sub strand
Make sure the materials needed are available for the lesson. For Activity 1, ensure that all
learners have a ruler. In Activity 2A, ensure that the learners have rulers, papers and a pair
of scissors to make the cut outs.
112
Sides of a right-angled triangle
Refer to Learner’s Book page 88
Activity 1A: In pairs
1. Guide learners to draw a right-angled triangle ABC. Let them use a ruler to measure
the length of each side of the triangle. Ask them to identify the longest side.
2. Instruct the learners to brainstorm and discuss the name given to the longest side of
a right-angled triangle. Guide them to mention the name given to each of the other
two shorter sides. This will develop communication and collaboration.
3. Guide the learners to identify the right angle in the triangle. Let them relate the position
of the longest side to the right angle. They should be able to discover that the hypotenuse
as the longest side of a right-angled triangle and it is the side that is opposite to the
right angle. This enhances critical thinking and problem solving.
4. Randomly select a few learners to present their findings to the rest of the class. Reinforce
their findings through probing and demonstration.
Activity 1B: In groups
1. Instruct learners to draw a ladder that is leaning on a wall as shown in the Learner’s
Book. Let them identify and mark the right angle formed on the drawing.
2. Guide the learners to identify the sides of the right-angled triangle that are represented
by the wall, ladder and the horizontal distance from the foot of the ladder to the wall.
3. Allow a few learners to present their ndings in class. Lead them in a discussion to
summarise of the concept.
4. Tell individual learners to do Practice exercise 1 in the Learner’s Book. is enhances
the values of honesty, responsibility and integrity.
Practice exercise 1: Expected answers (Page 89)
1. (a) Line BC is the base; Line AB is the height; Line AC is the hypotenuse.
(b) Line RQ is the base; Line PQ is the height; Line PR is the hypotenuse.
2. For each triangle, check and ascertain that the learner has correctly labelled the
longest side that is opposite the right angle.
3. Check for proportional drawings with correct labelling.
113
e Pythagorean relationship
Refer to Learner’s Book page 90
Identifying the Pythagorean relationship (page 90)
Activity 2A: In pairs
1. Guide learners to draw square A of side 3 cm, square B of side 4 cm and square C of
side 5 cm on a piece of paper. Let them draw smaller 1 centimetre squares on squares
A, B and C. Guide them to cut out squares A, B and C. Caution the learners to observe
their safety and that of others while using cutting instruments. This promotes the life
skill of safety as learners take care to avoid harm.
2. Guide the learners to arrange the cut-outs to form triangle KLM as shown in the
Learner’s Book. This will help develop creativity and imagination.
3. Guide the learners to mark the right angle on triangle KLM. Let them count the number
of 1 centimetre squares on the hypotenuse of the triangle. Let the learners count the
number of 1 centimetre squares on the two shorter sides of the triangle.
4. Let the learners draw the table provided in the Learner’s Book and record their findings.
5. Guide the learners in comparing the number of squares on the hypotenuse to the total
number of squares on the base and the height.
6. Guide the learners to conclude that the number of squares on the hypotenuse is equal
to the sum of the number of squares on the two shorter sides.
Activity 2B: In groups
1. Instruct learners to observe the triangles in the Learner’s Book. Let them measure the
lengths of the sides labelled x, y and z.
2. For each triangle, let the learners compare z
2
and x
2
+ y
2
. Guide them to realise that x
2
+ y
2
= z
2
. This develops critical thinking and problem solving.
3. Ask the learners to draw other right-angled triangles. For each right-angled triangle,
let the learners compare the square of the hypotenuse to the sum of the squares of the
two shorter sides. This enhances creativity and imagination.
4. Allow a few learners to present their finding in class. Probe and guide them to infer
that the Pythagorean relationship states that in a right-angled triangle, the square of
the hypotenuse is equal to the sum of the squares of the two shorter sides.
5. Guide the learners through Example 1 on page 92 of the Learner’s Book to help enhance
their understanding of the concept.
114
6. Instruct individual learners to do Practice exercise 2 in the Learner’s Book.
Practice exercise 2: Expected answers (Pages 92 and 93)
1. (a) e triangle is right angled; 20
2
+ 4.5
2
= 20.5
2
(b) e triangle is not right angled; 11
2
+ 8
2
≠ 14.5
2
(c) e triangle is not right angled; 4
2
+ 6
2
≠ 8.2
2
(d) e triangle is right angled; 24
2
+ 10
2
= 26
2
2. e groups of numbers in (c), (e), (f) and (g) form right-angled triangles.
3. (a) a
2
+ b
2
= c
2
(b) z
2
+ x
2
= y
2
(c) j
2
– l
2
= k
2
(Accept: j
2
– k
2
= l
2
)
(d) f
2
– g
2
= e
2
Applying the Pythagorean relationship (page 93)
Activity 3: In pairs
1. Ask learners to read the story in the Learner’s Book. Let them brainstorm and discuss
how high the top of the ladder is from the foot of the wall. e learners develop social
cohesion and the values of unity and respect as they work together in pairs to nd a
common answer.
2. Randomly select a few learners to present their ndings to the class. Harmonise their
ndings through probing and demonstration. Guide them through Example 2 and
Example 3 on page 94 of the Learner’s Book.
3. In order to assess each individual learner’s level of understanding, ask him or her to
do Practice exercise 3.
Practice exercise 3: Expected answers (Page 95)
1. (a) m = 20 cm
(b) x = 2.5 cm
(c) y = 24 cm
2. (a) x = 40 cm (b) y = 39 cm
3. 25 cm
4. 0.5 m
5. 7.5 m
6. 5 cm
115
Digital learning
1. Guide learners to use a computer, a tablet or a smartphone to search for a game
involving number sequences.
They may use this link: https://www.mathgames.com/skill/8.57-pythagorean-theorem-
find-the-hypotenuse.
2. Walk around the class and encourage the learners to use the digital devices for their
intended purpose. Ensure that the learners are kept safe from insecure or indecent
sites and materials. This promotes cyber security and digital literacy.
Extended activity
Instruct learners to identify objects that form right-angled triangles. Allow them to do this
activity at their own free time and with the help of their parents, guardians or friends. ey
should name and recognise the sides of a right-angled triangle in each object. Tell them
to use sticks or wires to form right-angled triangles. ey should measure the sides of the
triangles and check if the sides satisfy the Pythagorean relationship.
Suggested assessment task
Encourage learners to carry out authentic tasks in order to enhance their vocational skills.
In this sub strand, encourage the learner to use right-angled triangular objects in their
immediate environment to identify, investigate and apply the concept of Pythagorean
relationship.
Assessment methods
(a) Written questions: Ask learners to do the Practice exercises in the Learner’s Book.
(b) Observation: Move around the classroom guiding learners in the dierent activities
as well as assisting those who may have diculties in understanding and application
of Pythagorean relationship.
(c) Oral questions: Ask varied questions to gauge a learner’s understanding of the
concepts as well as assess the process of learning.
Suggested assessment tools
1. Rating scale
A rating scale states the criteria and provides response selections to describe the quality or
frequency of the learner’s work. e teacher indicates the degree of frequency of occurrence
of competencies displayed by the learner.
116
Examples of descriptive words that indicate degree or frequency of occurrence.
• Always, usually, sometimes, never
• Very satisfactory, satisfactory, unsatisfactory
• Very satised, satised, unsatised, very unsatised
• Excellent, good, fair, weak
A sample rating scale is given below.
School: Sasale Secondary School Learning area: Mathematics
Learner’s name: Mercy Nyabile Grade: 7
Strand: measurement Sub strand: Pythagorean relationship
Learning activity: Making a ladder
Competence
(knowledge, skills,
attitudes, values)
assessed
Always (4) Usually(3) Sometimes(2) Never (1)
Selects appropriate
tools (hammer, nails
and pieces of timber).
Uses the tools and
pieces of timber
appropriately.
Positions the ladder
correctly to form a
right-angled triangle.
Comments on the learner’s performance:
Learner’s signature: __________________ Date: ____________
Teachers name: _______________ signature:______________ Date:___________
117
2. Oral presentation evaluation sheet
Use this tool during class presentations to assess the learner’s acquisition of skills,
development of the core competencies, organisation and delivery of concepts. A sample
oral presentation evaluation sheet is given below.
Mathematics presentation sheet
Name of learner: Charles Isaya
Date: 16/07/2022
Content feedback
Excellent
Good
Satisfactory
Fair
e learner exhibits mastery of content
in presentation.
e learner uses relevant and
accurate examples in presentation.
e learner correctly answered
questions asked by peers.
Overall impression
Excellent
Good
Satisfactory
Fair
Information was presented clearly.
Ideas were presented in a logical order.
e learner spoke loudly enough.
3.2 Length
Number of lessons: 6
Refer to Learner’s Book pages 96 to 113
Introduction
is sub strand is not new to learners as they have tackled it in lower and upper primary.
It is important to have them realise that in this grade they will be introduced to additional
units of length other than the ones they are already familiar with. It is imperative to
establish whether or not they can recall the units of length that they had interacted with
in upper primary.
Length being a practical oriented sub strand, it is obvious that the learners will literally
be involved in actual measurement of length and therefore encourage the learner to
participate in the hands-on activities.
Specic Learning Outcomes
By the end of the sub strand, the learner should be able to:
(a) Convert units of length from one form to another involving cm, dm, m, Dm and Hm
in learning situations.
118
(b) Perform operations involving units of length in dierent situations.
(c) Work out the perimeter of plane gures in dierent situations.
(d) Work out the circumference of circles in dierent situations.
(e) Use IT devices for more learning on length and for enjoyment.
(f) Promote use of length in real life situations.
Core Competencies to be developed
• Communication and collaboration: as learners work in groups when measuring
lengths of various objects and as they speak, listen and discuss the relationship between
circumference and diameter.
• Self-efficacy: as learners enhance their personal skills by performing different
operations involving length.
• Critical thinking and problem solving: as learners interpret, infer and relate
circumference to diameter.
Pertinent and contemporary issues (PCIs)
• Social cohesion: as learners work in pairs and in groups to measure the lengths of
various objects.
• Safety: as learners observe their safety and that of others when handling dierent
instruments of measuring length.
• Global citizenship: as learners appreciate units of measurements especially the SI
units of length.
Links to other subjects
• Integrated science: as learners interact with dierent units of measuring length.
• Pre-career and pre-technical: as learners acquire and practice skills needed in tailoring,
constructions, engineering and surveying.
Values
• Integrity: as learners carry out the activities and give the correct measurements of
length.
• Unity: as learners work in groups while measuring the lengths of various objects.
Key Inquiry Questions
1. Why do we use dierent units of measuring length?
2. How do we measure the perimeter of dierent objects?
119
Suggested teaching and learning resources
• Metre Rule • 1-metre sticks • Tape measure
• Rulers • geometrical sets • Scissors
• Strings • Straws • Digital devices
Teacher preparation for the lessons in this sub strand
You can ask learners to bring some of the required teaching and learning resources from
home. is may include pairs of scissors, straws and geometrical sets. In case you have
inadequate metre rules you can improvise by guiding the learners to make 1-metre sticks.
You can also improvise a tape measure using a string or a rope. Make sure you assemble
the required learning materials prior to the lesson.
Make sure you download the videos prior to the lesson and ensure that your digital devices
are in good working condition. When the learners will be using the digital devices, walk
around the classroom and ensure that they use them for the intended purpose. Ensure that
the learners are kept safe from insecure or indecent sites and materials.
Group your learners in groups of mixed abilities making sure that you have taken into
consideration those with special needs.
Suggestions on facilitating dierentiated learning and learners with special
needs
Facilitating dierentiated learning Facilitating learners with special needs
• Most of the activities in this sub strand
will involve the learners’ psychomotor
and observation skills. Take advantage
of such activities to vary the stimulus.
You can further enrich your learning
environment by using outdoor activities
to break the monotony of classroom
learning.
• Use your intuition to group learners
in such a way that the gied learners
are mixed with the time takers.
Nevertheless, make sure that the gied
learners do not over dominate the
activities as the time takers become
passive spectators.
• In doing individual tasks, give more
work to the gied learners as you work
on reinforcing concepts with the time
takers.
• Physically impaired learners must
be put into consideration when
doing Activity 3. Encourage the
other learners to assist them while
using cutting tools. Caution and
safety must be observed as learners
handle cutting tools in order to
avoid injuries.
• While watching the video in the
digital activity, minimise the glare
of the digital device to provide
appropriate lighting for visually
impaired learners.
• In Activity 10, learners are required
to collect circular objects from their
immediate environment. Cater for
learners with albinism by allowing
them to wear hats and long sleeved
shirts.
120
Suggested learning experiences
Converting units of measuring length
Refer to Learner’s Book page 96
Activity 1A: In groups
3. Encourage the learners to mention the units of measuring length that they know. Use
this to establish the learners’ entry behaviour on the concept.
4. Let the learners arrange the units that they have mentioned from the largest to the
smallest. Guide them to create a conversion table for the units of length.
5. Let the learners draw a table like the one in the Learner’s Book. is will encourage
global citizenship as learners appreciate units of measuring length, especially the SI
units.
Activity 1B: groups
1. Ask learners to draw a conversion chart like the one in the Learner’s Book. Use your
discretion to see whether they can come up with the chart on their own and guide
them if need be. Let them state what each symbol in the chart stands for.
2. Challenge the learners to relate the dierent units of length. Let them use the
relationship to work out conversions involving dierent units of measuring length.
3. Allow the learners to discuss and determine why length is measured using dierent
units. Listen carefully to their conversation as they discuss and reinforce accordingly.
Communication and collaboration is developed as learners work together in groups
to convert units of length.
4. Guide the learners through Example 1 and Example 2 on page 98 of the Learner’s
Book.
5. Tell individual learners to do Practice exercise 1 in the Learner’s Book.
Practice exercise 1: Expected answers (Page 98 and 99)
1. (a) 4 500 m (b) 1.2 m (c) 50 m (d) 25 m (e) 825 m (f) 0.018 m
2. (a) 4 Dm (b) 9.4 Dm (c) 7.8 Dm (d) 25 Dm (e) 121 Dm (f) 0.39 Dm
3. (a) 20 000 cm (b) 13 cm (c) 0.85 cm (d) 200 cm (e) 950 cm (f) 17 000 cm
4. 14.3 dm 5. 0.58 Hm 6. 220 Dm 7. 5 250 cm
8. 3.25 km 9. 1 900 m 10. 0.45 Dm
121
Digital learning
Guide the learner to use a computer, a tablet or a smartphone to search for a game involving
converting the units of length.
ey may use this link: https://www.iknowit.com/lessons/c-length-conversions-metric.
html.
Operations involving units of length
Refer to Learner’s Book page 99
Addition involving units of length (page 99)
Activity 2: In groups
1. Let learners study the gure in the Learner’s Book. Give them a few minutes to discuss
and internalise the information in the gure.
2. Instruct the learners to calculate the distance Kimunya covered by driving from his
home to the hospital via the shop. Let them work out the distance in metres from the
shop to the hospital via Kimunya’s home.
3. Allow a few learners to present the group’s ndings to the rest of the class. Emphasise
on adding values of length that have similar units.
4. Guide the learners through Example 3 and Example 4 on page 100 of the Learner’s
Book. Task them to explain what they have learnt.
5. Instruct individual learners to do Practice exercise 2 in the Learner’s Book.
Practice exercise 2: Expected answers (Pages 100 and 101)
1. (a) 7 m 91 cm (b) 14 m 2 dm (c) 23 m 90 cm 2 mm
(d) 10 Dm 21 dm (e) 70 Hm 5 Dm (f) 22 km 118 m
2. 21 m 18 cm 3. 51 dm 9 cm 4. 64 cm 6 mm
5. 11 m 6. 41 Hm 45 m
Subtraction involving units of length (page 101)
Activity 3: In groups
1. Instruct learners to measure and record the length of a drinking straw or stick. Let
them write their answers in centimetres and millimetres. Social cohesion is promoted
as learners work in groups to measure lengths of various objects.
122
2. Guide the learners to use a pair of scissors to cut out the straw into two unequal pieces.
The pertinent and contemporary issue of safety is enhanced as learners handle cutting
tools and different instruments of measuring length.
3. Tell the learners to measure and record the length of one piece of the straw. Ask them
to subtract the length of the piece from the length of the whole straw. Allow them to
measure the length of the other piece of straw. Ask them to compare their measured
value to their calculated value. Self-efficacy is enhanced as the learners perform
different operations involving units of length.
4. Guide the learners through Example 5 and Example 6 on pages 101 and 102 of the
Learner’s Book. Clearly explain to them the steps followed when subtracting units of
length.
5. Tell individual learners to do Practice exercise 3 in the Learner’s Book.
Practice exercise 3: Expected answers (Pages 102 and 103)
1. (a) 5 m 27 cm (b) 3 km 720 m (c) 4 Hm 46 m 47 cm
(d) 3 dm 4 cm (e) 13 cm 7 mm (f) 17 km 57 Dm 5 m.
2. 8.4 cm 3. 2 cm 4. 4 m 84 cm 5 mm
5. 11 m 3 dm 5 cm 6. 3 km 4 Hm 75 m
Digital learning
Guide the learners to use a computer, a tablet or a smartphone to search for a video
involving subtraction of units of length.
ey may use this link: https://tinyurl.com/lengthG7.
Multiplication involving units of length (page 103)
Activity 4: In pairs
1. Ask learners to use a ruler to measure the thickness of a Mathematics textbook in
centimetres and millimetres. The value of integrity is enhanced as the learners give
honest and accurate measurements.
2. Let the learners pile five similar textbooks and work out the height of the pile. To obtain
the height of the pile, the learners should multiply the thickness of each textbook by
the number of textbooks.
3. Allow a few learners to present their findings to the rest of the class. Consolidate their
findings by guiding the learners through Example 7 and Example 8 on pages 103 and
104 of the Learner’s Book.
4. Instruct individual learners to do Practice exercise 4 in the Learner’s Book.
123
Practice exercise 4: Expected answers (Pages 104 and 105)
1. (a) 21 Hm 126 cm (b) 14 m 4 dm (c) 49 km 78 m
(d) 25 Hm 8 Dm (e) 55 Dm 6 m 2 dm (f) 97 m 36 cm 5 mm
2. 6 Hm 120 dm 3. 35
1
5
m (Accept 35.2 m) 4. 13 m 50 cm
5. 14 Dm 4 m
Division involving units of length (page 105)
Activity 5: In groups
1. Instruct learners to use a ruler to measure a string of length 5 dm 6 cm.
2. Guide the learners to cut the string into four parts of equal length. Ensure the safety
of the learners as they handle the cutting tools.
3. Tell the learners to measure the length of one piece of the string. Challenge them to
write a division sentence for the set up. Critical thinking and problem solving is
developed as learners brainstorm and come up with a division sentence fortheir set ups.
4. Allow a few learners to present their division sentences to the class. Consolidate their
findings by guiding them through Example 9 and Example 10 on page 106 of the
Learner’s Book.
5. Assess the learners’ mastery of the concept of division involving units of length by
instructing them to attempt Practice exercise 5 individually.
Practice exercise 5: Expected answers (Page 106)
1. (a) 2 Dm 3 m (b) 3 m 20 cm (c) 3m 7 dm
2. 700 strides 3. 5 Hm 96 m 4. 9 dm 4 cm 5. 0.6 m (Accept 60 cm)
Perimeter of plane gures
Refer to Learner’s Book page 106
Perimeter of a square (page 106)
Activity 6: In pairs
1. Instruct learners to draw a square. Ensure that the learners use a ruler and either a set
square or a protractor to draw the square. Walk around the class to ensure that the
learners are able to draw accurate squares with sides of any length. Self-efficacy is
enhanced as learners make decisions on the length of each side of the square. Instruct
them to use a ruler to measure the sides of the square in centimetres, and a protractor
to measure the angles of the square.
124
2. Emphasise that a square has four equal sides and all the angles should be 90°. Guide
them to work out the distance all around the square.
3. Allow a few learners to present their answers to the rest of the class. Remind them
that perimeter is the distance round a plane figure or shape. Probe them to note that
when calculating the perimeter of a plane figure, they should add the length of all its
sides. Let them deduce that the perimeter of a square is equal to the length of one side
multiplied by 4.
4. Take the learners through Example 11 on page 107 of the Learner’s Book on how to
work out the perimeter of a square.
Perimeter of a rectangle (page 107)
Activity 7
1. Instruct learners to measure the length and the width of their classroom chalkboard.
2. Challenge the learners to work out the perimeter of the chalkboard. Allow them to
discuss and establish a formula to work out the perimeter of a rectangle. is develops
critical thinking and problem solving as the learners come up with the formula.
3. Emphasise that a rectangle has two pairs of opposite sides that are equal. erefore,
the perimeter of a rectangle = 2(length + width).
Perimeter of a triangle (page 108)
Activity 8: In pairs
1. Instruct learners to get two set squares from their geometrical set. Ask them to draw
the outline of each set square on a piece of paper.
2. Let the learners use a ruler to measure the sides of the triangles they have drawn. is
enhances Integrity as learners give the correct measurements
3. Allow the learners to work out the perimeter of each triangle
4. Instruct the learners to outline straight edges of paper or a piece of string around
each of the triangles drawn. ey can then place them on a ruler in order to obtain
the perimeters of the triangles. Let the learners draw other triangles and obtain their
perimeters.
5. Reinforce their understanding by guiding the learners through Example 13 on page
108 of the Learner’s Book.
6. Ask individual learners to do Practice exercise 6 in the Learner’s Book.
125
Practice exercise 6: Expected answers (Page 108 and 109)
1. (a) 40 cm (b) 36 cm (c) 78 cm
2. 14 m 3. 22.75 m 4. 1 510 m
5. 200 cm 6. (a) 30 m (b) 120 m
7. 18 cm 8. 30 m
Perimeter of combined shapes (page 109)
Activity 9: In groups
1. Instruct learners to use a ruler to measure the sides of the figures in the Learner’s Book.
Allow them to work out the perimeter of each figure. The competence of self-efficacy
and the value of integrity are enhanced as learners carry out the task and give correct
measurements.
2. Allow a few learners to present their findings to the rest of the class. This promotes
peer education and enhances self-esteem in the learners. Consolidate their findings
by guiding the learners through Example 14 on page 109 of the Learner’s Book.
