Teacher’s Guide - Grade 9 Mathematics

Mathematics
Teacher’s Guide

Grade 9
(Implemented from year 2018)

Department of Mathematics
Faculty of Science and Technology
National Institute of Education
Sri Lanka
www.nie.lk
 Teacher’s
Teacher’s Guide - Grade 9 Mathematics

Mathematics
Grade 9– Teacher’s Guide

© National Institute of Education

First Print 2017

Department of Mathematics
Faculty of Science and Technology
National Institute of Education

Print:
Education Publications Department
Isurupaya
Battaramulla

ii
 Teacher’s Guide - Grade 9 Mathematics

Message of the Director General

With the primary objective of realizing the National Educational Goals recommended by the
National Education Commission, the then prevalent content based curriculum was
modernized, and the first phase of the new competency based curriculum was introduced to
the eight year curriculum cycle of the primary and secondary education in Sri Lanka in the
year 2007

The second phase of the curriculum cycle thus initiated was introduced to the education
system in the year 2015 as a result of a curriculum rationalization process based on research
findings and various proposals made by stake holders.

Within this rationalization process the concepts of vertical and horizontal integration have
been employed in order to build up competencies of students, from foundation level to higher
levels, and to avoid repetition of subject content in various subjects respectively and
furthermore, to develop a curriculum that is implementable and student friendly.

The new Teachers’ Guides have been introduced with the aim of providing the teachers with
necessary guidance for planning lessons, engaging students effectively in the learning
teaching process, and to make Teachers’ Guides will help teachers to be more effective within
the classroom. Further, the present Teachers’ Guides have given the necessary freedom for the
teachers to select quality inputs and activities in order to improve student competencies. Since
the Teachers’ Guides do not place greater emphasis on the subject content prescribed for the
relevant grades, it is very much necessary to use these guides along with the text books
compiled by the Educational Publications Department if, Guides are to be made more
effective.

The primary objective of this rationalized new curriculum, the new Teachers’ Guides, and the
new prescribed texts is to transform the student population into a human resource replete with
the skills and competencies required for the world of work, through embarking upon a pattern
of education which is more student centered and activity based.

I wish to make use of this opportunity to thank and express my appreciation to the members
of the Council and the Academic Affairs Board of the NIE the resource persons who
contributed to the compiling of these Teachers’ Guides and other parties for their dedication
in this matter.

Dr. (Mrs.) Jayanthi Gunasekara

Director General
National Institute of Education
Maharagama

iii
 Teacher’s Guide - Grade 9 Mathematics

Message of the Deputy Director General

Education from the past has been constantly changing and forging forward. In recent years,
these changes have become quite rapid. Past two decades have witnessed a high surge in
teaching methodologies as well as in the use of technological tools and in the field of
knowledge creation.

Accordingly, the National Institute of Education is in the process or taking appropriate and
timely steps with regard to the education reforms of 2015.

It is with immense pleasure that this Teachers' Guide where the new curriculum has been
planned based on a thorough study of the changes that have taken place in the global context
adopted in terms of local needs based on a student-centered learning-teaching approach, is
presented to you teachers who serve as the pilots of the schools system.

An instructional manual of this nature is provided to you with the confidence that, you will be
able to make a greater contribution using this.

There is no doubt whatsoever that this Teachers' Guide will provide substantial support in the
classroom teaching-learning process at the same time. Furthermore the teacher will have a
better control of the classroom with a constructive approach in selecting modern resource
materials and following guide lines given in this book.

I trust that through the careful study of this Teachers Guide provided to you, you will act with
commitment in the generation of a greatly creative set of students capable of helping Sri
Lanka move socially as well as economically forward.

This Teachers' Guide is the outcome of the expertise and unflagging commitment of a team of
subject teachers and academics in the field Education.

While expressing my sincere appreciation of this task performed for the development of the
education system, my heartfelt thanks go to all of you who contributed your knowledge and
skills in making this document such a landmark in the field.

M.F.S.P. Jayawardhana
Deputy Director General
Faculty of Science and Technology

iv
Teacher’s Guide - Grade 9 Mathematics

Advice and Approval: Academic Affairs Board,

National Institute of Education

Supervision: Mr. K.Ranjith Pathmasiri, Director,

Department of Mathematics,
National Institute of Education

Coordination: Mr. G.P.H. Jagath Kumara

Project Leader of Grades 6-11 Mathematics

Curriculum Committee:
External:
Dr. U. Mampitiya Senior Lecturer, department of Mathematics,
University of Kelaniya

Dr. D.R. Jayewardena Senior Lecturer, department of Mathematics,

University of Colombo

Mr. M.S. Ponnambalam Retired Senior Lecturer,

Siyane National College of Education

Mrs. W.M.B Janaki Wijesekara Retired Director,Department of Mathematics,

National Institute of Education

Mr. W. Rathnayake Retired Project Officer,

Department of Mathematics,
National Institute of Education

Mr. W.M. Wijedasa Retired Director, Mathematics Branch,

Ministry of Education,Isurupaya,Battaramulla

Mr. B.D.C. Biyanwila Director, Mathematics Branch, Ministry of

Education,Isurupaya,Battaramulla
Internal

Mr. K. Ranjith Pathmasiri Director, Department of Mathematics,

National Institute of Education

Mr. G.P.H. Jagath Kumara Senior Lecturer, Department of Mathematics,

National Institute of Education

Mr. G.L. Karunarathna Senior Educationist, Department of Mathematics,

National Institute of Education

v
Teacher’s Guide - Grade
Grade 9 Mathematics

Mrs. M.N.P. peiris Senior Lecturer, Department of Mathematics,

National Institute of Education

Mr. S. Rajendram Lecturer, Department of Mathematics,

National Institute of Education

Ms. K.K.Wajeema Sumedani Asst. Lecturer, Department of Mathematics,

Kankanamge National Institute of Education

Mr. P. Wijaikumar Asst. Lecturer, Department of Mathematics,

National Institute of Education

Mr. C. Suthesan Asst. Lecturer, Department of Mathematics,

National Institute of Education

External Resource Support:

Mrs. D.M. Attanayake Retired In-service Advisor

Mr. H.M.A. Jayasena Retired In-service Advisor

Mrs. B.M. Bisomenike In-service Advisor, Divisional Education Office,

Wariyapola

Mr. M.S.P.K. Abeynayake Assistant Director of Education,

Zonal Education Office, Kantale

Mr. D.D. Anura weerasinghe In-service Advisor,Sri Rewatha M.P.,Mathara

Mrs. G.H.S. Ranjani de Silva Teacher Service,

Pannipitiya Dharmapala Viddiyalaya,Pannipitiya

Mrs. M.A.S. Rabel Teacher Service (Retired)

Language Editing: Mr. H.P. Susil Sirisena,

Lecturer, Hapitigama NCOE

Computer Type Setting: Mrs. K. Nelika Senani, Technical Assistant-I

Cover Page:

Plan: Mr. E.L.A. Liyanage, Technical Assistant-I,

Press, National Institute of Education

Pictures: Try outing the lesson plans in schools of Western

and North-western Provinces

vi
 Teacher’s Guide - Grade 9 Mathematics

Instructions on the use of the Teacher’s Guide

The Department of Mathematics of the National Institute of Education has been preparing for
the new education reforms to be implemented in 2015 for the first time since 2007, in
accordance with the education reforms policy which is implemented once every eight years.
The Grade 9 Mathematics Teacher’s Guide which has been prepared accordingly has many
special features.

The Grade 9 syllabus is included in the first chapter. The syllabus has been organized under
the titles Competencies, Competency Levels, Content, Learning Outcomes and Number of
Periods. The proposed lesson sequence is given in the second chapter. The Learning-
Teaching-Evaluation methodology has been introduced in the third chapter. A special
feature of this is that the best method to develop each of the subject concepts in students has
been identified from various methods such as the discovery method, the guided discovery
method, the lecture-discussion method etc and the lesson plan has been developed based on it.

Following the proposed lesson sequence, the relevant competency and competency levels as
well as the number of periods required for each lesson have been included at the beginning
under each topic. Specimen lesson plans have been prepared with the aim of achieving one or
two of the learning outcomes related to a selected competency level under each competency.
These lesson plans have been carefully prepared to be implemented during a period or a
maximum of two periods.

To create awareness amongst the students regarding the practical applications of the subject
content that is learnt, a section titled ‘Practical Use’ which contains various such applications
has been introduced in some of the lessons.

You have been provided with the opportunity to prepare suitable lesson plans and appropriate
assessment criteria for the competency levels and related learning outcomes for which
specimen lesson plans have not been included in this manual. Guidance on this is provided
under the title ‘For your attention ….’.

Another special feature of this Teacher’s Guide is that under each lesson, websites which can
be used by the teacher or the students, in the classroom or outside which contain resources
that include videos and games to enhance students’ knowledge is given under the title ‘For
further use’ and the symbol . Although it is not essential to make use of these, the
learning-teaching-evaluation process can be made more successful and students’ subject
knowledge can be enhanced by their use, if the facilities are available.

Further, in selected lessons, under the title “For the teacher only” and the symbol ,
facts which are especially for the teacher are included. This information is only to enhance the
teacher’s knowledge and is not given to be discussed with the students directly. The teacher
has the freedom to make necessary amendments to the specimen lesson plan given in the new
teacher’s manual which includes many new features, depending on the classroom and the
abilities of the students. We would be grateful if you would send any amendments you make
or any new lessons you prepare to the Director, Department of Mathematics, National Institute
of Education. The mathematics department is prepared to incorporate any new suggestions
that would advance mathematics educations in the secondary school system.
Project Leader
vii
 Teacher’s Guide - Grade 9 Mathematics

Contents

Chapter Page

01. Syllabus 1 - 25
1.1 Common National Goals 1 - 2
1.2 Common National Competencies 3 - 5
1.3 Aims of Learning Mathematics 6
1.4 Subject Content 7 - 25

02. Lesson Sequence 26

03. Instructions for the Learning-Teaching-Evaluation Process 27 - 157

vii
 1.0 Syllabus
1.1 Common National Goals
The national system of education should assist individuals and groups to achieve major national goals that are relevant to the
individual and society.

Over the years major education reports and documents in Sri Lanka have set goals that sought to meet individual and national needs.
In the light of the weaknesses manifest in contemporary educational structures and processes, the National Education Commission has
identified the following set of goals to be achieved through education within the conceptual framework of sustainable human
development.

I Nation building and the establishment of a Sri Lankan identity through the promotion of national cohesion, national integrity,
national unity, harmony and peace, and recognizing cultural diversity in Sri Lanka’s plural society within a concept of respect
for human dignity.

II Recognizing and conserving the best elements of the nation’s heritage while responding to the challenges of a changing world.

III Creating and supporting an environment imbued with the norms of social justice and a democratic way of life that promotes
respect for human rights, awareness of duties and obligations, and a deep and abiding concern for one another.

1
IV Promoting the mental and physical well-being of individuals and a sustainable life style based on respect for human values.

V Developing creativity, initiative, critical thinking, responsibility, accountability and other positive elements of a well-
integrated and balance personality.

VI Human resource development by educating for productive work that enhances the quality of life of the individual and the
nation and contributes to the economic development of Sri Lanka.

VII Preparing individuals to adapt to and manage change, and to develop capacity to cope with complex and unforeseen situations
in a rapidly changing world.

VIII Fostering attitudes and skills that will contribute to securing an honourable place in the international community, based on
justice, equality and mutual respect.

2
1.2 Common National Competencies

The following Basic Competencies developed through education will contribute to achieving the above National Goals.

(I) Competencies in Communication

Competencies in Communication are based on four subsets; Literacy, Numeracy, Graphics and IT proficiency.

Literacy: Listen attentively, speak clearly, read for meaning, write accurately and lucidly and communicate ideas
effectively.

Numeracy: Use numbers for things, space and time, count, calculate and measure systematically.

Graphics: Make sense of line and form, express and record details, instructions and ideas with line form and
colour.

IT proficiency: Computer literacy and the use of information and communication technologies (ICT) in learning, in the
work environment and in personal life.

(II) Competencies relating to Personality Development

• Generic skills such as creativity, divergent thinking, initiative, decision making, problem solving, critical and
analytical thinking, team work, inter-personal relations, discovering and exploring;

• Values such as integrity, tolerance and respect for human dignity;

• Emotional intelligence.
(III) Competencies relating to the Environment

These competencies relate to the environment: social, biological and physical.

3
 Social Environment: Awareness of the national heritage, sensitivity and skills linked to being members of a plural
society, concern for distributive justice, social relationships, personal conduct, general and legal
conventions, rights, responsibilities, duties and obligations.

Biological Environment: Awareness, sensitivity and skills linked to the living world, people and the ecosystem, the trees,
forests, seas, water, air and life- plant, animal and human life.

Physical Environment: Awareness, sensitivity and skills linked to space, energy, fuels, matter, materials and their links
with human living, food, clothing, shelter, health, comfort, respiration, sleep, relaxation, rest,
wastes and excretion.

Included here are skills in using tools and technologies for learning working and living.

(IV) Competencies relating to Preparation for the World of Work

Employment related skills to maximize their potential and to enhance their capacity

• to contribute to economic development,

• to discover their vocational interests and aptitudes,

• to choose a job that suits their abilities, and

• to engage in a rewarding and sustainable livelihood.

(V) Competencies relating to Religion and Ethics

Assimilating and internalizing values, so that individuals may function in a manner consistent with the ethical, moral and
religious modes of conduct in everyday living, selecting that which is most appropriate.
4
(VI) Competencies in Play and the Use of Leisure

Pleasure, joy, emotions and such human experiences as expressed through aesthetics, literature, play, sports and athletics,
leisure pursuits and other creative modes of living.

(VII) Competencies relating to “learning to learn”

Empowering individuals to learn independently and to be sensitive and successful in responding to and managing change
through a transformative process, in a rapidly changing, complex and interdependent world.

5
1.3 Aims of Learning Mathematics

The following objectives should be aimed at and achieved to further develop the mathematical concepts, creativity and sense of
appreciation in students entering the junior secondary stage, so that their mathematical thinking, understanding and abilities are
formally enhanced.

(1) The development of computational skills through the provision of mathematical concepts and principles, as well as
knowledge of mathematical operations, and the development of the basic skills of solving mathematical problems with
greater understanding.

(2) The development of correct communication skills by enhancing the competencies of the proper use of oral, written,
pictorial, graphical, concrete and algebraic methods.

(3) The development of connections between important mathematical ideas and concepts, and the use of these in the study and
improvement of other subjects. The use of mathematics as a discipline that is relevant to lead an uncomplicated and
satisfying life.

(4) The enhancement of the skills of inductive and deductive reasoning to develop and evaluate mathematical conjectures and
conversations.

(5)The development of the ability to use mathematical knowledge and techniques to formulate and solve problems, both
familiar and unfamiliar and which are not limited to arithmetic or the symbolical or behavioral, which arise in day to
day life.
6
2.4 Subject Content
Competency Competency Content Learning Outcomes Periods
Level
Competency – 1 1.1
Manipulates the Organizes • Scientific notation • Identifies writing a number as the product of a 03
mathematical numbers in • Large numbers (Up number greater or equal to 1 and less than 10, and
operations in the ways that to a million) a power of ten as representing a number in
set of real facilitate their • Decimal numbers scientific notation.
numbers to fulfill manipulation. • Writes numbers greater than one in scientific
the needs of day notation.
to day life. • Writes numbers less than one in scientific notation.
1.2
Determines • Rounding off • Identifies the rules that are used when rounding off 02
approximate • Whole numbers numbers.
values to (Up to the millions • Rounds off whole numbers to the nearest ten.
facilitate period) • Rounds off whole numbers to the nearest hundred.
manipulation. • To the nearest 10 • Rounds off whole numbers to the nearest thousand.
• To the nearest 100 • Rounds off a decimal number to a given decimal
• To the nearest place.
1000 • Solves problems related to rounding off.
• Decimal numbers
(To a given decimal
place)
1.3
Develops • Binary numbers • Identifies binary numbers. 03
relationships • Introduction • Converts a binary number into a decimal number.
between • Conversion • Converts a decimal number into a binary number.
numbers in • Base two Base • Adds binary numbers.
different bases. ten • Subtracts binary numbers.
• Addition • Investigates instances in the modern world where
7
 Competency Competency Content Learning Outcomes Periods
Level
• Subtraction the binary number system is used.
Competency – 2 2.1
Makes decisions Develops the • General term • Writes the general term of a number pattern. 03
for future general term by • Of a given number • Writes the number pattern when its general term is
requirements by identifying the pattern given.
investigating the relationship • Solves problems related to number patterns.
various between the
relationships terms of a
between numbers. number pattern.

Competency – 3 3.1
Manipulates units Methodically • Simplifying fractions 05
and parts of units simplifies • Laws of • Simplifies expressions of fractions that contain
under the expressions simplification “of”.
mathematical involving (BODMAS) • Accepts that the laws on the order in which
operations to fractions. simplification should be carried out (BODMAS)
easily fulfill the need to be followed when simplifying fractions
requirements of under the basic mathematical operations.
day to day life. • Simplifies expressions of fractions that contain
brackets.
• Simplifies expressions of fractions that contain the
basic mathematical operations, brackets and “of”.
• Solves problems involving fractions by applying
the BODMAS Laws.

Competency – 4 4.1
Uses ratios to Engages in • Introducing direct • Identifies proportion 06
facilitate day to calculations by proportions • Explains direct proportions using examples.
day activities. considering • Problems related to • Writes the relationship between two quantities
direct direct proportions which are directly proportional in the form .
8
 Competency Competency Content Learning Outcomes Periods
Level
proportions. • Unitary method • Solves problems related to direct proportions by
• Based on the applying the unitary method.
definition of • Solves problems related to direct proportions by
proportion using the definition of proportion.
• Foreign currency • Solves problems involving the conversion of
• Representing direct foreign currency by applying the knowledge on
proportions direct proportions.
algebraically • Solves problems on direct proportions by
• ; is expressing the relationship algebraically.
a constant
•
• Solving problems
using
Competency - 5 5.1
Uses percentages Makes decisions • Profit, Loss • Identifies the profit/loss. 06
to make by comparing • Identifies the profit/loss percentage.
successful profits and • Uses of percentages • Performs calculations related to purchase price,
transactions in the losses. selling price, profit/loss percentage.
modern world. (Discounts,
Commissions) • Explains what a discount is.
• Performs calculations related to discounts.
• Explains what a commission is.
• Performs calculations related to commissions.
• Solves problems by applying the knowledge on
profit/loss/discounts/commissions.
Competency – 6 6.1
Uses logarithms Simplifies • Laws of indices • Identifies the laws of indices that are applied when 03
and calculators to powers by • Multiplication multiplying powers and dividing powers
easily solve applying the • Division • Identifies the laws of indices that are applied when
problems in day laws of indices. • Power of a power finding the power of a power.
9
 Competency Competency Content Learning Outcomes Periods
Level
to day life. • Simplifying indices • Recognizes that and .
• Including zero index • Applies the laws of indices to simplify expressions
• Including negative involving indices.
indices
6.2
Uses the • Scientific calculator • 1. Identifies the keys On , Off , + , - , × , ÷ and = 02
calculator to • Using the keys of in the scientific calculator
facilitate a calculator • Uses scientific calculator using the keys On , Off ,
calculations. • =, %, + , - , × , ÷ and =
• Identifies the keys % , x and √x in the scientific
2

calculator.
• Uses the keys % , x and √x in the scientific
2

calculator.
• Accepts that efficiency can be increased by using
the scientific calculator.
• Check the accuracy of the answers by using the
scientific calculator.
Competency – 7 7.1 • Circle • Measures the diameter and the circumference of
Investigates the Applies the • Measuring the circular laminas using various methods. 05
various methods relationship diameter • Develops a formula for the circumference by
of finding the between the • Measuring the considering the relationship between the diameter
perimeter to carry diameter and circumference and the circumference of a circle.
out daily tasks circumference • Relationship • Performs calculations related to the circumference
effectively. of a circle when between the of a circle by applying the formulae and
performing circumference and .
various the diameter • Finds the circumference of a circle.
calculations. • Application of the • Finds the perimeter of a semi-circle.
formulae and • Solves simple problems involving the circum-
ference of a circle.
10
 Competency Competency Content Learning Outcomes Periods
Level
• Perimeter of a semi-
circle
Competency – 8 8.1
Makes use of a Investigates the • Area • Develops a formula for the area of a parallelogram. 05
limited space in area of simple • Parallelogram • Finds the area of a parallelogram.
an optimal geometrical • Trapezium • Develops a formula for the area of a trapezium.
manner by shapes in the • Circle • Finds the area of a trapezium.
investigating the environment. • Develops the formula for the area of a
area. circle.
• Performs calculations by applying the formula
.
• Solves problems related to the areas of
parallelograms, trapeziums and circles.
Competency – 11 11.1
Works critically Develops • Relationships between • Identifies the relationship between and 3. 03
with the relationships the units of liquid • Develops the relationship between and 3.
knowledge on between units of measurements • Develops the relationship between and 3.
liquid measures to liquid • Milliliter and cubic • Converts liquid measurements in one unit to
fulfill daily needs. measurements. centimeter another, by using the relationships between and
• Liter and cubic 3
, between and 3, and between and 3.
centimeter • Solves problems related to the conversion of units
• Liter and cubic of liquid measurements.
meter

Competency – 13 13.1
Uses scale Indicates the • Location of a place • Explains “bearing”. 05
diagrams in direction of a • By means of • Accepts that the bearing and the distance are
practical location by “bearing” needed to describe the location of a place with
situations by means of an respect to another place on a horizontal plane.
11
 Competency Competency Content Learning Outcomes Periods
Level
exploring various angle. • Identifies the clinometer as an instrument that is
methods. used to measure bearing and uses it.
• Describes various locations in terms of bearing and
distance.
• Performs calculations related to bearing.
13.2
Investigates • Two dimensional • Draws scale diagrams of locations in a horizontal 03
various scale diagrams plane when the relevant bearings and distances are
locations in the • On a horizontal given.
environment plane • Obtains measurements in relation to locations in a
using scale horizontal plane using scale diagrams.
diagrams.
Competency – 14 14.1
Simplifies Simplifies • Algebraic expressions • Finds the value of an algebraic expression which 02
algebraic expressions by • Substitution does not involve powers or roots by substituting
expressions by substitution. (without roots but directed numbers.
systematically including fractions)
exploring various
methods.
14.2
Simplifies • Simplifies algebraic expressions involving 03
binomial • Simplification binomial expressions which are of the form
expressions • Algebraic , where .
expressions with • Simplifies algebraic expressions of the form
brackets , where .
• Of the form • Validates the product of two binomial expressions
, using areas.
where .
• Of the form,
, where
12
 Competency Competency Content Learning Outcomes Periods
Level
.

Competency – 15 15.1
Factorizes Presents • Factors of algebraic • Factorizes an algebraic expression with up to four 02
algebraic algebraic expressions terms by taking two terms at a time.
expressions by expressions in a • The common factor • Factorizes an algebraic expression with four terms,
systematically simple form by a binomial where the factors are binomial expressions.
exploring various factorizing. expression; up to 4
methods. terms
• Of the form

• Of the form

15.2
Factorizes • Trinomial quadratic • Organizes an algebraic expression of the form 03
quadratic expressions of the into a form that can be factored, by
expressions to form separating the term into two terms.
fulfill • Difference of two • Factorizes an algebraic expression of the form
mathematical squares (not including .( a perfect square)
requirements. algebraic expressions) • Writes down the factors of the difference of two
squares that includes algebraic terms.

Competency - 16 16.1
Explores the Analyses • Algebraic fractions • Identifies algebraic fractions. 03
various methods relationships in • Introduction • Adds and subtracts algebraic fractions with equal
of simplifying daily life by • Addition and integral denominators.
algebraic fractions simplifying subtraction • Adds and subtracts algebraic fractions with
to solve problems algebraic • With integral unequal integral denominators.
encountered in fractions. denominators • Adds and subtracts algebraic fractions with equal
day to day life.
13
 Competency Competency Content Learning Outcomes Periods
Level
(equal/unequal algebraic denominators.
denominators)
• With algebraic
denominators
(equal
denominators)
Competency – 17 17.1
Manipulates the Easily solves • Solving linear • Solves linear equations containing algebraic terms 03
methods of problems in day equations with fractional coefficients.
solving equations to day life by • With two types of • Solves linear equations with two types of brackets.
to fulfill the needs solving linear brackets
of day to day life. equations. • With fractions

17.2
Solves problems • Solving simultaneous • Solves a pair of simultaneous equations by 03
by using the equations eliminating an unknown, when the coefficient of
methods of • The coefficient of one unknown is of equal numerical value in both
solving one unknown being equations.
simultaneous of equal numerical • Uses other algebraic methods to solve pairs of
equations. value in the two simultaneous equations when the coefficient of one
equations unknown is of equal numerical value in both
equations.
• Selects the most suitable method to solve a pair of
simultaneous equations.
Competency – 18 18.1
Analyzes the Uses the • Solving inequalities • Solves inequalities of the form ( ∈ ). 03
relationships relationship • Of the form • Solves inequalities of the form when
between various between two ( ∈ ) • Solves inequalities of the form when
quantities related quantities to
14
 Competency Competency Content Learning Outcomes Periods
Level
to real-life solve problems. ( is an integer or a fraction)
problems. • Represents the integral solutions of an inequality
• Of the form on a number line.
• Represents the solutions of an inequality on a
( ) number line.
• Representation of the
solutions on a number
line

• Integral solutions

• Intervals of
solutions
Competency – 19 19.1
Explores the Changes the • Changing the subject • Changes the subject of a formula that does not 02
methods by which subject of a of simple formulae contain squares and square roots.
formulae can be formula that has (Without squares and • Performs calculations by substituting values for the
applied to solve been developed square roots) unknowns in a simple formula.
problems to show the • Substitution
encountered in relationship
day to day life. between
variables.
Competency – 20 20.1
Easily Analyses • Introducing functions • Identifies that the relationship between and 04
communicates the graphically • Straight line graphs given by a linear equation in and is a function.
mutual mutual linear • Of the form • Draws the graph of a function of the form .
relationships that relationship • Of the form • Draws the graph of a function of the
exist between two between two form .
variables by variables. • Of the form • Explains how the graph of a function changes

15
 Competency Competency Content Learning Outcomes Periods
Level
exploring various depending on the sign and magnitude of the
methods. (for a given domain) gradient .
• Introducing the • States that is the gradient and is the intercept of
gradient and the the graph of a function of the form .
intercept • Writes down the gradient and the intercept of the
graph of a function of the form by
examining the function.
• Draws the graph of a function of the form
for a given domain.
• Analyses the gradients of straight line graphs
which are parallel to each other.
Competency – 21 21.1
Makes decisions Establishes the • Application of the • Identifies the theorem “The sum of the adjacent 03
by investigating relationships theorem “The sum of angles formed by a straight line meeting another
the relationships between the the adjacent angles straight line is two right angles”.
between various angles related to formed by a straight
angles. straight lines. line meeting another • Verifies the theorem “The sum of the adjacent
straight line is two angles formed by a straight line meeting another
right angles” (Proof straight line is two right angles”.
not expected)
• Solves problems by applying the theorem “The
• Proof and application sum of the adjacent angles formed by a straight
of the theorem “If two line meeting another straight line is two right
straight lines intersect angles”.
one another, the • Identifies the theorem “If two straight lines intersect
vertically opposite one another, the vertically opposite angles are
angles are equal” equal”.
• Verifies the theorem “If two straight lines intersect
one another, the vertically opposite angles are
equal”.
16
Competency Competency Content Learning Outcomes Periods
Level

• Solves problems by applying the theorem “If two

straight lines intersect one another, the vertically
opposite angles are equal”.
• Proves the theorem “If two straight lines intersect
one another, the vertically opposite angles are
equal”.
21.2
Investigates the • The angles formed • Identifies the alternate angles, corresponding 01
angles formed when a transversal angles and allied angles that are formed when a
by various intersects a pair of transversal intersects a pair of straight lines.
intersecting straight lines
straight lines. • Alternate angles
• Corresponding
angles
• Allied angles
21.3
Identifies the • Application of the • Identifies the theorem, “When a transversal 03
relationships following theorem and intersects a pair of straight lines, if a pair of
between the its converse; “When a alternate angles is equal, or a pair of corresponding
angles related to transversal intersects a angles is equal or the sum of a pair of allied angles
parallel lines. pair of straight lines, if equals two right angles, then the pair of straight
a pair of alternate lines is parallel”
angles is equal, or a
pair of corresponding • Verifies the theorem, “When a transversal intersects
angles is equal or the a pair of straight lines, if a pair of alternate angles is
sum of a pair of allied equal, or a pair of corresponding angles is equal or
angles equals two the sum of a pair of allied angles equals two right
right angles, then the angles, then the pair of straight lines is parallel”
pair of straight lines is
17
Competency Competency Content Learning Outcomes Periods
Level
parallel”
(Proof not expected) • Solves problems by applying the theorem, “When a
transversal intersects a pair of straight lines, if a pair
of alternate angles is equal, or a pair of
corresponding angles is equal or the sum of a pair
of allied angles equals two right angles, then the
pair of straight lines is parallel”

• Identifies the following converse of the above

theorem, “When a transversal intersects a pair of
parallel straight lines,
- pairs of alternate angles formed are equal
- pairs of corresponding angles formed are equal
- the sum of each pair of allied angles formed
equals two right angles.

• Verifies the following converse of the above

theorem, “When a transversal intersects a pair of
parallel straight lines,
- pairs of alternate angles formed are equal
- pairs of corresponding angles formed are equal
- the sum of each pair of allied angles formed
equals two right angles.

• Solves problems by applying the following

converse of the above theorem, “When a transversal
intersects a pair of parallel straight lines,
- pairs of alternate angles formed are equal
- pairs of corresponding angles formed are equal
- the sum of each pair of allied angles formed
18
 Competency Competency Content Learning Outcomes Periods
Level
equals two right angles.
Competency – 23 23.1
Makes decisions Geometrically • Introducing axioms • Identifies the five basic axioms. 04
regarding day to analyses the through geometry • Develops relationships using the five basic axioms.
day activities relationships • Quantities that are
based on between equal to the same
geometrical quantities. quantity are equal to
concepts related each other
to rectilinear • If equal quantities
plane figures. are added to equal
quantities, the
resultant quantities
will also be equal
• If equal quantities
are subtracted from
equal quantities, the
resultant quantities
will also be equal
• If equal quantities
are multiplied by
equal quantities the
resultant quantities
will be equal
• If equal quantities
are divided by equal
quantities, the
resultant quantities
will be equal

19
Competency Competency Content Learning Outcomes Periods
Level

23.2
Formally • Application of the • Identifies the theorem, “The sum of the three 04
investigates the theorem interior angles of a triangle is 180o”.
sum of the three “The sum of the three • Verifies the theorem, “The sum of the three
interior angles interior angles of a interior angles of a triangle is 180o”.
o
of a triangle. triangle is 180 ” • Solves simple geometric problems using the
theorem, “The sum of the three interior angles of a
triangle is 180o”.
23.3 • Application of the • Identifies the theorem, “If a side of a triangle is
Investigates the theorem produced, the exterior angle so formed is equal to 04
relationship “If a side of a triangle the sum of the two interior opposite angles”.
between the is produced, the • Verifies the theorem, “If a side of a triangle is
exterior angle exterior angle so produced, the exterior angle so formed is equal to
formed by formed is equal to the the sum of the two interior opposite angles”.
producing a side sum of the two • Solves simple geometric problems using the
of a triangle and interior opposite theorem, “If a side of a triangle is produced, the
the interior angles” exterior angle so formed is equal to the sum of the
opposite angles. two interior opposite angles”.
23.4
Performs • Application of the • Identifies the theorem, “The sum of the interior 05
calculations theorem angles of an n-sided polygon equals (2n – 4) right
using the sums “The sum of the angles”.
of the interior interior angles of an • Verifies the theorem, “The sum of the interior
and exterior n-sided polygon angles of an n-sided polygon equals (2n – 4) right
angles of a equals (2n – 4) angles”.
polygon. right angles” • Solves simple geometric problems using the
theorem, “The sum of the interior angles of an n-
• Application of the sided polygon equals (2n – 4) right angles”.
theorem
20
 Competency Competency Content Learning Outcomes Periods
Level
“The sum of the • Identifies the theorem, “The sum of the exterior
exterior angles of an angles of an n-sided polygon is four right angles”.
n-sided polygon is • Verifies the theorem, “The sum of the exterior
four right angles” angles of an n-sided polygon is four right angles”.
• Solves simple geometric problems using the
theorem, “The sum of the exterior angles of an n-
sided polygon is four right angles”.
23.5
Applies • Identifying and • Identifies Pythagoras’ relationship. 04
Pythagoras’ applying Pythagoras’ • Verifies Pythagoras’ relationship.
relationship to relationship (For • Solves simple problems by applying Pythagoras’
solve problems whole number values) relationship.
in day to day • Solves problems in day to day life by applying the
life. subject content related to Pythagoras’ relationship.
Competency – 27 27.1
Analyzes Uses the • Introducing the basic • Identifies what a locus is. 05
according to knowledge on loci • Identifies the four basic loci.
geometric laws, the basic loci to • The locus of a point • Constructs a perpendicular to a straight line from a
the nature of the determine the moving at a constant point on the line.
locations in the location of a distance from a • Constructs a perpendicular to a straight line from
surroundings. point. fixed point an external point.
• The locus of a point • Constructs a perpendicular to a straight from an
moving at an equal end point.
distance from two • Constructs the perpendicular bisector of a straight
fixed points line.
• The locus of a point • Solves problems in day to day life by using the
moving at a constant knowledge on the basic loci.
distance from a
straight line

21
 Competency Competency Content Learning Outcomes Periods
Level
• The locus of a point
moving at an equal
distance from two
intersecting straight
lines. (without
constructions)
• Construction of a
line perpendicular to
a straight line
• From an external
point
• From a point on
the line
• From an end point
• Perpendicular
bisector
27.2
Uses geometric • Bisection of an angle • Constructs the bisector of an angle. 04
constructions in • Construction of 60o, • Constructs angles of magnitude 60o, 30o, 120o.
various 90o, 30o, 45o, 120o • Constructs angles of magnitude 90o, 450.
activities. • Copying an angle • Constructs other angles that can be constructed
equal to a given angle using the construction of angles of magnitude 60o,
• Construction of 90o, 30o, 45o, 120o.
parallel lines • Studies methods of validating the accuracy of the
constructions.
Competency – 28 28.1
Facilitates daily Represents data • Representation of data • Identifies a frequency distribution. 04
work by such that • In tables • Presents a given group of data in a frequency
investigating the comparison is • Ungrouped distribution without class intervals.

22
 Competency Competency Content Learning Outcomes Periods
Level
various methods facilitated. frequency • Identifies what a class interval is.
of representing distribution • Identifies presenting data in class intervals as
data. (clustering without grouping data.
class intervals) • Represents a given group of data in a frequency
• Grouped frequency distribution with class intervals.
distribution
Competency – 29 29.1
Makes predictions Investigates • Interpretation of data • Identifies the central tendency measurements of 06
after analyzing frequency • Measures of central mode, median and mean as representative values of
data by various distributions tendency of an a frequency distribution.
methods, to using ungrouped • Identifies the score that occurs the most in a group
facilitate daily representative frequency of data as the mode of that group.
activities. values. distribution • Identifies the score in the middle of a group of data
• Mode when it is in either ascending or descending order
• Median as the median of that group.
• Mean • Identifies the value that is obtained when the
• Measures of values of all the data are added together and
dispersion of an divided by the number of data as the mean of that
ungrouped frequency group.
distribution • Calculates the mean of a group of data using the
• Range formula , when it has been presented in a
• Grouped frequency frequency distribution.
distribution • Identifies the difference between the greatest value
• Modal class and the least value of a group of data as its range.
• Median class • Identifies grouped frequency distributions.
• Writes down the modal class of a grouped
frequency distribution.
• Writes down the median class of a grouped
frequency distribution.
23
 Competency Competency Content Learning Outcomes Periods
Level
• Makes decisions in day to day life by considering
representative values.
Competency – 30 30.1
Manipulates the Performs set • Types of sets • Identifies finite sets and infinite sets. 07
principles related operations by • Finite sets • Concludes with reasons whether a given set is a
to sets to facilitate identifying • Infinite sets finite set or an infinite set.
daily activities. various systems. • Relationship between • Writes down all the subsets of a given set.
two sets • Explains the difference between equivalent sets
• Subsets of a set and equal sets.
• Equal sets • Identifies disjoint sets.
• Equivalent sets • Identifies the universal set.
• Disjoint sets • Writes down the elements in the intersection of
• Universal set two sets.
• Set Operations • Writes down the elements in the union of two sets.
• Intersection • Identifies the complement of a set.
• Union • Identifies the symbols relevant to set operations.
• Complement of a set • Accepts that if the intersection of two sets is the
empty set, then the two sets are disjoint.
• Solves problems using the knowledge on sets.
• Represents subsets, the intersection of two sets, the
union of two sets, disjoint sets and the complement
of a set in Venn diagrams and writes these sets
using the symbols used for set operations. (For two
sets only)
Competency – 31 31.1
Analyzes the Investigates the • Randomness • Identifies random experiments. 05
likelihood of an likelihood of an • Sample space • Identifies the set of all possible outcomes of an
event occurring to event by • Probability of an event experiment as the sample space of that experiment.
predict future considering the in a sample space • Writes down the sample space of a given
24
 Competency Competency Content Learning Outcomes Periods
Level
events. outcomes of the when the outcomes experiment.
experiment. are equally likely • Identifies equally likely outcomes.
• Writes down examples of equally likely outcomes.
• Performs calculations using the formula
for an event of a random experiment with
equally likely outcomes, having a sample space .
• Makes decisions in day to day life using the
knowledge gained on probability.

Total 142

25
 Lesson Sequence
Contents Competency Number of
Levels periods

1st Term
1. Round off and Scientific Notation 1.1, 1.2 05
2. Number base two 1.3 03
3. Number Patterns 2.1 03
4. Fractions 3.1 05
5. Percentages 5.1 06
6. Algebraic Expressions 14.1, 14.2 05
7. Factors of the algebraic expressions 15.1, 15.2 05
8. Angles related to strait lines and parallel lines 21.1, 21.2, 21.3 07
9. Liquid Measurements 11.1 03
42
2nd Term
10. Direct proportion 4.1 06
11. Calculator 6.2 02
12. Indices 6.1 03
13. Loci and Constructions 27.1, 27.2 09
14. Equations 17.1, 17.2 06
15. Axioms 23.1 04
16. Angles of a triangle 23.2, 23.3 09
17. Formulae 19.1 02
18. Circumference of a circle 7.1 05
19. Pythagoras relationship 23.5 04
20. Graphs 20.1 04
54
3rd Term
21. Inequalities 18.1 03
22. Sets 30.1 07
23. Area 8.1 05
24. Probability 31.1 05
25. Angles of polygons 23.4 05
26. Algebraic fractions 16.1 03
27. Scale drawings 13.1, 13.2 08
28. Data representation and prediction 28.1, 29.1 10
46
26 Total 142
Teacher’s Guide - Grade 9 Mathematics

1. Rounding off and Scientific Notation

Competency 1: Manipulates the mathematical operations in the set of real
numbers to fulfill the needs of day to day life.

Competency Level 1.1: Organizes numbers in ways that facilitate their manipulation

Number of Periods: 03

Introduction:
• Scientific notation is used as a method of indicating large numbers (e.g.
5 900 000 000 which is the distance to the pluto from the sun in kilome-
tres) and small numbers (e.g. 0. 000 000 000 753 which is the mass of
an sand atom in kilorams) in shortened form.
• In scientific notation , the relevant numbers (1 or greater than 1 or less
than 10) are written as a product of a number and a power of 10.
• Any fraction that can be indicated as terminating or recurring decimals
and integers belong to the set of rational numbers.
• When A is a number ( 1 or greater than 1 but less than 10) and n is an
integer , the scientific notation is indicated in generalised form by A×10n.
• This section expects to direct students to write large numbers greater 1
and small numbers less than 1 by scientific notation.

Learning outcomes relevant to Competency Level 1.1:

1. Identifies writing a number as the product of a number greater or equal to 1

and less than 10, and a power of ten as representing a number in scientific
notation.
2. Writes numbers greater than one in scientific notation.
3. Writes numbers less than one in scientific notation.

Glossary of terms:

Integes - ksÅ, - epiwntz;fs;

Power - n,h - tY
Scientific notation - úoHd;aul wxlkh - tpQ;QhdKiwf; Fwpg;gL
P

Instructions to plan the lesson:

A specimen lesson that would adopt guided inquiry method to

develop in students the first and second learning outcomes relevant
to competency level 1.1 is given below.

27
Teacher’s Guide - Grade 9 Mathematics

Time: 40 minutes

Quality inputs:
• The demy paper containing the information in Annex I
• Copies of Annex I , one for each student.

Instructions for the teacher:

Approach:
• Distribute the copies of Annex I to the students
• Show the demy paper containing the information in Annex I to the students.
• Engage the students in the activity of completing the table 1.1 in the annex
and revise their Knowledge about 1 and the numbers greater than 1 and
less than 10.