3. Instruct individual learners to do Practice exercise 7 in the Learner’s Book.
Practice exercise 7: Expected answers (Page 110)
1. (a) 8.8 cm (b) 7.3 cm (c) 9.7 cm
For number 1 (a), (b) and (c) above accept ± 0.2 cm as the margin of error in the
learner’s measurements.
2. (a) 78 cm (b) 52 cm
3. 136 m
Digital learning
1. Guide the learners to use a computer, a tablet or a smartphone to search for a
game involving perimeter of plane figures. This will enhance their digital literacy
competence.
They may use this link: https://www.iknowit.com/lessons/e-perimeter.html.
2. Walk around the classroom and encourage the learners to use the digital devices for
their intended purpose. Ensure that the learners are kept safe from insecure or indecent
sites and materials. This promotes cyber security and digital literacy.
126
Relationship between circumference and diameter
Refer to Learner’s Book page 111
Activity 10: In groups
1. Ask learners to get circular objects like tins, lids and coins. Instruct them to wrap a
strip of paper or a string once around each object. Let them mark the end of the paper
where it completes the round.
2. Tell the learners to use a ruler to measure the length of the paper that wraps around
each object.
3. Let the learner come up with a strategy to measure the diameter of each object. Allow
them to use their creativity and imagination but guide them if required.
4. Emphasise to the learners that:
• e circumference is the distance around a circular object or shape.
• e diameter is the length of a straight line from one end of a circle to the other
end, passing through the centre. Radius on the other hand is the length of a line
from the centre of a circle to any point on its circumference. e radius is half
the diameter of a circle.
5. Ask the learners to divide the circumference of each object by its diameter. Critical
thinking and problem solving is developed as learners exercise their autonomy and
make an inference that relates circumference to diameter.
6. Guide the learners to draw and fill a table like the one in the Learners’ Book.
7. Allow the learners to share their work with other learners in the class. Assist them to
deduce that when the circumference (C) of any circle is divided by its diameter (d),
the answer is always the same number that is referred to as pi(π). π is about
22
7
.
is means that
C
d
= π
Circumference of Circles
Refer to Learner’s Book page 111
Activity 11: In groups
1. Ask the learner to write down the relationship between the circumference and the
diameter of a circle (
C
d
= π). Allow them to discuss how they can use the relationship
to work out the circumference of a circle. is develops communication and
collaboration as learners speak and listen to one another while working as a team.
127
2. Let the learners use a pair of compasses to draw a circle of radius 3.5 cm. Taking π to
be
22
7
, let them work out the circumference of the circle.
3. Guide the learners to measure the circumference of the circle they have drawn using a
string and a ruler. Let them compare their calculated circumference and their measured
circumference. Allow some learners to present their group’s ndings to other learners
in the class.
4. Harmonise the concepts the learners have learnt using Example 15 and Example 16 on
page 112 of the Learner’s Book.
5. Tell them to work out practice exercise 8 with the help of their friends, parents or
guardians
Practice exercise 8: Expected answers (Page 113)
1. (a) 44 cm (b) 88 cm (c) 22 cm
2. (a) 31.4 cm (b) 47.1 cm (c) 56.52 cm (d) 125.6 cm
3. 220 m 4. 330 m 5. 17.6 m 6. 22 cm
7. 1 650 m 8. 1 500 revolutions 9. 220 m 10. 2.1 cm
Digital learning
Guide learners to use a digital device such as a calculator to compute the circumference of
circles with the specied radii. (Take π = 3.14)
(a) 4.5 cm (b) 12.25 cm (c) 20 cm (d) 28 cm
Extended activity
In this activity the learners shall work with the help of their parents or guardian. ey are
required to establish the perimeter of a room in their houses. Give them specic guidelines
on how to go about the exercise. Creativity and imagination is developed as the learner’s
device ways to measure the perimeter of dierent rooms in their houses at home.
Suggested assessment task
Instead of focusing on grades, a competency-based assessment task emphasises on every
individual learner actively demonstrating mastery of the concepts. In this sub strand,
encourage the learner to come up with a factual explanation on how the dierent units of
length have useful in his or her day to day activities and experiences.
128
Assessment methods
• Written questions: Ask learners to do the practice exercises in the Learner’s Book.
• Observation: Observe the learners as they work and do activities in teams, for example,
when determining the diameter of circular objects.
• Oral questions: Ask question to probe the learners’ understanding of the concepts.
Suggested assessment tools
1. Learner’s prole
A learner’s prole is a summary of the teacher’s opinion on a learner’s mastery of
competencies based on the assessment made. It enables the teacher to understand the
competencies developed by the learner and the challenges he or she is experiencing.
e competencies can be assessed by peers, teachers, parents, and community members.
You may consider using information obtained from an observation schedule, learner’s
journal, checklist, portfolio or a learner’s involvement in projects to construct a learner’s
prole. A sample learner’s prole is given below.
Learner’s Name: Sospeter Kazungu Grade: 7
Teacher: Yassin Seyyid Learning area: Mathematics
Strand: Measurement Sub strand: Length
Learning outcome: Convert units of length from one form to another involving cm, dm,
m, Dm and Hm in learning situations
Criteria Learner’s Strengths Learner’s
Weaknesses
Learner’s
Preferences/Interests
Identifying
units of
measuring
length
He knows all the units
of measuring length.
He confuses the
Decametres and
decimetres.
He prefers using an
acronym to recall the
units of measuring
length in descending
order.
Relating units
of measuring
length
He comfortably
relates the m to km,
Hm, cm and mm
He has challenges
relating the Dm and
dm.
He prefers relating the
units of measurement
to metres.
Converting
units of
measuring
length
He comfortably does
conversions involving
the m with km, Hm,
cm and mm.
He has challenges
doing conversions
of units without rst
relating them to
metres.
He prefers tackling
questions involving
conversion of metres
to other units and
vice versa.
129
2. e Know, Want, Learnt (KWL) Chart
e KWL Chart is a model that helps the learner organise information before, during and
aer a lesson. In this chart learners brainstorm about what they Know about a concept,
what they Want to know, and what they have Learnt by the end of the lesson. is is a tool
that directs the learner to initiate his or her background knowledge, develop a purpose for
learning and summarise the competencies acquired. It gives a learner an opportunity to
self-assess.
At the start of the lesson, instruct the learners to ll in the rst two columns. e last
column should be lled in aer the lesson. A sample of the KWL Chart is given below:
Name of the learner: Sospeter Kazungu Date: 02/09/2022
Learning outcome: Convert units of length from one form to another involving
cm, dm, m, Dm, Hm in learning situations.
What do I already
Know about this
concept?
What do I Want to know about this
concept?
What have I Learnt
during this lesson?
I know how to
convert metres to
centimetres and
vice versa.
I want to know how to convert and
relate other units of length.
e learner may write
that he or she has
learnt how to carry out
conversions involving
cm, dm, m, Dm and
Hm.
3.3 Area
Number of lessons: 8
Refer to Learner’s Book pages 114 to 130
Introduction
In Grade 5, learners were introduced to the square centimetre as a unit of measuring
area. In Grade 6, they explored area of plane shapes and combined shapes. In this sub
strand, they will build on their knowledge of area to larger units of measurement such
as square metres, acres and hectares which are commonly used in real life situations. As
you introduce this sub strand, assist your learners understand the rationale of studying
the larger units of measuring area. Enrich their experiences from the onset by explaining
how the measurement of area in acres, square metres or hectares is applied in surveying,
building and construction, farming and other day to day activities.
130
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) Identify square metres (m
2
), acres and hectares as units of measuring area.
(b) Work out the area of rectangle, parallelogram, rhombus and trapezium in dierent
situations.
(c) Work out the area of circles in dierent situations.
(d) Calculate the area of borders and combined shapes in real life situations.
(e) Use IT devices for more learning on area and for enjoyment.
(f) Appreciate the use of area in real life situations.
Core Competencies to be developed
• Critical thinking and problem solving: as learners cut out a circle into small sectors
and then joining them to create a parallelogram and generate formula of getting the
area of a circle.
• Creativity and imaginations: as learners creatively combine dierent shapes to make
patterns.
• Self-ecacy: as learners enhance their personal skills and demonstrate how to derive
the formula for the area of a circle.
Pertinent and contemporary issues (PCIs)
• Safety: as learners handle dierent instruments or tools to make cut outs and grids of
dierent materials.
• Environmental education: as learners use locally available materials in measuring
the area of dierent shapes.
Links to other subjects
• Pre-career and pre- technical: as learners determine the correct area of dierent
shapes like it is done in surveying.
• Creative arts: as learners use dierent shapes to make patterns and combined shapes.
• Integrated science: as learners relate area to friction and pressure.
131
Values
• Responsibility: as the learner cuts out the small sectors of the circle and joins them
up to form a parallelogram.
• Integrity: as learners work out exact areas of dierent shapes.
• Unity: as learners work in groups and share tasks in measuring the area of objects.
Key inquiry questions
1. What are plane gures?
2. How do we work out the areas of plane gures?
Suggestions on facilitating dierentiated learning and learners with special
needs
Facilitating dierentiated learning Facilitating learners with special needs
• Rene the learning strategies
and experiences to target
dierent senses in the learners.
You may consider using videos,
infographics, realia, audio books,
role-playing, pictures, both
spoken and written directions
to tasks among others. is
variety of resources enables a
large number of learners with
dierent interests to be exposed
to learning experiences that suit
their wide range of preferences.
• Allot time for the learners to
assess themselves and suggest
learning styles that suit their
needs.
• In Activity 2 and Activity 6, learners are
required do make paper cut outs. is can
be challenging to learners with physical
impairment. Allow them some extra
time to perform these activities. Ensure
that they are grouped with other learners
so that their contribution in the entire
learning process is enhanced.
• Use your discretion to see to it that
visually impaired learners are facilitated.
You can encourage other learners to assist
them to visualise the shapes of dierent
plane gures as they calculate the area.
• Ensure that learners with hearing
impairment are sitting in appropriate
positions that gives them an unobstructed
line of view to the speaker. is enables
them to read the lips of speaker.
Suggested teaching and learning resources
Locally available materials such as cartons, geometrical construction instruments,
measuring instruments such as metre rule, measuring tapes, ropes, strings or sticks.
132
Teacher preparation for the lessons in this sub strand
Assemble all the learning materials prior to the lesson. Consider using locally available
materials such as cartons to make square metre cut-outs that can be used in estimating or
measuring actual areas of larger objects.
For every activity, ensure that the sitting arrangement of the learners is conducive for the
type of activity.
In Activity 2, Activity 3 and Activity 7, make sure learners have enough paper and cutting
tools to make cut-outs.
Suggested learning experiences
Square metres, acres and hectares
Refer to Learner’s Book page 114
Activity 1A: In groups
1. Ask the learners to estimate the size of their school compound. This links to the learning
area of Pre-career and pre-technical as learners survey their school compound.
2. Let the learners mention the units that they used to estimate the size of the compound.
Allow them to discuss the units that can be used to measure large areas such as farms
and plots of land. Emphasise to the learners that large areas like farms and pieces of
land can be measured in m
2,
acres or hectares.
Activity 1B: In groups
3. Direct learners to observe the grid in the Learner’s Book. Allow them to study and
interpret the details in the grid.
4. Challenge the learners to estimate the number of square metres that make 1 acre. Let
them also relate square metres to hectares and acres to hectares. Emphasise that
1 hectare = 10 000 m
2
, and that the area covered by an acre of land is about 4 046.86 m
2
.
This means that 1 hectare (ha) of land is about 2.47 acres.
5. Guide the learners to create a conversion table involving square metres, acres and
hectares. Allow different groups to share and discuss their conversion tables.
6. Consolidate their conversion charts through probing and demonstration. Guide them
through Example 1, Example 2 and Example 3 on pages 115 and 116 of the Learner’s
Book. Reinforce the concepts that the learners have learnt by asking them at random
to convert the different units of area.
7. Ask individual learners to do Practice exercise 1 in the Learner’s Book.
133
Practice exercise 1: Expected answers (Page 116)
1. (a) 40 468.6 m
2
(b) 23 000 m
2
(c) 153 780.68 m
2
(d) 71 250 m
2
2. (a) 1 acre (b)
1
2
acres (c) 17.29 acres (d) 123.5 acres
3. (a) 3 Ha (b) 0.1 Ha (c) 11 Ha (d) 0.05 Ha
4. 1.44 Ha
5. 10 acres
Area of plane gures
Refer to Learner’s Book page 116
Area of a rectangle (page 116)
Activity 2: In groups
1. Instruct learners to make 6 square cut-outs of side 1 metre from cartons, cardboards
or timber. is promotes environmental education as learners use locally available
materials to make rectangles.
2. Guide the learners to arrange the cut-outs in two equal rows to form a rectangle. Let
them work out the area of the rectangle by counting the number of unit squares.
3. Instruct the learners to measure the length and the width of the rectangle using a tape
measure. Allow them to multiply the length and the width of the rectangle to get the
area. is encourages the value of integrity as learners give correct measurements.
4. Direct the learners to compare the area they got by counting unit squares with the area
they obtained by multiplying the length and the width.
5. Allow two or three volunteer learners to present their ndings to the rest of the class.
Emphasise that opposite sides of a rectangle are equal and parallel. Let them understand
that the area of a rectangle is obtained by multiplying the length and the width.
6. Guide the learners through Example 4 on page 117 of the Learner’s Book. Clearly
explain to them the steps followed when working out the area of a rectangle.
7. Tell the learners to do Practice exercise 2 in the Learner’s Book with the help of their
parents or guardian. is will promote parental empowerment and engagement.
Practice exercise 2: Expected answers (Page 117)
1. (a) 4 650 m
2
(b) 2 784 m
2
(c) 5 508 m
2
(d) 11 837 m
2
2. 24 ha 3. 20.0 acres 4. 340 m
2
5. 34 m
134
Area of a parallelogram (page 118)
Activity 3: In groups
1. Ask learners to draw and cut out a rectangle. Let them label the rectangle as ABCD.
2. Guide the learners to draw and cut out triangle ABE from rectangle ABCD as shown
in the Learner’s Book. Safety is promoted as learners observe their safety and that of
others as they use cutting tools.
3. Guide the learners to join the cut-out for triangle ABE to line CD to form a new shape
as shown in the Learner’s Book. Let them name the new shape that is formed. Creativity
and imagination is developed as learners form a parallelogram from a rectangle.
4. Ask the learners to brainstorm and compare the area of rectangle ABCD to the area
of the parallelogram. Communication and collaboration is developed as learners
mention whether or not there has been a change in the area of the shape.
5. Guide the learners through Example 5 and Example 6 on pages 118 and 119 of the
Learner’s Book. Emphasise the formula for calculating the area of a parallelogram.
6. Since a parallelogram is made from a rectangle, its area is equal to the area of the
rectangle.
Area of rectangle = length × width
Area of parallelogram = base length × perpendicular height
7. Tell individual learners to do Practice exercise 3 in the Learner’s Book.
Practice exercise 3: Expected answers (Pages 119 and 120)
1. (a) 165 cm
2
(b) 150 cm
2
2. 4.56 ha 3. 37.8 cm
2
4. (a) 45 m (b) 1.78 acres
5. 30 m
Area of a rhombus (page 120)
Activity 4A: In groups
1. Direct learners to observe figure KLMN in the Learner’s Book. Instruct them to trace
the figure on a piece of paper.
2. Let the learners use a ruler to measure the sides of the figure. Let them discuss what
they have observed. Communication and collaboration is developed as learners
express their answers and opinions.
135
3. Instruct the learners to draw diagonals KM and LN as shown in the Learner’s Book.
Let them state the angle at which the diagonals bisect each other. Assist them to deduce
that the diagonals bisect each other at right angles.
4. Tell the learners to measure the length of the diagonals. Let them work out the area of
triangles KLN and LNM and add the areas together. The value of integrity is enhanced
as learners give the actual lengths that they have measured.
5. Guide the learners to work out the area of triangle KOL and multiply it by 4.
6. Direct the learners to discuss the different methods of calculating the area of a rhombus.
Give them a few minutes to discuss and harmonise their findings.
Activity 4B: In groups
1. Direct learners to use gure KLMN in Activity 4A. Ask them to work out a half of the
product of the two diagonals.
2. Guide the learners to draw a perpendicular bisector from K to line LM. Let them
measure the length of the bisector.
3. Guide the learners to multiply the length of the base by the length of the perpendicular
bisector. Instruct them to compare their answers for this activity to the answers they
got in Activity 4A.
4. Allow two or three volunteer learners to present their ndings to the rest of the class.
Let them mention the dierent methods of calculating the area of a rhombus.
Additional information
A rhombus is a parallelogram whose sides are all equal. e length of the
perpendicular bisector is the height. Area of a rhombus can be calculated as follows:
Area of a rhombus = base length × perpendicular height
=
1
2
× the product of the two diagonals
= 4 × area of one of the four equal triangles
= 2 × area of one of the two equal triangles
5. Guide the learners through Example 7 and Example 8 on page 121 of the Learner’s
Book. Emphasise the formula for calculating the area of a rhombus.
6. Tell individual learners to do practice exercise 4 in the Learner’s Book.
Practice exercise 4: Expected answers (Pages 121 and 122)
1. (a) 0.9438 m
2
(b) 1 295 m
2
(c) 0.0096 m
2
(d) 0.084 m
2
2. (a) 2.882 ha (b) 1.6274 ha
3. 96 m
2
4. 864 m
2
5. 20.25 m
2
136
Area of a trapezium (page 122)
Activity 5: In groups
1. Challenge learners to name the shape shown in the Learner’s Book. They should be
able to identify the shape as a trapezium.
2. For each figure in the Learner’s Book, guide the learners as they work out the area of
triangle ABD, area of triangle BCD and the value of;
1
2
(a + b)h. The value of unity is
enhanced as learners work in groups and share tasks in working out the area.
3. Ask the learners to record their results in a table like the one in the Learner’s Book.
Let them compare their answers for the total area of the triangles with the value of
1
2
(a + b)h. Critical thinking and problem solving is developed as they establish the
relationship between the total area of the triangles and the value of
1
2
(a + b)h.
4. Allow a few volunteer learners to present their findings to the rest of the class.
Consolidate their findings through probing and demonstrations. Emphasise to the
learners that:
• A trapezium has one pair of opposite sides that are parallel but not equal.
• To calculate the area, they can add the areas of the triangles that make the trapezium.
• Area of a trapezium =
1
2
× sum of parallel sides × height
5. Take the learners through Example 9 on page 123 of the Learner’s Book. Let them
apply the formula;
1
2
(a + b)h.
6. Let the learners put in practice the concepts learnt through working out Practice
exercise 5 in the Learner’s Book.
Practice exercise 5: Expected answers (Page 124)
1. (a) 1 120.5 m
2
(b) 2 928 m
2
(c) 4 170 m
2
2. 288 cm
2
3. (a) 19 764 m
2
(b) 15 067 m
2
(c) 34 831 m
2
4. 15 cows
Area of a circle (page 124)
Activity 6: In groups
1. Instruct learners to draw a circle of radius 7 cm on a manila paper. Ask them to cut
out the circle.
137
2. Guide the learners to fold and divide the circle into 24 equal parts as shown in the
Learner’s Book. This will not only arouse their curiosity but will also enhance their
critical thinking and problem solving as they figure out what the activity is all about.
3. Guide the learners to open the circle and cut along the folds to get 24 equal parts
of the circle they had at the beginning. Enhance safety as learners handle different
instruments and tools to make and divide cut outs.
4. Guide the learners to arrange the equal parts as shown in the Learner’s Book to form
a shape that looks like a parallelogram. Responsibility is enhanced as the learners
cuts out the small sectors of the circle and joins them up to form a shape that looks
like a parallelogram.
5. Tell the learners to measure the length (l) and the perpendicular height (h) of the shape.
Let them compare the length (l) to half the circumference of the circle. Allow them to
also compare the perpendicular height (h) to the radius of the circle. Give them a few
minutes to analyse their arrangement and make inferences.
6. Guide the learners to derive the formula for calculating area of a circle. This enhances
self-efficacy.
Additional information
Smaller equal parts of a circle can be arranged to form a shape that looks like a
parallelogram.
e two lengths represent the circumference of the circle.
One of the lengths is equal to half the circumference of the circle.
e perpendicular height is equal to the radius of the circle.
Area of the parallelogram = base length × perpendicular height
=
1
2
c × r
=
1
2
× circumference × radius (c = 2πr)
=
1
2
× 2πr × r
1
1
= πr
2
e parallelogram came from the circle and has the same area as the circle. is
means:
Area of the circle = Area of the parallelogram
Area of a circle = πr
2
7. Consolidate their findings by guiding the learners through Example 10 and Example 11
on page 125 of the Learner’s Book. Reinforce the concept that the learners have learnt
by asking them to mention the formula for calculating the area of a circle.
8. Ask individual learners to do Practice exercise 6 in the Learner’s Book.
r
138
Practice exercise 6: Expected answers (Page 126)
1. (a) 3 850 cm
2
(b) 4 658.5 cm
2
(c) 6 506.5 cm
2
2. (a) 77 cm
2
(b) 173.25 cm
2
(c) 19.25 cm
2
3. 3.465 m
2
4. 1 256 m
2
5. 6.16 m
2
Digital learning
1. Guide learners to use a computer, a tablet or a smartphone to search for more
information on the area of a circle.
They may use this link: https://byjus.com/maths/area-of-circle/.
2. Instruct learners to watch a video on cutting out circles into small sectors. Let them
demonstrate how to derive the formula for the area of a circle.
Area of boarders (page 126)
Activity 7: In groups
1. Tell learners to place a Mathematics textbook on a manila paper. Let them trace the
outline of the textbook.
2. Instruct the learners to put a Mathematics exercise book on top of the traced outline.
Let them trace the outline of the exercise book. Communication and collaboration is
developed as work together in groups to ascertain that the uncovered part that remains
when a small area sits on a big area is called a margin or a boarder.
3. Ask the learners to identify the book that has a larger surface. Let them shade the area
of the larger outline that is uncovered by the smaller outline.
4. Guide the learners to use a ruler to measure the length and the width of each outline
and work out the area. Instruct them to also calculate the area of the shaded part.
Critical thinking and problem solving is developed as learners establish that area of
a margin is calculated by subtracting the smaller area from the larger area.
5. Harmonize their findings by guiding the learners through Example 12 on page 127 of the
Learner’s Book.
Area of combined shapes (page 127)
Activity 8: In groups
1. Ask learners to trace the combined shapes in the Learner’s Book. Let them draw dotted
lines to show the plane figures in each combined shape. Creativity and imagination
is developed as learners identify the plane figures that are in each combined shape.
139
2. Guide the learners to calculate the area of each combined shape. Self-efficacy is
developed as learners work out the area of different combined shapes.
3. Allow a few volunteer learners to present their answers to the rest of the class.
Harmonize their findings by probing and demonstrations.
4. Guide the learners through Example 13 on page 128 of the Learner’s Book.
5. Ask individual learners to do Practice exercise 7 in the Learner’s Book.
Practice exercise 7: Expected answers (Pages 128 and 130)
1. (a) 296 m
2
(b) 10.5 cm
2
(c) 224 cm
2
(d) 28 cm
2
2. (a) 7 336 cm
2
(b) 245 cm
2
(c) 280 cm
2
(d) 468 cm
2
3. 144 cm
2
4. (a) 10 800 m
2
(b) 11 224 m
2
(c) 424 m
2
5. 17.27 m
2
6. 20 m (b) 961 m
2
7. 1578.5 m
2
8. 8 624 m
2
Assessment methods
(a) Written questions: Allow the learners to do the practice exercises in the Learner’s Book.
(b) Observation: Walk around the classroom and monitor the learners’ practical skills
as they manipulate objects while carrying out the activities.
(c) Oral questions: Ask question to probe the learners’ understanding of the concepts.
Listen to their feedback and reinforce accordingly.
Adaptation of assessment tools for learners with special needs
Ensure you make modications on the assessment methods and tools used for learners
with special needs. In circumstances where they are incapacitated to do a task based on
physical challenges, purpose to group them with other learners so that their physical
challenge doesn’t lead to a dismal performance.
However, ensure that this privilege is not abused thereby making learners with special
needs to be passive spectators as activities are being done by the rest.
Suggested assessment tool
Assessment rubric
e assessment tool that can be used to interpret and eectively assess the learner’s
performance in a task. It consists of 3 sections namely: Criteria, Descriptors and
Performance Levels.
140
ere are two types of rubrics namely:
(i) Analytic Rubric: Breaks down content or tasks being assessed into parts and assesses
each part separately.
(ii) Holistic Rubric: Assesses overall performance on a task as a single entity. Scores the
overall competencies of the learner.
A sample holistic rubric is given below.
Indicators Exceeds
Expectations
Meets
Expectations
Approaches
Expectations
Below
Expectations
Ability to
identify
square
metre (m
2
),
acres and
hectares
as units of
measuring
area
e learner
accurately and
prociently
identies square
metres (m
2
), acres
and hectares
as units of
measuring area.
e learner
accurately
identies
square metres
(m
2
), acres and
hectares as units
of measuring
area.
e learner
partially
identies
square metre
(m
2
), acres
or hectares
as units of
measuring
area.
e learner
identies
square metres
(m
2
), acres
and hectares
as units of
measuring area
with diculties.
Ability to
work out
the area of
rectangles,
paral-
lelogram,
rhombus
and trape-
zium
e learner
accurately
and prociently
works out the
area of rectangles,
parallelograms,
rhombi or
trapezia.
e learner
accurately
works out
the area of
rectangles,
parallelogram,
rhombus and
trapezium.
e learner
partially works
out the area of
rectangles or
parallelogram
or rhombus or
trapezium.
e learner
works out
the area of
rectangles,
parallelogram,
rhombus and
trapezium
with
diculties.
Ability to
work out
the area of
circles
e learner
accurately and
systematically
works out the area
of circles.
e learner
works out the
area of circles
accurately.
e learner
partially works
out the area of
circles.
e learner
works out
the area of
circles with
diculties.
Ability to
calculate
the area of
borders and
combined
shapes
e learner
accurately and
systematically
calculates the
area of borders
and combined
shapes.
e learner
calculates the
area of borders
and combined
shapes
accurately.
e learner
partially
calculates the
area of borders
and combined
shapes.
e learner
calculates
the area of
borders and
combined
shapes with
diculties.
141
3.4 Volume and capacity
Number of lessons: 8
Refer to Learner’s Book pages 130 to 142
Introduction
e learner has already been introduced to calculating the volume of cubes and cuboids in
Grade 6. In this sub strand, the learners will identify the cubic metre as a unit of volume,
convert m
3
into cm
3
and vice versa, work out the volume of cylinders, identify the relationship
between cm
3
, m
3
and litres and also work out the capacity of dierent containers. Volume
is the space that a 3-D object occupies. Capacity, on the other hand, describes how much
a container can hold. Learners oen get confused by these two concepts. e activities in
this sub strand will enable the learner to compare volume and capacity so as to determine
the relationship. e learner will also be required to think intuitively about the dierence
between volume and capacity.
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) Identify metre cube (m
3
) as a unit of volume in measurements.
(b) Convert metre cube (m
3
) into centimetre cube (cm
3
) and vice versa in dierent situations.
(c) Work out the volume of cubes, cuboids and cylinder in dierent situations.
(d) Identify the relationship between cm
3
, m
3
and litres in real life situations.
(e) Relate volume to capacity in real life situations.
(f) Work out the capacity of containers in real life situations.
(g) Use IT devices for more learning on volume and capacity and for enjoyment.
(h) Appreciate use of volume and capacity in real life situations.
Core competencies to be developed
• Critical thinking and problem solving: as learners create a conversion table involving
units of volume.
• Creativity and imagination: as learners create models of cubes and cuboids using
locally available materials.
Pertinent and contemporary issues (PCIs)
• Environmental education: as the learners use big and small containers of dierent
volume from locally available resources.
• Safety: as learners keep safe while making models of cubes and cuboids.
• Education for Sustainable Development (ESD): as learners observe water conservation
using containers of dierent capacities.
142
Links to other subjects
• Visual arts: as the learners create models of cubes and cuboids using locally available materials.
• Pre-career and pre-technical: as learners create models of cubes and cuboids using
locally available materials.
• Integrated science: as learners work out volume of dierent substances.
Values
• Responsibility: as learners work in groups and share dierent tasks in making models
of cubes and cuboids.
• Peace: as learners discuss and work together as a team to make models of dierent
volumes and capacities.
Key inquiry questions
1. Where do we use volume and capacity in daily capacities?
2. Why do we measure volume?
3. Why do we convert volume to capacity?
Suggestions on facilitating dierentiated learning and learners with special
needs.
Facilitating dierentiated learning Facilitating learners with special needs
• Give both the time takers and the
gied learners equal chances to
participate in class activities. Ensure
that they accommodate one another
and work together despite their
dierences.
• Give gied learners additional
challenging activities and more
responsibilities that require creativity
and exploration to keep them
busy and prevent them from being
frustrated when they are repeatedly
required to carry out simple tasks.
Avoid the temptation of delivering
concepts at the pace of the gied
learners. is will inconvenience the
time takers.
• Identify each learner’s needs and
characteristics and adjust the content
delivery process accordingly. is will help
learners with dierent abilities to learn and
acquire information in their own way.
• Ensure the short-sighted learners sit at the
front of the class and the long-sighted ones
sit at the back to ensure appropriate distance
from the chalkboard during lessons.
• In Activity 2 learners are required to draw
a cube and label its sides. Encourage the
learners to draw large cubes and label them in
large print to assist visually impaired learners.
• Encourage learners to speak clearly and
audibly during the group activities. e
learners can also use gestures and sign
language if possible, to assist learners with
hearing impairment. During the digital
learning activities, provide speech to text
captioning for the videos or you may also
avail headphones with amplied sound for
learners with hearing impairment.
• In Activity 5B encourage the learners who
stammer when reading to read aloud slowly. is
will help them to reduce stress and the symptoms
of stuttering. Encourage other learners to be
patient with learners who stammer.
143
Suggested teaching and learning resources
• Cartons, cardboards
• Cylindrical containers of dierent capacities
• Manila papers, 1 metre sticks/wires/papyrus reeds
Teacher preparation for the lessons in this sub strand
Ask the learners to collect the dierent containers required for the dierent activities in
the sub strand. Assemble the learning materials prior to the lessons. Ensure to organise
the sitting arrangement of the learners according to the type of activities. Group together
learners of mixed abilities and encourage each one of them to participate actively.
e cubic metre (m
3
) as a unit of measuring volume
Refer to Learner’s Book page 130
Activity 1: In groups
1. Ask learners to assemble the cartons, cardboards or pieces of timber that had been
collected prior to the lesson.
Guide the learners to cut out 1 metre square pieces from the cartons, cardboards or
pieces of timber. Let them join the pieces to form a cube like the one shown in the
Learner’s Book. This promotes creativity and imagination
The learners can also make cubic structures using 1 metre sticks or wires, papyrus reeds
or bamboo sticks and cover them using either manila papers or newspapers. This will
promote education for sustainable development. It also enhances environmental
education as they interact with cubes in their surroundings.
2. Guide the learners in calculating the volume of the cube. Randomly choose a few
learners to present their findings to the rest of the class. This will help promote
self-efficacy and peer education. Harmonise their findings through probing and
demonstration.
3. Guide the learners in identifying the cubic metre as a unit of measuring volume.
Converting m
3
into cm
3
Refer to Learner’s Book page 131
Activity 2: In pairs
1. Ask learners to draw a cube and label its sides in metres. Guide them in labelling the
sides of the same cube in centimetres. This promotes critical thinking and problem
solving.
144
2. Let the learners work out the volume of the cube in metres and in centimetres.
3. Guide the learners in comparing the volume of the cube in cubic metres and in cubic
centimetres. Allow them to discuss and infer that 1 000 000 cm
3
make 1 m
3
.
4. Enhance the learners’ understanding by guiding them through Example 1 on page
131 of the Learner’s Book.
5. Ask individual learners to do Practice exercise 1 in the Learner’s Book.
Practice exercise 1: Expected answers (Pages 131 and 132)
1. (a) 6 000 000 cm
3
(b) 11 000 000 cm
3
(c) 500 000 cm
3
(d) 4 500 000 cm
3
(e) 24 000 000 cm
3
(f) 672 000 cm
3
(g) 60 000 cm
3
(h) 5 250 000 cm
3
2. 128 900 000 cm
3
3. 10 975 000 cm
3
4. 560 000 cm
3
Converting cm
3
into m
3
Refer to Learner’s Book page 132
Activity 3: In pairs
1. Guide learners to make practice cards like the ones in the Learner’s Book. Let them
brainstorm and mention the number of cubic centimetres that make a cubic metre.
2. Guide the learners to convert the cubic centimetres on each card into cubic metres.
3. Randomly choose a few learners to present their findings to the rest of the class. This
develops communication and collaboration. Harmonise their findings by guiding
the learners through Example 2 on page 132 of the Learner’s Book.
4. Tell individual learners to do Practice exercise 2 in the Learner’s Book.
Practice exercise 2: Expected answers (Page 132)
1. (a) 4 m
3
(b) 7.5 m
3
(c) 0.4 m
3
(d) 0.0567 m
3
(e) 12.6 m
3
(f) 0.5 m
3
(g) 1.809 m
3
(h) 0.3034 m
3
(i) 0.8753 m
3
2. 4.5 m
3
3. 0.216 m
3
4. 0.01 m
3
145
Volume of a cube
Refer to Learner’s Book page 133
Activity 4: In groups
1. Ask the learners to collect cubes of any dimensions. You can guide the learners to make
the cubes using carton boxes or manila papers prior to the lesson. This will develop
creativity and imagination as come up with innovative ways of making teaching and
learning resources.
2. Let the learner use a ruler to measure the sides of the cube they have collected. This
promotes integrity and honesty as the learners give the correct measurements.
3. Ask the learners to name the shape of each face of the cube. They can name the faces
using letters.
4. Guide them in calculating the area of the base of the cube.
5. Let the learners multiply the area of the base of the cube by its height. This enhances
the values of respect, unity and peace as they work harmoniously with each other.
Lead them into a discussion to ascertain that:
• Volume of a cube = side (s) × side (s) × side (s)
= s
3
6. Reinforce the concept by guiding learners through Example 3 on page 133 of the
Learner’s Book. Consolidate their findings through probing and demonstration.
Volume of a cuboid
Refer to Learner’s Book page 133
Activity 5A: In groups
1. Instruct the learners to observe the cuboid in the Learner’s Book and name the shape
of its base. Ask them to measure the length, width and height of the cuboid.
2. Instruct the learners to calculate the area of the base of the cuboid. Let them multiply
the area of the base that they have obtained by the height of the cuboid.
3. Lead the learners to brainstorm and deduce the formula that can be used to calculate
the volume of a cuboid. Critical thinking and problem solving is developed as the
learners obtain the formula. Emphasise that:
• Volume of a cuboid = area of the base × height
• e base of a cuboid can either be a rectangle or a square.
• Since the area of a rectangle or a square = length × width
• en, the volume of a cuboid = length × width × height
= l × w × h
146
Activity 5B: In pairs
1. Instruct learners to read the story in the Learner’s Book. This will help the learner
develop communication and collaboration as they read aloud. Encourage each of
them to read the story clearly and audibly. To enhance love and respect amongst the
learners, let them be patient with learners who stammer and those who are shy.
2. Let them discuss and calculate the volume of one brick.
3. Guide the learners to brainstorm and calculate the volume each pile of bricks. Guide
them on how to express the volume of each pile of bricks in cubic metres.
4. Harmonise what they have learnt by guiding them through Example 4 on page 134 of
the Learner’s Book to enhance their understanding.
5. Tell the learners to do Practice exercise 3 in the Learner’s Book with the help of their
parents or guardian. This promotes parental empowerment and engagement.
Practice exercise 3: Expected answers (Pages 134 and 135)
1. (a) 1 728 cm
3
(b) 540 cm
3
(c) 1 224 cm
3
(d) 5.4 m
3
2.
Shelf Length Width Height Base area Volume
(a) Q 14 cm 6 cm 5 cm 84 cm
2
420 cm
3
(b) P 18 cm 6.5 cm 8 cm 117 cm
2
936 cm
3
(c) R 60 cm 12 cm 4 cm 720 cm
2
2 880 cm
3
(d)
S 8 m
3
1
2
m 2
1
2
m
28 m
2
70 m
3
3. 15 312 500 cm
3
4. 406 000 000 cm
3
5. 25 600 cm
3
6. 2.5 m
Volume of cylinders
Refer to Learner’s Book page 135
Activity 6A: In pairs
1. Instruct the learners to collect cylindrical objects prior to the lesson. ey can come
with empty tins from home. Ask them to place each cylinder on a piece of paper and
trace its base.
147
2. Instruct the learners to mention the shape traced from the base of the cylinder. ey
should be able to recognise that the base of the cylinder is a circle. Let them come up
with dierent strategies to determine the radius of the circle. is develops creativity
and imagination.
3. Guide the learners in working out the area of the base. ey should be able to use the
formula for area of a circle (πr
2
) with ease.
4. Let the learners measure the height of the cylinder. Ask them to multiply the area of
the base by the height of the cylinder. Let them discuss and ascertain the quantity of
measurement represented by their answer. ey should be able to do this by using
the units in their answer to infer the quantity of measurement. is develops critical
thinking and problem solving.
5. Randomly choose a few learners to present their ndings to the rest of the class. Lead
them into a discussion to determine the formula used to calculate the volume of a
cylinder: Volume of a cylinder = Area of the base × Height
= πr
2
× h
6. Consolidate their ndings through probing and demonstration.
Activity 6B: In groups
1. Guide the learners to use the cylinders that they used in Activity 6A. Ask them to use
a string and a ruler to measure the radius and the height of the cylinders.
2. e learners can also sandwich each cylinder between two textbooks and measure
the length AB, which is the diameter as shown below. is promotes Education for
Sustainable Development (ESD) as learners use locally available resources in learning.
A
Textbook
Textbook
Base of the
cylinder
B
3. Ask the learners to divide the diameter by 2 to get the radius of each cylinder.
4. Instruct them to measure the height of each cylinder and calculate the volume of each
cylinder.
5. Randomly select a few learners to present their ndings to the rest of the class. is
will help develop self-ecacy and peer-education in the learners. For the learners to
internalise the concept, guide them through Example 5 on page 136 of the Learner’s
Book.
6. Tell individual learners to do Practice exercise 5 in the Learner’s Book. is enhances
the values of honesty, responsibility and integrity.
148
Practice exercise 4: Expected answers (Pages 136 and 137)
1. (a) 6 160 cm
3
(b) 21 560 cm
3
(c) 3.08 m
3
(d) 95.04 m
3
2. 75.36 m
3
3. 3.85 m
3
4. 0.1386 m
3
5. 23 cm
Relationship between cm
3
and litres
Refer to Learner’s Book page 137
Converting litres into cm
3
Activity 7: In groups
1. Ask learners to collect dierent containers of capacity 100 cm
3
and 1 litre, prior to the
lesson. Let them label the containers as either 100 cm
3
or 1 litre. Ask them use the
smaller container to ll the larger container with water. Encourage learners use water
sparingly and avoid spillage. is promotes Education for Sustainable Development
and enhances the values of responsibility and integrity.
2. Ask the learners to count the number of 100 cm
3
containers that can ll a 1 litre bottle.
Guide them to interpret their results and make the inference that 1 000 cm
3
make 1
litre.
3. Harmonise the concept learnt using Example 6 on page 137 of the Learner’s Book.
4. Tell individual learners to do Practice exercise 5 in the Learner’s Book.
Practice exercise 5: Expected answers (Page 138)
1. (a) 5 000 cm
3
(b) 14 000 cm
3
(c) 250 cm
3
(d) 2 400 cm
3
(e) 9 600 cm
3
(f) 894 cm
3
2. 18 000 cm
3
3. 48 350 cm
3
4. 250 cm
3
5. 203 500 cm
3
Converting cm
3
into litres (page 138)
Activity 8: In groups
1. Guide learners to re-use the containers that they used in Activity 7. Each group should
have a 1 litre container and several 100 cm
3
containers. Ensure that all the containers
are labelled accordingly.
2. Instruct the learners to ll the 1 litre container with water. Let them empty water from
the 1 litre container into the 100 cm
3
containers. is develops critical thinking and
problem solving.
149
3. Let the learners count the number of 100 cm
3
containers it takes to empty a 1 litre bottle.
4. Guide learners through Example 7 on page 138 of the Learner’s Book to help improve
understanding of the concept.
5. Tell individual learners to do Practice exercise 6 in the Learner’s Book.
Practice exercise 6: Expected answers (Pages 138 and 139)
1. (a) 3 litres (b) 12 litres (c) 1.306 litres
(d) 23.45 litres (e) 0.532 litres (f) 0.1 litres
2. 4 litres 3. 56 litres 4. 10.5 litres
5. 0.54 litres
Relationship between m
3
and litres
Refer to Learner’s Book page 139
Converting m
3
into litres (page 139)
Activity 9: In groups
1. Instruct learners to collect dierent 1 litre containers that have the shape of a cube or
a cuboid prior to the lesson.
2. Ask them to measure the length, width and height of the containers they have collected.
is enhances the value of integrity and responsibility in the learners as they give
honest and accurate dimensions.
3. Instruct the learners to calculate the volume of the containers in cubic centimetres. Let
them convert the volume into cubic metres.
4. Guide the learners to compare the volume and the capacity of the containers. Let a few
learners present their ndings to the rest of the class. Lead them into a discussion to
discover that 1 m
3
= 1 000 litres. is develops communication and collaboration.
5. Reinforce the concept by guiding learners through Example 8 on page 139 of the
Learner’s Book.
6. Tell individual learners to do Practice exercise 7 in the Learner’s Book.
Practice exercise 7: Expected answers (Pages 139 and 140)
1. (a) 7 000 litres (b) 28 000 litres (c) 875 litres
(d) 11 200 litres (e) 15 700 litres (f) 12 litres
2. 75 litres
3. 13 824 litres
4. 9 000 litres
5. (a) 2 310 cm
3
(b) 2.31 litres
150
Converting litres into m
3
(page 140)
Activity 10: In groups
1. Instruct learners to draw a table like the one shown in the Learners Book. Let the
learners brainstorm and discuss how the conversions can be done. Let them complete
the table. is enhances critical thinking and problem solving.
2. Guide the learners to make a conversion table involving cm
3
, m
3
and litres.
3. Let the learners present their tables to the rest of the learners in class. is will enhance
self-ecacy and peer-education. Consolidate their ndings through probing and
demonstration.
4. Guide the learners through Example 9 on page 140 of the Learner’s Book.
5. Instruct individual learners to do Practice exercise 8 in the Learner’s Book.
Practice exercise 8: Expected answers (Page 140)
1. (a) 9 m
3
(b) 35 m
3
(c) 27.5 m
3
(d) 80.05 m
3
(e) 0.02 m
3
(f) 0.205 m
3
2. 8.506 m
3
3. 32.4 m
3
4. 0.0172 m
3
Capacity of containers in real life situations
Refer to Learner’s Book page 141
Activity 11: In pairs
1. Instruct learners to observe the containers provided in the Learner’s Book. Ask them
to write the formula that can be used to calculate the volumes of each of the containers.
2. Guide learners into a discussion about how volume can be used to determine the
capacity of a container. is enhances critical thinking and problem solving.
3. Guide the learners through Example 10 on page 141 of the Learner’s Book.
4. Instruct individual learners to do Practice exercise 9 in the Learner’s Book.
Practice exercise 9: Expected answers (Page 141)
1. 10.5 litres 2. 141 300 litres 3. 15.16 litres 4. 6 600 litres
Digital learning
1. Guide learners to use a computer, a tablet or a smartphone to search for a video involv-
ing working out capacity of containers.
ey may use this link: https://tinyurl.com/capacityG7.
151
2. Walk around and encourage the learners to use the digital devices for their intended
purpose. Ensure that the learners are kept safe from insecure or indecent sites and
materials. is promotes cyber security and digital literacy.
Extended activity
Instruct learners to collect containers of dierent capacities at home or in the
school compound. Allow them to do this activity at their own free time and with the help
of their parents, guardians or friends.
ey should determine and record the volume of each container in cubic centimetres. Tell
them to compare the volume and the capacity of each container and make an inference.