Development of the lesson:

• Using the examples such as those given below , show how a number can
be shown in terms of powers of ten.
30 = 3 × 10 = 3 × 101
300 = 3 × 100 = 3 × 102
• Reinforce students’ knowledge by getting them to complete table 1.2 ,
given in the annex.
• After completing table 1.2, establish in students the idea that a number can
be represented by the product of either 1 or a number greater than but less
than 10 and a power of 10 and that this is called scientific notation.
• Also draw students’ attention to the relationship between the change in the
decimal place and the power of 10.
Assessment and evaluation:
• Assessment criteria:
• Identifies scientific notation as a method of abbreviating large numbers.
• Writes large numbers given in the scientific notation.
• Accepts that writing large numbers in the scientific notation is easier. .
• Engages correctly in the activity following the instructions given.
• Works cooperatively within the group.
• Direct the students to do the relevant exercises in lesson 1 of the textbook.
For your attention...
Development of the lesson:

• Discuss with students about writing the numbers less than one by scientific
notation in relation to the learning outcome 3.

28
Teacher’s Guide - Grade 9 Mathematics

• Explain the writing of numbers below 1 by scientific notation presenting

examples such as follows.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 1 of the text
book.

7 1
0.7 = = 7  = 7  101
10 10

12 12 1
0.12 = =  = 1.2  101
100 10 10

3.52 1
0.0352   3.52   3.52  102
100 100
For further reference:

• http://www.youtube.com/watch?v=cK1egPBjJXE
• http://www.youtube.com/watch?v=OPxzx75bAfk
• http://www.youtube.com/watch?v=DaoJmvqU3FI
• http://www.youtube.com/watch?v=pf41fDSWeoA
• http://www.youtube.com/watch?v=3jBfLaLrk6I
• http://www.youtube.com/watch?v=_qzs1zozTBo
• http://www.youtube.com/watch?v=fh8gkPW_6g4
• http://www.youtube.com/watch?v=BkwI6Uu0vi4
http://www.youtube.com/watch?v=_MIn3zFkEcc

29
Teacher’s Guide - Grade 9 Mathematics

Annex I
Table 1.1

Of the following numbers, select either 1 or numbers greater than 1 but less than
10 and underline them.

0.1, 9.2, 8.32, 10.1, 0.9, 1.0, 2.35, 8.09

Table 1.2
Complete the blanks.

4 4  1 4  100
40 4  10 4  101
400 4  100 4
4000 4   103
40000  10000 4
4  100000 
52 5.2   101
638  100 

Table 1.3
Complete the blanks.

Number Scientific notation

5  100
52 5.2 
502  102
173 1.73 
6072  103
4807 
5.31  103

30
Teacher’s Guide - Grade 9 Mathematics

2. Binary Numbers
Competency 1: Manipulates the mathematical operations in the set of real
numbers to fulfill the needs of day to day life.

Competency Level 1.3: Develops relationships between numbers in different bases.

Number of Periods: 03

Introduction:
• The number system written using only the two digits 0 and 1 is referred to
as the number system to base two or the binary number system.
• The digits used in the number system to the base two are only 0 and 1.
• When writing binary numbers it is a must that the base is written as two.
e.g. 11two
• As in the case of the number system to the base 10, the place value is
expressed by the powers of 10 , in the number system to the base two ,
the place value is indicated by the powers of two as 20, 21, 22, ...
• Numbers to the base two can be represented by the abacus and maximum
number of counting objects in a rod of it can be one.
• Numbers to the base ten can be converted to numbers to base two by
repeated division by two until the quotient is zero.
• In a binary number, by finding the values according to place value, binary
numbers can be converted to numbers to base ten.
• 0two + 0two = 0two 0two - 0two = 0two

0two + 1two = 1two 10two - 1two = 1two

1two + 0two = 1two 1two - 0two = 1two

1two + 1two = 10two 1two - 1two = 0two

By using above bonds, addition and subtraction of binary numbers
can be done.
• The devices such as calculators and computers in the modern world use
base two numbers.

Learning outcomes relevant to Competency Level 2.3:

1. Identifies binary numbers.
2. Converts a decimal number into a binary number.
3. Converts a binary number into a decimal number.
4. Adds binary numbers.
5. Subtracts binary numbers.
6. Investigates instances in the modern world where the binary number system is
used.

31
Teacher’s Guide - Grade 9 Mathematics

Glossary of terms:

Base - mdoh - mb
Place Value - ia:dkSh w.h - ,lg;ngWkhdk;
Binary numbers - oaùuh ixLHd - Jtpj vz;fs;
Conversion - mßj¾;kh - khw;wy;

Instructions to plan the lesson:

Given below is a specimen lesson that incorporates a group activity

planned to achieve the learning outcomes 1 and 2 relating to the
competency level 1.3.
Time: 40 minutes

Quality inputs:
• Tooth picks or small pieces of eakles, 25 for each group
• Rubber bands or twine
• Halfsheets
• Copies of the activity sheet

Instructions for the teacher:

Approach:
• Through a discussion with students, emerge the fact that 0, 1, 2, 3, 4, 5, 6,
7, 8 and 9 are the digits that are being used in the presently used system of
numbers of base ten.
• Using the abacus , explain the value of the respective digits in the number
3234 written using those numbers.

3  103  2  102  3  101  4  100

3000 + 200 + 30 + 4
3234
103 102 101 100
• Stress that the maximum number of counting objects that can be
accommodated by a single rod in the abacus is 9.
• Recall that not putting any counting objects to a rod of the abacus indicates 0.
• State that likewise there can be other number bases as well.
• Recall that numbers such as 1, 2, 4, 8, 16, ....... can be written as powers
of 2 as follows.
1 = 20, 2 = 21,14 = 22, 8 = 23

32
Teacher’s Guide - Grade 9 Mathematics

Development of the lesson:

• Divide the class into groups as appropriate.
• Distribute quality inputs and activity sheets among the students.
• Give instructions to engage in the activity and record the results individually
while discussing within the group.
• Assess students while moving with the groups and helping them when
necessary.
• Introduce numbers to the base two to the students using examples in the
activity.
• Explain how the binary numbers are represented in the abacus.

- 1 0 1 0Two
23 22 21 20

• Build up the whole surfacing the students’ findings and how a number to the
base ten is converted to a number of base two by repeated division till the
quotient is zero.
2 15 2 10
27 1 25 0
23 1 22 1
21 1 21 0
0 1 0 1

15Ten = 1 1 1 1Two 10Ten = 1 0 1 0Two

Activity sheet for the Students :

Group Relevant numbers

A 9, 12
B 11,14
C 15, 20

• Take pieces of eakles equal to the first number you have received.
• Using rubber bands, make bundles of two pieces of eakles in each. If there
are single pieces keep them aside.
• Tie up into bundles of twos again the two-eakle bundles. If any two eakle
bundles are left, keep them aside.
• If possible tie up the four-eakle bundles in pairs. If any four-eakle bundles are
left, keep them aside.

33
Teacher’s Guide - Grade 9 Mathematics

• Using the results of your activity, complete the following table. If there are no
relevant bundles put 0

Bundles of 8 Bundles of 4 Bundles of 2 Bundles of 1

------- ------ ------ ------

Number of pieces of eakles you got = -- of 8 + -- of 4 + -- of 2 + -- of 1

----------------------------- = 8 ×---- + 4 ×---- + 2 ×---- + 1 ×----

------ Ten = 8 4 2 1
--- --- --- ---

-------- = 2 2 2 2
--- --- --- ---

• Do the same activity for the second number you have got and write the result
as above.

Assessment and evaluation:

• Assessment criteria:
• Indicates a number to the base two as a sum of the powers of 2.
• Identifies the number system with 0 and 1 as the number system of base
ten.
• Describes the value of a number to the base 2 in terms of the place value.
• Indicates a base ten number in base two.
• Accepts that in calculators and computers base two is used.
• Direct the students to do the relevant exercises in lesson 2 of the textbook.

Practical situations:
• Discuss with the students that base two is used in calculators and computers.

For your attention.....

Development of the lesson:

• After the establishment of learning outcomes 1 and 2 relevant to the

competency level 1.3 in students, they may be involved in the following joyful
game.
• Make five cards as shown in the diagram and write those numbers in the
cards.
• Let students think of a number below 31.

34
Teacher’s Guide - Grade 9 Mathematics

• Give 5 cards to a students and ask to separate the cards which bear the
number he has thought.
• If he says that number is seen in cards 1, 2, 4 say that the number is
1+2+4 = 7
• When the students become aware of the game, let them play the game in pairs.
• Say that this game can be played for other number bases as well.

16 8 4 2 1
17 8 4 2 1
17 9 5 3 3
18 10 6 6 5
19 11 7 7 7
20 12 12 10 9
21 13 13 11 11
22 14 14 14 13
23 15 15 15 15
24 24 20 18 17
25 25 21 19 19
26 26 22 22 21
27 27 23 23 23
28 28 28 26 25
29 29 29 27 27
30 30 30 30 31
31 31 31 31

• Taking the place value in to consideration, make students aware of writing the
numbers in base two in the number base of ten.
• Remembering well the additive and subtractive bounds in base two, practice
addition and subtraction of binary numbers.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 2 of the text
book.

For further reference:

35
Teacher’s Guide - Grade 9 Mathematics

3. Number Patterns
Competency 2 : Makes decisions for future requirements by investigating the
various relationships between numbers.

Competency Level 2.1: Develops the general term by identifying the relationship between
the terms of a number pattern.

Number of Periods: 03

Introduction:
• By identifying the relationship between the terms of some number patterns,
there is a possibility of obtaining the other terms in the pattern. These
number patterns are called as number sequences.
• The general term of a number pattern is decided by the value of each term
of the number pattern, the place of the term and the relationship between
thesuccessive terms. In grade 8, students have learnt the general term in
natural numbers, odd numbers, triangular numbers, square numbers and
multiples.
• Under the competency level 2.1 in grade 9, students are expected to find
out the general term in any number pattern in which the difference between
any two successive terms is equal.

Learning outcomes relevant to Competency Level 2.1:

1. Writes the general term of a number pattern.
2. Writes the number pattern when its general term is given.
3. Solves problems related to number patterns.

Glossary of terms:

Number sequence - ixLHd wkql%u - vz; njhlup

nth term - n jk moh - n Mk; cWg;G
1st term - m<uq moh - Kjyhk; cWg;G
Difference of terms - mo w;r fjki - cWg;Gf;fSf;fpil Naahdtpj;jpahrk;
General term - idOdrK moh - nghJ cWg;G

Instructions to plan the lesson:

This aims to build up in students the subject concepts relating to

the learning outcome 1 under the competency level 2.1. For this, a
specimen lesson planned to make students build up the general
term of a given pattern using the guided inquiry method is presented
below.

36
Teacher’s Guide - Grade 9 Mathematics

Time: 40 minutes
Quality inputs:
• Copies of the activity sheet, one for each student

Instruction for the teacher:

Approach:
• Display a number pattern with multiples learned in grade 8 on the board and
recall how the general term was found.
• Ask students about the difference between the first term and the successive
terms in a given number pattern of equal difference of terms.
• In order to obtain the general term of this number pattern, conduct a
discussion about the make of the first term and second term.
• On that basis, make a review with regard to the finding out of the general term
of a number pattern in which the difference between the successive term is
equal.

Development of the lesson:

• Group the students as appropriate, give one copy of the activity sheet to each
group and engage them in the activity.
• After completion of the activity, give an opportunity for students to present how
they discovered the general term of the pattern.
• Conduct a discussion explaining to the students that the general term of the pattern
can be easily built up in relation to the difference between successive terms.
Activity sheet for the Students:

In the number pattern 4, 7, 10, 13, .........

• What is the first term?
• What is the difference between two successive terms? ..................
• In order to obtain a general term using the first term and the difference
between two successive terms in the above pattern, fill in the following blanks.

1st term  4 = 4+3  0

2nd term  7 = 4 + ............  1
3rd term  10 = ............ + ............  .......
4th term  13 = ............ + ............  .......
5th term  ........ = ............ + ............  .......
8th term  ........ = ............ + ............  .......
10th term  ........ = ............ + ............  .......
nth term   ............ + ............  .......
= ............ + 3 (n - 1)
= ............
=

37
Teacher’s Guide - Grade 9 Mathematics

• Obtained a general term for the nth term in the following pattern as was done
above.

Group A 4, 9, 14, 19, ..............

Group B 2, 5, 8, 11, .............
Group C 3, 7, 11, 15, .............
Group D 8, 11, 14, 17, .............

• Write two uses of obtaining the general term.

Assessment and evaluation:

• Assessment criteria:
• Writes the initial term and the difference between the successive terms of
the number pattern.
• Builds up the relationship between the terms in the number pattern.
• Writes the general term of any number pattern in which the difference
between successive terms is equal.
• Seeks relationships reviewing information.
• acts cooperatively within the group.
• Direct the students to do the relevant exercises in lesson 3 of the textbook.

For your attention...

Development of the lesson:

• Design and implement activities suitable for obtaining the terms and solve the
problems related to number patterns when the general term is given in relation
to the learning outcomes 2 and 3.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 3 of the text
book.

For further reference:

• http://www.youtube.com/watch?v=Muba9-W2FOQ
• http://www.youtube.com/watch?v=HXg_a9oJ5nA
• http://www.youtube.com/watch?v=KSrnZMAfwTM
• http://www.youtube.com/watch?v=mFftY8Y_pyY
• https://www.youtube.com/watch?v=Zj-a_9cd5jc

38
Teacher’s Guide - Grade 9 Mathematics

4. Fractions
Competency 3 : Manipulates units and parts of units under the mathematical
operations to easily fulfill the requirements of day to day life.

Competency Level 3.1: Methodically simplifies expressions involving fractions.

Number of Periods: 05

Introduction:
In an expression in which either whole numbers or fractions are connected
by mathematical operations , each of those operations are effected in a cer-
tain sequence. The sequence in which those mathematical operations are
placed in the expression is always not the sequence that should be followed
when simplifying it. The verbal description of the expression brings into view
the order of working out the mathematical operations. In grade 7 students
have learnt how to find the value of an expression in which whole numbers
are combined by basic mathematical operations.
When solving problems with fractions, the students should know how to
manipulate brackets and “of” when they are coupled with the mathematical
operations ÷, ×, + and - . So, in the simplification of fractions, the following
order should be followed.
1. Simplifying the part within the brackets
2. Simpliifying the part with “of”
3. Operating division
4. Operating multiplication
5. Operating addition
6. Operating subtraction
The rule that indicates the sequence of operation when simplifying fractional
numbers according to basic mathematical operations along with brackets
and ‘of’ is known as ‘BODMAS’. This section aims to develop the ability of
simplifying fractions using the ‘BODMAS’ rule.

Learning outcomes relevant to Competency Level 3.1:

1. Simplifies expressions of fractions that contain “of”.

2. Accepts that the laws on the order in which simplification should be carried
out (BODMAS) need to be followed when simplifying fractions under the
basic mathematical operations.
3. Simplifies expressions of fractions that contain brackets.
4. Simplifies expressions of fractions that contain the basic mathematical
operations, brackets and “of”.
5. Solves problems involving fractions by applying the BODMAS Law.

39
Teacher’s Guide - Grade 9 Mathematics

Glossary of terms:
Fractions - Nd. - fzpjr; nra;iffs;;
Brackets - jryka - ml;rufzpj cWg;G
Division - fn§u - ml;rufzpjf; Nfhit
Multiplication - .=K lsÍu - $w;W
Addition - tl;= lsÍu - milg;G
Subtraction - wvq lsÍu - njupahf;fzpak
Mathematical Operation - .Ks; l¾u - fzpjr; nra;iffs;

Instructions to plan the lesson:

Given below is a specimen lesson designed to develop in students the

forth learning outcome adopting guided inquiry method with teacher
demonstration after reinforcing in them the subject concepts relevant
to learning outcomes 1, 2 and 3 under the competency level 3.1.

Time: 40 minutes

Instructions for the teacher:

Approach:
• Identify the knowledge gained by students about fractions in the former classes
and start the lesson with an inquiry into the simplification of fractions
1 1
• Discuss with students about the solving of problems 2     and
4 5
1 1
2 
4 5
• Discuss with students about the difference in the values of answers obtained
for the above problems.
• Through it elicit from students the need of a sequence for solving problems
relating to fractions.

Development of the lesson:

• Using an example, explain to students that arbitrary use of brackets doesn’t
lead to identical answers when simplifying fractions using several mathematical
operations.
• Emphasize to students, that in an instance of a simplification involving the
mathematical operations ÷ and ×, it has to be decided which operation is
worked out first.
• Simplify some examples such as the ones given below while discussing with
students. In each, draw students attention to the content within brackets.

40
Teacher’s Guide - Grade 9 Mathematics

1 1 1 2 1 3
(1)     (2)  
 2 3 4 5 3 4

(First simplifying part (Simplify × and ÷ from left

within brackets.) to right respectively )

2 1 3 1 1 1
(3)  of (4)  
5 3 4 2 3 4
(First simplify (Simplify + and - from left
the part with ‘of’ to right respectively)
1 1 1
(5)  
2 3 4

( If there are  or  and  or - , first  or  and then

 or - should be simplified)

• Accordingly make the students understand that a sequence is essential in the

simplifications related to fractions which include brackets, ‘of’ and basic
mathematical operations. Recall them the folowing order.
Step (1) Simplifying the part with brackets
Step (2) Simplifying the part with ‘of’
Step (3) Using the mathematical operation division
Step (4) Using the mathematical operation multiplication
Step (5) Using the mathematical operation addition
Step (6) Using the mathematical operation subtraction

Assessment and evaluation:

• Assessment criteria:
• Accepts the need of an order in the multiplication of mathematical operation
when simplifying expressions with fractions that include basic mathematical
operations.
• Simplifies expressions with fractions within brackets.
• Simplifies expressions with fractions that include + and - from left to right
respectively.
• Simplifies expressions with fractions that includes ÷ and × from left to right
respectively.
• Simplifies expressions with fractions that include basic mathematical
operations, brackets and ‘of’ using the BODMAS rule.
• Direct the students to do the relevant exercises in lesson 4 of the textbook.

41
Teacher’s Guide - Grade 9 Mathematics

For your attention...

Development of the lesson:

• Plan and implement suitable lessons to develop in students abilities relevant to

the learning outcomes 5 under competency level 3.1.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 4 of the text book.

For further reference:

•
•

42
Teacher’s Guide - Grade 9 Mathematics

5. Percentage
Competency 5 : Uses percentages to make successful transactions in the modern
world.

Competency Level 5.1: Makes decisions by comparing profits and losses.

Number of Periods: 06

Introduction:
• In trade, always the seller tries to sell a good at a price greater than the
buying price of it. Then the seller gets a profit. But in some instances it has to
be sold at a price less than that spent for buying it. Then the merchant suffers
a loss. The profit or loss can be calculated by the difference between the
buying price and the selling price. It is easier to make decision about the
more profitable transactions by indicating the profit or loss as a percentage.
• With the hope of attracting consumers, in many trade activities, the goods
are sold at a price less than the price marked on them. By this, more profit
can be earned by the increased sales. The amount of the price reduced in
such occasions is known as the discount and it is indicated as a percentage
of the marked price.
• When selling high valued items such as a land or a vehicle or when selling
some goods in stocks, the service of a middleman is sought. Such a person is
called broker. The amount paid to the broker for his service is called the
commission. This is indicated as a percentage of the amount obtained by
the relevant act of trade.

Learning outcomes relevant to Competency Level 5.1:

1. Identifies the profit/loss.

2. Identifies the profit/loss percentage.
3. Performs calculations related to purchase price, selling price, profit/loss
percentage.
4. Explains what a discount is.
5. Performs calculations related to discounts.
6. Explains what a commission is.
7. Performs calculations related to commissions.
8. Solves problems by applying the knowledge on profit/loss/discounts/
commissions.

43
Teacher’s Guide - Grade 9 Mathematics

Glossary of terms:

Profit/Loss - ,dNh$w,dNh - ,yhgk; / el;lk;

Purchase price - .;añ, - nfhs;tpiy
Selling price - úl=Kqï ñ, - tpw;wtpiy
Marked price - ,l=Kq l< ñ, - Fwpj;j tpiy
Discount - jÜgu - fopT
Commission - fldñia - juF (fkp\d;)
Broker - ;e/õlrejd - jufu;

Instructions to plan the lesson:

Given below is a specimen lesson that adopts lecture-discussion

method and an individual activity aimed at developing subject matter
related to the learning outcomes 1, 2 and 3 under the competency
level 5.1.
Time: 40 minutes

Quality inputs:

• Copies of the activity sheet

Instructions for the teacher:

Approach:
• Display some newspaper advertisement and posters with the words profit,
loss, discount, commission in the classroom and discuss about the profits and
losses as instances where percentages are used in trade.
• Write a few fractions on the board and discuss how they are written as
percentages recalling previous knowledge.