Suggested assessment tasks
e Extended activity in the Learner’s Book is an authentic task that the learner is required
to perform. It gives an opportunity for the learners to demonstrate that they have the
understanding and the ability to apply their learning in relevant and meaningful ways. Use
the learners’ results to assess their understanding by letting them:
1. Explain the method they used to determine the volume and the capacity of each
container.
2. Explain why they think their answers are correct.
Assessment methods
(a) Written questions: Ask learners to do the Practice exercises in the Learner’s Book.
(b) Observation: Walk around the classroom and monitor the learners’ practical skills
as they carrying out the activities.
(c) Oral questions: Ask questions to probe a learner’s understanding of the concepts.
Suggested assessment tool
Rating scale
A rating scaleis an assessment tool that allows teachers to indicate the frequency of the
knowledge, skills, attitudes and values displayed by the learner. A sample rating scale is
given below:
(a) Administrative information
School: Jumba Junior Secondary School Class: Grade 7 Central
Learner’s name: Simon Bateri Teacher’s name: Josephine Kago
Subject: Mathematics Strand: Measurement
Sub strand: Volume and Capacity Learning activity: Relating volume to
capacity in real life
152
(b) Competency assessed
(knowledge, skills, attitude, values)
Always
4
Usually
3
Sometimes
2
Never
1
• e learner can relate volume to
capacity
• e learner completes the activity
within the assigned time.
• e learner conserves water when
relating capacity to volume.
(c) Comment on learner’s performance
Learner’s signature: _______________ Date: _______________
Teacher’s signature: _______________ Date: _______________
3.5 Time, Distance and Speed
Number of lessons: 8
Refer to Learner’s Book pages 142 to 151
Introduction
e learners are already familiar with the concepts of time and distance. In upper primary,
time and distance were taught in two dierent sub strands. is sub strand looks to bring
together and relate the concepts of time and distance so as to introduce the concept of
speed. erefore, lay emphasis on learners identifying and recognising the relationship
between time, distance and speed.
e learning activities in this sub strand engage learners in individual, pair and group
tasks that allows most learners to absorb the concepts. Learners will also be given with
an opportunity to apply the concepts that they have learnt in a variety of ways including
practical and written assignments. In the course of delivering the concepts in this sub
strand, it is advisable to use diverse learning resources and varied pedagogical approaches
to make the experiences more engaging.
Specic Learning Outcomes
By the end of the sub strand, the learner should be able to:
(a) Identify units of measuring time in real life situations.
(b) Convert units of time from one form to another in learning situations.
(c) Convert units of measuring distance in learning situations.
(d) Identify speed as distance covered per unit time in dierent situations.
(e) Work out speed in km/h and m/s in real life situations.
153
(f) Convert units of speed from kilometres per hour (km/h) to meters per second (m/s)
and vice versa in real life situations.
(g) Use IT devices to learn more on time, distance and speed for planning.
(h) Appreciate the use of time, distance and speed in real life situations.
Core competencies to be developed
• Critical thinking and problem solving: as learners create conversion tables and as
they interpret, infer, relate and determine distance, time and speed.
• Self-ecacy: as learners observe punctuality in attending to dierent activities.
Pertinent and Contemporary Issues (PCIs)
• Disaster Risk Reduction (DRR) and Safety: as learners observe safety on the road
and as they control the speed of dierent machines.
Links to other subjects
• Integrated science: as learners observe time as they carry out dierent experiments.
• Sports and Physical Education:as learners participate in athletics and work out their speeds.
Values
• Patriotism: as learners observe road safety rules including speed limits.
• Integrity: as learners observe punctuality and work out correct distances.
Key inquiry question
1. Why do we relate distance, time and speed?
2. What is the importance of speed in daily activities?
Suggestions on facilitating dierentiated learning and learners with special
needs
Facilitating dierentiated learning Facilitating learners with special needs
• Engage learners in the varied
activities provided in the Learner’s
Book so that the specic interests of
all the learners are satised.
• Give additional tasks and activities
to gied learners. Simultaneously,
you can use individualised
approach to support the time
takers. is way all learners will be
actively engaged.
• Ensure that all learners are involved
in the activities regardless of their
impairments. Treat all learners as equals
and encourage the learners to do the
same.
• In Activity 1 and Activity 4A, consider
using talking clocks or talking watches
to cater for learners with visual
impairment.
154
Suggested teaching and learning resources
• Field
• Measuring tapes
• Analogue and digital clocks
• Digital watches
• Stopwatches or clocks
Teacher preparation for the lessons in this sub strand
Ensure that the instruments for measuring time are assembled prior to the lesson. In case
you have insucient wall clocks you can improvise by having your learners make them
on a cardboard or manila paper sheet. If need be you can guide your learners to prepare
charts and conversion tables in advance. In case you shall use videos during the lessons,
download the videos prior to the lesson and ensure that your digital devices are in good
working condition.
Make sure you review the prerequisite knowledge in prior lesson. Manila papers and
writing materials required for creating charts and conversion tables should be availed
beforehand.
e learners are already conversant with the concept of length. If possible, give them
an assignment prior to the lesson so that they can estimate the distance as they walk
from home to school or to other specied destinations. is way Activity 3 will be
done with ease. For Activity 4, mark tracks that will be used for running prior to the
lesson. Ask learners to come with sporting attire on the scheduled day of the lesson.
You may consider scheduling the lesson on a day that learners also have a Sports and
Physical Education lesson. Some of the activities in this sub strand will involve actual
participation of learners in sporting activities. Organise yourself so that the learners are
well informed of such activities so that they are not only psychologically prepared but
also prepared in terms of the correct dressing. Ensure that your learners are grouped in
such a way that their individual dierences are taken care of.
Suggested learning experiences
Units of measuring time
Refer to Learner’s Book page 142
Activity 1: In groups
1. Provide digital and analogue clocks or watches. Ask learners to identify the hour,
minute and seconds hands in an analogue clock. Let them identify the unit of time
shown by each hand of the clock.
2. Instruct the learners to read and tell the time shown by the digital clock. Let them
identify the units that have been used to tell the time.
155
3. Allow the learner to discuss the units of time that they know with other groups. is
develops communication and collaboration.
Converting units of time
Refer to Learner’s Book page 143
Activity 2: In pairs
1. Allow learners to use their prior knowledge to come up with a conversion chart like
the one shown in the Learner’s Book.
2. Ask the learners to use the conversion chart to complete the table in the Learner’s
Book as shown below.
Seconds, Minutes and Hours
What I have What I want What I do
Seconds Minutes Divide by 60
Minutes Seconds Multiply by 60
Minutes Hours Divide by 60
Hours Minutes Multiply by 60
Seconds Hours Divide by 3 600
Hours Seconds Multiply by 3 600
Allow the learners to brainstorm and determine how many seconds make an hour.
4. Allow a few learners to present their ndings to the rest of the class. is enhances
communication and collaboration. It also promotes self-ecacy and peer education.
Consolidate their ndings by guiding the learners through Example 1 and Example 2
on pages 143 and 144 of the Learner’s Book.
5. Tell the individual learners to do Practice exercise 1 in the Learner’s Book.
Practice exercise 1: Expected answers (Page 144)
1. (a) 300 seconds (b) 1 410 seconds (c) 1 812 seconds
(d) 3 600 seconds (e) 7 650 seconds (f) 1 620 seconds
2. (a) 3 minutes (b) 1
1
2
minutes (c) 2
1
2
minutes
(d)180 minutes (e) 450 minutes (f) 12 minutes
3. (a)10 hours (b) 4
7
12
hours (c) 2
2
5
hours
(d) 1 hour (e) 1
1
2
hours (f)
1
6
hours
4. 3 000 seconds 5. 90 minutes 6.
7
12
of an hour
7. 5
1
4
hours 8. 162 seconds
156
Converting units of measuring distance
Refer to Learner’s Book page 145
Activity 3: In pairs
1. Ask the learner to estimate the distance in metres from the school to a nearby market
or shopping centre. Tell the learners to convert the estimated distance into kilometres.
Creativity and imagination is developed as learners deliberate and estimate distances.
2. Guide the learners estimate the distance in kilometres from their home to the chief’s
oce. Instead of the chief’s oce, the learners could estimate the distance to a local
church, mosque or dispensary. Allow the learners to convert the estimated distance
into metres.
3. Guide the learners through Example 3 and Example 4 on page 145 of the Learner’s Book.
4. Instruct individual learners to do Practice exercise 2.
Practice exercise 2: Expected answers (Pages 145 and 146)
1. (a) 10 000 m (b) 27 000 m (c) 1 800 m
(d) 6 850 m (e) 12 250 m (f) 15 125 m
2. (a) 4 km (b) 19.25 or 19
1
4
km (c) 8.5 or 8
1
2
km
(d) 30.05 km (e) 0.924 km (f) 0.48 km
3. 405 200 m 4. 2 500 m 5. 80 500 m
6. 1.27 km 7. 3 260 m 8. 0.95 km
Speed
Refer to Learner’s Book page 146
Activity 4A: In groups
1. Ask learners to use a tape measure or a 1 metre stick to measure a distance of 100 m on
the school playground as shown in the Learner’s Book.
2. Allow the learners to take turns to run from the starting point to the nishing point.
is promotes health education as learners participate in athletics and perform
physical exercises.
3. Guide the learners to use a stopwatch to measure the time in seconds, taken by each
learner in the group to cover the distance. Tell them to record the time taken by each
learner to cover the distance. is inculcates the value of integrity in the learners as
they give correct readings of time for each participant without bias or prejudice.
4. Guide the learners to work out the distance in metres covered by each learner in one
second. Let them discuss how fast each learner in the group can run.
157
5. Allow the learners to brainstorm and infer that speed is the distance an object covers in
a given time. Critical thinking and problem solving is developed deduce that speed is
calculated by dividing the distance covered by the time.
Activity 4B: In groups
1. Direct learners to refer to the information on the time taken by dierent means of
transportation to cover 400 km as mentioned in the Learner’s Book. Ask them to work
out the speed in km/h for each means of transportation. Self-awareness is enhanced as
learners determine the speed of dierent means of transportation.
2. Allow the learners to discuss and identify the means of transportation that would be
the best to use for transporting fresh owers. is develops creativity and imagination.
3. Let the learners identify the means of transportation that travels at the slowest speed.
Allow a few learners to present their ndings to the rest of the class. Encourage other
learners in class to ask questions to the learner who is presenting. Allow the learner who
is presenting to respond to the questions and give guidance if required. is enhances
communication and collaboration. It also promotes self-ecacy and peer education.
4. Consolidate their ndings by guiding the learners through Example 5 and Example 6
on pages 147 and 148 of the Learner’s Book.
5. Instruct individual learners to do Practice exercise 3 in the Learner’s Book.
Practice exercise 3: Expected answers (Page 148)
1. 72 km/h 2. 48 km/h 3. 16 m/s 4. 2.4 km/h
5. 1 m/s 6. 545 km/h 7. 100 km/h 8. 53.5 km/h
Converting of units of speed
Refer to Learner’s Book page 148
Converting km/h to m/s (page 148)
Activity 5: In groups
1. Direct learners to observe a picture of a speedometer shown in the Learner’s Book
Probe them to explain where they have seen the speedometer and what it is used for.
You can choose to use a video or an animation of the speedometer of a moving vehicle.
2. Let the learners identify the unit of measuring speed that is shown in the speedometer.
Guide them to convert the speed shown on the speedometer to m/s.
3. Harmonise their findings by guiding them through Example 7 on page 149 of the
Learner’s Book.
158
Practice exercise 4: Expected answers (Page 149)
1.
Speed in km/h 18 km/h 81 km/h 108 km/h 72 km/h 31.5 km/h
Speed in m/s 5 m/s 22.5 m/s 30 m/s 20 m/s 8.75 m/s
2. 26
2
3
m/s 3. 12.5 m/s 4. 33
1
3
m/s 5. 42.5 m/s
Converting to m/s into km/h (page 150)
Activity 6: In groups
1. Allow learners to read the story in the Learner’s Book. Ask them probing questions to
deepen their comprehension of the story.
2. From the story, instruct the learners to calculate; the perimeter of the eld in metres,
Simeone’s speed in m/s, perimeter of the eld in kilometres, and the number of hours
Simeone took to jog around the eld.
3. Guide the learners to divide the distance covered in kilometres by the time taken in
hours to get Simeone’s speed in km/h.
4. Tell the learners to compare the speeds in m/s and in km/h. Lead them in a
discussion on how to convert m/s to km/h.
Practice exercise 5: Expected answers (Page 151)
1.
Speed in m/s 5 m/s 10 m/s 18 m/s 36 m/s 12.5 m/s
Speed in km/h 18 km/h 36 km/h 64.8 km/h 129.6 km/h 45 km/h
2. 144 km/h 3. 24 km/h 4. 6 km/h 5. 1 224 km/h
Suggested assessment task
Instruct learners to make posters about observing safety on the road in relation to speed.
Guide them to display the posters during the next parents’ meeting.
Assessment methods
(a) Written questions: Ask learners to do the practice exercises in the Learner’s Book.
(b) Observation: Walk around the classroom and monitor the learners’ practical skills
as they carry out the activities like measuring speeds of their peers.
(c) Oral questions: Ask questions to probe the learners’ understanding of the concepts
and reinforce accordingly.
159
Suggested assessment tool
Learner observation sheet
is tool gathers information based on observation of individual or group of learners.
You can use this tool to assess their behaviour, values and competency in Mathematics
and then analyse the feedback to adjust your pedagogy to suit diverse needs of individual
learners. A sample observation sheet is given below.
Mathematics observation sheet
Name of learner: Joseph Segei Date: 05/10/2022
Skill Mastered Needs practice Needs to be retaught
Working out speed in km/h
and m/s
P
Observations: e learner needs more practice in working out speed in m/s.
3.6 Temperature
Number of lessons: 4
Refer to Learner’s Book pages 152 to 158
Introduction
In their daily activities, learners tell the hotness or coldness of objects using arbitrary
methods such as seeing and touching. ey also describe the weather in their surroundings
in terms of temperature. Even though Temperature is a new sub strand to the learners,
these real life experiences form part of the learners’ prior knowledge in this concept.
Understanding the basics of this concept is vital, and as a result the learning activities
have been carefully arranged to enable the learner to progress from known to unknown.
You can use the concepts in this sub strand to sensitise the learners on the phenomenon
of climate change and harsh weather conditions. Enlighten them on the need to exercise
good citizenry on matters of environmental conservation and become ambassadors of the
same in their local communities.
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) Describe the temperature conditions of the immediate environment as warm, hot or
cold.
(b) Compare temperature using hotter, warmer, colder and same as in dierent situations.
160
(c) Identify units of measuring temperature as degree Celsius and Kelvin in dierent
situations.
(d) Convert units of measuring temperature from degree Celsius to Kelvin and vice-versa.
(e) Work out temperature in degree Celsius and Kelvin in real life situations.
(f) Use IT devices to learn about temperature conditions of dierent places.
(g) Appreciate temperature changes in the environment.
Core competencies to be developed
• Communication and collaboration: as learners work together in groups and use tools
of measuring temperature.
• Digital literacy: as learners interact with technology and determine the temperature
of dierent places and objects using digital thermometers.
Pertinent and Contemporary Issues (PCIs)
• Self-awareness: as learners take their body temperatures.
• Safety: as learners work in groups and exercise caution when dealing with hot
substances.
Links to other subjects
• Health Education: as learners consider their body temperatures to establish their
health status and dressing appropriately.
• Social Studies: as learners consider climatic temperature changes and adverse weather
conditions.
Values
• Responsibility: as learners carefully handle tools of measuring temperature.
• Integrity: as learners give correct measurements of temperature.
Key inquiry questions
1. How does temperature affect our everyday lives?
2. How do we measure temperature?
161
Suggestions on facilitating dierentiated learning and learners with special
needs
Facilitating dierentiated learning Facilitating learners with special needs
• In Activity 1A, the learner is
guided to move to the eld and
observe the temperature in the
environment and discuss the
temperature conditions as warm,
hot or cold. Make maximum
utility of this chance to engage
your kinaesthetic learners
actively as they showcase their
psychomotor skills in the hands
on activities.
• Take advantage of the outdoor
activities to vary the stimulus
and learning environment from
the classroom setting. is
will be a good time to evaluate
your learners’ self-ecacy and
leadership skills.
• If you are planning to use an analogue
thermometer to measure temperature,
preferably get an alcohol thermometer
because the red liquid is more visible
compared to the silver colour of a
mercury thermometer. For visually
impaired learners, you can consider
providing them with a hand lens to
magnify the image and make clear
observations of the readings.
• In Activity 2, caution, guide and counsel
learners with behavioural disorders. Give
them a clear set of rules and expectations
to ensure their safety and that of others
while comparing the temperature of hot,
warm and cold substances.
Suggested teaching and learning resources
ermometers, water containers including those that can be used for heating, source of
heat, ice or ice cold water
Teacher preparation for the lessons in this sub strand
e thermometer will be a vital teaching and learning resource in this sub strand. Ensure
that you have assembled various types of analogue and digital thermometers including a
thermo gun if it is available. Get pictures or photographs of other types of thermometers
that are not available within your locality. Ensure that you have thermometers that are
functional as Activity 4 will be done practically by the learners so that the concept is well
illustrated and understood.
Have the learners understand how to use dierent types of thermometers to measure
temperature. Observation skills must be emphasised to give the learners an insight and basic
skills of measurement of physical quantities in the STEM subjects. You can also explain to
them the science behind the working of the mercury or alcohol thermometers since they
will probably nd it fascinating to see how the liquid levels rise and fall depending on the
various temperature conditions.
162
As you group learners for Activity 3, ensure each group has a responsible learner who can
serve as the group leader. Instruct the group leaders to encourage their peers to handle
thermometers with utmost care to avoid breakages. is is to ensure that thermometers
are well taken care of and the learners are kept safe. Keep a close eye on the learners as they
do this activity and ensure that they do not come into contact with mercury or pieces of
glass in case their thermometers break.
Temperature conditions in the environment
Refer to Learner’s Book page 152
Activity 1A: In groups
1. Allow learners to observe the temperature condition around their school. Ask them to
describe the temperature condition as hot, warm or cold. This links to Social Studies
as learners consider climatic temperature changes.
2. Allow the learners to explain their answers to other learners in their class. This develops
the competence of communication and collaboration.
Activity 1B: In pairs
1. Direct learners to observe the pictures provided in the Learner’s Book. Ask them to
discuss what they can see in each of the pictures.
2. Let them deliberate and describe the temperature condition in each picture.
3. Allow the learners to discuss and determine how temperature affects their day to day
activities. This enhances critical thinking and problem solving competence. Tell
them to share their answers with other learners in the class.
Comparing temperature
Refer to Learner’s Book page 153
Activity 2: In groups
1. Ask learners to rub the palms of their hands together for about a minute and then
touch their faces. Let them mention whether their faces are warmer or colder than their
hands and if their hands warmer or colder than their faces. This enhances the value
of integrity as learners compare the temperature and give honest answers. Encourage
learners to touch their cheeks and caution them not to touch their mouths, noses or
eyes. This will prevent the spread of Covid-19.
2. Allow learners to wash their hands with running water from a tap. Tell them to compare
the temperature of their hands to that of the water.
163
3. Take learners to the school kitchen. With the help of cooks and other workers in the
kitchen, guide learners to compare the temperature of water in different containers. Let
them use terms such as use hotter, warmer, colder and same as. Ensure that learners
are kept safe from hot substances while doing this activity. You can ask workers at the
kitchen and other teachers to assist you in monitoring the learners.
4. Tell individual learners to do Practice exercise 1 in the Learner’s Book.
Practice exercise 1: Expected answers (Pages 153 and 154)
1. (a) hotter than (b) colder than (c) same as
2. (a) warmer (b) colder (c) hotter
Extended activity
Ask learners to keep a daily record of temperature conditions in the environment at
8.00 a.m. and 1.00 p.m. and 4.00 p.m, for a period of one week. Let them compare the
temperature conditions for the dierent days of the week and record in a journal.
Based on the learners’ responses you can encourage them to appreciate the signicance of
the dierent temperature conditions in the environment. For example, ‘How hot weather
enables grains and clothes to dry quickly’ and ‘how hot or cold weather inuences their
dressing’.
Units of measuring temperature
Refer to Learner’s Book page 154
Activity 3: In groups
1. Provide learners with thermometers like the ones in the Learner’s Book. Allow them
to name the instrument and mention its use. They should be able to discover that the
instrument is called a thermometer and it is used to measure temperature.
2. Ask the learners to identify the units that they can see on the thermometers. Guide
them to observe that the units of measuring temperature are degrees Celsius or degrees
Centigrade (written in short form as °C) and Kelvin (written in short form as K).
3. Allow the learners to present their findings to other learners in the class. Harmonise
their findings by asking probing questions. Demonstrate to them that zero degrees
Celsius can be written in short form as 0 °C and a temperature of three hundred Kelvin
can be written in short form as 300 K.
164
Extended activity
Ask the learner to use a thermometer to take the temperature of his or her body aer doing
dierent physical exercises at dierent times of the day. Let him or her record the readings
and keep the results in a portfolio. is links with Health Education as learners will
consider their body temperatures to establish their health status and dressing appropriately.
Practice exercise 2: Expected answers (Page 155)
1. 30 °C 2. 340 K 3. 18.5
°C
4. 85 °C 5. 1 007 K
Converting units of measuring temperature in degrees Celcius and Kelvin
Refer to Learner’s Book page 155
Activity 4: In groups
1. Instruct learners to study the conversion chart in the Learner’s Book. Ask them to
compare the temperature readings in degrees Celsius and in Kelvin.
2. Challenge the learners to discuss how to convert degrees Celsius to Kelvin. Allow them
to brainstorm and deduce how to convert Kelvin to degrees Celsius? This encourages
critical thinking and problem solving competence.
3. Ask them to share their answers with other learners in the class.
Practice exercise 3: Expected answers (Page 156)
1. (a) 312 K (b) 338.4 K (c) 295 K (d) 287.8 K
2. (a) 40 °C (b) 156.6 °C (c) 0.5 °C (d) 630.8 °C
3. 28 °C 4. 373 K 5. 37.5 °C 6. 458 K
7. 5 505 °C 8. 368.4 K 9. 64.9 °C 10. 303.5 K
Working out temperature in degrees
Refer to Learner’s Book page 157
Activity 5: In pairs
1. Provide learners with cold and hot water in dierent containers. Guide them to set up
the containers as shown in the Learner’s Book. is ensures learners’ safety.
2. Tell the learners to measure and record the temperature of the water in each container
165
in degrees Celsius. is encourages integrity as the learners give accurate information
of the thermometer readings. It also enhances digital literacy as learners interact
with thermo gun thermometer and other types of digital thermometers to determine
temperature of dierent places or substances.
3. Ask the learners to nd the dierence in temperature between the hot and cold water.
Practice exercise 4: Expected answers (Page 158)
1. (a) 71 °C (b) 78 K (c) 42.8 °C
(d) 133.3 °C (e) 303 K (f) 633.8 K
2. (a) 38 K (b) 6.6 °C (c) 75 K
(d) 17.7 °C (e) 149.3 °C (f) 178.5 K
3. 44.5 °C 4. 20.7 K 5. 39.8 °C
6. 366.5 K 7. 31.4 °C 8. 122.2 K
9. 53.5 °C
10. (a) 15.9 °C (b) 14.4 °C (c) 2.2 °C
Digital learning
Guide the learner to use a computer, a tablet or a smartphone to search for a game
involving temperature.
ey may use this link: https://www.iknowit.com/lessons/a-temperature-celsius.html.
Additional information
• You may consider guiding your learners into a debate on the type of weather condition
that is conducive for dierent human activities. is will help them understand and
appreciate how changes in weather conditions aect our day to day activities. In
addition, it will sensitise them on environmental awareness and make them conscious
of how pollution can adversely aect mankind leading to responsible citizenry.
• Randomly pick a learner and ask him to measure and record the temperature of a
given substance. is helps you to assess the learner’s observation skills. Check the
reading on the thermometer and reinforce accordingly.
Suggested assessment task
Have the learners observe and record temperature conditions in their immediate
environment over a given period of time and write about their results in a journal.
166
Assessment methods
(a) Written questions: Ask learners to do the practice exercises in the Learner’s Book.
(b) Observation: Walk around the classroom and monitor the learners’ practical skills
as they carry out the activities like measuring temperatures of dierent substances.
(c) Oral questions: Ask questions to probe the learners’ understanding of the concepts
and reinforce accordingly.
Suggested assessment tool
A journal
A journal entails the learner keeping a record of their personal feelings, thoughts,
experiences and activities on a daily basis or regularly in a specied period of time. e
learner’s development of competencies or achievement of learning outcomes can be
deduced from the writings in the journal especially on matters regarding attitude and
feelings towards the subject matter. e teacher gets a basis to assess the learner and
reinforces positive attitudes. A sample assessment journal is given below.
School: Jitahidi Academy Grade: 7
Learner’s name: Sheila Nekesa Date of entry: 23
rd
March 2023
Competency: Observing weather conditions in the immediate environment
Learner’s thoughts e weather condition today is warm. e temperature is
neither hot nor cold. I feel good as I sit under a tree to read my
storybook.
Teacher’s comment Well done Sheila! Taking advantage of the warm weather
condition to read a book is quite commendable.
3.7 Money
Number of lessons: 12
Refer to Learner’s Book pages 159 to 183
Introduction
Money is a universal concept and has been discussed widely in the competency-based
curriculum. In Grade 6, learners made a simple budget, identied types of taxes and
calculated prot and loss. In this sub strand, the learners will explore prot, loss,
percentage prot, percentage loss, discount, percentage discount, commission, percentage
commission, bills, postal charges and mobile money transactions.
167
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) Work out prot and loss in real life situations.
(b) Calculate the percentage prot and loss in dierent situations.
(c) Calculate the discount and percentage discount of dierent goods and services.
(d) Calculate commission and percentage commission in real life situations.
(e) Interpret bills at home.
(f) Prepare bills in real life situation.
(g) Work out postal charges in real life situations.
(h) Identify mobile money services for dierent transactions.
(i) Work out mobile money transactions in real life situations.
(j) Use IT devices to learn more about money for expenditure and investment.
(k) Recognise use of money in day to day activities.
Core competencies to be developed
• Critical thinking and problem solving: as learners work out prots, losses, discounts,
commissions and as they interpret charts to determine mobile money transactions,
bills and postal charges.
• Communication and collaboration: as learners speak, listen and role play on
negotiating for discounts and commissions.
• Citizenship: as learners work out discounts, bills, commissions and mobile money
transactions in Kenyan currency.
Pertinent and contemporary issues (PCIs)
• Financial literacy: as learners work out discounts, commissions and mobile money
as well as postal charges and bills.
• Decision making: as learners use money in paying bills and postal charges.
Links to other subjects
• Business studies: as learners work out bills, skills, discounts, commissions and postal
charges.
• Life skills: as learners apply negotiation skills in discounts and commissions.
• English: as learners gather information on postal services and charges.
Values
• Patriotism: as learners work out and pay bills in Kenyan currency.
• Integrity: as learners pay bills and appreciate use of money.
Key inquiry questions
1. Why do we use money in daily activities?
2. What considerations would we make when buying or selling?
3. What is involved in mobile money transactions?
168
Suggestions on facilitating dierentiated learning and learners with special
needs
Facilitating dierentiated learning Facilitating learners with special needs
• Grouping learners with diverse
abilities, characteristics or qualities
is a common practice during the
teaching and learning process. In
this sub strand, you may consider
grouping learners with similar
learning styles (visual, auditory,
kinaesthetic, read and write). is
should not be confused with grouping
learners based on similar level of
ability or understanding. Grouping
learners based on similar learning
styles allowslike-minded learners to
support each other’s learning. You
can oer themspecic instructions
to suit each group’s common needs
and preferences. is encourages
collaboration through common work
and thinking practices.
• At the end of this sub strand, organise
small groups of learners in circles
and inform them to take turns in
discussing the concepts they have
learnt. Encourage them to make their
explanations as detailed as possible.
is helps auditory and participatory
learners retain more information.
• Activity 8B and Activity 9C involve
interpretation of postal charts and
money transaction charts. Ensure
that the charts are conspicuous and
in large print to make them legible
for learners with visual impairment.
• Encourage learners to speak clearly
and audibly during the group
activities. e learners can also
use gestures and sign language if
possible, to assist learners with
hearing impairment.
• Ensure the short-sighted learners
sit at the front of the class and the
long-sighted ones sit at the back to
ensure appropriate distance from
the chalkboard during lessons.
• In activity 8A, give more time to
physically impaired learners so that
they can move around at the post
oce. Encourage the other learners
support them too. For example,
helping in pushing a wheelchair for
them.
Suggested teaching and learning resources
• Charts
• Mobile phones
• Bills
169
Teacher preparation for the lessons in this sub strand
Instruct learners to collect dierent types of bills at home or in school prior to Activity 6A. Liaise
with parents, guardians, other teachers, a nearby post oce and the school administration
to visit a post oce prior to Activity 8A.
In cases where the post oce is far away from the school, the teacher can organise and
obtain a resource person from the post oce who can deliver the required information to
the learners.
Suggested learning experiences
Prot and loss
Refer to Learner’s Book page 159
Activity 1A: In pairs
1. Let learners use a dictionary or a digital device to search for the meaning of the
words ‘prot’ and ‘loss’. Let them read aloud the meaning of each word as given in the
dictionary or by the digital device.
2. Let the learners explain the meaning of prot and loss to one another in class.
3. Guide the learners as they discuss how business people can make prots or losses. Let
them share experiences and ideas on how business people can make prots or losses.
Activity 1B: In groups
1. Guide learners to study the table in the Learner’s Book about Gabriel’s transactions.
2. Instruct learners to read about Gabriel buying a house and a car then later selling both
at the prices shown in the Learner’s Book. Let them determine whether Gabriel made
a prot or a loss on the sale of the house and car. Guide them to make the conclusion
that Gabriel made a prot on the sale of the house because the selling price was higher
than the buying price. e learners should also note that Gabriel made a loss on the
sale of the car because the selling price was lower than the buying price. Financial
literacy is enhanced as learners determine how to make prots in businesses.
3. Challenge the learners to work out the amount of prot or loss he made on the sale
of each item.
4. Guide the learners through Example 1 and Example 2 on page 160 of the Learner’s
Book. Emphasise that buying price is the price at which an item is bought and selling
price is the price at which an item is sold.
170
Additional information
To make a prot, the selling price should be higher than the buying price of the
item.
Prot = Selling Price – Buying Price
When the buying price is higher than the selling price, a loss is made.
Loss = Buying price – Selling price
5. Instruct the learners to do Practice exercise 1 in the Learner’s Book.
Practice exercise 1: Expected answers (Page 160)
1. Ksh 400 2. Ksh 690 000 3. Ksh 17 000
4. Ksh 29 000 5. Ksh 40 200 6. Ksh 45
7. Ksh 1 600 000 8. (a) Ksh 220 (b) Ksh 93 500
Percentage prot and loss
Refer to Learner’s Book page 161
Activity 2: In pairs
1. Tell learners to read aloud the story in the Learner’s Book. Ask them to also read the
story silently and discuss the information in the story.
2. From the story, instruct the learners to calculate the selling price of each goat. Guide
them to work out the total percentage profit Anita made from the sale of the goats.
3. Challenge the learners to calculate the loss Anita made from the sale of the remaining
cows in the story. Let them express the loss as a percentage of the buying price.
Additional information
Percentage prot is the prot expressed as a percentage of the buying price.
Percentage prot
Prot
Buying price
= × 100%
Percentage loss is the loss expressed as a percentage of the buying price.
Percentage loss
Loss
Buying price
= × 100%
4. Reinforce their grasp of the content by guiding the learners through Example 3, Example 4,
Example 5 and Example 6 on pages 161 and 162 of the Learner’s Book.
5. Instruct the learners to do Practice exercise 2 in the Learner’s Book.
171
Practice exercise 2: Expected answers (Page 171)
1.
Buying price
(Ksh)
Selling price
(Ksh)
Prot
(Ksh)
Loss
(Ksh)
Percentage
prot
Percentage
loss
(a) 7 200 8 352 1 152 - 16% -
(b) 1 800 1 899 99 -
5
1
2
%
-
(c) 8 500 8 000 - 500 -
5
15
17
%
(d) 19 400 14 550 - 4 850 - 25%
2. 40% 3. 40% 4. Ksh 10 200 5. 2%
6. 60% 7. Ksh 14 400 8. 12.5%
Discount
Refer to Learner’s Book page 163
Activity 3: In pairs
1. Ask learners to read the conversation between Mwakideu and Alicia in the Learner’s
Book. Let them discuss and comprehend the information they have read in the
conversation. Let the learners give an equal opportunity to the learners with impaired
speech. Encourage them to read slowly, clearly and audibly. Ask the other learners be
patient with them in order to enhance love and respect amongst the learners.
2. Instruct the learners to role play the conversation in the Learner’s Book. Let them
identify the marked price and the buying price of the television from the conversation.
is will develop critical thinking and problem solving.
3. rough discussion, let the learners brainstorm and calculate the dierence between
the marked price and the buying price. Challenge them to recognise this dierence as
the discount.
4. Guide the learners through Example 7 and Example 8 on page 164 of the Learner’s
Book.
5. Instruct the learners to do Practice exercise 3.
Practice exercise 3: Expected answers (Page 164)
1. Ksh 700 2. Ksh 6 500 3. Ksh 31 500 4. Ksh 2 500
5. Ksh 5 250
172
Percentage discount
Refer to Learner’s Book page 165
Activity 4: In groups
1. Let the learners discuss the picture shown in the Learner’s Book.
2. Guide them to discuss the meaning of a 50% discount. Challenge them to compare
the buying price and the marked price of an item with a 50% discount. Guide the
learners to understand that for an item with 50% discount, the buying price is half of
the marked price.
3. Guide the learners to work out the discount offered on two litres of soda. Let them
express the discount as a percentage of the marked price. This will develop critical
thinking and problem solving.
4. Allow a few learners to present their findings in class. For learners to internalise the
concept, allow them to ask and respond to questions from their peers. This promotes
communication and collaboration.
Additional information
Discount can be indicated either as an amount of money or as a percentage of the
marked price.
Percentage discount =
Discount
Marked price
× 100%
5. Guide the learners through Example 9 on page 165 of the Learner’s Book as a way of
enhancing the concept.
6. Instruct the learners to do Practice exercise 4 in the Learner’s Book.
Practice exercise 4: Expected answers (Page 166)
1.
Marked price
(Ksh)
Selling price
(Ksh)
Discount
(Ksh)
Percentage
discount
(a) 4 800 4 400 400
8
1
3
%
(b) 7 200 5 400 1 800 25%
(c) 2 200 1 980 220 10%
(d) 6 300 5 040 1 260 20%
2. (a) Ksh 2 100 (b) 14
2
7
%
3. Ksh 105 000 4. Ksh 125 000 5. Ksh 92 000
173
Commission and percentage commission
Refer to Learner’s Book page 166
Activity 5A: In pairs
1. Instruct learners to read about Hekima Company in the Learner’s Book. Let them
discuss to further comprehend the information that they have read.
2. Guide the learners as they discuss the meaning of the word ‘commission’. Lead them to
note that commission is the amount of money that is paid to an agent or a salesperson
depending on the value of goods he or she sells.
3. Guide the learners as they calculate the commission earned by a salesperson who sold
a car worth Ksh 1 500 000, a lorry worth Ksh 4 800 000 and a bus worth Ksh 7 000 000
in one month. Give guidance to learners who may have challenges.
Activity 5B: In groups
1. Guide learners to read the story in the Learner’s Book. Allow them to discuss and
internalise the information provided in the story.
2. Challenge the learners to calculate the commission earned by Mathew. Ask them to
also calculate the commission earned by Mary. Walk around the classroom and make
observations as they calculate the commissions. Give guidance to learners who may
have challenges in carrying out the calculations. Encourage the gifted learners to guide
the time takers. This will enhance unity and co-operation amongst the learners.
3. Challenge the learners to interpret their answers and make a conclusion on who earned
more money. Allow them to share and discuss their answers their peers in class.
Additional information
Commission is the amount of money that is paid to an agent or a salesperson
depending on the value of goods he or she sells.
It is a form of payment that is given to a person who sales goods on behalf of
another person or company.
Percentage commission =
Commission
Total sales
× 100%
4. Guide the learners through Example 10, Example 11 and Example 12 on pages 167 and
168 of the Learner’s Book. Probe learners to summarise the concept by mentioning
what they have learnt.
5. Instruct the learners to do Practice exercise 5 individually.
174
Practice exercise 5: Expected answers (Page 168)
1. (a) 4% (b) Ksh 15 000
2. 2%
3. Ksh 27 000 4. Ksh 14 750 5. Ksh 54 000 6. 1.8%
7. Ksh 8 000 8. 7.5%
Interpreting bills
Refer to Learner’s Book page 169
Activity 6A: In pairs
1. Guide learners to discuss the meaning of a bill. Ask the learners to take dierent bills
that have been collected at home or in school and stick them on a chart.
2. Ask the learners to observe and discuss the information found in the bills? ey
should be able to infer that a bill is a list showing money owed for goods and services
provided. Let them know that in buying and selling, a bill shows items bought and the
amount of money charged.
3. Allow a few learners to present their charts in class. Lead them in a discussion to
consolidate their understanding on the components of bills. ese components vary
depending on the type of bill. For example, an electric bill may have the following
components; fuel cost charge, forex charge, EPRA charge, REP charge, VAT, WRA
charge, ination adjustment and consumption charge among others.
Activity 6B: In groups
1. Guide learners to study the electricity bill in the Learner’s Book. Let them observe the
components of the bill.
2. Tell the learners to read the units of electricity used by Brian. Challenge them to check
the amount of VAT that Brian paid.
3. Instruct the learners to determine Brian’s total bill for the month of August.
4. Reinforce their understanding of the concept by taking the learners through Example 13
on page 170 of the Learner’s Book.
5. Ask individual learners to do Practice exercise 6 in the Learner’s Book.
Practice exercise 6: Expected answers (Pages 170 and 171)
1. (a) Ksh 600 (b) Ksh 4 800 (c) Ksh 4 000
2. (a) 6 000 litres (b) Ksh 1 080 (c) Ksh 920
175
Preparing bills
Refer to Learner’s Book page 171
Activity 7: In groups
1. Guide learners to discuss the bill in the Learner’s Book. Let them brainstorm and
discuss the meaning of @ as used in bills. ey should be able to note that @ in bills
means the price per item.
2. Guide the learners to deliberate on the meaning of the word ‘for’ as used in bills. Let
them determine that the word ‘for’ in bills means total cost of all the items bought.
3. Instruct the learners to copy and complete the bill in the Learner’s Book.
4. Guide learners through Example 14 on page 172 of the Learner’s Book as a way of
reinforcing the concepts.
5. Ask the learners to do Practice exercise 7 in the Learner’s Book.
Practice exercise 7: Expected answers (Pages 172 and 173)
1. (a) Ksh 1 760 (b) Ksh 2 760
2. (a)
Item Ksh cents
2 cabbages @ Ksh 50 100 00
2 kg of carrots @ Ksh 70 140 00
10 kg of potatoes for Ksh 250 250 00
3 kg of tomatoes @ Ksh 100 300 00
2 kg of onions for Ksh 90 90 00
Kales for Ksh 25 25 00
Total 905 00
(b) Ksh 95
3. (a) Ksh 80
(b)
Item Ksh cents
40 packets of chalk @ Ksh 55 2 200 00
20 bottles of glue @ Ksh 80 1 600 00
100 sheets of manila charts @ Ksh 30 3 000 00
5 bottles of white out @ Ksh 80 400 00
Total 7 200 00
176
4. (a)
Item Ksh cents
5 kg of sugar @ Ksh 120 600 00
4 kg of maize our @ Ksh 62.50 250 00
2 litres of cooking oil @ Ksh 270 540 00
Total 1 390 00
(b) Ksh 110
5. (a)
Item Ksh cents
5 litres of cooking oil @ Ksh 270 1 350 00
400 g of salt @ Ksh 10 for 200 g 20 00
2 bars of soap @ Ksh 160 320 00
6 kg of rice @ Ksh 200 1 200 00
2 litres of milk @ Ksh 60 for 500 ml 240 00
2 kg of wheat our for Ksh 145 145 00
Total 3 275 00
(b) Ksh 3 275 (c) Ksh 275
Extended activity
Instruct learners to discuss and identify the information that can be seen on a restaurant
bill. Tell them to create their own restaurant bills. Allow the learners to do this activity
at their own free time and with the help of their friends, parents or guardians. is will
enhance learning to learn.
Postal charges
Refer to Learner’s Book page 174
Activity 8A: As a class
1. Organise for learners to visit a nearby post office. Liaise with parents, guardians, other
teachers, a nearby post office and the school administration to make this visit happen.
2. Prior to the visit, instruct learners to prepare questions that they will ask while at the
post office. Ensure that at least one more teacher of the opposite gender accompanies
you and the learners during this visit.
3. While at the post office encourage learners to ask workers at the post office about the
services they offer.
177
Additional information
Some of the services oered by the post oce include:
• Mail services – Sending and receiving mail items such as letters and postcards
among others.
• Courier services – Transporting and delivering goods, documents or items to
dierent places.
• Payment services – Sending and receiving money using the post oce.
4. Assist the learners to get the current inland and international postal charges from the
postal office. Challenge them to use the postal charges to determine the cost of sending
a 20 g letter and a postcard to other places in Kenya.
5. Challenge the learners to write a journal about the visit to the post office and what they
have learnt during the visit. Use the learners’ journals to assess their understanding.
Activity 8B: In groups
1. Instruct learners to study Table 1 in the Learner’s Book. Let them discern that the
table is for inland postal charges and it shows the prices of sending mail items to
dierent places in Kenya.
2. Guide the learners to work out the total charge for sending 450 g of newspapers, 1.5 kg of
printed papers and 2 kg of literature for the blind. Let them also calculate the postage
bill for Fiona who sent two letters of mass 260 g and 500 g, two postcards and a small
packet of mass 750 g.
3. Allow a few learners to present their answers in class. Lead them in a discussion to
harmonise their understanding of the concept.
4. Guide the learners through Example 15 on page 176 of the Learner’s Book.
5. Guide learners to observe Table 2 in the Learner’s Book. Let them study the table and
discuss the information provided in it.
6. Ask a volunteer learner to take the class through Example 16 on page 178 of the
Learner’s Book. Listen to the learner’s explanation as you reinforce, correct or
emphasise accordingly. is promotes peer education.
7. Ask individual learners to do Practice exercise 8 and Practice exercise 9 in the Learner’s
Book.
178
Practice exercise 8: Expected answers (Page 176)
1. Ksh 565 2. Ksh 690 3. Ksh 3 825
4. (a) Ksh 320 (b) Ksh 325 (c) Lydia; By 5 shillings
Practice exercise 9: Expected answers (Pages 178 and 179)
1. (a) Ksh 345 (b) Ksh 1 500 (c) Ksh 3 730 (d) Ksh 4 930
2. (a) Ksh 790 (b) Ksh 1 100 (c) Ksh 2 055 (d) Ksh 2 705
3. Ksh 6 450 4. Ksh 14 435 5. Ksh 2 455
6. (a)
Item Ksh cents
One hundred and twenty 1 kg parcels…..120 × Ksh 58 6 960 00
Forty nine 6 kg parcels…………….…….49 × Ksh 350
Twenty 4 kg parcels……………….…..…20 × Ksh 220
17 150
4 400
00
00
Fiy seven 10 kg parcels………………....57 × Ksh 430 24 510 00
Total 53 020 00
(b) Ksh 53 020
Extended activity
Instruct learners to research and determine how people used to send money in the
years between 1980 and 2000. Allow them to do this activity at their own free time and
with the help of their friends, parents, guardians, grandparents and other members of
the community. However, agree with the learners on the timelines of when to complete
collecting the information for this extended activity. Allow learners to present their
ndings to other learners in the class.