Development of the lesson:

• Presenting each of the following instances verbally, ask students about the
profit /loss incurred in rupees.
1. Selling for Rs. 100 an item bought for Rs. 80
2. Selling for Rs. 95 an item bought for Rs. 80
3. Selling for Rs. 150 an item bought for Rs. 120
4. Selling for Rs. 150 an item bought for Rs. 115
5. Selling for Rs. 2080 an item bought for Rs. 1350
6. Selling for Rs. 2150 an item bought for Rs. 1500
7. Selling for Rs. 900 an item bought for Rs. 960

44
Teacher’s Guide - Grade 9 Mathematics

• Discuss that a profit is resulted when purchase price < selling price and a loss
is incurred when purchase price > selling price and the profit/loss can be
formed by the difference between the purchase price and the selling price.
• Discuss with students that from transactions 1 and 2 , 1 is profitable and from
transactions 3 and 4, 4 is profitable.
• Discuss that case 5 and 6, such a comparison cannot be made on the basis of
percentages.
• Give an opportunity for students to complete the activity sheet individually and
discuss about the calculation of the percentages of profits and losses.
Emphasize that here, profit / loss should be written as a fraction of the
purchase price.
Activity sheet for the Students :

• Copy the following table and complete it.

Item Purchasing Selling Profit Pr ofit / loss Percentage

price (Rs.) price(Rs.) /loss Purchase price of profit /loss
20 20
A 80 100 20  100% = 25%
80 80
B 80

C 80

D 80

E 80

(i) What are the occasions of getting the same percentage?

(ii) According to the percentage of the profit ,by what item the highest
profit is obtained?

Assessment and evaluation:

• Assessment criteria:
• Finds profit/loss when purchase price and selling price are known.
• Calculate the percentage of profit/loss.
• States that when calculating the percentage of profit /loss, the profit/loss
should be written as a fraction of the purchase price.
• Decides on the more profitable trade on the basis of the percentage.
• Contributes to the discussion of relevant facts with others while actively
engaging in the activity

45
Teacher’s Guide - Grade 9 Mathematics

• Direct the students to do the relevant exercises in lesson 5 of the textbook.

For your attention...
Development of the lesson:

• Orient to exercises presenting examples on finding the profit/loss and selling

price when the percentage of profit/ loss and purchase price are given.
• Reinforce the relevant subject matter following suitable methods for the other
learning outcomes as well.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 5 of the text
book.

For further reference:

•
•
•

46
Teacher’s Guide - Grade 9 Mathematics

6. Algebraic Expressions
Competency 14 : Simplifies algebraic expressions by systematically exploring
various methods.

Competency Level 14.1: Simplifies expressions by substitution.

Competency Level 14.2: Simplifies binomial expressions.

Number of Periods: 02

Introduction:
• The value of simple algebraic expressions can be found by substituting a
value for the algebraic terms in them. The algebraic expressions presented
in this grade are devoid of roots but contain fractions. The values are
found by substituting directed numbers. They also include algebraic
expressions with parentheses of the following form.
a ( x  y )  b( x  y )
• In this section, it is also expected to simplify two simple algebraic
expressions of the type ( x  a )( x  b); a, b   .The product of two
binomial expressions such as these can also be obtained through area
also.

Learning outcomes relevant to Competency Level 14.1:

1. Finds the value of an algebraic expression which does not involve powers
or roots by substituting directed numbers.

Glossary of terms:

Algebraic expression - ùÔh m%ldYkh - ml;rufzpjf; Nfhitfs;

Algebraic term - ùÔh moh - ml;rufzpj cWg;G

Instructions to plan the lesson:

Given below is a specimen lesson adopting an activity in pairs for

developing in students the subject concepts relating to competency
level 14.1.

Time: 40 minutes

Quality inputs:
• Copies of the work sheet

47
Teacher’s Guide - Grade 9 Mathematics

Instructions for the teacher:

Approach:
• Recall how the knowledge of simplifying integers is used when finding the value
of an algebraic expression by substituting the given value of an algebraic term.
• Draw students’ attention to the use of BODMAS rule when simplifying
algebraic expressions.
• Reinforce students’ knowledge of multiplying a whole number by a fraction.

Development of the lesson:

• Distributes work sheets, one for two students.
• Guide the students to copy the work sheet and fill in the blanks,
• Move among the students, help them when required and assess them while the
students are involved in the activity.
• After completion of the activity, build up the whole of the lesson taking
students’ findings into consideration and recalling how algebraic expressions
are simplified by substituting a given value to an algebraic term.5

Activity sheet for the Students :

• Observe the work sheet well and complete it while discussing.

• Find the value of each algebraic expression according to the values of x given.
Algebraic expression Values of x
1
+2 -2 2
(i) 2x + 3 ........ ......... 1
2  3
........ ......... 2
1 3
4

(ii) 2x-3 ....... ......... .........

2 2  (  2)  3
(iii) 2(2x - 3) ........ 2  4  3 .........
2 x  7   14

1
1  2  2  3
(iv) (2x +3) 2
2 1
 4  3
2
1 ............ ..........
7
2
7
2

48
Teacher’s Guide - Grade 9 Mathematics

Assessment and evaluation:

• Assessment criteria:
• Substitutes a given value in an algebraic expression correctly.
• Simplifies integers correctly.
• Simplifies fractions correctly.
• Works cooperatively and completes the relevant activity sheet correctly.
• Direct the students to do the relevant exercises in lesson 6 of the textbook.

For your attention...

Development of the lesson:

• Plan lesson as appropriate for the learning outcomes relating to the

competency level 14.2 and implement.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 6 of the text
book.

For further reference:

• http://www.youtube.com/watch?v=fGThIRpWEE4

49
Teacher’s Guide - Grade 9 Mathematics

7. Factors of algebraic Expressions

Competency 15 : Factorizes algebraic expressions by systematically exploring
various methods.

Competency Level 15.1: Presents algebraic expressions in a simple form by factorizing.

Competency Level 15.2: Factorizes quadratic expressions to fulfill mathematical

requirements.

Number of Periods: 02

Introduction:
In grade 8, students have learnt how the common factor of an algebraic
expression consisting of up to three terms can be isolated. In this section, it is
expected to separate common factors in an algebraic expression of four
terms taking two terms each time. This ability of factorisation is essential for
the separation of factors of trinomial quadratic equations in the future. There-
fore, factorisation of algebraic expressions is very importance for the stu-
dents. This can also be used to find the length and breadth of rectangles of
given area in which the length and breadth are given as algebraic terms or
expressions.

Learning outcomes relevant to Competency Level 15.1:

1. Factorizes an algebraic expression with up to four terms by taking two

terms at a time.
2. Factorizes an algebraic expression with four terms, where the factors are
binomial expressions.

Glossary of terms:

Factors - idOl - fhuzpfs;

Commom factor - fmdÿ idOl - nghJf;fhuzpfs

Instructions to plan the lesson:

Given below is a specimen lesson adopting lecture-discussion

method coupled with an individual activity for developing in students
the concept of factorising four terms algebraic expressions in which
the common factor is binomial relevant to the learning outcome 1
under the competency level 15.1.

50
Teacher’s Guide - Grade 9 Mathematics

Time: 40 minutes

Instructions for the teacher:

Approach:
• Recall how the common factor of an algebraic expression comprising two
algebraic terms with a common factors is isolated.
• Extends this up to expressions with three algebraic terms while discussing.
• Also recall how the area of rectangles in which the length and breadth are
given in algebraic terms is found.

Development of the lesson:

• Present the figure with rectangles in the annex I to the students. Obtain as
ax + ay an algebraic expression for the area of the rectangle CDEF
represented as part 1.
• Separate the common factor of that algebraic expression ax + ay and indicate
it as a product of two factors (x+y)
• Obtain from students that the length of the rectangle so is (x+y) and its
breadth is a.
• Similarly, by separating the area of the rectangle FEGH into two factors elicit
from students that its length is (x+y) and the breadth is b.
• Show that the length and breadth of the rectangle CDGH are (x+y) and (a+b)
respectively and its area is (a+b)(x+y).
• Through a discussion with students, obtain the fact that the sum of the areas
of the rectangles CDEF and FEGH is ax+ay+bx+by.
• Obtained from students that the sum of the four parts of the rectangle
ax+ay+bx+by is equal to (a+b)(x+y)
i.e. ax+ay+bx+by = (a+b)(x+y)
• Factorise an expression such as ax+ay+bx+by without equating the areas.
• After reinforcing the subject concept in students by solving several problems,
direct them to factorise other types of algebraic expressions such as
x2+ax+bx+ab

Assessment and evaluation:

• Assessment criteria:
• Writes the area of a rectangle separated in to parts as the sum of the areas
of those parts.
• Separates the common factors of an algebraic expression with two terms.
• Accepts that by factorising an algebraic expression given in the form of the
area of the rectangle, its length and breadth can be obtained.

51
Teacher’s Guide - Grade 9 Mathematics

• Factorises an algebraic expression with four terms by writing the area of a

rectangle in two different ways.
• Participates actively to the activity giving correct answers.
• Direct the students to do the relevant exercises in lesson 7 of the textbook.

For your attention...

Development of the lesson:

• After factorising four term algebraic expressions such as x2+ax+bx+ab, guide

the students to factorise expressions with other signs.
• Discuss how the signs should be manipulated when factorising expressions
with terms such as k2-k+1-k.
• Establish the concepts through extra exercises.
• Plan and implement a suitable activity to achieve the subject concepts relevant
to the learning outcome 2 of the competency level 15.1.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 7 of the text
book.

For further reference:

• http://www.youtube.com/watch?v=HXIj16mjfgk
• http://www.youtube.com/watch?v=nOZTe8jU2g4
• http://www.youtube.com/watch?v=fVIZmOQBS5M
• http://www.youtube.com/watch?v=jmbg-DKWuc4
• http://www.youtube.com/watch?v=YahJQvY396o
• http://www.youtube.com/watch?v=tvnOWIoeeaU

52
Teacher’s Guide - Grade 9 Mathematics

Annex - 1

C D

Part I ax ay

F
E

Part II
by
bx

H G

53
Teacher’s Guide - Grade 9 Mathematics

8. Angles Related to Straight Lines and Parallel Lines

Competency 21 : Makes decisions by investigating the relationships between

various angles.

Competency Level 21.1: Establishes the relationships between the angles related to straight
lines.

Competency Level 21.2: Investigates the angles formed by various intersecting straight
lines.

Competency Level 21.3: Identifies the relationships between the angles related to parallel
lines.

Number of Periods: 07

Introduction:
The boundary that separates a surface into two parts is a line. When two
points are given, the interval that connects them is a straight line. A straight
line indefinitely spreads to either side. Therefore, in mathematical works we
draw segments of straight lines but not straight lines.
The theorems given in the work ‘The Elements’ written by the mathematician
Euclid in the third century B.C. are built up on plane figures. This lesson
introduces three theorems presented in that book with regard to straights
lines. As the theorems frequently used in geometric deduction, these are very
important.

Learning outcomes relevant to Competency Level 21.3:

1. Identifies the theorem, “When a transversal intersects a pair of straight lines, if

a pair of alternate angles is equal, or a pair of corresponding angles is equal or
the sum of a pair of allied angles equals two right angles, then the pair of
straight lines is parallel”

2. Verifies the theorem, “When a transversal intersects a pair of straight lines, if a

pair of alternate angles is equal, or a pair of corresponding angles is equal or
the sum of a pair of allied angles equals two right angles, then the pair of
straight lines is parallel”

54
Teacher’s Guide - Grade 9 Mathematics

3. Solves problems by applying the theorem, “When a transversal intersects a

pair of straight lines, if a pair of alternate angles is equal, or a pair of corre-
sponding angles is equal or the sum of a pair of allied angles equals two right
angles, then the pair of straight lines is parallel”

4. Identifies the following converse of the above theorem, “When a transversal

intersects a pair of parallel straight lines,
- pairs of alternate angles formed are equal
- pairs of corresponding angles formed are equal
- the sum of each pair of allied angles formed equals two right angles.

5. Verifies the following converse of the above theorem, “When a transversal i

ntersects a pair of parallel straight lines,
- pairs of alternate angles formed are equal
- pairs of corresponding angles formed are equal
- the sum of each pair of allied angles formed equals two right angles.

6. Solves problems by applying the following converse of the above theorem, “When
a transversal intersects a pair of parallel straight lines,
- pairs of alternate angles formed are equal
- pairs of corresponding angles formed are equal
- the sum of each pair of allied angles formed equals two right angles

Glossary of terms:
Parallel line - iudka;r f¾Ldj - rkhe;juf; NfhLfs;
Transversal line - ;S¾hla f¾Ldj - FWf;Nfhb
Vertically opposite angles - m%;suqL fldaK - Fj;njjpu;f;Nfhzq;fs;
Corresponding angles - wkqrEm fldaK - xj;jNfhzq;fs;
Alternate angles - taldka;r fldaK - xd;Wtpll ; Nfhzq;fs;
Allied angles - ñ;% fldaK - Neaf;Nfhzq;fs;
Theorem - m%fïhh - Njw;wk;;
Converse - úf,dauh - kWjiy

Instructions to plan the lesson:

A specimen lesson designed with adoption of a student activity is given below

to introduce the theorem relating to learning outcome 1 and verify that theorem
relating to outcome 2 under competency level 21.3 after establishing in students
the learning outcomes relevant to competency level 21.1 and 21.2.

Time: 80 minutes
Quality inputs:
• 10 cm × 10 cm oil papers, three for each group
• Copies of the activity sheet, three for each group
• Poster given in annex 1

55
Teacher’s Guide - Grade 9 Mathematics

Instructions for the teacher:

Approach:
• Display the diagram on the board and discuss with students
E about the straight lines and angles in it.
• During the discussion recall students about the transversal,
F B the paired angles corresponding, alternate and allied, the
A approximate relationship of the positions of corresponding
and alternate angles to letters Z and F and the situation of
C G the pair of allied angles.
D • Recall that the parallelism of two straight lines can be
examined with the ruler and the set square with a right angle
and how it is examined. Direct the students to investigate
H the geometric relationship between these angles and lines.
Development of the lesson:

• Display the poster with the theorem in annex 1. Show that the straight lines
forming the angles are parallel when alternate angles are equal or
corresponding angles are equal or the sum of the allied angles is equal to 1800
and introduce the theorem.
• Divide students into groups of four to get them ready for the activity designed
to verify the theorem.
• To each group distributea copy of the activity sheet, three pieces of oil papers.
• While the students are engaged in the activity, help the students who need
assistance.
• At the end of the activity , discuss about the students’ findings and confirm that
the theorem is true.

Activity sheet for the students:

T
E
L
A B P Q
V
C D
M S
R W
F U
figure  figure 

• Copy the two diagrams given to you separately on oil papers. Labels the
diagrams with the letters similar to those in the diagram.

56
Teacher’s Guide - Grade 9 Mathematics

• Mark in both copies the angle at vertex L corresponding angle to FMD ˆ in

ˆ ˆ
figure  . Using the oil paper see whether the angles FMD and ELB in the
activity sheet are equal. Accordingly note the relationship between
corresponding angles in figure  .
• Measure those two angles with the protractor and confirm the above decision
made.
• Repeat the same activity with figure  , find the corresponding angle to RWU ˆ
and see whether those two angles have same relationship mentioned above.
• Mark in both copies the angle at vertex M alternate angle to ALMˆ in figure
 . Using the oil paper see whether the angles ALM ˆ and LMD ˆ in the activity
sheet are equal. Accordingly note the relationship between alternate angles in
figure 
• Measure those two angles with the protractor and confirm the above decision
made.
• Repeat the same activity with figure  , find the alternate angle to QVWˆ
and see whether those angles have same relationship mentioned above.
ˆ at vertex M, measure those two angles with
• Identify the allied angle to BLM
the protractor and obtain the sum of those two angles. Accordingly note the
relationship between allied angles in figure  .
ˆ
• Identify the allied angle to PVW at vertex W, measure those two angles with
the protractor and obtain the sum of those two angles. See whether those
angles have same relationship mentioned above.
• Using the right angle corner made with a paper, examine whether CD and AB
are parallel. Confirm same using the set square and the ruler.
• Using the paper corner ,examine whether the lines PQ and RS are parallel and
confirm same using the set square and the ruler.
• Get ready to present how the theorem can be verified using your results.

Assessment and evaluation:

• Assessment criteria:
• States that the theorem related to parallel lines correctly.
• Verifies that when the corresponding angles and alternate angles are equal
of the angles formed when two straight lines are intersected by a transver-
sal, the straight lines are parallel.
• Accepts that the lines are parallel when the sum of two allied angles is equal
to two right angles.
• Examines the parallelism of two lines using a right angle corner.
• Uses verification to interpret specific occasions.
• Direct the students to do the relevant exercises in lesson 8 of the textbook.

57
Teacher’s Guide - Grade 9 Mathematics

For your attention.....

Development of the lesson:

• Plan and implement a suitable lesson to deveop in students the abilities relevant
to the learning outcome 3,4,5 and 6 under competency level 23.1.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 8 of the text
book.

For further reference:

• http://www.youtube.com/watch?v=wRBMmiNHQaE
• http://www.youtube.com/watch?v=2CZrkdtgeNU
• http://www.youtube.com/watch?v=gRKZaojKeP0
• http://www.youtube.com/watch?v=H-E5rlpCVu4
• http://www.youtube.com/watch?v=2WjGD3LZEWo
• http://www.youtube.com/watch?v=Ld7Vxb5XV6A
• https://www.youtube.com/watch?v=aq_XL6FrmGs

Annex 1

Poster

When two straight lines are intercepted by a transversal, those straight lines are
parallel if
• the corresponding angles are equal or
• the alternate angles are equal or
• the sum of a pair of allied angles is equal to two right angles.

58
Teacher’s Guide - Grade 9 Mathematics

9. Liquid Measurements
Competency 11 : Works critically with the knowledge on liquid measures to fulfill
daily needs.

Competency Level 11.1: Develops relationships between units of liquid measurements.

Number of Periods: 03

Introduction:
The volume of a certain quantity of a liquid can be measured by the units by
which the capacity of a container of that liquid is measured. The capacity of
a container is the volume of the liquid which completely fills that container.
The volume of an object is the space occupied by that object whereas the
volume of a liquid is the extent of space occupied by that liquid. Therefore
there should be a relationship between the units of measuring capacity and
volume. Capacity is measured by unit such as ml and l whereas volume is
measured by such as mm3, cm3 and m3. Since the conversion from one unit
of measurement to another is essential in day to day life , it is essential to
understand the relationship among these units. Thus the aim of this section is
the understanding of the relationship among these units of measurement, con-
version of the units of liquid measurement using those relationships and solv-
ing problems related to them.

Learning outcomes relevant to Competency Level 11.1:

1. Identifies the relationship between and 3.

2. Develops the relationship between and cm 3.
3. Develops the relationship between and m3.
4. Converts liquid measurements in one unit to another, by using the relationships
between ml and cm3, between and cm 3, and between l and m 3.
5. Solves problems related to the conversion of units of liquid measurements.

Glossary of terms:
Volume - mßudj - FiwepYit
Capacity - Odß;dj - $l;L tl;b -
Cube - >klh - khj myFfspd; vz;zpf;if
Cuboid - >kldNh - jtiz -

59
Teacher’s Guide - Grade 9 Mathematics

Instructions to plan the lesson:

This lesson expects to develop in students the subject concepts

relevant to the learning outcome 1 under the competency level
11.1.
Time: 40 minutes

Quality inputs:
• The following objects made with a transparency so that water doesn’t leak
• a 2 cm × 2 cm × 2cm cube
• a 2 cm × 2 cm × 3cm cuboid
• a 2 cm × 3 cm × 3cm cuboid
• a 2 cm × 3 cm × 4cm cuboid
• a 2 cm × 3 cm × 5cm cuboid
• Several syringes
• Vessels of water
• Rulers
• Copies of work sheets

Instructions for the teacher:

Approach:
• Show several vessels and bottles, ask about their capacity and volume and
lead a discussion.
• Explain that capacity of a container is the volume of a liquid required to fill that
container completely, the volume of an object is the space it occupies and
liquid volume is the space occupied by that liquid.
• Discuss that units of measuring capacity are ml and l which the units of
measuring volume are mm3, cm3 and m3.
• Recalling the need of the relationship among these unit types when solving
problems in everyday life, approach the lesson by inquiring into the relationship
among them.

Development of the lesson:

• Divide the students into group as appropriate and distribute to each group a
copy of the work sheet, a cuboid, a vessel of water, a syringe and a ruler.
• Engage the students in the relevant activity.
• Give an opportunity to present students’ findings.
• Based on the students’ findings, obtain the relationship between cm3 and ml is
1cm3 = 1ml

60
Teacher’s Guide - Grade 9 Mathematics

Activity sheet for the Students :

• Using the ruler, measure to the nearest centemtre the length, breadth and
height of the cuboid provided to you.
• Thereby, calculate the volume of the cuboid.
• Draw water in to the syringe given and fill the cuboid completely with
water.
• Express in ml the volume of water required to fill the cuboid completely.
• Comparing those two volumes, obtain a relationship between cm3 and ml.
• Present the relationship you obtained to the class.