Mobile money services
Refer to Learner’s Book page 179
Activity 9A: In pairs
1. Direct learners to discuss and mention the mobile money services that they know.
2. Provide learners with a mobile phone. Allow them to scroll and click on the SIM
toolkit app.
3. Guide the learners to identify the mobile money services listed in the SIM toolkit app.
Instruct them note down the mobile money services.
179
Activity 9B: In groups
1. Guide the learners to read the list of mobile money services as provided in the Learner’s Book.
2. Let the learners mention other mobile money services that they know.
Activity 9C: In groups
1. Guide learners to study Table 3 in the Learner’s Book. Give them a minute to discuss
and comprehend the information in the table.
2. Instruct the learners to determine the amount of transaction charge paid by Mwende
for sending Ksh 4 950 to her son who is a ZE-Money user? Let them work out Mwende’s
balance after sending the money to her son. Guide the learners to also calculate the
largest amount of money that Mwende’s son can withdraw after receiving the money
from his mother.
3. Guide the learners through Example 17 on page 181 of the Learner’s Book to enhance
their grasp of the concept.
4. Ask the learners to do Practice exercise 10 in the Learner’s Book.
Practice exercise 10: Expected answers (Page 181)
1. (a) Ksh 24 (b) Ksh 96 (c) Ksh 114 (d) Ksh 114
2. (a) Ksh 45 (b) Ksh 180 (c) Ksh 390 (d) Ksh 450
3. (a) Ksh 38 (b) Ksh 105 (c) Ksh 405 (d) Ksh 405
4. Ksh 2 469 5. Ksh 238 6. Ksh 450 7. Ksh 555
8. Ksh 935 9. Ksh 375 10 Ksh 158 11. Ksh 2 700
12. Ksh 1 647
Extended activity
1. Instruct learners to determine the procedure followed when carrying out the following
mobile money transactions:
(a) Sending money
(b) Withdrawing money from an agent
(c) Paying for bills
(d) Paying for goods and services using till numbers
(e) Saving money
2. Allow the learners to collect the required information for this activity with the help of
their parents or guardians. This activity can take three days to one week or over the
school holidays. Let the learners present the information they have gathered to the
rest of the class.
180
Assessment tasks
Instruct learners to tell each other stories about their real life experiences that involved
receiving discounts during shopping and using mobile money transactions.
Assessment methods
(a) Written questions: Ask learners to do the practice exercises in the Learner’s Book.
(b) Observation: move around the class room guiding learners in the dierent activities as
well as assisting those who may have diculties in forming and solving linear equations.
(c) Oral questions: Ask questions to involve the learners in the learning process as well
as assess process of learning.
Suggested assessment tool
Rating scale
A rating scaleis an assessment tool that allows teachers to indicate the frequency of the
knowledge, skills, attitudes and values displayed by the learner. A sample rating scale is
given below:
(a) Administrative information
School: Malake Junior secondary school Class: Grade 7 West
Learner’s name: Antony Mzumbe Teacher’s name: Eric Mutuma
Subject: Mathematics Strand: Measurement
Sub strand: Money Learning activity: Role play shopping
and selling activities
(b) Competency assessed
(knowledge, skills, attitude, values)
Always
4
Usually
3
Sometimes
2
Never
1
• e learner can make a price list
• e learner can bargain and obtain
discounts.
• e learner is able to apportion the
money they have to buy the item they
require,
• e learner is able to engage traders.
• e learner is able to calculate
discounts and percentage discounts.
(c) Comment on learner’s performance
Learner’s signature: _______________ Date: _______________
Teacher’s signature: _______________ Date: _______________
181
4.1 Angles
Number of lessons: 10
Refer to Learner’s Book page 184
Introduction
An angle is formed when two-line segments meet at a vertex. e angles 45°, 60°, 90°
and 180° have dierent sizes that can be measured using a protractor. Types of angles on
a straight line include acute, right, obtuse and reex angles. is sub strand is important
since it further develops the learners’ understanding of angle properties involving dierent
shapes up to a hexagon. e learners will be engaged in mastering a range of skills including
drawing, using a protractor and calculations involving angles. Before the learners embark
on the concepts in this sub strand, it is expected that they can identify angles on a straight
line, measure angles on a straight line and determine the sum of angles in a triangle. ey
learnt these concepts in Grade 6.
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) Relate dierent types of angles on a straight line in dierent situations.
(b) Solve angles at a point in learning situations.
(c) Relate angles on a transversal in dierent situations.
(d) Solve angles in a parallelogram in dierent situations.
(e) Identify angle properties of polygons up to hexagon in dierent situations.
(f) Relate interior angles, exterior angles and the number of sides of a polygon up to
hexagon in dierent situations.
(g) Solve angles and sides of polygons up to hexagon in learning situations.
(h) Use IT devices to learn more about angles and for leisure.
(i) Admire use of angles in objects.
Core competencies to be developed
• Communication and collaboration: as learners discuss in groups to identify the
positions of objects in the immediate environment in relation to angles.
• Critical thinking and problem solving: as learners draw, measure, interpret, infer and
relate dierent types of angles.
• Digital literacy: as learners interact with technology and use digital devices to learn
more on angles.
4.0 Geometry
182
Pertinent and contemporary issues (PCIs)
• Safety: as learners handle cutting tools and use cut outs or drawings of dierent
polygons up to hexagon.
Links to other subjects
• Pre- career and pre-technical: as learners use cut outs or drawings of dierent polygons
up to hexagon, in tailoring, survey or architecture.
Values
• Responsibility: as learners explore positions of objects in the immediate environment
in relation to
• Unity: as learners work together in groups to use cut outs or drawings of dierent
polygons up to hexagon.
Key inquiry questions
1. What are angles?
2. Where do we use angles in real life situations?
Suggestions on facilitating dierentiated learning and learners with special
needs
Facilitating dierentiated learning Facilitating learners with special needs
• Give the time takers and gied
learners equal opportunities to
participate in class presentations.
Encourage them to accommodate
one another and work together as
a team despite their dierences.
• Encourage the time takers to
participate in class activities such
as discussions, role play and
demonstrating the procedure
followed when measuring angles.
• Understand each learner’s needs
and characteristics and organise
the content delivery process
accordingly. is will help learners
with dierent abilities to learn and
acquire information in their own
way.
• Ensure the short-sighted learners
sit at the front of the class and the
long-sighted ones sit at the back to
ensure appropriate distance from the
chalkboard during lessons.
• In Activity 1A, give more time to
physically impaired learners so that they
can participate in the marking of angles
on the playground. Encourage the other
learners to help in pushing wheelchairs
for them.
• In Activity 6 learners are required to
draw parallel lines and a transversal.
Encourage learners to make large
drawings to assist visually impaired
learners.
183
Suggested teaching and learning resources
• Unit angles
• Protractors
• Rulers
• Pencils
• Straight edges
Teacher preparation for the lessons in this sub strand
Ensure that there are enough unit angles, protractors, rulers and charts with drawn images
of dierent angles. In Activity 1, ensure that you have enough ropes and objects such as
stones, sticks or pegs.
Suggested learning experiences
Types of angles on a straight line
Refer to Learner’s Book page 184
Activity 1A: In groups
1. Take learners outside to the playground. Guide them to mark the playground using
ropes and objects as shown in the Learner’s Book. Let them measure and name the
types of angles formed by the objects. The objects they use can be either stones, sticks
or pegs.
2. Instruct the learners to compare the sizes of the angles. Critical thinking and problem
solving is developed as learners determine the types of angles formed by the position
of the objects.
3. Guide the learners to identify different objects in the school compound and establish
the angles formed by the position of the objects. This could include the position of
an object with its shadows. Let them discuss their results with the others in the class.
Activity 1B: In pairs
1. Guide learners to draw angles like the ones in the Learner’s Book. Remind them how
to use a protractor to measure the angles. First, they should place the Centre of the
protractor on top of the vertex. Emphasise that the zero line of the protractor should
be aligned to one side of the angle to be measured. Stress on the importance of always
reading the scale that starts at 0° when measuring an angle.
2. Let the learners measure and compare angle x and angle y in gure A. Instruct them
to work out the sum angles x and y. Let them note that the two angles add up to 180°
and they are called supplementary angles.
184
3. Direct the learners to measure and compare angle m and angle n in gure B. Instruct
them to calculate the sum of angles m and n. Let them note that the two angles add
up to 90° and they are called complementary angles.
4. Harmonise the concepts the learners have learnt by guiding them through Example 1 on
page 185 of the Learner’s Book. Let them nd the value of angle x in the given gure.
Give them more angles to work out their values using the concept of supplementary
and complementary angles that they have learnt.
5. Tell individual learners to do Practice exercise 1 in the Learner’s Book.
Practice exercise 1: Expected answers (Page 186)
1. Accept correct and accurate drawings.
2. (a) 157° (b) 56°
(c) 22° (d) 74°
3. x = 70°
Solving angles at a point
Refer to Learner’s Book page 186
Activity 2: In groups
1. Instruct learners to observe the figures in the Learner’s Book. Let them measure the
angles in each figure using a protractor.
2. Ask the learners work out the sum of the angles in each of the figures. Allow a few
learners to present the group’s findings to the rest of the class. This will help enhance
self-efficacy and peer-education. Emphasise that angles at a point add up to 360°.
3. Guide the learners through Example 2 on page 187 of the Learner’s Book. Instruct them
to draw different other figures involving angles at a point. Let them measure the angles
and find their sum. This develops learning to learn. It also promotes self-efficacy.
4. Tell the learners to do Practice exercise 2 in the Learner’s Book.
Practice exercise 2: Expected answers (Page 187)
1. t = 202° 2. x = 80° 3. b = 120° 4. d = 55°
185
Relating angles on a transversal
Refer to Learner’s Book page 188
Vertically opposite angles (page 188)
Activity 3: in groups
1. Instruct learners to study the figure in the Learner’s Book. Using a protractor, ask the
learners to measure angles w, x, y and z. Let them compare angle w to angle y and
angle x to angle z.
2. Lead learners in a discussion to infer that angles that are on opposite sides of a vertex
are called vertically opposite angles. They should also conclude that vertically opposite
angles are always equal.
Corresponding angles (page 188)
Activity 4: In groups
1. Let the learners draw a pair of parallel lines and also draw a straight-line CD crossing
the parallel lines. Guide them to identify line CD to be a transversal. Emphasise that
a straight line intersecting two or more parallel lines is called a transversal.
2. Guide the learners to make a paper cut-out of angle a and slide the cut-out along
transversal CD on the drawing. Let them spot that the cut-out fits exactly on angle b.
3. Using a protractor, instruct the learners to measure angle a and angle b. Let them
note that angle a and angle b are corresponding angles. Assist them to establish that
corresponding angles are usually on the same side of the transversal and are always
equal.
Alternate angles (page 189)
Activity 5: In pairs
1. Direct learners to study the figure in the Learner’s Book. Using a protractor, instruct
the learners to measure angles j and k. Let them compare angle j to angle k.
2. Lead learners in a discussion to infer that alternate angles are usually formed between
the parallel lines but on the opposite sides of the transversal. They should also deduce
that alternate angles are always equal. This develops critical thinking and problem
solving.
3. Challenge the learners to mark and name two other angles in the figure that are similar
to angle j and angle k.
186
Co-interior angles (page 190)
Activity 6: In groups
1. Guide learners to draw a pair of parallel lines and a transversal. Let them mark two
angles formed between the parallel lines but on the same side of the transversal.
2. Instruct the learners to use a protractor to measure the two angles and calculate their
sum.
3. Randomly select a few learners to present their findings to the rest in class. Harmonise
their findings through probing and demonstration. Lead them to conclude that
co-interior angles are usually formed between the parallel lines but on the same side
of the transversal. Emphasise that co-interior angles are also called allied angles and
they always add up to 180°.
4. In order to assess the skills that the learners have learnt, ask them at random to identify
vertically opposite angles, corresponding angles, alternate angles and co-interior angles
using the transversal given in Example 3 on page 190 of the Learner’s Book.
5. Tell individual learners to do Practice exercise 4 in the Learner’s Book.
Practice exercise 3: Expected answers (Pages 190 and 191)
1. a = 101° b = 79° c = 101° d = 101°
2. e = 56° f = 124° g = 56°
3. x = 64° y = 30°
4. q = 140° w = 40° x = 112° y = 68° z = 72°
Solving angles in a parallelogram
Refer to Learner’s Book page 191
Activity 7: In pairs
1. Instruct learners to draw a parallelogram ABCD like the one in the Learner’s Book.
Let them measure angles DAB, ABC, BCD and ADC.
2. Ask the learners to work out the sum of angle DAB and angle ABC. Let them also
calculate the sum of angle ADC and angle BCD. Challenge the learners to interpret
their results and make inferences. This will enhance critical thinking and problem
solving.
3. Instruct the learners to compare angles ADC and angle ABC.
4. Randomly allow a few learners to present the pair’s findings to the rest of the class.
187
Emphasise that:
• e opposite sides of a parallelogram are equal and parallel.
• e opposite angles of a parallelogram are equal.
• e four angles in a parallelogram add up to 360°.
• Any two angles on the same side add up to 180°.
5. Consolidate and reinforce the concept by guiding learners through Example 4 on
page 191 of the Learner’s Book. Give them worksheets involving angle properties
of parallelograms and let them work out the size of some missing angles in the
parallelograms.
6. Tell individual learners to do Practice exercise 4 in the Learner’s Book.
Practice exercise 4: Expected answers (Page 192)
1. (a) x = 65° y = 115° z = 65°
(b) x = 30° y = 45° z = 135°
2. x = 20°
Angle properties of polygons
Refer to Learner’s Book page 192
Activity 8: In groups
1. Guide learners to use drinking straws and pins to make the polygons in the Learner’s
Book. Ensure that the drinking straws are of the same size so that learners end up
with regular polygons. Challenge the learners to give a general name for the shapes
they have made.
2. Guide the learners to use a protractor to measure the interior angles of the shapes.
Encourage them to calculate the sum of the interior angles in each shape.
3. Task the learners to state the angle properties of each of the shapes. Emphasise on the
following points:
(a) Triangle
• e sum of interior angles is 180°.
• In a triangle with three equal sides (equilateral triangle), all angles are 60°.
• In a triangle with two equal sides (isosceles triangle), two angles are equal.
• In a triangle with no equal sides (scalene triangle), no angles are equal.
• e sum of two interior opposite angles in a triangle is equal to the exterior
angle.
188
(b) Square
• Each of the interior angles measures 90°.
• e sum of all the interior angles is 360°.
(c) Rectangle
• Each of the interior angles measures 90°.
• e sum of all the interior angles is 360°.
(d) Trapezium
• It has only one pair of parallel sides.
• e sum of all the interior angles is 360°.
• e sum of two angles on the transversal sides of a trapezium is 180°.
(e) Pentagon
• It has ve sides.
• Each interior angle of a regular pentagon is 108°.
• e sum of all the interior angles is 540°.
(f) Hexagon
• It has six sides.
• Each interior angle of a regular hexagon is 120°.
• e sum of all the interior angles is 720°.
Relating interior angles, exterior angles and number of sides
Refer to Learner’s Book page 193
Activity 9: In groups
1. Direct learners to observe the polygons in the Learner’s Book. Let them trace the
polygons given on a sheet of paper.
2. Instruct the learners to count the number of sides in each of the polygons. Tell them
to extend the sides of the polygons and then measure each interior and exterior angle.
is will enable the learner to determine that in a regular polygon, all the sides and all
the interior angles are equal.
3. Let the learners draw and ll in their results in a table like the one in the Learner’s
Book. Guide them to add the interior angle to the exterior at each vertex and make
an inference.
4. Instruct the learners to divide 360° by an exterior angle for each polygon. Let them
compare their answer to that the number of sides for each polygon.
189
5. Lead learners in a discussion to ascertain the number of right angles that make the
sum of the interior angles of each polygon. Let them compare the number of right
angles to the number of sides for each polygon.
6. Given that the number of sides is n, challenge the learners to form an expression that
can represent the comparison they made. Emphasise the following:
• For a polygon with n sides, the sum of interior angles is (2n – 4)right angles.
• Sum of interior angles = (2n – 4)right angles (A right angle is 90°)
= (2n – 4)90°
• Number of sides (n) =
360°
Exterior angle
Solving for angles and sides of a polygon
Activity 10: in groups
1. Instruct learners to name polygons with 3 sides, 5 sides and 6 sides. Guide them to
calculate the size of an interior angle in each of the polygons.
2. Tell learners to work out the size of an exterior angle in each of the polygons. Move
around the classroom and observe the learners as they calculate the size of interior
angles and exterior angles. Give guidance to learners who may be having challenges.
Allow a few learners to present the group’s findings to the rest of the class.
3. Consolidate their findings by demonstrating to them how to solve for angles and sides
of a polygon using Example 5, Example 6 and Example 7 on page 195 of the Learner’s
Book.
4. Tell individual learners to do Practice exercise 5 in the Learner’s Book.
Practice exercise 5: expected answers (Page 196)
1.
Name of
regular polygon
Number
of sides
Sum of all
interior angles
Size of an
interior angle
Size of an
exterior angle
(a) Triangle 3 180° 60° 120°
(b) Square 4 360° 90° 90°
(c) Rectangle 4 360° 90° 90°
(d) Pentagon 5 540° 108° 72°
(e) Hexagon 6 720° 120° 60°
2. (a) y =120° (b) w = 72° x = 108° (c) b = 60° a = 120°
3. 144° 4. 5
190
Digital learning
Ask the learners to use a computer, a tablet or a smartphone to search for a game involving
polygons.
ey may use this link: https://www.iknowit.com/lessons/c-geometry-polygons.html.
Extended activity
Instruct the learners to cut out drawings of dierent polygons and use them to make
patterns.
Assessment methods
1. Written tasks: Ask learners to do the practice exercises in the Learner’s Book.
2. Observation: Observe and check the work of the learners as they discuss the activities
and practice exercises provided.
3. Oral questions: Ask oral questions as learners discuss and make class presentations
of the concepts that they have learnt.
4. Take away assignment: Make worksheets with questions on the concepts they have
studied. Give the worksheets to learners as take away assignments which can be done
with the help of their parents or guardians.
Suggested assessment tasks
Develop authentic assessment tasks that will enable learners to apply the knowledge and
skills that they have studied in class. You may consider letting the learners engage in games
that involve angles. Challenge them to write and recite poems that will give them an insight
on angle properties of polygons.
Suggested assessment tool
Frayer model
e Frayer Model is a graphic organiser used for building the learner’s vocabulary. is
technique requires the learner to dene a specic vocabulary and apply his or her knowledge
by generating examples and non-examples, giving characteristics, and/or drawing a picture
to illustrate the meaning of the word. is tool can be used by an individual learner or in
groups.
191
is information is placed on a chart that is divided into four sections to provide a visual
representation for learners. A sample is given below.
Name of the learner: Muli Wambua Learning outcome: Identify angle
properties of a triangle
Denition
e learner can dene a triangle.
Characteristics
e learner can write some of the
properties of a triangle.
Examples
e learner can identify angle
properties of a triangle.
Non-examples
e learner can identify angle properties
of other polygons that are not properties
of triangles.
Angle properties
of triangles
4.2 Geometrical constructions
Number of lessons: 10
Refer to Learner’s Book pages 197 to 207
Introduction
In Grade 5, learners were introduced to measuring angles in degrees in dierent situations.
In Grade 6, the learners were introduced to measuring angles on a straight line, determining
the sum of angles in a triangle, constructing parallel lines, bisecting lines and constructing
perpendicular lines. In this sub-strand, learners will build on their learning experience by
measuring dierent angles, constructing dierent angles, triangles and circles using a ruler
and a pair of compasses in dierent situations.
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) Measure dierent angles in learning situations
(b) Bisect angles using a ruler and a pair of compasses only in learning situations.
(c) Construct 90°, 45°, 60°, 30°, and other angles that are multiples of 7.5° using a ruler
and a pair of compasses only in dierent situations.
(d) Construct dierent triangles using a ruler and a pair of compasses only in dierent situations.
(e) Construct circles using a ruler and a pair of compasses only in dierent situations.
192
(f) Use digital devices to learn about geometric constructions for skills development.
(g) Recognise the use of geometric constructions in real life situations.
Core competencies to be developed
• Creativity and imagination: as learners construct angles, triangles and circles and
make observations and inferences.
• Digital literacy: as learners use and interact with digital devices to learn more on
construction of angles, triangles and circles.
Pertinent and contemporary issues (PCIs)
Safety: as learners use geometrical instruments such as pair of compasses and dividers.
Links to other subjects
Pre-tech and pre-career: as learners construct angles, triangles and circles which they can
use to make geometrical patterns.
Values
• Responsibility: as learners use geometrical instruments for construction of angles and
circles.
• Unity: as learners work in groups to draw and measure dierent angles.
Key inquiry questions
1. Where do we use geometric constructions in real life situations?
2. Why do we use geometric constructions?
Suggestions on facilitating dierentiated learning and learners with special
needs
Facilitating dierentiated learning Facilitating learners with special needs
• Give both the time takers and gied
learners equal chances to participate
in class activities. Ensure that they
accommodate one another and work
together despite their dierences.
• Identify each learner’s needs and
characteristics and adjust the content
delivery process accordingly. is will
help learners with dierent abilities to
learn and acquire information in their
own way.
• Encourage learners to use large print
when making bar models in Activity 3
to assist visually impaired learners.
• Encourage learners to speak clearly
and audibly during the group
activities. e learners can also
use gestures and sign language if
possible, to assist learners with
hearing impairment.
193
Suggested teaching and learning resources
• Geometrical set.
• Learner’s book.
• Plane papers or plane books.
Teacher preparation for the lessons in this sub strand
Make sure the required teaching and learning resources are available prior to the lesson.
In all activities in this sub-strand ensure the learners have a pair of compasses, ruler, and
a protractor.
Suggested learning experiences
Measuring angles
Refer to Learner’s Book page 197
Activity 1: In pairs
1. Guide learners in using of a ruler to draw different angles on a piece of paper. Instruct
them to use a protractor to measure the size of each angle. Walk around the classroom
and observe them as they measure the angles and offer guidance to those who may
have challenges. Ensure that the learners are able to place the centre of the protractor
at the vertex, align the zero line of the protractor to the straight lines and use the scale
that starts at 0° to measure the angles.
2. Ask the learners to identify the scale of the protractor that they have used to measure
each of the angles. Allow them to discuss their findings with other learners in class.
3. Guide the learners through Example 1 on page 197 of the Learner’s Book to help them
enhance their knowledge on measuring of angles.
Additional information
A common error made by learners when using a protractor is reading the inner
scale instead of the outer scale and vice versa. To remedy this error, emphasise that
the learners should always measure the size of an angle using the scale that begins
from 0°.
4. Ask the learners to do Practice exercise 1 in the Learner’s Book.
Practice exercise 1: Expected answers (Pages 197 and 198)
1. 70° 2. 100° 3. 51° 4. 140° 5. 220° 6. 85°
194
Bisecting angles using a ruler and a pair of compasses
Refer to Learner’s Book page 198
Activity 2: In pairs
1. Tell learners to draw an acute angle. Let them label the angle as WXY.
2. With X as the centre and using any radius, guide them to make an arc cutting line WX
at P and line XY at Q as shown in the Learner’s Book.
3. With P and Q as the centres and using the same radius, let them make arcs that meet
at a point. Let them label Z to be the point of where the arcs meet.
4. Let the learners use a ruler to join point Z and point X. Instruct them to use a protractor
to measure angle WXZ and angle ZXY. They should be able to notice that the angles
are equal. Emphasise that an angle bisector is a line that divides a given angle into two
smaller equal angles.
5. Tell individual learners to do Practice exercise 2 in the Learner’s Book. This will promote
self-efficacy and self-esteem.
Practice exercise 2: Expected answers (Page 199)
1. Check for correct and accurate procedure in the bisection of the angles.
2. Allow learners to draw angles of different sizes. Check for correct and accurate
procedure in the bisection of the angles.
Constructing an angle of 90°
Refer to Learner’s Book page 200
Activity 3: In pairs
1. Instruct learners to draw a line of any length and mark a point P on it. With P as the
centre, let them draw arcs to intersect the line on either side of P. Ask them to mark
the arcs as Q and R as shown in the Learner’s Book.
2. Guide the learners to open their pairs of compasses so that the radius is longer than
QP. With Q as the centre, they should draw an arc above P. With R as the centre and
using the same radius, let the learners draw another arc to cut the first arc. Let the
point where the arcs meet be labelled as Z.
3. Ask the learners to use a ruler to draw a line that passes through points P and Z. Let
them measure angle QPZ and angle RPZ. They should be able to determine that each
of the angles is equal to angle 90°.
4. Instruct the learners to discuss the steps followed when constructing an angle of 90°.
195
Constructing an angle of 45°
Refer to Learner’s Book page 201
Activity 4: In pairs
1. Instruct learners to construct an angle of 90°. Walk around the classroom and observe
them as they construct the angle and offer guidance to those who may have challenges.
2. Guide the learners to bisect the angle of 90°. Let them use a protractor to measure
the size of the angle bisector. They should be able to realise that each angle bisector
is equal to 45°.
3. Guide the learners to interpret their constructions and make a conclusion that an angle
of 45° can be constructed by bisecting an angle of 90°.
Constructing an angle of 60°
Refer to Learner’s Book page 201
Activity 5: In pairs
1. Tell learners to draw a line of any length and mark a point M on it. With M as the
centre and at any radius, let them use a pair of compasses to draw an arc cutting the
line at point T. Self-awareness is enhanced as learners use geometrical instruments
to make constructions.
2. Maintaining the same radius and using T as the centre, guide the learners to make
another arc to meet the first arc at S. Let them use a ruler to draw a line through points
M and S.
3. Instruct the learners to measure angle SMT. They should be able to determine that
angle SMT is equal to 60°.
4. Lead the learners in a discussion about the steps followed when constructing an angle
of 60°.
Constructing an angle of 30°
Refer to Learner’s Book page 202
Activity 6: In pairs
1. Instruct learners to construct an angle of 60°. Walk around the classroom and observe
them as they construct the angle and offer guidance to those who may have challenges.
2. Guide the learners to bisect the 90° angle. Let them use a protractor to measure the
size of the angle bisector. They should be able to realise that each angle bisector is
equal to 30°.
196
3. Guide the learners to interpret their constructions and make a conclusion that an angle
of 30° can be constructed by bisecting an angle of 60°. Critical thinking and problem
solving is developed as learners interpret their constructions and make an inference.
Constructing an angle of 120°
Refer to Learner’s Book page 203
Activity 7: In pairs
1. Guide learners to construct an angle of 60°; angle HGY as shown in the Learner’s Book.
Let them use a protractor to measure angle EGY.
2. Randomly allow a few learners to present their findings to the class. Harmonise their
findings through probing and demonstration. They should be able to deduce that to
construct an angle of 120°, one can construct an angle of 60° and use the supplement
angle on the straight line. Creativity and imagination is developed as learners make
demonstrate how to construct an angle of 120°.
Constructing an angle of 105°
Refer to Learner’s Book page 203
Activity 8: In groups
1. Guide learners to construct an angle of 120° and label it as shown in the Learner’s
Book. Instruct them to construct an angle of 90° at point B.
2. Guide the learners to bisect angle TBR. Let them measure the size of angle CBS. They
should observe that the size of angle CBS is 105°.
3. Ask the learners to brainstorm and deliberate on other ways of constructing an angle
of 105°. They should be able to infer that an angle of 105° can also be constructed by
constructing an angle of 60° and an angle of 45°. Lead them to also deduce that to
construct an angle of 75°, one can construct an angle of 105° and use the supplement
angle on the straight line. As they work together in groups, the values of social cohesion,
unity and peace are enhanced. Creativity and imagination is also developed as they
describe different ways of constructing angle of 105° and an angle of 75°.
197
Practice exercise 3: Expected answers (Page 204)
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i)
198
(j) (k)
Constructing triangles
Refer to Learner’s Book page 205
Activity 9A: In groups
1. Tell learners to draw a straight line and mark points X and Y, 6 cm apart. With Y as
the centre and a of radius 5 cm, instruct them to mark an arc above line XY.
2. With X as the centre and a radius of 4 cm, ask the learners to draw an arc above XY
to intersect the first arc. Let Z be the point where the two arcs intersect. Let them use
a ruler to join point Z to points X and Y.
3. Let the learners name the shape they have constructed. Tell them to measure the length
of line YZ and line XZ.
Activity 9B: In groups
1. Guide learners to read the statement in the Learner’s Book and let them draw a labelled
sketch of triangle ABC.
2. Instruct them to draw line AB of length 3 cm and construct an angle of 75° at point B.
Let them measure a length of 4 cm and mark point C as shown in the Learner’s Book.
3. Tell the learners to join point C and point A to complete the triangle. Ask them to
measure the length of line AC.
4. Allow a few learners to present their constructions to the class. Consolidate their
findings through probing and demonstration.
5. Ask individual learners to do Practice exercise 4 in the Learner’s Book.
Practice exercise 4: Expected answers (Page 206)
For this Practice exercise, check on correct and accurate constructions.
199
Digital learning
1. Guide learners to use a computer, a tablet or a smartphone to search for a video
involving constructing triangles.
ey may use this link: https://tinyurl.com/constructingtrianglesG7.
2. Walk around and encourage the learners to use the digital devices for their intended
purpose. Ensure that the learners are kept safe from insecure or indecent sites and
materials. is promotes cyber security and digital literacy.
Constructing circles
Refer to Learner’s Book page 207
Activity 10A: In pairs
1. Guide learners to draw a line and mark a point G on it.
2. With G as the centre, let them draw a circle of any radius. Ask them to measure the
diameter of the circle.
Activity 10B: In pairs
1. Guide learners to measure 5 cm on a ruler using a pair of compasses. Let them use the
radius to draw a circle. Allow the learners to share and fault on another’s construction.
2. Ask individual learners to do Practice exercise 5 in the Learner’s Book.
Practice exercise 5: Expected answers (Page 207)
For this Practice exercise, check on correct and accurate constructions.
Extended activity
1. Tell learners to draw a circle of any radius.
2. Guide learners in using a pair of compasses and same radius to make six marks on the
circumference of the circle at equal distance from each other.
200
3. With the same radius and each of these marks as the centre, guide them to draw arcs
to cut the circumference as shown below.
(a) (b) (c)
4. Let the learners shade the patterns with different colours.
5. Allow the learners to create other patterns involving construction. Let them show their
patterns to their friends.
Suggested assessment task
e Extended activity in the Learner’s Book is an authentic task that the learner is required
to perform. It gives an opportunity for the learners to demonstrate that they have the
understanding and the ability to apply their learning in relevant and meaningful ways.
Aer learners have created patterns involving construction, use the patterns to assess their
construction skills by letting them:
1. Display their patterns in the classroom.
2. Explain the procedure they followed to construct the patterns.
Assessment methods
(a) Written questions: Ask learners to do the Practice exercises in the Learner’s Book.
(b) Observation: Move around the classroom guiding learners in the dierent activities
as well as assisting those who may have diculties in forming and solving linear
equations.
(c) Oral questions: Ask probing questions to reinforce the learner’s understanding of
the concepts as well as assess process of learning.
201
Suggested assessment tools
1. Portfolio
is is a record of activities, projects, drawings, journals and assessments that a learner has
done. ese records can be kept in a physical le or in a digital folder. Digital portfolios
involve creating folders on a computer where each learner’s records are kept. A teacher can
easily track a learner’s performance over a period of time by looking records that are kept
in the portfolio.
2. Checklist
School: Feza Secondary School
Period of assessment: October 2022 Teacher’s name: Layla Mengi
Class: Grade 7 North Subject: Mathematics
Strand: Numbers Sub strand: Factors
Name
Competence (knowledge, skills, attitude, values)
Tick appropriately
Construct an angle of
90° 45° 60° 30° 120° 105°
Yes No Yes No Yes No Yes No Yes No Yes No
Duncan √ √ √ √ √ √
Jane √ √ √ √ √
Pius √ √ √ √ √
Harriet √ √ √ √ √ √
202
5.1 Data handling
Number of lessons: 10
Refer to Learner’s Book pages 208 to 230
Introduction
In Grade 6, the learners were introduced to presentation of data on bar graphs. In this sub
strand, the learners will build on their experiences on data collection and its representation
on pictographs, bar graphs, pie charts, line graphs and travel graphs. ey will also learn
how to interpret data presented on bar graphs, pie charts, line graphs and travel graphs
in real life situations. Encourage learners to link the concepts in this sub strand to real
life situations and also to other subjects. e learners may for instance, use data from
experiments in Integrated Science such as length of growing plants to create line graphs.
ey may also collect and represent data from Sports and Physical Education such as
distances covered in triple jumps and long jumps.
Specic learning outcomes
By the end of the sub strand, the learner should be able to:
(a) State the meaning of data in a learning institution.
(b) Collect data from dierent situation.
(c) Draw frequency distribution table of data from dierent situations.
(d) Determine suitable scale for graphs.
(e) Draw pictographs of data from real life situations.
(f) Draw bar graphs of data from dierent situations.
(g) Interpret bar graphs of data from real life situations.
(h) Draw pie charts of data from real life situations.
(i) Interpret pie charts of data from dierent situations.
(j) Draw a line graph of data from dierent situations.
(k) Interpret travel graphs from real life situations.
(l) Use IT devices to represent data.
(m) Appreciate use of data in real life situations.
Core competencies to be developed
• Creativity and imagination: as learners present data in form of pie charts and
pictographs.
5.0 Data handling and probability
203
• Critical thinking and problem solving: as learners interpret and analyse data from
bar graphs.
Pertinent and Contemporary Issues (PCIs)
• Education for Sustainable Development (ESD): as learners choose careers in research
related elds such as surveying.
• Decision making: as learners present data that can be used to make informed choices.
Links to other subjects
• Visual arts: as learners draw pictographs and pie charts.
• Social Studies: as learners present data in pie charts, bar graphs, line graphs and
pictographs.
Values
• Responsibility: as learners collect and present data involving dierent resources in
pictographs.
• Peace: as learners work in groups to collect and represent data.
Key inquiry questions
1. Why do we collect data?
2. How do we represent data?
3. How do we interpret data?
Suggestions on facilitating dierentiated learning and learners with special
needs
Facilitating dierentiated learning Facilitating learners with special needs
• Give both the time takers and
gied learners equal chances
to participate in class activities.
Ensure that they accommodate
one another and work together
despite their dierences.
• Identify each learner’s needs
and characteristics and adjust
the content delivery process
accordingly. is will help learners
with dierent abilities to learn and
acquire information in their own
way.
• is sub strand engages learners in
drawing pictographs, bar graphs, line
graphs, and pie charts. As physically
impaired learners take time to draw
these graphs, encourage other learners
to be patient and accommodate them.
• Encourage learners to speak clearly and
audibly during the group activities. e
learners can also use gestures and sign
language if possible, to assist learners
with hearing impairment.
204
Suggested teaching and learning resources
• Class registers
• Graph books or papers
• Manila papers
• Pairs of scissors
• Learner’s Book
Teacher preparation for the lessons in this sub strand
Make sure the required teaching and learning resources are available prior to the lesson. In
Activity 4, ensure there are enough one shilling coins. In Activity 6, Activity 7, Activity 10
and Activity 11 ensure that the learners have graph books or papers.
Suggested learning experiences
e meaning of data
Refer to Learner’s Book page 208
Activity 1: In groups
1. Guide learners to brainstorm and discuss the meaning of the word data. is enhances
communication and collaboration. Allow them to use a dictionary or other reference
books from the library to search for the meaning of the word data. ey should be
able to determine that data is a collection of information that has been gathered and
organised to help in decision-making.
2. From their research, guide the learners to mention some of the sources of data in
the school. is could include the library, games oce, kitchen store, class register,
staroom, classrooms, deputy principal’s oce and the principal’s oce.
3. Guide the learners to mention ways in which data can be collected and organised.
is will invoke their critical thinking and problem solving skills. ey should be
able to determine that some of the ways through which data can be collected include
using questionnaires, surveys, interviews, eld observation and experiments.
4. Tell individual learners to do Practice exercise 1 in the Learner’s Book.
Practice exercise 1: Expected answers (Page 208)
1. Data is a collection of information that has been gathered and organised to help in
decision-making. (Accept any other relevant denition)
2. Library, games oce, classroom, staroom, kitchen store, deputy principal’s oce
and principal’s oce. (Accept any other relevant answer)
3. e data can be recorded in a frequency table and represented in a graph. (Accept
any other relevant answer)
205
Collecting and organising data
Refer to Learner’s Book page 208
Activity 2A: As a class
1. Guide learners to name clubs, groups or teams that are available in the school. is
could include music club, scouts club and football team among others.
2. Let the learners mention the number of learners in the class who are members of the
dierent clubs, groups or teams.
3. Allow learners to name other activities that are available at the school. ese could
include learners’ council, swimming, peer tutoring, trivia quizzes, sewing, sculpture,
animation, woodwork among others.
4. Let the learners discuss how they can collect, organise and display data about the
activities available at their school.
5. Instruct individual learners to do Practice exercise 2 in the Learner’s Book. is
enhances self-ecacy and responsibility.
Activity 2B: In groups
1. Ask learners to draw a table like the one in the Learner’s Book and record the data
they have collected in Activity 2A. Allow them to change and organise the table to
suit their data.
2. Walk around the classroom and observe as the learners represent their data in a
frequency table and give guidance to those who are having challenges.
3. Instruct individual learners to do Practice exercise 2 in the Learner’s Book.
Practice exercise 2: Expected answers (Page 209)
For this practice exercise, accept frequency tables that are well organised with any
reasonable values of data.
Representing data in tables
Refer to Learner’s Book page 209
Activity 3: In groups
1. Guide learners to identify the head and the tail of a coin. Let them take turns to toss
the coin. Let them allow each learner in the group to toss the coin 5 times. is fosters
respect and social cohesion.
206
2. Ask the learners to draw a table like the one in the Learner’s Book. Let them record
the number of times the head or the tail show up.
3. Let learners in dierent groups compare their frequency tables. Lead them to
participate in a discussion for them to understand that frequency is the number of
times a certain data occurs.
4. Guide learners through Example 1 on page 210 of the Learner’s Book to enhance their
understanding of the concept.
5. Tell individual learners to do Practice exercise 3 in the Learner’s Book.
Practice exercise 3: Expected answers (Page 210)
1.
Learning area Tally Frequency (f)
Mathematics //// //// //// 14
English //// //// 9
Integrated science //// //// // 12
Kiswahili //// // 7
Business studies //// //// / 11
2.
Number of cows per family Tally marks Frequency (f)
0 //// 4
1 // 2
2 //// 5
3 //// / 6
4 //// 4
5 //// 4
3.
Number of pens bought Tally Frequency (f)
1 //// /// 8
2 //// // 7
3 //// 4
4 /// 3
5 / 1
6 // 2
207
4.
Days of the week Monday Tuesday Wednesday ursday Friday
Number of babies
vaccinated
25 18 19 21 14
Tally marks //// ////
//// ////
////
//// ////
//// ///
//// //// ////
////
//// ////
//// //// /
//// ////
////
Choosing suitable scales for graphs
Refer to Learner’s Book page 211
Activity 4: In groups
1. Ask learners to write the following values on dierent pieces of paper: Integrity,
Honesty, Peace, Responsibility and Unity. Let them fold the pieces of paper.
2. Allow the learners to take turns to pick a paper. ey should check the value written
on it and fold it again. Aer every pick encourage the learners to reshue the pieces
of paper before the next pick. Each learner should have 5 chances to pick the paper.
3. Guide the learners to draw and represent the data in a frequency distribution table.
4. Guide the learners to study and interpret the data they have and decide the one they
will put on the vertical axis and the one they will put on the horizontal axis. ey
should be able to agree to have the values on the horizontal axis and the frequency on
the vertical axis.
5. Let them choose a suitable scale that can be used on the horizontal axis and another
suitable scale that can be used on the vertical axis. Critical thinking and problem
solving is developed as learners brainstorm on the suitable scale to use for each axis.
6. Allow a few learners to present their data and scales of choice to the class. Ask probing
questions about why they chose their scales. is enhances their communication
skills. Let them explain to the rest of the class the factors they considered when
choosing the scale. ese factors could include the number of items and the size of
the grid on the graph paper among others. ey should be able to acknowledge that
a suitable scale should make it easy to draw and read a graph. It should allow all the
data to t on the graph paper so that it is not too large or too small.
7. In order to assess the skills and competencies developed in the learners, ask them at
random to choose a scale for dierent groups of data. Creativity and imagination is
developed as learners study the groups of data and choose suitable scales.
208
Drawing pictographs
Refer to Learner’s Book page 211
Activity 5A: In pairs
1. Let learners read and observe the information provided in the Learner’s Book. Let
them discuss the means of transportation used by the ten learners to go to school in
the morning. is enhances communication and collaboration. It also promotes the
values of honesty and respect as learners mention and appreciate the various means
of transportation used by their locality.
2. Guide the learners to determine the scale that has been used to represent the
information. Lead them into a discussion to identify the name given to a graph in
which information has been represented using pictures. ey should be able to tell
that such graphs are called pictographs.
3. Let the learners discuss their answers with other learners in the class.
Activity 5B: In groups
1. Let learners draw a table like the one in the Learner’s Book and write the name of each
learner in their group.
2. Let the learners choose a picture and use a scale of a picture to represent a person, to
represent the number of family members for each learner in the group. Acknowledge
the learners who portray creativity in their choice of pictures and reinforce them
positively
3. Let the learners compare their pictographs with those of other learners in their
class. Reinforce the concept by guiding them through Example 2 on page 212 of the
Learner’s Book.
4. Instruct individual learners to do Practice exercise 4 in the Learner’s Book.
209
Practice exercise 4: Expected answers (Page 213)
1.
represents 50 books
Year Number of books
2017
2018
2019
2020
2021
2.
represents 5 houses
Month Number of houses
January
February
March
April
May
210
3.
represents 50 fruits
Type of fruit Number of fruits
Mangoes
Oranges
Pawpaws
Watermelons
4.
represents 3 cars
Venue Number of cars
Imani church
Zahir mosque
Tamu hotel
Elimu school
Digital learning
Guide learners to use a computer, a tablet or a smartphone to search for a game involving
pictographs.
ey may use this link: https://www.mathgames.com/skill/2.14-create-pictographs.
211
Drawing bar graphs
Refer to Learner’s Book page 213
Activity 6: As a class
1. Guide learners to take turns and mention their favourite sports. Ensure that every
learner in the class mentions his or her favourite sport. The value of respect is enhanced
as learners take turns and appreciate each other’s choices.
2. Guide the learners to represent the data in a frequency distribution table. Let them
choose a suitable scale and use it to draw a bar graph.
3. Allow the learners to compare their bar graph with those of other groups. Let them
discuss the importance of using a bar graph to represent data. Self-awareness is
enhanced as learners deliberate on the importance of using a bar graph to represent
data from real-life.
4. Guide the learners through Example 3 on page 214 of the Learner’s Book.
5. Instruct individual learners to do Practice exercise 5 in the Learner’s Book. Learning
to learn is developed as learners take charge of their own learning by working out the
questions in the Practise exercise.
Practice exercise 5: Expected answers (Page 215)
1.
Day of the week
Mon
Tue Wed ur
Fri
0
5
10
15
20
25
30
35
40
45
50
55
60
65
Mass in kg
212
2.
Day of the week
Mon
Tue Wed ur
Fri
0
10
20
30
40
50
Number of Learners
3.
Name of the month
Jan
Feb
Mar April
May
0
50
100
150
200
250
Number of learners
300
June
213
4.
Name of the learner
Emily James
Sylvia Ian
0
2
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Number of trees
Michael
Interpreting bar graphs
Refer to Learner’s Book page 216
Activity 7: In groups
1. Instruct learners to study the bar graph in the Learner’s Book. Let them observe the
number of fish sold by Moses in one week.
2. Guide the learners to interpret the bar graph and identify the number of fish Moses
sold on Friday. Let them mention the day that Moses sold 40 fish.
3. Instruct the learners to interpret the bar graph and identify the two days that Moses
sold the same number of fish. Let them work the difference between the number of
fish that Moses sold on Sunday and on Thursday. This enhances their critical thinking
and problem solving skills.