Assessment and evaluation:

• Assessment criteria:
• State that the capacity of a container is the volume of a liquid filling it
completely and the volume of an object is the total amount of space it
occupies.
• Calculates the volume of a cuboid by measuring its length, breadth and
height.
• By comparing, states that 1cm3 = 1ml.
• Facilitates day to day affairs by comparing the units of measuring capacity
and volume.
• Acts in the group respecting the ideas of the others.
• Direct the students to do the relevant exercises in lesson 9 of the textbook.

For your attention...

Development of the lesson:

• Plan and implement lessons as appropriate to achieve the other learning

outcomes under competency level 11.1

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 9 of the text
book.

For further reference:

•
•

61
Teacher’s Guide - Grade 9 Mathematics

10. Direct Proportionality

Competency 4 : Uses ratios to facilitate day to day activities.

Competency Level 4.1: Engages in calculations by considering direct proportions.

Number of Periods: 06

Introduction:
• A ratio is a relationship between two similar quantities whereas a propor-
tion is a numerical relationship between two dissimilar quantities.
• When there is definite numerical relationship among the corresponding ele-
ments in two quantities belonging to the proportional relation, the quantities
are said to have a proportion.
• On the property that the ratio between any two elements in the first
quantity is equal to the ratio between the two corresponding elements in
the other quantity and when the value of the first quantity increases, the
corresponding value of the other quantity too increases, the two quantities
are said to have a direct proportion.

a > c
a:b=c:d
b d
>

• When the first quantity is x and the second quantity is y, the fact that x is
directly proportional to y is indicated as x y .
Then x = ky
x
 k
y
• The problems on directly proportional quantities can also be solved using
properties of proportionality , by unitary method and also algebraically.
• The aim of this lesson is to introduce proportionality and direct
proportionality and give guidance to solve numerical problems related to
them.

Learning outcomes relevant to Competency Level 4.1:

1. Identifies proportion.
2. Explains direct proportions using examples.
3. Writes the relationship between two quantities which are directly proportional
in the form .
4. Solves problems related to direct proportions by applying the unitary method.

62
Teacher’s Guide - Grade 9 Mathematics

5. Solves problems related to direct proportions by using the definition of

proportion.
6. Solves problems involving the conversion of foreign currency by applying the
knowledge on direct proportions.
7. Solves problems on direct proportions by expressing the relationship
algebraically

Glossary of terms:
Proportion - iudkqmd;h - gq;Ffs;
Direct Proportion - wkqf,dau iudkqmd;h - %yjdk;
Quantities - rdYs - gq;nfhd;wpd; gpujpg;gad
Foreign Currencies - úfoaY uqo,a - tiuaWf;fg;gl;l fk;gdp
Algebraic form - ùÔh wdldrh - fhzg;gl;l %yjdk;

Instructions to plan the lesson:

Given below is a specimen lesson designed to develop in students

the concepts of proportionality relevant to the learning outcomes 1
and 2 under the competency level 4.1 adopting lecture-discussion
method with an individual activity.
Time: 40 minutes

Instructions for the teacher:

Approach:
• Display the following clauses on the board.
• The ages of A and B respectively are 10 years and 15 years.
• A wheel rotates 40 rounds in 2 minutes.
• Asking students’ ideas about the above two statements, let student present in
the simplest form the ratio of ages of A and B
• Recall that the statement the wheel rotates 20 rounds in 2 minutes
indicates a proportion.
• Involve students in the following activity to identify the characteristics of a
proportionality.

Development of the lesson:

• Display the following table on the board and let students complete it
individually.

63
Teacher’s Guide - Grade 9 Mathematics

The price of a pen is Rs. 12.

First quantity(Numbers of pens) Second quantity (Cost Rs.)
1 12
2 .......
3 .......
4 .......
5 .......
6 .......
7 .......
8 .......
9 .......
10 .......

• Show that the first column of the table gives the number of pens and the
second column gives the cost.
• Assign students to write in the simplest form the numerical relationship existing
between an element in the first quantity and the corresponding element in the
second quantity as a ratio as follows.
1 : 12 = ...................
2 : 24 = ...................
3 : 36 = ...................
4 : 48 = ...................
• Surface that, as per the ratio above , there is a constant ratio between the
elements of the two quantities and say that such a relationship is called a
proportion.
• Instruct to write in the above table itself in the simplest form the ratio between
any two elements in the first quantity and the ratio between the corresponding
elements in the second quantity as follows.
Ratio between two elements The ratio between the two corresponding
in the first quantity elements in the second quantity and its
simplest form
1:3 12:36 = 1:3
..... : ..... ..... : .... = .... : ....
..... : ..... ..... : .... = .... : ....
..... : ..... ..... : .... = .... : ....
..... : ..... ..... : .... = .... : ....

• On the basis of the answers and also in the light of the following clause, discuss
the relationship between those two ratios.

64
Teacher’s Guide - Grade 9 Mathematics

The ratio between any two elements in the first quantity is equal to the
ratio between the two corresponding elements in the second quantity.

• Discussing about the increase in the value of the corresponding element with
the increase in value of an element in the first quantity and the number of pens
and their cost, introduce direct proportionality.
• In the light of the characteristics shown above, show that there is a direct
proportionality between the books the same size and their mass.
• Directing students to select direct proportionalities from the following
proportionalities, recall again about what is meant by ‘directly proportional’
• Equal size eggs and their price
• The length of a side of a square and its perimeter.
• The length of a side of a square and its area.
• The distance travelled by a vehicle running with a constant speed and
the time spent.

Assessment and evaluation:

• Assessment criteria:
• Of two quantities different from each other, identifies as a proportionality
the relationships where the ratio between an element in the first quantity and
the corresponding element in the second quantity is constant.
• Describes as a direct proportion a relationship in which the value of the
second quantity increases with the increase in the value of the first quantity.
• Presen89 ts the characteristics of a direct proportion.
• Selects direct proportionalities from given relationships.
• Participates actively in the discussion and gains learning experiences.
• Direct the students to do the relevant exercises in lesson 10 of the textbook.
For your attention...
Development of the lesson:
• Give guidance to write in algebraic form the relationship between two
quantities which are directly proportional.
• Plan and implement suitable learning teaching method to achieve the learning
outcomes 3, 4, 5, 6, and 7 under the competency level 4.1.
Assessment and evaluation:
• Direct the students to do the relevant exercises in lesson 10 of the text book.
For further reference:

• http://www.youtube.com/watch?v=4ywTWCaLmXE
• https://www.youtube.com/watch?v=d7rAlcNHDUI
• https://www.youtube.com/watch?v=Zm0KaIw-35k
• http://www.youtube.com/watch?v=KiVGac1aBt8

65
Teacher’s Guide - Grade 9 Mathematics

11. Calculator
Competency 6 : Uses logarithms and calculators to easily solve problems in day to
day life.

Competency Level 6.2: Uses the calculator to facilitate calculations.

Number of Periods: 02

Introduction:
The ancient human has restored to pebble keeping and drawing lines on a
tablet of clay for counting. In that, no calculation has be made .Afterwards,
it seems that man has used the set of fingers as a calculator. In about 100
B.C., Egyptians and the Chinese had used the abacus.
Abacus is also type of a calculator. Napierian logarithms too is a sort of
calculators. Blaise Pascal produced the mechanical calculator and in 1833
Charles Babage invented the analysis machine. As the modern computer is
designed on his principles, Charles Babage is known as the father of com-
puter science.
Given above is a diagram of a scientific calculator.
In any calculator there four keys for the four math-
ematical operations + , - , × , ÷ .Key On starts
the action of the calculator while Off deactivate it.
The key = gives the result of the mathematical
operation. Under the competency level 6.2, it is
expected that the students will identify and use the
keys + , - , × , ÷ , = , % , x2 and x in
the scientific calculator.

Learning outcomes relevant to Competency Level 6.2:

1. Identifies the keys On , Off , + , - , × , ÷ and = in the scientific

calculator
2. Uses the scientific calculator using the keys On , Off , + , - , × , ÷ and =
3. Identifies the keys % , x2 and x in the scientific calculator..
4. Uses the keys % " x2 and x in the scientific calculator..
5. Accepts that efficiency can be increased by using the scientific calculator.
6. Check the accuracy of the answers by using the scientific calculator.

66
Teacher’s Guide - Grade 9 Mathematics

Glossary of terms:
Scientific calculator - úoHd;aul .Klh - tpQ;QhdKiwf; fzpfUtp
Key - h;=r - rhtp
Key board - h;=re mqjrej - rhtpg;gyif
Multiplication - .=K lsÍu - ngUf;fy;

Instructions to plan the lesson:

The aim of this is to build up in students the subject concepts related

to learning outcomes 1 and 2 under the competency level 6.2. The
sequel gives a specimen lesson that adopts guided inquiry method
to achieve this aim.
Time: 40 minutes

Quality inputs:
• Scientific calculator (one for each group)
• Copies of the activity sheets
• A felt pen and an A4 sheet

Instructions for the teacher:

Approach:
8.625
• Direct the students to get the answer for the problem .
3.75
• Ask about the answer that can be obtained.
• Say that it is easy to solve this using a calculator and display a scientific
calculator and approach the lesson by asking about its keys.

Development of the lesson:

• Make the students aware about the keys of a scientific calculator and their
functions.
Key Function
On Putting on the calculator
Off Putting off the calculator
+ Adding two numbers
- Subtracting two numbers
× Multiplying two numbers
÷ Dividing one number by another
= Obtaining the answer

• After introducing the keys in the calculator, show that the problem presented
on the board can easily be solved by using the calculator.

67
Teacher’s Guide - Grade 9 Mathematics

• Show that the relevant process can be indicated as

On  8.625  ÷  3.75  =  2.3

• Group the students as appropriate and give each group a copy of the activity
sheet.and assign the work for each group.
• Distribute the necessary equipment and materials to the groups and engage in
the activity.
• At the end of the activity conduct a discussion. During the discussion explain
that the calculator should be switched on by the key and in simplifications
under basic mathematical operations first the number and then the relevant
mathematical operation should be entered. Thereafter, the second number
should be entered and relevant key should be used to obtain the answer.

Activity sheet for the students:

• Study the activity sheet you have got well.

A B C D
25 + 31 45 + 11 52 + 63 74 + 29
73 - 20 54 - 12 48 - 23 57 - 41
82  3 58  2 73  8 64  7
175  5 536  4 528  4 508  2

• Select the part assigned to your group.

• Obtain the value of the mathematical expressions given using the scientific
calculator.
• Using a flow diagram show how you obtained that value.
• Present the answer you got to the whole class.

Assessment and evaluation:

• Assessment criteria:
• Identifies correctly the calculator key relevant to the calculation.
• Simplifies a mathematical expression correctly using the calculator.
• Shows by a correct arrow diagram how the answer was obtained by
solving the mathematical expression.
• Accepts that it is easier to use the scientific calculator to simplify
mathematical expression with mathematical operations.
• Learns through experience.
• Direct the students to do the relevant exercises in lesson 11 of the textbook.

68
Teacher’s Guide - Grade 9 Mathematics

For your attention.....

Development of the lesson:
• Plan and implement suitable activities to develop in students the subject
concepts relevant to learning outcomes 3, 4, 5 and 6.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 11 of the text
book.

For further referenc:

• http://www.youtube.com/watch?v=cK1egPBjJXE
• http://www.youtube.com/watch?v=OPxzx75bAfk
• http://www.youtube.com/watch?v=DaoJmvqU3FI
• http://www.youtube.com/watch?v=pf41fDSWeoA
• http://www.youtube.com/watch?v=3jBfLaLrk6I
• http://www.youtube.com/watch?v=_qzs1zozTBo
• http://www.youtube.com/watch?v=fh8gkPW_6g4
• http://www.youtube.com/watch?v=BkwI6Uu0vi4
• http://www.youtube.com/watch?v=_MIn3zFkEcc

69
Teacher’s Guide - Grade 9 Mathematics

12. Indices
Competency 6 : Uses logarithms and calculators to easily solve problems in day to
day life

Competency Level 6.1: Simplifies powers by applying the laws of indices.

Number of Periods: 03

Introduction:
Logarithms are based on the concept of indices. In previous grades the stu-
dents have learnt identification of powers, index notation, identification of
powers whose base is an algebraic symbol, expansion of powers, finding
values by substituting positive integers for the algebraic terms in powers with
algebraic terms and expansion of powers in a product.
This section aims to develop in students the ability to recognize the applica-
tion of indices rules and use them for simplification of expression with indices
in multiplication and division of powers with equal bases and in finding the
power of a power. Hence under this section the subject matter a m  a n  a m  n ,
am n 1
an
 
 a mn , am n
 a mn , a 0  1 and a  n are discussed.
a

Learning outcomes relevant to Competency Level 6.1:

1. Identifies the laws of indices that are applied when multiplying powers and
dividing powers.
2. Identifies the laws of indices that are applied when finding the power of a power.
n 1
3. Recognizes that and a 
an
4. Applies the laws of indices to simplify expressions involving indices.

Glossary of terms:
Index - o¾Ylh - Rl;bfs;
Rules for indices - n,h - Rl;b tpjpfs;
Power - o¾Yl kS;s - tY
Division - fn§u - tFj;jy;
Multiplication - .=K lsÍu - ngUf;fy;

Instructions to plan the lesson:

Given below is a specimen lesson plan that adopts a group activity

for developing in students the subject concepts related to the first
learning outcome 1 under the competency level 6.1.
Time: 40 minutes

70
Teacher’s Guide - Grade 9 Mathematics

Quality inputs:
• Copies of the activity sheets
• A felt pen and an A4 sheet ( for each group )

Instructions for the teacher:

Approach:
• Ask what is a power and write a power such as 25 on the board.
• Have access to the lesson by involving students to expand that power.
• Surface the need of multiplying two or more powers and dividing two or more
powers.

Development of the lesson:

• Group the students as appropriate.

• Distribute a copy of the activity sheet and an A4 sheet to every group and let
them do the activity according to the instructions given.
• After completion of the group activity, elicit ideas from the groups and make a
review.
• Surface index rules used when multiplying or dividing two or more powers and
give a summery as follows.
• a m  a n  a m n
am
•  a mn
an
Activity sheet for the students:

• Observe the activity sheet well, discuss it within the group and fill in the
blanks as appropriate.(In first, fill in the blanks in first column.)

Fill in the blanks Fill in the blanks and obtain

the final answer obtained on
the left hand side by another
method

2 2  23 22  23
= (......  ....... )  (.......  ........  ......) = 2 ..... + .....
= ......  ......  ......  ......  .......... = 2 .....
= 2 .....

a3  a a3  a
= (......  ......  ......) = a .....+.....
= a .... = a ....

71
Teacher’s Guide - Grade 9 Mathematics

35
35
32
32
......  .....  ......  .......
  3(.......)  (.......)
.......  .........
 ............  .........  ...........  3........
 3........

x4
x4
x2
x2
......  .....  ......  .........
  x(.......)  (.......)
.......  .........
 ............  .........  ...........  x..........
 x..........

• Using the above findings simplify the following.

b3
( a) y 4  y 2 (b)
b2

Assessment and evaluation:

• Assessment criteria:
• Identifies the index rule used in the multiplication of powers.
• Identifies the index rule used in the division of powers.
• Multiplies and divides powers using index rules.
• Accepts that index rules facilitate multiplication and division of powers.
• Direct the students to do the relevant exercises in lesson 12 of the textbook.

For your attention...

Development of the lesson:

• Plan lesson as appropriate and implement to develop the learning outcomes 2,

3 and 4 under competency level 6.1.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 12 of the text
book.
For further reference:
• http://www.youtube.com/watch?v=-TpiL4J_yUA
• http://www.youtube.com/watch?v=tvj42WdKlH4
• http://www.youtube.com/watch?v=U8kmaUXaPJY
• http://www.youtube.com/watch?v=jYOfMszfzAQ
• http://www.youtube.com/watch?v=Of8ezQj1hRk

72
Teacher’s Guide - Grade 9 Mathematics

13. Loci and Constructions

Competency 27 : Analyzes according to geometric laws, the nature of the locations
in the surroundings.

Competency Level 27.1: Uses the knowledge on the basic loci to determine the location of
a point.

Competency Level 27.2: Uses geometric constructions in various activities.

Number of Periods: 09

Introduction:
In this section it is expected to discuss identification of the four basic loci,
construction of a bisector to a line, construction of a bisector of an angle,
copying an angle equal to a given angle and constructions of angles of given
values relevant to competency level 27.1 and 27.2.
In the dynamic world, we frequently see objects moving. These move mostly
under external influences. Based on the external forces or factors affecting
the motion of an object, a prediction can be made about the path of that
object. The path of a point moving under the influence of an external force is
called a locus. It is the dynamic concept of a locus. As regards the static
concept, the combination of all the locations of a point too gives rise to a
locus.
This section includes facts about basic loci and selected geometrical con-
structions. Further, this section encompasses facts relating to the correct us-
age of geometrical instruments in geometrical constructions and how the
constructions made are validated.

There are four basic types of loci.

1. The locus formed by the union of all the points on a plane equidistant
from a fixed point or the locus of a point moving at a constant
distance from fixed a point is a circle.
2. All the points located on a plane equidistant from two fixed points or
the locus of a point moving at an equal distance from two fixed points is
the perpendicular bisector of the line joining those two points.
3. The locus formed by the union of the all the points located at an equal
distance from a fixed line or the locus of a point moving at a constant
distance from a fixed line are two straight lines parallel to the fixed line
with a constant gap.

73
Teacher’s Guide - Grade 9 Mathematics

4. The locus formed by the union of all the points on a plane equidistant
from two non parallel lines or the locus of a point moving at an equal
distance from two non parallel lines is the bisector of the angle formed
at the meeting point of those two lines.

By discussing with students phenomena seen in the natural environment such

as the path of a tip of a clock arm, the path taken by finger tips when opening
a tap and the path of a rain drop falling from the edge of a roof a practical
knowledge regarding loci can be given.

Learning outcomes relevant to Competency Level 27.2:

1. Constructs the bisector of an angle.

2. Constructs angles of magnitude 60o, 30o, 120o.
3. Constructs angles of magnitude 90o, 450.
4. Constructs other angles that can be constructed using the construction of
angles of magnitude 60o, 90o, 30o, 45o, 120o.
5. Copies an angle equal to a given angle.
6. Studies methods of validating the accuracy of the constructions

Glossary of terms:
Locus - m:h - xOf;F
Circle - jD;a;h - mtl;lk;
Fixed point - wp, ,laIHh- - epiyahd Gs;sp
Constant distance - ksh; ÿr -khwhj; J}uk;rk
Equal distance - iudk ÿr - rk J}uk;
Bisector - iuÉfþolh - ,U$whf;fp
Perpendicular - ,ïnh - nrq;Fj;J
Perpendicular bisector - ,ïn iuÉfþolh - ,Urkntl;br; nrq;Fj;J
Parallel lines - iudka;r f¾Ld - rkhe;juf;NfhLfs;
Construction - ks¾udKh - mikg;G
Intersection - fþokh - ,ilntl;Ljy;
Straight line - ir, f¾Ldj - Neu;NfhL

A specimen lesson designed as a stepwise, individual student activity

coupled with a teacher demonstration for developing in students
the subject concepts related to the learning outcomes 1 and 2
under the competency level 27.2 after achieving the subject
concepts relevant to the learning outcomes under the competency
level 27.1 is given below.
Time: 40 minutes

74
Teacher’s Guide - Grade 9 Mathematics

Quality inputs:
• Compass
• Ruler

Instructions for the teacher:

Approach:
• Conduct a short discussion about the instruments used in constructions and
how the compass and the ruler are used.

Developments of the lesson:

• Follow the steps given below to develop the ability of bisecting an angle in
students. While demonstrating by the teacher guide the students to do the
constructions.
( It is necessary that the teacher uses the compass and the ruler.)
• Bisecting an angle

Step 01 - 
Draw the angle. Name it ABC
Step 02 - Taking a suitable radius on the compass and making B the centre,
draw an arc intersecting lines BA and BC. Name the point of
intersection D and E.
Step 03 - Making point D the centre draw an arc again within the angle.
Step 04 - Taking the same radius draw another arc making E the centre
so that the arc drawn in steps 3 is intersected.
Step 05 - Name X the point of intersection of the two arcs and join BX.
ˆ .Confirm the bisecting
Explain that line BX is the bisector of ABC
ˆ by measuring the angles ABX
of ABC ˆ
ˆ and CBX

• Constructing an angle of 600

Step 01 - Draw a segment of a straight line and name it EF.
Step 02 - Taking a suitable radius on the compass and making E the centre,
draw an arc intersecting lines EF. Name the point of intersection
G.
Step 03 - Taking the same radius used in step 02 above and placing the
pointer of the compass on point G draw an arc intersecting the
other arc. Name that point H.