214
4. Challenge the learners to determine horizontal scale and vertical scale.
5. Guide the learners through Example 4 on page 217 of the Learner’s Book.
6. Instruct individual learners to do Practice exercise 6 in the Learner’s Book.
Practice exercise 6: Expected answers (Page 218)
1. (a) 2 learners (b) 16, 12, 12, 10, 8 (c) 58 years
2. (a) 510 children (b) 120 children (c) 840 children
3. (a) June (b) April (c) 170 mm
Digital learning
Guide the learners to use a computer, a tablet or a smartphone to search for a game
involving bar graphs. ey may use the link:
https://www.iknowit.com/lessons/d-interpreting-bar-graphs.html.
Drawing pie charts
Refer to Learner’s Book page 221
Activity 8: In groups
1. Guide learners to make a circular paper cut-out. Let them fold and divide the cut-out
into 8 equal parts.
2. Guide the learners to use 3 parts of the cut-out to represent books, 2 parts to represent
pens, 1 part to represent erasers and 2 parts to represent rulers as shown in the Learner’s
Book.
3. Guide them to write fractions for each item represented on the cut-out.
4. Reinforce their understanding of the concept by guiding them through Example 5 on
page 221 of the Learner’s Book.
5. Instruct individual learners to do Practice exercise 7 in the Learner’s Book.
215
Practice exercise 7: Expected answers (Page 222)
1. (a) 16 hectares (b) grazing
3
8
, maize
2
8
, sorghum
2
8
, beans
1
8
(c)
Grazing
Maize
Sorghum
Beans
2.
February
January
March
April
3.
Week 1
Week 3
Week 2
Week 4
216
4.
Kenya
Ethio p i a
Rwanda
N igeria
Interpreting pie charts of data
Refer to Learner’s Book page 222
Activity 9: In groups
1. Instruct learners to study the pie chart in the Learner’s Book. Direct them to recognise
that the pie chart shows a representation of crops grown on a 32 hectare farm.
2. Tell the learners to write fractions to show the parts occupied by coffee and potatoes.
Guide them to calculate the size of the farm that is occupied by tea and maize.
3. Allow a few learners to present their answers to the class. As much as possible,
allow room for constructive peer criticism so that learners can fault one another’s
interpretation of the pie charts. Encourage learners to respect each other’s opinion
regardless of whether or not they agree with them. Caution the learners from demeaning
their peers in the guise of criticising them.
4. Guide the learners through Example 6 on page 223 of the Learner’s Book.
5. Instruct individual learners to do Practice exercise 8 in the Learner’s Book.
Practice exercise 8: Expected answers (Page 223)
1. (a)
1
3
(Accept
2
6
) (b) Ksh 500 (c) Ksh 500
2. (a) 80 goats (b) 160 cows
(c) 160 more chickens than goats (d) 80 more chickens than cows
3. (a) 16 learners (b) Table tennis and basketball (c) 8 learners
217
Drawing line graphs
Refer to Learner’s Book page 224
Activity 10: In groups
1. Instruct learners to collect eight similar pencils from members of the group. Guide
them in determining the price for one pencil. Let them use the same cost to work
out the cost of different number of pencils. Let them draw a table like the one in the
Learner’s Book and fill it in.
2. Guide the learners to draw horizontal and vertical axes of a graph. Let them label the
cost in shillings on the vertical axis, and the number of pencils on the horizontal axis.
3. Instruct the learners to choose a suitable scale. Let them use the data from the table to
plot points on the graph. Tell them to join the points to obtain a straight line.
4. Allow learners to share and discuss their graphs with other learners in the class. This
fosters communication and collaboration.
5. Guide the learners through Example 7 on page 224 of the Learner’s Book and then
compare with what they have done as a way of enhancing the concept.
6. Direct individual learners to do Practice exercise 9 in the Learner’s Book.
Practice exercise 9: Expected answers (Page 225)
1.
Milk in litres
1 2 3 4 5 6 7 8
90
45
0
135
180
225
Cost in shillings
*
*
*
*
*
218
2.
Number of days
1 2 3 4 5 6 7 8
40
20
0
60
80
100
120
140
Amount of honey in litres
*
*
*
*
*
*
3.
Number of litres
1 2 3 4 5 6 7 8
24
12
0
36
48
60
Distance in kilometres
*
*
*
*
*
*
72
84
219
Interpreting travel graphs
Refer to Learner’s Book page 226
Activity 11: In groups
1. Guide learners to study the graph in the Learner’s Book. Direct them to observe Noah’s
journey as he cycled from his home to the market.
2. Guide the learners to determine the distance Noah covered every 30 minutes. This
promotes critical thinking and problem solving. Let them interpret the travel graph
and mention the distance Noah covered between 9.00 a.m. and 9.15 a.m.
3. Challenge the learners to discern the time that Noah had covered half of his journey.
Guide them to calculate Noah’s speed in km/h and state how long Noah’s journey took?
4. Guide learners through Example 8 on page 227 of the Learner’s Book. Emphasise that
a travel graph is a type of line graph that shows the distance covered over a certain
period of time.
Practice exercise 10: Expected answers (Pages 228, 229 and 230)
1. (a) 120 km (b) 3 hours (c) 60 km/h
2. (a) (i) Horizontal scale: 1 cm represents 30 minutes
(ii) Vertical scale: 1 cm represents 25 km
(b) 30 minutes (c) 180 km (d) 150 km (e) 1.00 p.m. (f) 60 km/h
3. (a) None (b) 4.00 p.m. (c) 30 km (d) 48 km (e) 12 km/h
Extended activity
Instruct learners to carry out a research on dierent economic activities in the community.
Learning to learn is developed as learners do this activity at their own free time and with
the help of their friends. Let them collect data and determine the most common economic
activities in their community. ey should represent their data in a bar graph, pie chart
and line graph.
Suggested assessment task
e Extended activity in the Learner’s Book is an authentic task that the learner is required
to perform. It gives an opportunity for the learners to demonstrate that they have the
understanding and the ability to apply their learning in relevant and meaningful ways.
Aer learners have carried out their research and collected data, use their results to assess
their understanding by letting them:
1. Explain the tools they used to collect and organise the data.
2. Show a graphical representation of the data they collected.
3. Analyse their data and make reasonable inferences.
220
Assessment methods
(a) Written questions: Ask learners to do the Practice exercises in the Learner’s Book.
(b) Observation: Move around the classroom guiding learners in the dierent activities
as well as assisting those who may have diculties in forming and solving linear
equations.
(c) Oral questions: Ask probing questions to reinforce the learner’s understanding of the
concepts as well as assess the process of learning.
Suggested assessment tools
1. Rating scale
Use a rating scale like the one shown below to evaluate your learners.
Indicators Always Sometimes Rarely
e learner draws pictographs of data
from real life situations.
✓
e learner draws and interprets bar
graphs of data from dierent sources.
✓
e learner draws and interprets pie
charts of data from real life situations.
✓
e learner draws and interprets line
graphs of data from dierent situations
✓
2. Peer assessment form
Use peer assessment to allow learners evaluate the performance of their classmates.
Peer assessment is useful in developing decision-making skills, critiquing abilities and
self-awareness in the learners. Use peer assessment to evaluate individual learner’s
contributions to the group’s common goal during projects and other activities.
Peer assessment can be done openly, encouraging comparison and discussion, or
anonymously depending on the assessment activity and context.
Create a peer assessment form for the learner to ll in. An example is given below.
Peer assessment form
Name of group member: Jared Okelo Date: 07/11/2022
Learning outcome: Collecting data from the immediate environment.
What was good about the activity? Areas that need improvement.
Jared did a good job in collecting data on
dierent economic activities in the community.
I think Jared should learn more on
representing data on pie charts.
221
Guidelines for Community Service Learning Project
Introduction
Following the dynamic demands of the 21
st
century, coupled with the sudden global crisis
of the COVID-19 pandemic, it is more evident that exibility is inevitable and Kenyan
institutions of learning have not been spared. Subsequently, there is need for learning to
take place beyond the connes of theclassroom. A project is an alternative assessment
tool that facilitates teaching and learning experiences to occur outside the classroom.
e project the learners will be exposed to in this grade will give them an opportunity to
apply Mathematics and other subjects to identify and solve problems in the immediate
community. is will require learners to communicate, collaborate and increasingly
engage with the community around the school. In order to enhance the community’s
participation in assisting the learners, it is essential to promote a school environment
where members of the community feel respected, listened to and needed. Encourage
learners to be incorporated into community activities as volunteers and interns so as
to make them responsible members of the community in addition to preparing them
for senior school. is gives learners opportunities to participate in activities in their
community as they seek for or enhance their knowledge, skills and competencies within
a stipulated subject matter. e learners get a rst-hand experience of interacting with
members of their community in addressing real-life issues that need intervention. In
so doing, the learners gain a wealth of knowledge, experience and life skillsthat can be
utilised in their careerseven as they give back to the community. e learner will develop
a sense of belonging to the community even as he or she empathises and seeks solutions
to the pertinent and contemporary issues.
Community Service Learning (CSL) is therefore a form of experimental education that
enables learners to apply their knowledge and skills in addressing meaningful needs in the
community over a stipulated period of time. Aer successful completion of the project,
the learners will support each other to analyse what they have learnt by taking part of the
Community Service Learning activity and how it might be applied to their academic and
personal development.
Some of the advantages of Community Service Learning include:
• The projects have authenticity and provide solutions to pertinent issues in the
community.
• e learners have a choice to select and solve issues that are most meaningful to them.
• e learners don’t have to wait until the end, they can self-assess and measure their
progress during the project. ey can set their own targets to track their learning.
222
• e project enables the learners and the community to work together in collaboration
towards a common goal.
• Finding innovative ways to solve real-life problems in the society develops critical
thinking and problem solving in the learner.
Project-based learning would be the best approach to carry out the community service
learning since the two are quite similar since the both focus on authenticity and meaningful
work.
When project-based learning approach is used for Community Service Learning, there is
a highly eective impact on the learners and the community at large.
Project-based learning is constructive, collaborative, contextual and self-directed.
The main stages of a project-based CSL activity include:
• Problem identication
• Goal or objective setting
• Designing of the methodology
• Data collection
• Data representation
• Data analysis
• Conclusion
• Recommendations
Procedure for creating a community service learning activity using project-
based learning approach
• Needs assessment
• Outline the desired content, skills, competencies and learning outcomes
• Emphasize on collaborative learning between learners and the community
• Reection
• Action planning
• Evaluation and Impact Assessment
• Feedback
Rationale for Community Service Learning
Pedagogy must be dynamic and be tailor-made to suit the vast needs of the diverse learners.
Community service learning oers learners an opportunity to build capacity in their
knowledge, skills and competencies within dierent subjects as they address problems in
their communities thereby fostering social cohesion and citizenship.
223
Purpose of the activity: To identify a problem in the school community through research.
Learners to use and apply the community service learning project skills they have been
exposed to in Life Skills Education.
Skills and competencies to be developed
• Research: Learners will develop research skills as they identify the Pertinent and
Contemporary Issues (PCIs) to address during the project, ways and tools to use in
investigating and collecting the data, manner in which they will analyse information
and present their ndings.
• Communication and collaboration: Learners will develop eective communication
skills as they engage with peers and school community members. ese will include
listening actively, asking questions and presentation skills using varied modes.
• Citizenship: Learners will be able to explore opportunities for engagement as
members of the school community and providing a service for the common good.
• Leadership and responsibility: Learners develop leadership and responsibility skills
as they take up various roles within the project.
• Financial literacy skills: Learners consider how they can undertake the project as well
as sourcing and utilising resources eectively and eciently.
• Entrepreneurship: Learners consider innovative ways of generating income for the
community service learning project.
Key Inquiry Questions
1. How does one determine community needs?
2. Why is it necessary to be part of a community?
3. What can one do to demonstrate a sense of belonging?
Preparation for the community service learning activity
Ensure that learners brainstorm and identify all the resources that they will require for
the activity. Let them consider improvising and utilising locally available materials as this
will make the project to be cost eective thereby promoting Education for Sustainable
Development (ESD).
Guidelines for administering the activity
1. Learners should undertake the activity as a class.
2. The project should be done outdoors and not within the allocated classroom time.
3. The activity should take a maximum of two weeks.
224
4. Allow enough time for learners to investigate, brainstorm and identify pertinent and
contemporary issues in the community that need attention. Brainstorming sessions
can be held during breaktime.
5. Encourage learners to discuss and come up with possible solutions to the issues they
have identified.
6. Let the learners propose the most appropriate solution to the problem.
7. Guide learners to choose the best tools for use in the collection of information about the
problem they have identified. Suggested information gathering tools are observation
sheets, questionnaires and interviews.
8. Guide learners in developing tools for collecting the data.
9. Guide the learners to develop various reporting documents on their findings. This could
be in form of frequency tables, bar graphs, pictographs, line graphs or pie charts.
10. Guide learners in developing reporting tools for their findings.
11. Guide the learners in collecting feedback from peers and the school community. This
can be done through assembly and club meetings.
12. Guide the learners to discuss the strengths and weaknesses of the implemented activity
and also the lessons they have learnt.
13. Allow the learners to reflect on how the project enhanced their learning and how it
was relevant to the issues facing their community.
Assessment Rubric
Indicator Exceeds
Expectation
4
Meets
expectation
3
Approaches
Expectation
2
Below
expectation
1
e ability
to identify
and analyse
a pertinent
issue in
society to be
addressed.
Learner critically
denes and
elaborately
discusses a
pertinent issue to
be addressed.
Learner denes
and discusses a
pertinent issue
to be addressed.
Learner denes
and discusses a
pertinent issue
to be addressed
with minimal
support.
Learner
requires
support to
critically
examine and
select the
appropriate
issue.
225
e ability to
plan to solve
the identied
problem
Learner
correctly and
systematically
establishes
resources
needed, develops
plans, assigns
responsibilities,
and generates
data on the CSL
project.
Learner
correctly
establishes
resources
needed,
develops
plans, assigns
responsibilities,
and generates
data on the CSL
project.
Learner
sometimes
establishes
resources
needed,
develops
plans, assigns
responsibilities,
and generates
data on the CSL
project.
Learner has
diculty
establishing
resources
needed,
developing
plans,
assigning
responsibilities
and generating
data on the
CSL project.
e ability
to design
solutions to
the identied
problem and
implement
them.
Learner
constantly
applies the
knowledge and
skills gained
in subjects to
address the
identied issue.
Learner
applies the
knowledge and
skills gained
in subjects to
address the
identied issue.
Learner
applies the
knowledge and
skills gained
in subjects to
address the
identied issue
with some
support.
Learner
requires a lot
of probing
to apply the
knowledge and
skills gained
in subjects
to address
the identied
issue.
Ability to
share ndings
to relevant
actors
Learner
comprehensively
and condently
shares ndings
of the issue
addressed in the
activity.
Learner
condently
shares ndings
of the issue
addressed in
the activity.
Learner shares
some of the
ndings of the
issue addressed
in the activity.
Learner briey
shares ndings
of the issue
addressed in
the activity,
lacks necessary
details.
e ability to
reect on own
learning and
relevance of
the activity
Learner
distinctively and
clearly outlines
the benets of
the CSL activity
on the target
community and
own learning.
Learner clearly
outlines the
benets of the
CSL activity
on the target
community and
own learning.
Learner outlines
the benets of
the CSL activity
on the target
community and
own learning, a
few unclear.
Learner
struggles to
outline the
benets of the
CSL activity
on the target
community
and own
learning.
226
Appendix 1
Sample scheme of work
School: Baharini Secondary School Subject: Mathematics Term 1 Grade 7 Date: 15/05/2022
Week Lesson Strand Sub
strand
Specic
learning
outcome
Learning
experiences
Key inquiry
questions(s)
Learning
resources
Assessment
methods
Reection
1 1 1.0
Numbers
1.1
Whole
numbers
By the end of
the lesson the
learner should
use place value
of digits up to
hundreds of
millions in real
life.
In pairs or
in groups,
learners to
identify and
write place
value of
digits using
place value
apparatus.
Where is
place value
used in real
life?
• Mathematics
Grade 7
Learner’s Book
• Teacher’s
Guide
• Place value
apparatus
• Number cards
• Videos
• Digital
devices
• Oral
questions
• Written
tests
• Observation
• Class
activities
By the end of
the lesson the
learner should
use total value
of digits up to
hundreds of
millions in real
life.
In pairs or
in groups,
learners to
identify and
write total
value of
digits using
place value
apparatus.
Where is
total value
used in real
life?
• Mathematics
Grade 7
Learner’s
Book
• Teacher’s
Guide
• Place value
apparatus
• Number
cards
• Videos
• Digital
devices
• Oral
questions
• Written
tests
• Observation
• Class
activities
227
By the end of
the lesson the
learner should
read and write
numbers in
symbols up to
hundreds of
millions in real
life situations.
In pairs or
in groups,
learners
to read
and write
numbers
in symbols
from number
cards or
charts.
Why do
we write
numbers in
words or
symbols?
• Mathematics
Grade 7
Learner’s
Book
• Teacher’s
Guide
• Place value
apparatus
• Number
cards
• Videos
• Digital
devices
• Oral
questions
• Written
tests
• Observation
• Class
activities
By the end of
the lesson the
learner should
read and write
numbers in words
up to millions for
uency.
In pairs or
in groups,
learners to
read and write
numbers in
words from
number cards
or charts
and practice
writing
dummy
cheques for
different sums
of money.
Where do we
write numbers
in words or
symbols?
• Mathematics
Grade 7
Learner’s Book
• Teacher’s
Guide
• Place value
apparatus
• Number cards
• Dummy
cheques
• Videos
• Digital devic
es
228
Appendix 2
Sample lesson plan
School Subject Grade Date Time Roll
Baharini Secondary
School
Mathematics 7 14/01/2022 9.30 a.m. –10.10 a.m. 40
Strand: Numbers
Sub strand: Whole numbers
Specic learning outcome
By the end of the lesson, the learner should be able to use place value of digits up to
hundreds of millions in real life.
Key inquiry question
Where is place value of numbers used in real life?
Teaching and learning resources
• Mathematics Grade 7 Learner’s Book
• Mathematics Grade 7 Teacher’s Guide
• Chalkboard, chalk and chalkboard
duster
• Resources from the environment
• Abacus
• Videos
• Digital devices
• Pens and notebooks
• A place value chart
• Number cards
• Number charts
Core competencies to be developed
• Critical thinking and problem solving: as learners identify place value of digits in
numbers.
• Digital literacy: as learners use digital devices to learn and play digital games involving
place value.
• Self-ecacy: as learners share or lead others in groups to nd the place value of digits
in numbers.
Pertinent and Contemporary Issues (PCIs)
1. Safety: as learners handle place value apparatus and put objects on an abacus.
2. Career awareness: as learners discuss where numbers are used and then calculate the
place value in prices of dierent items.
229
3. Gender issues and peace education: as learners nd the place value of digits in
the amount of money raised by people who are doing business in a harmonious
environment.
Link to other subjects
Language: as learners discuss in pairs and in groups and as they take part in classroom
presentations.
Values
• Respect: as learners work in pairs and in groups to come up with a common answer.
• Unity: as learners work towards achieving group goals.
• Social cohesion: as learners work in groups irrespective of their backgrounds.
Information for the teacher
In this lesson, it is important that the learner understands the dierence between place
value and total value. rough practice and use of place value apparatus, the learner will
be able to tell the dierence.
Lesson development
Step 1
Given that this is the rst lesson, introduce yourself and welcome the learners to Junior
Secondary. Assure the learners that the concepts they are going to learn will build on their
learning experiences from upper primary. is will help calm down the learners and allay
any anxieties that may hinder the learning process.
Step 2
Guide learners to make a card with the number 9 999 999. Ask the learners to count
forward and mention the whole number that follows 9 999 999. is will help the learners
to make a transition from the place value of millions which they are familiar with to the
place value of tens of millions which is part of what they are going to learn.
Step 3
Guide learners to draw a place value chart. Let them write the number 416 928 305 in the
place value chart. Give them an opportunity to discuss and determine how to write the
number in the place value chart. is will help you gauge the learners’ entry behaviour.
Encourage the learners to discuss and nd the place value for each digit in the number 416
928 305. Let them give priority to nding the place value of the digit 4 because this falls on
the hundreds of millions place value and that is the scope for this concept. Let the learners
discuss and identify the digit that is in the place value of tens of millions in the number
416 928 305.
230
Step 4
Emphasise that the place values of the digits in a number increases from right towards
the le. Randomly choose a few learners to present the group’s ndings to the rest of the
class. Harmonise the concepts the learners have learnt using Example 1 in the Learner’s
Book. Let them write down numbers of their own choice then discuss and write their place
values.
Conclusion
End the lesson by asking the learners to summarise what they have learnt in this lesson.
Tell individual learners to do Practice exercise 1 in the Learner’s Book.
Reection of the lesson
e lesson was well taught. e learners were able to use place value of digits up to hundreds
of millions in real life.
Extended activity
Learners to nd out other dierent uses of place value of digits up to hundreds of millions
in real life.
231
Appendix 3
Sample record of work
Name of school: Baharini Secondary School Teacher: Patrick Haji
Grade: 7
Subject: Mathematics
Date: 15/11/2022
Strand: Measurement
Sub strand: Pythagorean relationship
Week
Lesson
Work covered
Remarks
1 1 In this lesson, the learners
were introduced to the
Pythagorean relationship.
The learners were able to identify
the sides of a right-angled triangle.
e learners were able to identify
and recognise the Pythagorean
relationship.
Subject head:
Signature:__________ Date: ___________
Head teacher:
Signature:________ Date: _______
232
Appendix 4
Assessment record book
A sample assessment record sheet is given below.
Name of school: Baharini Secondary School
Name of learner: Ruth Moraa Teacher: Ezekiel Too
Strand: Measurement Sub strand: Pythagorean relationship
Grade 7 Subject: Mathematics Date: 02/07/2022
Specic learning
outcome
Competencies to
be
acquired
Work covered
Remarks
e learner
should be able
to identify and
recognise the
Pythagorean
relationship.
• Communication
and
collaboration
• Self-ecacy
• Learning to
learn
In this sub
strand, the
learner was
taken through
activities
involving
identication
of the
Pythagorean
relationship.
Ruth Moraa is able
to consistently and
accurately identify
the Pythagorean
relationship.