Step 04 - ˆ . Show that it is

Join EH and produce. Measure the angle HEF
0
60 .
• Constructing of an angle 300
Step 01 - Construct an angle of 600. Name it FGH
ˆ .

75
Teacher’s Guide - Grade 9 Mathematics

Step 02 - Taking a suitable radius on the compass and making G the centre,
draw an arc intersecting lines GF and GH. Name the points of
intersection K and L.
Step 03 - Making K and L as centres draw two arcs of equal radii
intersecting each other. Name the point of intersection M.

Step 04 - Join GM. Measure angles FGM ˆ and HGM ˆ . Confirm that FGH
ˆ
is bisected by GM and the resulting angle is 300

• Construct of an angle 1200 with students, using the steps used for construc-
tion of an ange 600.

Assessment and evaluation:

• Assessment criteria:
• Uses compass and ruler correctly.
• Involves in the constructions according to instructions given.
• Bisects an angle given.
• Confirms the accuracy of the construction.
• Completes the work patiently according to a plan.
• Direct the students to do the relevant exercises in lesson 13 of the textbook.

For your attention...

Development of the lesson:

• Subsequent to the development of skills relevant to learning outcomes 1 and 2

of competency level 27.2, give an opportunity to develop stepwise the skills
of constructing another angles and copying angles.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 13 of the text book.

For further reference:

76
Teacher’s Guide - Grade 9 Mathematics

14. Equations
Competency 17 : Manipulates the methods of solving equations to fulfill the needs of
day to day life.

Competency Level 17.1: Easily solves problems in day to day life by solving linear
equations.

Competency Level 17.2: Solves problems by using the methods of solving simultaneous
equations.

Number of Periods: 06

Introduction:
An equality of two mathematical expressions can be indicated by an equa-
tion. An equation with one unknown of power one is a linear equation. This
section aims to find the solution of linear equations with two types of brack-
ets in which the coefficients are fractions.
In this section solving of simultaneous equations with equal coefficient is also
expected.
The knowledge of solving equations is very important not only in mathemat-
ics but also in the learning of other subjects such as science and economics.

Learning outcomes relevant to Competency Level 17.1:

1. Solves linear equations containing algebraic terms with fractional coefficients.

2. Solves linear equations with two types of brackets.

Glossary of terms:

Simple equations - ir, iólrK - njupahf; fzpak;

Unknown - w{d;h - Unknown
Simultancous equations - iu.dó iólrK - Simultaneous equations

Instructions to plan the lesson:

Given below is a specimen lesson designed to develop in students

the learning outcomes 1 under the competency level 17.1

Time: 40 minutes

Quality inputs:
• Copies of the work sheets

77
Teacher’s Guide - Grade 9 Mathematics

Instructions for the teacher:

Approach:
• In order to revise the facts learnt so far about solving linear equations, discuss
with students the solving of one of the following types of equations.
Type ax + b = c
1
Type x =c
2
1
Type xb  c
2
• Also discuss how the accuracy of the solution is checked by substituting the
solution in the above equations.

Development of the lesson:

• Distribute work sheet to all the students and engage them in the activity.
• While engage in the activity, move among the students, help them when
necessary and assess them.
• Finally discuss students about their findings and reinforce in them how the
linear equations carrying algebraic terms with fractional coefficients are solved.

Students’ work sheet:

• Writes the terms filling into the blank boxes observing well, the following
steps of solving linear equations.

a 3x x
1' 2 7 2'   10
3 3 4
a x x
2  72    12  10 
3 3 4
a   120
 3  5
3 x
a

3'

4'

78
Teacher’s Guide - Grade 9 Mathematics

a a
3  5
2 3 (Multiplying all the terms by the
a a
    5 6 LCM of the denominators.)
2 3
3a   30
3x x
 30 4.   10
3 4
30 x x
    12  10  (Multiplying
3 4
all the terms
a  ......   120
by the LCM
x of the
denominators.)
5. Solve the following linear equations following the above steps.
x 2x
i.)   6
3 3
x x
ii.)   7
3 4
• Check the accuracy of your answers by substituting them in the equations.

Assessment and evaluation:

• Assessment criteria:
• Follows the sequence of steps when solving linear equations.
• When solving linear equations containing algebraic terms with fractional
coefficients, multiply all the terms by the LCM of the denominators
• Solves linear equations containing algebraic terms with fractional
coefficients.
• Checks the correctness of the solution by substituting the solution in the
equation given.
• Solves problems using the knowledge of linear equations.
• Direct the students to do the relevant exercises in lesson 14 of the textbook.

For your attention...

Development of the lesson:

• In order to establish in students the subject matter relevant to the learning

outcome 2 under the competency level 17.1, plan and implement lessons
following suitable methods.
• Adopting interesting methods, reinforce in students the subject matter relating
to competency level 17.2.

79
Teacher’s Guide - Grade 9 Mathematics

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 14 of the text
book.

For further reference:

•
•
•

80
Teacher’s Guide - Grade 9 Mathematics

15. Axioms
Competency 23 : Makes decisions regarding day to day activities based on
geometrical concepts related to rectilinear plane figures.

Competency Level 23.1: Geometrically analyses the relationships between quantities.

Number of Periods: 04

Introduction:
The expressions that are already accepted as true without proof are known
as axioms. They can be understood correctly without verification. Axioms
can be described as an indispensable tool to explain facts logically, to come
to conclusions and to build up various relationships in learning mathematics.
Under the themes of algebra axioms are often used when solving equations
and inequalities. In geometry they are frequently useful in verification and
when solving problems with calculations. In subjects such as logic, axioms
are used to build up relationships logically and come to conclusions. Though
there are many axioms in use, five most frequently used axioms have been
identified. This section deals with those five axioms.

Learning outcomes relevant to Competency Level 23.1:

1. Identifies the five basic axioms.

2. Develops relationships using the five basic axioms.

Glossary of terms:
Axioms - m%;HlaI - fzpjr; nra;iffs;;

Instructions to plan the lesson:

A specimen lesson plan suitable to build up in students subject

concepts relevant to the first learning outcome under the
competency level 23.1 is presented below. It is proposed that this
is implemented on individual basis.
Time: 40 minutes

Quality inputs:
• An enlarge copy of the activity sheet

81
Teacher’s Guide - Grade 9 Mathematics

Instructions for the teacher:

Approach:
• Present the following instances and discuss about the relationship that can
be drawn from the information given.
Price of a pen = Rs. 10, Price of an eraser = Rs. 10
 Price of a pen = Price of an eraser

• AB = PQ
AB = XY
 PQ = XY

• Price of 1 kg of sugar = Rs. 98

 Price of 5 kg of sugar = Rs. 98  5
• AB = 10 cm
AB 10
 cm
 5.AB = 10  5 cm and 2 2
• PQ = XY
PQ XY
 2PQ = 2.XY and 
3 3

Development of the lesson:

• Make the students aware of the fact that under each instance they need to
study the information given within the box and should write the relationships
that can be obtained from the figures or facts given.
• Display the enlarged activity sheet (or draw it on the board) and engage
students in the activity individually.
• After completion of the activity, have a discussion with students and explain
that the statements which we understand true right away are called axioms.
• Taking into consideration the students’ findings and the examples used at the
approach, build up the five axioms and ask the students about them.

That is to say,
Axioms 1: The quantities equal to the same quantity are equal themselves.
If a = b and b = c, a = c

Axioms 2: The quantities obtained by adding the same quantity to two equal
quantities are equal.
If a = b, a + c = b + c

82
Teacher’s Guide - Grade 9 Mathematics

Axioms 3: The quantities obtained by subtracting the same quantity from two
equal quantities are equal.
If a = b, a - c = b - c

Axioms 4: The quantities obtained by multiplying two equal quantities by the

same quantity are equal.
If a = b , na = nb

Axioms 5: The quantities obtained by dividing two equal quantities by the

same quantity are equal.
a b
If a = b,  ; where n is not zero
n n

Activity sheet for the students:

• Study the example given in the box in situation 1, 2 and 3 and build up
relationships in each according to the information or figure is given.
figures.
Situation 1
Example:
XY = 5cm
AB = BC
PQ = 5cm
AB = AD
 XY = PQ

M D
Situation 2
K
Example: C B
ˆ  550
PQR N
ˆ  350
XYZ
ˆ ˆ  550  350  900
PQR+XYZ
L A
ˆ = ABC
KLM ˆ
ˆ = CBD
MLN ˆ

Situation 3 Z Y
Example:
AB = 15cm X
P R
BC = 4cm
AB - BC = 15cm - 4 cm = 11 cm XY = PQ Q

83
Teacher’s Guide - Grade 9 Mathematics

Assessment and evaluation:

• Assessment criteria:
• Writes various relationships that can be derived from the information given.
• Expresses the opinions of self about the relationships derived by others
from the information given.
• Identify expressions that clearly appear to be true as axioms.
• Describe five basic axioms.
• Accepts that identification of axioms is very important in mathematics.
• Direct the students to do the relevant exercises in lesson 15 of the textbook.

For your attention...

Development of the lesson:

• Direct students to do exercises on building up various relationships using

axioms in relation to the learning outcome 2 under the competency level 23.1.
• Build up and present other appropriate examples.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 15 of the text
book.

For further reference:

•

84
Teacher’s Guide - Grade 9 Mathematics

16. Angles of a Triangle

Competency 23 : Makes decisions regarding day to day activities based on
geometrical concepts related to rectilinear plane figures.

Competency Level 23.2: Formally investigates the sum of the three interior angles of a
triangle.

Competency Level 23.3: Investigates the relationship between the exterior angle formed by
producing a side of a triangle and the interior opposite angles.

Number of Periods: 09

Introduction:
The theorem “The sum of the interior angles of a triangles is equal to 1800” is
a fundamental theorem. In most of the instances in the future this theorem has
to be made use of in geometry. Therefore, it is very important to verify this
theorem and understand its validity and in this section this aspect is discussed.
In this section , it is also expected to verify the theorem “ the exterior angle
formed by producing aside of a triangle is equal to the sum of the two interior
opposite angles” and discuss its applications. So, in the calculations relating
to triangles, these theorem can be used.

Learning outcomes relevant to Competency Level 23.2:

1. Identifies the theorem, “The sum of the three interior angles of a triangle is
180o”.
2. Verifies the theorem, “The sum of the three interior angles of a triangle is
180o”.
3. Solves simple geometric problems using the theorem, “The sum of the three
interior angles of a triangle is 180o”.

Glossary of terms:
Triangle - ;%sfldaKh - Kf;Nfhzk;
Interior angles - wNHka;r fldaK - mff;Nfhzq;fs;
Theorem - m%fïhh - Njw;wk;
Verification - i;Hdmkh - tha;g;Gg;ghu;j;jy;

85
Teacher’s Guide - Grade 9 Mathematics

Instructions to plan the lesson:

A specimen lesson planned to introduce and verify the theorem “The

sum of the interior angles of a triangles is equal to 1800” relevant to
learning outcomes 1 and 2 under the competency level 23.2 adopt-
ing the lecture-discussion method with an activity in pairs is present-
ed below.

Time: 40 minutes

Quality inputs:
• Copies of the work sheet

Instructions for the teacher:

Approach:
• Recall again about the magnitudes of the acute angles, obtuse angles and
straight angle learnt before.
• Recall that the sum of the adjacent angles meeting at a point on a straight line is
equal to 1800.

Development of the lesson:

• Introduce the theorem “The sum of the interior angles of a triangles is 1800” by
writing it on a panel and displaying it.
• Tell students that they are going to do an activity in pairs to verify the above
theorem.
• Display an enlarge copy of the work sheet in front of the class.
• Engage all the students in the activity in pairs.
• After completing the activity, elicits from the students that according to the
result the sum of the three interior angles of a triangle is 1800 irrespective of its
type.
• Instruct to confirm what they have discovered by drawing another type of a
triangle different from the previous and measuring its angles.

86
Teacher’s Guide - Grade 9 Mathematics

Activity sheet for the students:

• Draw any one of the following types of triangles of your choice on a paper.
a a a

b c b b c
c
• Label as a, b and c the three angles of the triangle you have drawn.
• With the help of your friend separate the triangle in to three parts each with an angle.
• Paste the parts so that their vertices meet at a point touching their arms and
see whether a straight line is obtained.
• So, discuss with your friend that by this method, the theorem “The sum of
the interior angles of a triangles is 1800” can be verified.

Assessment and evaluation:

• Assessment criteria:
• Draw an acute-angled, obtuse-angled and right-angled triangles.
• State that their angles lie on a straight line when pasted so that their vertices meet.
• Accepts that, whatever the type of the triangle, the sum of their three
interior angles is 1800.
• Engage in an activity to come to a conclusion through a generalisation.
• Shares the results obtained with the others.
• Direct the students to do the relevant exercises in lesson 16 of the textbook.

For your attention...

Development of the lesson:

• After verifying that the sum of the three interior angles of triangle is 1800,
engage in exercises applying it.
• Include into exercises, various types of triangles as well as triangles with
parallel lines learnt before.
• Design and implement lesson plan to achieve the learning outcomes relevant to
the competency level 23.3.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 16 of the text book.

For further reference:

• http://www.youtube.com/watch?v=hmj3_zbz2eg
• https://www.youtube.com/watch?v=6s1CI3uuhko
• http://www.youtube.com/watch?v=0gzSreH8nUI

87
Teacher’s Guide - Grade 9 Mathematics

17. Formulae
Competency 19 : Explores the methods by which formulae can be applied to solve
problems encountered in day to day life.

Competency Level 19.1: Changes the subject of a formula that has been developed to
show the relationship between variables.

Number of Periods: 06

Introduction:
• The general relationship existing between two or more quantities is a
formula.
• In a formula, when one quantity becomes equal to other quantities
organised in an order, that single quantity is referred to as the subject of
the formula.
• Formulae are used in subjects like mathematics and science as well as in
other subjects. In calculations, one variable has to be made the subject
according to the need
• In this section it is expected to change the subject of formula without
powers and roots and substitute value for an unknown in a simple
equation and simplify.

Learning outcomes relevant to Competency Level 19.1:

1. Changes the subject of a formula that does not contain squares and square
roots.
2. Performs calculations by substituting values for the unknowns in a simple
formula.

Glossary of terms:
Formula - iQ;%h - nrq;Nfhz Kf;Nfhzp
Subject - Wla;h - nrk;gf;fk;
Unknown - w{d;h - igjfurpd; Njw;wk;
Substitution - wdfoaYh - igjfurpd; Kk;ik
Quantity - rdYsh - igjfurpd; Kk;ik

88
Teacher’s Guide - Grade 9 Mathematics

Instructions to plan the lesson:

Given below is a specimen lesson that adopts lecture discussion

method to achieve the first learning outcomes relevant to
competency level 19.1

Time: 40 minutes

Quality inputs:
• Copies of the activity sheet
• Kits of the cards prepared according to annex I
• Half sheets

Instructions for the teacher:

Approach:
• If p is the perimeter of a rectangle of length l and l
breadth b, p = 2(l+b). if the area of the above
r ectangle is A, A = lb b

• Presenting formulae such as above, introduce that the single algebraic term on
one side of a formula is the subject of the formula.
• Explain that it is required to change the subject during calculations according to
the situation.
• Recall giving examples how axioms are used when solving equations.

Development of the lesson:

• Group the students as appropriate.
• Distribute activity sheets, card kits and half sheets among the groups.
• Move among the groups while they are at work and give necessary
instructions.
• After completion of work, discuss with students how the unknown is made the
subject of the given formulae.
• Discussing with students explain how the subject is change in an equation with
n 2
parentheses such as S  180( n  2), S= (a  l ), S = (a  b)
2 5

89
Teacher’s Guide - Grade 9 Mathematics

Activity sheet for the students:

Group 1 Group 2 Group 3

v = u + ft (t) y = mx + c (x) A = 2  rh + a(h)

• Observe carefully the term to be made the subject opposite the formula
given to your group and the set of cards.
• In order to make the term given inside parentheses opposite the formula the
subject, arrange the set of cards in the correct order.
• Write the order you prepared in the half sheet.

Assessment and evaluation:

• Assessment criteria:
• Identifies the subject of a given formula.
• Identifies the correct order that should be used to make a given term the
subject of a formula.
• Makes given term in a formula the subject of it.
• Sees the relationship among the terms of a given formula.
• Involves in the given task following the correct steps.
• Direct the students to do the relevant exercises in lesson 17 of the textbook.

For your attention...

Development of the lesson:
• Following appropriate methods, develop in students the learning outcome 2
relevant to competency level 19.2.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 17 of the text
book.

For further reference:

•
•

90
Teacher’s Guide - Grade 9 Mathematics

Annex I
Group 1 Group 2 Group 3
v  u  ft y  mx  c ( x) A  2 rh  a
v  u ft y c A  a  2 rh  a  a
 m
f f x
A  a 2 rh

v  u  u  ft  u y  c  mx  c  c 2 r 2 r

v u y  c mx Aa
t  h
f x x 2 r

v  u  ft y  c  mx A  a  2 rh

91
Teacher’s Guide - Grade 9 Mathematics

18. Circumference of a Circle

Competency 7 : Investigates the various methods of finding the perimeter to carry out
daily tasks effectively.

Competency Level 7.1: Applies the relationship between the diameter and circumference
of a circle when performing various calculations.

Number of Periods: 05

Introduction:
Most of the objects that come across our day to day life are round or circular
shapes. So it is important to know the relationship between the circumfer-
ence and diameter. Discuss the following concepts according to the compe-
tency level 7.1. For any circle the ratio between the circumference and the
diameter is nearly around 3 and is named as . For calculations we assumed
22
the value of  as or 3.14. Through this competency level it is expected
7
to develop the skill to solve the problems relating circumfarane of a circle.

Learning outcomes relevant to Competency Level 7.1:

1. Measures the diameter and the circumference of circular laminas using

various methods.
2. Develops a formula for the circumference by considering the relationship between
the diameter and the circumference of a circle.
3. Performs calculations related to the circumference of a circle by applying the
formulae and .
4. Finds the circumference of a circle.
5. Finds the perimeter of a semi-circle.
6. Solves simple problems involving the circumference of a circle.

Glossary of terms:
Circle - jD;a;h - tl;lk;
Circumference - mßêh - gupjp
Diameter - úIalïNh -tpl;lk;
Radius - wrh - Miu

Instructions to plan the lesson:

Given below is an exemplar lesson plan to achieve the learning

outcomes 1, 2 and 3 of competency level 7.1 using group activity
method.

92
Teacher’s Guide - Grade 9 Mathematics

Time: 40 minutes

Quality inputs:
• Measuring tape
• Cicular discs with differant sizes
• A4 sheets
• Calculator
• Pair of scissors

Instructions for the teacher:

Approach:
• Discuss about finding the perimeter of rectilinear plane figures.
• Begin the lesson discussing about method of measuring the circular lengh of a
circular object.

Development of the lesson:

• Divide the class into groups according to the number of students.

• Give a copy of activity sheets, three different size circular discs, a measring tape,
A4 sheets, a calculator, a pair of scissors to every group.
• Give time to the students to present their findings
• During the presentation, pay attention to the value of the ratio between the
circumference and the diameter of a circle.
• Stress the above value is near to three.
• Make the student clear that the above ratio is named as  and its value is
22
assumed as 3.14 or for calculation.
7
• Make clear the above ratio is true for any circle.
c
• Make clear about the formula   from their discovery and discuss about
d
the different forms of the formular such as c   d and when d  2r is
given c  2 r .
• Tell the students to use the formula in solving problems relating to the
circumfrance of the circle.

Activity Sheet for the Students :

• Mark a point on the edge of the circular discs (different sizes).
• Draw a straight line on the paper give and mark a point on the straight line.
• By holding the disc vertically put the point on the straight line such that coin-
ciding the two points on the edge of the disc and the straight line.
• Now roll the disc along the line.
• When the point on the disc touches the straight line again mark the touching
point on the straight line.
• Measure the distance between the two points on the staight line.

93
Teacher’s Guide - Grade 9 Mathematics

• Put the disc on a paper and draw the outline of it.

• Cut and seperate the outline you drew and by folding symmetrically find the
diameter of the disc.
• Using the measures you have fill the following table.
c
Circular discs circumfrance (c) diameter (d)
d
i. ..............................
ii. ..............................
iii. ..............................

c
• Find the value of using calculator..
d
• What dicesion you can make with your calculations.
• Present your findings to the class.

Assessment and evaluation:

• Assessment criteria:
• Measures the circumference of the disc accurately.
• Measures the diameter of the disc accurately.
• Express the ratio between the circumference and the diameter is nearly 3.
• Works cooperatively within the group.
• Finishes the work on time.
• Direct the students to the relevant exercises in lesson 18 of the text book.

For your attention...

• Organise activities to achieve the learnig out comes 4, 5 and 6 of competency

level 7.1.

Assessment and evaluation:

• Direct the students to the relevant exercises in lesson 18 of the text book.
For further reference:

• hhttp://www.youtube.com/watch?v=04N79tItPEA
• http://www.youtube.com/watch?v=jyLRpr2P0MQ

For teachers only ........

It came to know that in ancient times mankind had the knowledge about the
ratio between the circumference and the diameter of a circle. Ludolph Van
ceulen (1540-1610) calculated the value of  to 35 decimal points.

Archemedes (287- 212 BC) calculated the value of  lies between 3 10 and
71
1
3 . Now the value of  is calculated to million decimal points by the computer..
7

94
Teacher’s Guide - Grade 9 Mathematics

19. Pythagoras Relationship

Competency 23 : Makes decisions regarding day to day activities based on
geometrical concepts related to rectilinear plane figures.

Competency Level 23.5: Applies Pythagoras’ relationship to solve problems in day to day
life.

Number of Periods: 04

Introduction:
The side opposite the right angle in a right angled triangle is called hypote-
nuse. It is the longest side of the triangle. In sixth century B.C., the Greek
mathematician Pythagoras had presented for the first time a relationship among
the side of a right angled triangle. The relationship states that in any right
angled triangle the area of the square drawn on the hypotenuse is equal to
the sum of the areas of the squares drawn on the other two sides of the
triangle.
In this section it is expected to veify Pythagoras’ relationship for whole num-
ber values , to solve simple problems using the subject content related to the
Pythagoras relationship and to use Pythagoras relationship to solve various
problems relating to the practical life.

Learning outcomes relevant to Competency Level 23.5:

1. Identifies Pythagoras’ relationship.

2. Verifies Pythagoras’ relationship.
3. Solves simple problems by applying Pythagoras’ relationship.
4. Solves problems in day to day life by applying the subject content related to
Pythagoras’ relationship.

Glossary of terms:
Right angle - RcqfldaKh - jpir
Diagonal - l¾Kh - J}uk;
Pythagoras’ relationship - mhs;.ria iïnkaOh - mikT
Right angle triangle - RcqfldaKS ;%sfldaKh - gUk;gb glk;

Instructions to plan the lesson:

This aims to establish in students the subject matter relevant to the

fourth learning outcome following the achievement of subject
content relating to learning outcomes 1, 2 and 3 under the
competency level 23.5. Given below is a specimen that involves
students in an outdoor activity for this.

95
Teacher’s Guide - Grade 9 Mathematics

Time: 40 minutes

Quality inputs:
• 30 m measuring tapes (one for each group)
• Hammer (one for each group)
• Ropes
• 5” iron nails (10 for each group)
• Copies of the activity sheet

Instructions for the teacher:

Approach:
• Recall Pythagoras relationship explaining that the area of the square drawn on
the hypotenuse of a right angled triangle is equal to the sum of the areas of the
squares drawn on the other sides using either a diagram or Pythagoras triads.
• Inform students that how Pythagoras relationship is applied in practical life and
how problems related to it are solved will be explored.

Development of the lesson:

• Divide the class into groups of six as appropriate.
• To each group give an activity sheet, a hammer, ten 5” iron nails, enough ropes
and a 30 m measuring tape.
• Assign different places in the outdoor for the groups.
• Orient the students to the activity giving instructions to position the true figure
given on the earth.
• At the end of the student activity, measure the lengths of the diagonal of the
rectangle and asking the accuracy of the placement of the rectangle make a
review.

Activity sheet for the students :

• Observe the following diagram. Fill in the blanks using the scale given.
3cm

2cm

scale 1:300
• The name by which this figure is known is .......................
• The true length of this is ..............................
• The true breadth of this is .........................

96
Teacher’s Guide - Grade 9 Mathematics

• The vertex angle of this figure is .................

• According to the measurements you obtained and the scale given, place that
figure on earth. Use the measuring tape, hammer, ropes, iron nails provided to
you for this.
• State an instance where you used subject content related to the Pythagoras
relationship when you are installing the above figure on earth
.....................................................................
• Name two instances wheresubject content related to the Pythagoras rela-
tionship is practically used in real life.
1. .........................................................................................
2. .........................................................................................

Assessment and evaluation:

• Assessment criteria:
• Fills in the blanks according to information given.
• Accepts that a rectangle can be correctly obtained using the subject con-
tent related to the Pythagoras relationship.
• Explains the importance and need of the subject content related to the
pythagoras relationship when positioning a rectangle or square on earth.
• Accepts the convenience of working together in a group.
• Complete the assigned task within a given period of time.
• Direct the students to do the relevant exercises in lesson 19 of the textbook.

Practical situations:
• Discuss with students an occasion such as placing the plan of a house on
ground or construction of a volleyball or netball court.

For your attention.....

• Plan and implement activities as follows to verify Pythagoras relationship in

relation to the learning outcome 2.
• Draw a right angled triangle on a square ruled paper and draw squares on all
the three sides of it.

97
Teacher’s Guide - Grade 9 Mathematics

T
X Y

B S
A

R
C
D

P Q Z

\
• PQR is the right angled triangle.
• According to the measurements given in the figure length of PR is 4 squares,
length of PQ is 7 squares.
• Draw PXYZ square so that PR = QZ and PQ = RX.
• As in the figure below , draw the rectangles RXTD, TYSA, BSZQ and
PQCR so that PR and PQ are length and breadth.
• Obtain the square RTSQ by joining the diagonals (RT, TS, SQ, RQ) of those
rectangles.
• Confirm Pythagoras relationship using the number of squares in the squares
drawn on the sides of the right angled triangle.
• Guide the students to explore different methods to verify the truth of
Pythagoras relationship . Using it, instruct students to prepare a portfolio of
learning as a method of school -based learning.

For further reference:

• http://www.youtube.com/watch?v=s9t7rNhaBp8
• http://www.youtube.com/watch?v=AEIzy1kNRqo
• https://www.youtube.com/watch?v=JVrkLIcA2qw

98
Teacher’s Guide - Grade 9 Mathematics

Only for the teacher...

• Given below is a method which can be used to genarate Pythagoras triads.

• When the length of a side of a right angled triangle except the hypotenuse is
an odd number,
• Take the odd number length of a smaller side of the triangle.
• Square it.
• Divide the number that was squared to two consecutive numbers so that
their sum is equal to the number squared.
• of the two consecutive numbers, the large number is the hypotenuse
while the other is the length of the other side.
5
5
3 3 2
 9 3
4
4
13
5 2  25 13
5 12  5

12
25
7 2  49 25
7 24
7
24

• When the length of a side of a right angled triangle except the hypotenuse is
an even number,
• Take the even number length of a smaller side of the triangle.
• Take exactly half of it.
• Square it.(the halved number)
• Take the two numbers, one greater than and one less than the number
obtained by squaring.

5
4 24 5
4 3
4
3
10
6  3 9 6 10
6
8
8
26
26
10 10  5  25  10
24

24

99
Teacher’s Guide - Grade 9 Mathematics

20. Graphs
Competency 20 : Easily communicates the mutual relationships that exist between
two variables by exploring various methods

Competency Level 20.1: Analyses graphically mutual linear relationship between two
variables.

Number of Periods: 07

Introduction:
In a straight line graph the equation of the function is given as y = mx + c. In
this m is known as the gradient of the graph and c is called the intercept.
Under this section it is expected to discuss about the identification of gradient
and intercept in a graph of the form y = mx + c , the behaviour of the graph
when the gradient and the intercept change, gradients of straight line graphs
that are parallel to one another and drawing a graph of a function of the form
ax + by = c.

Learning outcomes relevant to Competency Level 20.1:

1. Identifies that the relationship between and given by a linear equation in

and is a function.
2. Draws the graph of a function of the form y = mx .
3. Draws the graph of a function of the form y = mx + c.
4. Explains how the graph of a function changes depending on the sign and
magnitude of the gradient .
5. States that is the gradient and is the intercept of the graph of a function of
the form y = mx + c.
6. Writes down the gradient and the intercept of the graph of a function of the
form y = mx + c by examining the function.
7. Draws the graph of a function of the form ax + by = c for a given domain.
8. Analyses the gradients of straight line graphs which are parallel to each
other.

Glossary of terms:
Graph - m%ia;drh - tiuG
Gradient - wkql%uKh - gbj;jpwd;
Intercept - wka;(LKavh - ntl;Lj;Jz;LIntercept
Function - Y%s;h - rhu;G
Parallel - iudka;r - rkhe;juk;

100
Teacher’s Guide - Grade 9 Mathematics

Instructions to plan the lesson:

Given below is a specimen lesson adopting group work and lecture

-discussion method to achieve learning outcomes 4, 5 and 6 after
reinforcing in students the subject matter relevant to learning
outcomes 1, 2 and 3 under the competency level 20.1

Time: 40 minutes

Quality inputs:
• Copies of the activity sheet
• Coordinate planes prepared with x and y axes extending from -6 to +6

Instructions for the teacher:

Approach:
• Recall how the values of y is obtained by substituting values for x in an equa-
tion of the form y = 2x showing the relationship between y and x.
• Recall how the values of y are obtained by substituting values within the range
1  x  2 in an equation such as y = 3x + 2.
• Recall how a straight line graph is drawn on a coordinate plane.

Development of the lesson:

• Divide the students into group as appropriate.
• Give students the activity sheets and coordinate planes prepared.
• Engage students in the activity as indicated in the activity sheet.
• After completion of the activity, conduct a discussion eliciting findings to
surface following facts.
• In an equation of the form y = x or y = mx + c, the graph forms an acute
angle with the positive direction of x axis when the coefficient of x is
positive while an obtuse angle with positive direction of x axis when the
coefficient of x is negative.
• In a straight line graph of an equation of the form y = x or y = mx + c,
when the value of m>0 and increase, the angle formed by that line and the
positive direction of the x axis increases.
• They coordinate of the point at which the graph intersects the y axis is the
intercept of the graph.
• In an equation presented in the form y = mx + c , m indicates the gradient
while c represents intercept.
• At the end of the lesson present several equations of the form y = mx + c.
Observing them and questioning about gradient and intercept , lead a
discussion.

101
Teacher’s Guide - Grade 9 Mathematics

Activity sheet for the students :

I II III IV
y = 2x y = 4x y = 2x y = 3x
y = 4x - 1 y = 3x - 2 y = -3x + 1 y = -2x + 2
y = -3x + 2 y = -2x + 2 y = 2x - 3 y = 2x - 3

• Pay attention to the pair of equations you have got.

• Substitute suitable values for x, find the corresponding value of y and draw
their graphs on the coordinate plane provided.
• Observing the graphs drawn by your group answer the following questions.
• Will the angle formed by the graph with axis increase or decrease when the
coefficient of x in the equation increases positively?
• Is the angle formed by the graph with x axis an acute angle or obtuse angle
when the coefficient of x is negative?
• What is the relationship between the coordinates of y and the constant term
of the equation at the pont at which the graph relating to second and third
equations you have got intersect y axis.

Assessment and evaluation:

• Assessment criteria:
• Accepts that in a function of the form y = mx + c, when the value of m>0
and increases, the angle formed by the graph with the positive direction of x
axis increases.
• States the gradient and intercept of the graph of a given function.
• States that in a function of the form y = mx + c , when the value of m is
positive, the angle formed by the graph with the positive direction of x axis
is an actue angle.
• States the gradient and the intercept of the grsph of a given function without
drawing the graph.
• Complete the assigned task within a given period of time.
• Direct the students to do the relevant exercises in lesson 20 of the textbook.

For your attention...

Development of the lesson:

• Plan and implement suitable lession to develop in students subject concepts
relavant to learning outcomes 7 and 8 under competency level 20.1.

102
Teacher’s Guide - Grade 9 Mathematics

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 20 of the textbook.

For further reference:

• http://www.youtube.com/watch?v=0eWm-LY23W0
• http://www.youtube.com/watch?v=LoKEPEPaNm4
• http://www.youtube.com/watch?v=qo5jU_V6JVo
• http://www.youtube.com/watch?v=KV_XLL4K2Fw

103
Teacher’s Guide - Grade 9 Mathematics

21. Inequalities
Competency 18 : Analyzes the relationships between various quantities related to
real-life problems.

Competency Level 18.1: Uses the relationship between two quantities to solve problems.

Number of Periods: 03

Introduction:
In the use of quaantitative values we encounter in our day to day life, very
often we need to indicate greatness, lessness or equality. In mathematics
following symbols are used for these.
Meaning Symbol

Equal to 
Greater than 
Less than 
Either greater or less than 
Either less than or equal to 
Either greater than or equal to 
Greater than or less than or equal to 

It is required to have solutions not only for equations but also for inequalities.
This section explains how algebraic methods and number line are used for
this purpose.

Learning outcomes relevant to Competency Level 18.1:

1. Solves inequalities of the form (  ).

2. Solves inequalities of the form when
3. Solves inequalities of the form when a<0
(a; a  0 is an integer or a fraction)
4. Represents the integral solutions of an inequality on a number line.
5. Represents the solutions of an inequality on a number line.

104
Teacher’s Guide - Grade 9 Mathematics

Glossary of terms:
Inequality - wiudk;dj - rkdpyp
Equal - iudk fõ - rkd;
Greater than - úYd, fõ - ngupJ;
Less than - l=vd fõ - rpwpJ

Instructions to plan the lesson:

Given below is a specimen lesson that adopts guided inquiry

method to develop in students the skill of solving inequalities
relevant to the learning outcome 1 under the competency level
18.1.

Time: 40 minutes

Quality inputs:
• Copies of the activity sheet (one for each student )

Instructions for the teacher:

Approach:
• Recall the meaning of the following symbols learnt in grade 6 and 7.
=, >, <,  , 
• Show that the values 4, 5, 6, .... fit in for x when x > 3
• Write the equations x + 2 = 7 and x -1 = 5 on the board and solve them while
discussing with students.
• Show that instead of the inequality in above equations, relationships with
inequality signs may also exist.
• Have access to the lesson pointing out the need of solving a relationship with
such an inequality.

Development of the lesson:

• Distribute a copy of the activity sheet to every student.
• Direct the students to act according to the instructions given in it.
• Move among the students and give necessary assitance and instructions.
• After completion of the activity, make review eliciting responses randomly.
• During the review, explain if an inequality has a maximum or minimum whether
an inequality is characterised by a maximum or minimum.
• At the end of the review give a note that describes how a relationship with an
inequality is solved to be entered in the exercise books.

105
Teacher’s Guide - Grade 9 Mathematics

Activity sheet for the students :

• Solve the algebraic inequalities given in verbal clauses in the following table
applying your knowledge of solving simple equations and studying the
following examples.

Example (i) Example (ii)

x25 x -2 < 1
x  2  2  5  2 (use of axioms) x -2 + 2 < 1 + 2 (use of axioms)
x3 x <3
The set of whole numbers which The set of positive whole numbers which
is the solution of x ={3, 4, 5, 6, ...} is the solution of x ={2, 1}

• Rows A and B have been completed.Studying them complete the rest of the
table.
When Possible Values which x
wtitten in whole can assume
Statement
algebraic numbers Maximum Minimum
form for x (If exist) (If exist)
When 2 is added to the
A number presented by x, 5 is x + 2 = 5 3 - -
obtained.
The sum of the number
represented by x and 2 is
B either greater than or equal x + 2  5 3,4,5,6,... No 3
to 5
The sum of the number
represented by x and 5 is
i
either greater than or equal
to 8

9 is greater than the

ii answer obtained by sub-
tracting 2 from the number
represented by x
The answer obtained by
subtracting by 3 from the
iii number represented by x is
either equal to or greater
than 10

106
Teacher’s Guide - Grade 9 Mathematics

Assessment and evaluation:

• Assessment criteria:
• Writes the set of solutions that can be assumed by the algebraic term in an
inequality.
• Writes the maximum and minimum value that can be assumed by the
algebraic term in an inequality.
• Accepts that an inequality has more than one solutions.
• Solves inequalities using the algebraic method of solving simple equations.
• Complete the task following the instructions given.
• Direct the students to do the relevant exercises in lesson 21 of the textbook.

For your attention...

Development of the lesson:
• Plan and implement suitable lessons to develop in students subject concepts
relevant to learning outcomes 2, 3, 4, and 5 under the competency level 18.1

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 21 of the textbook.

For further reference:

• http://www.youtube.com/watch?v=nFsQA2Zvy1o

107
Teacher’s Guide - Grade 9 Mathematics

22. Sets
Competency 30 : Manipulates the principles related to sets to facilitate daily
activities.

Competency Level 30.1: Performs set operations by identifying various systems.

Number of Periods: 07

Introduction:

• Students have already learnt to identify a set and to write the elements of
a set. The sets in which the number of elements can be indicated by a
definite number are finite sets. The sets whose number of elements can-
not be indicated by a definite number are infinite sets.
• The sub sets of a given set are the sets written by picking up one or more
elements of that set , null set and the same set itself.
• If n is the number of elements in a set, it is maximum number of subsets is
2n.
• The sets with similar elements are equal sets whereas the sets with equal
number of elements are equivalent sets. Therefore equal sets always
equivalent sets but equivalent sets are always not equal sets.
• A set included elements of a set or sets is the universal set of those sets.
• The set that includes all the elements in the sets A and B is the union of
set A and B and is given the notation A  B .
• The set that includes the elements common to two sets A and B is the
intersection set of A and B is given the notation A  B .
• The sets in which the intersection is a null set are disjoint sets.
• The set that indicates the elements in the relevant universal set except the
elements of set A is the complement of set A. It is given the notation A/.
This section deals with the subject concepts related to the sets described
above.

Learning outcomes relevant to Competency Level 30.1:

1. Identifies finite sets and infinite sets.

2. Concludes with reasons whether a given set is a finite set or an infinite set.
3. Writes down all the subsets of a given finite set.
4. Explains the difference between equivalent sets and equal sets.
5. Identifies disjoint sets.
6. Identifies the universal set.

108
Teacher’s Guide - Grade 9 Mathematics

7. Writes down the elements in the intersection of two sets.

8. Writes down the elements in the union of two sets.
9. Identifies the complement of a set.
10. Identifies the symbols relevant to set operations.
11. Accepts that if the intersection of two sets is the empty set, then the two
sets are disjoint.
12. Solves problems using the knowledge on sets.
13. Represents subsets, the intersection of two sets, the union of two sets,
disjoint sets and the complement of a set in Venn diagrams and writes these
sets using the symbols used for set operations. (For two sets only)

Glossary of terms:

Finite sets - mßñ; l=,l - KbTs;s njhilfs;

Infinite sets - wmßñ; l=,l - Kbtpy; njhilfs;
Sub sets - Wml=,l - cgnjhilfs;
Equivalent sets - ;=,H l=,l - rktYj; njhilfs;
Equal sets - iul=,l - rk njhilfs;
Disjoint sets - úhqla; l=,l - %l;lw;w njhilfs;
Union of sets - l=,l fï,h - njhil xd;wpg;G
Intersection of sets - l=,l fþokh - njhil ,ilntl;L
Complement of a set - l=,lhl wkqmQrlh - epug;gpj; njhil

Instructions to plan the lesson:

Given below is a specimen lesson prepared adopting the lecture-

discussion method with a group activity to develop in students the
subject concepts related to the learning outcomes 1 and 2 under
the competency level 30.1.
Time: 40 minutes

Quality inputs:
• Copies of the activity sheet

Instructions for the teacher:

Approach:
• Start discussion by recalling previous knowledge and asking what is a set.
• Display the sets,
X = {even numbers between 0 - 10}
Y= {multiples of 3 between 0 - 25}
on the board. Continue the discussion asking about the elements of X and Y.

109
Teacher’s Guide - Grade 9 Mathematics

Development of the lesson:

• Divide the class into groups of four, give a copy of the activity sheet to each
group and engage the students in the activity.
• Once the activity is over, displays the findings of each group on the board.
• After the students’ presentations, conduct the discussion highlighting the
following.
• Can all the elements of the set A and b be written or not? Can the number
of all the elements in sets A and B be stated definitely or not?
• Can all the elements of the sets C and D be written or not? Can the number
of all the elements in sets C and D be stated definitely or not?
• The sets in which the number of elements can be given by a definite
quantitative value are called finite sets.
• The sets in which the number of elements cannot be given by a definite
quantitative value are called infinite sets.
• Display some other finite and infinite sets on the board and reinforce the
concept in students by asking to what type those sets belong.

Activity sheet for the students :

• If can write all elements of the following sets, write the elements of the sets and
the number of elements in each.
• If can’t write all elements of the sets, write some of elements of these sets and
put dotted line. As well as, indicate the sentence “can’t tell” instead the
number of elements in each.
(i) A = { odd numbers between 0 - 10 }
A={ } Number of elements in A =

(ii) B = {multiples of 5 between 0 -50}

B={ } Number of elements in B =

(iii) C ={multiple of 2 }
C={ } Number of elements in C =

(iv) D = { counting numbers }

D={ } Number of elements in D =

• Display the facts you found on the board.

110
Teacher’s Guide - Grade 9 Mathematics

Assessment and Evaluation:

• Assessment criteria:
• Writes the elements and the number of elements in a given finite set.
• Identifies as finite sets the sets whose number of elements can be given by a
definite quantitative value.
• Identifies as infinite sets the sets whose number of elements cannot be given
by a definite quantitative value.
• Acts cooperatively within the group.
• Completes the work within the allocated time.
• Direct the students to do the relevant exercises in lesson 22 of the textbook.

For your attention...

Development of the lesson:
• Plan and implement an activity to enable students to write the sub sets of a
given sub set.
• Introduce equal sets and equivalent sets and conduct an activity to explain the
difference between them.
• Adopt a suitable activity to introduce the universal set, intersection of sets,
union of sets and disjoint sets.
• Plan and implement and activity suitable to introduce the complement of a set.
• Design and implement activities to illustrate sets, sub sets, intersection of two
sets, union of sets, complement of a set and disjoint set by Venn diagrams.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 22 of the textbook.

For further reference:

• http://www.youtube.com/watch?v=jAfNg3ylZAI

111
Teacher’s Guide - Grade 9 Mathematics

23. Area
Competency 08 : Makes use of a limited space in an optimal manner by
investigating the area.

Competency Level 8.1: Investigates the area of simple geometrical shapes in the
environment.

Number of Periods: 05

Introduction:
The extent of a given surface is called its area. In previous grades it is learnt
how to derive formulae to find the areas of the plane figures squares, rectan-
gles and triangles and find areas of such figures using them. In this grade it is
expected that the student will derive formulae to find the areas of the plane
figures bounded by parallelogram, trapeziums and circles and find areas of
such shapes.

Learning outcomes relevant to Competency Level 8.1:

1. Develops a formula for the area of a parallelogram.

2. Finds the area of a parallelogram.
3. Develops a formula for the area of a trapezium.
4. Finds the area of a trapezium.
5. Develops the formula for the area of a circle.
6. Performs calculations by applying the formula A =  r2.
7. Solves problems related to the areas of parallelograms, trapeziums and circles.

Glossary of terms:
Parallelogram - iudka;rdi%hh -
Trapezium - ;%mi
S shu -
Circle - jD;a;h -

Instructions to plan the lesson:

Given below is a specimen lesson designed with the adoption of

discussion method coupled with an individual activity for developing
in students the subject matter related to the learning outcomes 1
and 2 under the competency level 8.1.
Time: 40 minutes

112
Teacher’s Guide - Grade 9 Mathematics

Quality inputs:
• Copies of the activity sheet
• Glue/pairs of scissors/squared ruled papers

Instructions for the teacher:

Approach:
• Ask what is area and discuss about the formulae used to find the area of a
square and rectangle in previous grades.
• Draw a few figures on the chalk board as appropriate and let the students find
the area of the rectangle.
• Surface through the discussion that the areas of the plane figures that overlap
are equal.

Development of the lesson:

• Divide the class into groups and to each group distribute quality input
materials adequately.
• Let the students know that they should do the activity individually and assess
them while assisting as required.
• After completion of the activity, conduct a discussion and reinforce learning
outcomes 1 and 2

Activity sheet for the students :

Part A
• Cut two parallelogram shapes the size in Figure 1 from a square ruled paper

A B
>

h
>

D
>C
>
a

Figure 1
.

113
 Teacher’s Guide - Grade 9 Mathematics

• In one of the parallelograms cut,

draw a triangular part as in Figure 2
and snip it out.

Figure 2

• Connect the snip out triangular part

with the remaining part and make a
rectangle as shown in Figure 3.

Figure 3
• Mark the length and breadth of that rectangle as a and h and write a formula
for the area in terms of them.
• Take the other parallelogram cut at the beginning and derive a formula for it in
terms of the area of the parallelogram.
• On the basis of them build up a formula for the area of a parallelogram A in
terms of the length of a side l and the perpendicular distance between that
side and the other equal side b.

Part B
•
• Using the formula you derived, find the area of each of the parallelograms
given below.. >>
>>
>

>>
>

5.5 cm
>

>

6 cm
>

7 cm 5 cm 12 cm
>

>> >> >>

10 cm 3 cm 8 cm

Assessment and evaluation:

• Assessment criteria:
• Reads and understands the instructions given and gets involved in the
activity.
• Derives a formula for the area of a parallelogram.
• Finds the area of a given parallelogram.
• Work cooperatively and efficiently with others.
• Accepts that when a shape is cut and another shape is made, the area
doesn’t change.
• Direct the students to do the relevant exercises in lesson 23 of the textbook.

114
Teacher’s Guide - Grade 9 Mathematics

For your attention...

Development of the lesson:

• Design and implement an activities to find the area of a trapezium and a circle
as appropriate.
• Get the students to drive formulae for their area and do exercises using them.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 23 of the textbook.

For further reference:

• http://www.youtube.com/watch?v=j3-XYLnxJDY
http://www.youtube.com/watch?v=ZyOhRgnFmIY

115
Teacher’s Guide - Grade 9 Mathematics

24. Probability
Competency 31 : Analyzes the likelihood of an event occurring to predict future
events.

Competency Level 31.1: Investigates the likelihood of an event by considering the

outcomes of the experiment.

Number of Periods: 05

Introduction:
• Characteristics of a random experiment are as follows.
* Knowing all the results before doing the experiment.
* Not knowing the result obtained at a particular instance.
* Repeatability of the experiment.
* lack of a pattern in the results though the experiment is repeated.

• The set that includes all the likely results of a random experiment is the sample
space of that experiment. If the results of an experiment have an equal likeli-
hood they are referred to as equally probable.
Ex:  In an experiment in which the side facing up is noted when a cubical fair
dice whose sides are marked with 1 - 6 is tossed, the results obtained are
equally probable.
Ex:  In an experiment in which the colour of the side facing up when a dice
whose 4 sides are painted white and 2 sides are painted black
is tossed, the result obtained are not equally probable.

• If A is an event in the sample space S with equally likely out comes and p(A) is
n(A)
the probability of happening A, p(A) = . Here, n(A) is the number of
n(S)
elements in the set of A while n(S) is the number of elements in the sample
space.

In this section, the subject concepts related to the probability described above
are studied.

Learning outcomes relevant to Competency Level 31.1:

1. Identifies random experiments.

2. Identifies the set of all possible outcomes of an experiment as the sample
space of that experiment.
3. Writes down the sample space of a given experiment.
4. Identifies equally likely outcomes.
5. Writes down examples of equally likely outcomes.

116
Teacher’s Guide - Grade 9 Mathematics

6. Performs calculations using the formula for an event of a random

experiment with equally likely outcomes, having a sample space .
7. Makes decisions in day to day life using the knowledge gained on probability.

Glossary of terms:

Random experiments - wyUq mÍlaIK - vOkhw;Wg; gupNrhjid

Sample space - ksheÈ wjldYh - khjpup ntsp
Equally Likely events - iufia NjH m%;sM, - rkkha; epfoj;jf;f
Event - isoaêh - epfo;r;rp
Out come - m%;sM,h - Event

Instructions to plan the lesson:

A specimen lesson designed to develop in students the subject

concept related to learning outcomes 2 and 3 adopting lecture
discussion method after the subject concepts relevant to the first
learning outcome under the competency level 31.1 are reinforced
in students is given below.
Time: 40 minutes

Quality inputs:
• Copies of the evaluation sheet prepared to distribute to students at the end of
the lesson for reinforcing the facts learnt. (one for each student)

Instructions for the teacher:

Approach:
• Initiate a discussion recalling the characteristics of a probability experiment
learnt before and giving examples for such experiments.

Development of the lesson:

• Discuss with students and consolidate in them that an implement of tossing an

unbiased coin is a probability experiment.
• Ask students which side of the coin faces up when the coin is tossed before
tossing it and record all the results.
• Show that the experiment of tossing a cubical fair dice with numbers 1 - 6 is a
probability experiment.
• Discuss all the probable results regarding the side facing up when tossing a
dice and write the set that includes all the results on the board.

117
Teacher’s Guide - Grade 9 Mathematics

• Explain that the set that includes all the results in the above example is the
sample space of those experiments.
• Discuss about the sample space of some other experiments also.
• Explain that sample space is symbolised by S.
• Distribute the question sheet to students, Let the students answer it and
discuss about the answers given by students.

Assessment and evaluation:

• Assessment criteria:
• Identifies all the likely results in a random experiment.
• States that all the results in a random experiment is its sample space.
• Writes the sample space of a given random experiment.
• Completes the task within the given period of time.
• Direct the students to do the relevant exercises in lesson 24 of the textbook.

Activity sheet with questions for reinforcement:

• Write the sample space relevant to each of the following random experiments.

(1) Recording the number on the side facing down when a tetrahedral dice
whose sides have numbers 1 - 4 is tossed.
Sample space, S = { }

(2) Recording the colour on the side facing up when a cubical dice with sides
painted in red, blue, white, black, yellow and green is tossed.
Sample space s ={ }

(3) Taking out a bead randomly from a bag containing three beads of colours
red, blue and white.
Sample space, S = { }

(4) Taking out a marked piece of paper from a bag containing rolled pieces of
paper numbered from 1 - 10.
Sample space, S = { }

(5) Taking out a ball randomly from a bag containing 4 identical balls of which
2 are red and numbered 1 and 2 while 2 are blue and numbered 1 and 2.
Sample space, S = { }

118
Teacher’s Guide - Grade 9 Mathematics

For your attention...

Development of the lesson:
• Plan suitable methods for learning outcomes 4, 5, 6 and 7 under the
competency level 31.1 and implement with students.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 24 of the textbook.

For further reference:

• http://www.youtube.com/watch?v=mLE-SlOZToc
• https://www.youtube.com/watch?v=sPQM-yZgGwc

119
Teacher’s Guide - Grade 9 Mathematics

25. Angles of Polygons

Competency 23 : Makes decisions regarding day to day activities based on
geometrical concepts related to rectilinear plane figures.

Competency Level 23.4: Performs calculations using the sums of the interior and exterior
angles of a polygon.

Number of Periods: 05

Introduction:
A polygon is a closed plane figure bounded by segments of straight lines. The
polygon in which each of the interior angle is less than 1800 are called convex
polygon whereas the polygons in which at least one interior angle is greater
than 1800 are known as concave polygons. The polygons in which all the
sides and angles are equal are known as regular polygons. A polygon only
with equal sides is an equilateral polygons.
The polygon with minimum number of sides is the triangle. In regular poly-
gons there are axes of symmetry equal in number to the number of sides. In
a regular polygon, the order of rotational symmetry is also equal to the
number of sides.
From the distant past many polygonal shapes have been used in various
creative works. Shapes of polygons takes a very important place in ancient
architecture. Polygonal shapes are used to create tessellations. Polygonal
shapes are seen even in natural creations such as the bee hives, spider webs
and cells.
Under this section it is expected to give an understanding about the sum of
the interior and exterior angles of a n-sided polygon in relation to competen-
cy level 23.4 . Accordingly it is expected to identify and verify the theorem ‘
The sum of all the interior angles of a n-sided polygon is equal to (2n-4) right
angles’ and solve simple geometry problems using it. It is also expected to
identify and verify the theorem’ the sum of all the exterior angles of n-sided
polygon is equal to 4 right angles’ and solve simple geometry problems using
it.

Learning outcomes relevant to Competency Level 23.4:

1. Identifies the theorem, “The sum of the interior angles of an n-sided polygon
equals (2n – 4) right angles”.
2. Verifies the theorem, “The sum of the interior angles of an n-sided polygon
equals (2n – 4) right angles”.
3. Solves simple geometric problems using the theorem, “The sum of the interior
angles of an n-sided polygon equals (2n – 4) right angles”.

120
Teacher’s Guide - Grade 9 Mathematics

4. Identifies the theorem, “The sum of the exterior angles of an n-sided polygon is
four right angles”.
5. Verifies the theorem, “The sum of the exterior angles of an n-sided polygon is
four right angles”.
6. Solves simple geometric problems using the theorem, “The sum of the exterior
angles of an n-sided polygon is four right angles”.

Glossary of terms:
Rectilinear closed plane figures - ir, f¾Çh ixjD; ;, rEm - vz;Nfhyk;
Triangle - ;%sfldaKh - nghJ cWg;G
Quadrilateral - p;=ri%h - klq;Ffs;
Pentagon - mxpdi%h - vz;Zk; vz;fs;
Hexagon - Ivi%h - ,ul;il vz;fs;
Interior angle - wNHka;r fldaKh - xw;iw vz;fs;
Exterior angle - ndysr fldaKh - rJu vz;fs;
Regular polygons - iúê nyqwi% - Kf;Nfhzp vz;fs;

Instructions to plan the lesson:

Given below is a group activity and guide inquiry method -based

specimen lesson design to develop in students the subject concepts
related to the learning outcomes 1 and 2 under the competency
level 23.4 .
Time: 40 minutes

Quality inputs:
• Copies of the activity sheet

Instructions for the teacher:

Approach:
• Start a discussion on the polygon with students drawing their attention to the
following facts.
– convex and concave polygons
– naming polygons from triangle to decagon
– instances where polygons are used for creative work
• Inquiring into the interior angles of polygon recall that the sum of the interior
angles of a triangles is 1800 and the sum of the interior angles of a quadrilateral
is 3600.

121
Teacher’s Guide - Grade 9 Mathematics

Development of the lesson:

• Divide the class into groups as appropriate and distribute copies of the activity
sheet one to each group.
• Show how one vertex is joined to the other in the polygons triangle,
quadrilateral, pentagon etc.
• Engage every student in the activity.
• At the end of the activity come to the generalization that the sum of the interior
angles of a polygon is (2n - 4) right angles.

Activity sheet for the students:

• In each polygon in the table, join on vertex with the other vertices by a straight
line.
• Write the number of triangles obtained when one vertex is joined with the
others.
• Build up a relationship between the number of sides of each polygon and the
number of triangles.
• Derive a relationship to find the sum of the interior angles of the polygon using
the sum of the interior angles of a triangle.
• Taking the sum of the interior angles of a triangle as two right angles, write the
sum of the interior angles of the polygon in terms of right angles.

No. of triangles No. of Sum of the interior angles

obtained by triangles
No. joining one obtained - No. As a multiple In terms of
Polygon Diagram of the interior the number
of vertex with of sides of the
sides others. polygon angles of a of triangles
triangle and sides

Triangle 3 1 3-2 1800  1 2(3 2)

Quadrilateral 4 2 4-2 1800  2 2(4  2)

Pentagon

Hexagon

Heptagon

Octagon

Polygon
with n sides

122
Teacher’s Guide - Grade 9 Mathematics

Assessment and evaluation:

• Assessment criteria:
• Joins the straight lines a vertex of a polygon with the others.
• Computes correctly the number of triangles obtained by joining one vertex
with other vertices.
• Finds a relationship between the number of sides of a polygon and the
number of triangles.
• Accepts that the sum of the interior angles of any polygon can be calculated
using the sum of the interior angles of the triangles.
• Direct the students to do the relevant exercises in lesson 25 of the textbook.

For your attention...

Development of the lesson:
• Let the students solve geometric problems containing simple calculations to
achieve the learning outcomes 3 and 6 relating to the competency level 23.4.
Design and implement a suitable activity for learning outcomes 4 and 5.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 25 of the textbook.

For further reference:

•

123
Teacher’s Guide - Grade 9 Mathematics

26. Algebraic Fractions

Competency 16 : Explores the various methods of simplifying algebraic fractions to
solve problems encountered in day to day life.

Competency Level 16.1: Analyses relationships in daily life by simplifying algebraic

fractions.

Number of Periods: 03

Introduction:
Either denominator or numerator or both denominator or numerator is/are
algebraic terms or algebraic expressions are called algebraic fractions.

1 1 x y 2a 1 2 x3
, , , , , , ,
x 2a 5 2 3b x  1 2a  b x  2

As in the case of common fractions, in the addition and subtraction of alge-

braic fractions, the denominators should be made equal.

Learning outcomes relevant to Competency Level 16.1:

1. Identifies algebraic fractions.

2 Adds and subtracts algebraic fractions with equal integral denominators.
3 Adds and subtracts algebraic fractions with unequal integral denominators.
4. Adds and subtracts algebraic fractions with equal algebraic denominators.

Glossary of terms:
ùÔh Nd. - vz;Nfhyk; - Algebraic fractions
yrh - nghJ cWg;G - Denominator
,jh - klq;Ffs; - Numerator
fmdÿ yrh - vz;Zk; vz;fs; - Common Denominator
l=vd u fmdÿ .=Kdldrh - ,ul;il vz;fs; - Least common multiple
;=,H Nd. - xw;iw vz;fs; - Equivalent fractions

Instructions to plan the lesson:

A specimen lesson with a group activity for developing in students

the subject concepts related to the learning outcomes 3 under the
competency level 16.1 is given below.

124
Teacher’s Guide - Grade 9 Mathematics

Time: 40 minutes

Quality inputs:
• Copies of the activity sheet
• Cards containing the following algebraic fractions

x x a a3 m n
3 4 2 5 3 6
x2 y b b m 1
5 3 3 4 4
y 3 y b1 n2
4 5 2 2
x 1 a1 n m
2 3 4 2

Instructions for the teacher:

Approach:
• Discuss with students about the addition and subtraction of numerical fractions
with equal and unequal denominators.
• Also discuss about the simplification of algebraic fractions carrying like terms
and unlike terms.
• Discuss with students about the simplification of two algebraic fractions with
5x x
equal denominators such as  .Emphasize that here too, the method used
3 3
in the simplification of numerical fraction is followed.

Development of the lesson:

• Divide the class into six groups as appropriate
• Distribute a copy of the activity sheet and a card with algebraic fractions to
each group and engage the students in the activity.
• Go to each group and give necessary support.
• After completion of the task, discuss step by step by asking questions how
two algebraic fractions with unequal numerical denominators are added.
• Discuss with students and emphasize that when adding fractions with unequal
numerical denominator, first the least common multiple of those two numbers
should be found.
• Stress that the answer can then be obtained by simplifying the numerator.

125
Teacher’s Guide - Grade 9 Mathematics

Activity sheet for the students:

• Pay attention to the card provided to your group.

• Of the algebraic fractions given in the card, select two algebraic fractions with
unequal denominators.
• Find the least common multiple of the denominators of those fractions.
• According to the least common multiple, write fractions equivalent to each
algebraic fraction.
• Recalling the addition of two fractions with equal denominators, add these two
fractions and get the answer.
• If possible, simplify the answer further.
• Of the two fractions, subtract the smaller fraction from the larger fraction and
obtain the answer.
• Select another pair of fractions with unequal denominators and add and
subtract them as was done before.

Assessment and evaluation:

• Assessment criteria:
• Identifies algebraic fractions.
• Obtain common denominator of integral denominators by finding the least
common multiple of the denominators of algebraic fractions with unequal
integral denominators.
• Accepts that the common denominator should be obtained when simplifying
algebraic fractions with unequal integral denominators.
• Obtains fractions equivalent to algebraic fractions according to the common
denominator.
• Adds and subtracts two algebraic fractions with unequal integral
denominators.
• Acts cooperatively within the group and reaches the target.
• Direct the students to do the relevant exercises in lesson 26 of the textbook.

For your attention...

Development of the lesson:
• Make students aware about the addition and subtraction of algebraic fractions
with equal algebraic denominators.

Assessment and evaluation:

• Direct the students to do the relevant exercises in lesson 26 of the textbook.

For further reference:

•

126
Teacher’s Guide - Grade 9 Mathematics

27. Scale Diagrams

Competency 13 : Uses scale diagrams in practical situations by exploring various
methods.

Competency Level 13.1: Indicates the direction of a location by means of an angle.

Competency Level 13.2: Investigates various locations in the environment using scale
diagrams.

Number of Periods: 07

Introduction:
Students have learnt in previous grades how to describe the location of a
place being at another position using directions. Bearing is used as a measure
of location in relation to northern direction. Bearing is obtained by a clock-
wise rotation from the direction of north identified using a compass. Indicat-
ing the angle of rotation by three digits is a convention. All the rotation should
be on the same plane. This section focuses on deciding the location of a
place by bearing and distance and solving problems related to it.

Learning outcomes relevant to Competency Level 13.1:

1. Explains “bearing”.
2. Accepts that the bearing and the distance are needed to describe the location
of a place with respect to another place on a horizontal plane.
3. Identifies the clinometer as an instrument that is used to measure bearing and
uses it.
4. Describes various locations in terms of bearing and distance.
5. Performs calculations related to bearing.

Glossary of terms:
Distance - ÿr - J}uk;;
Location - msysàu - mikT
Horizontal plane; - ;sria;,h - fpilj;jsk
Bearingjp - È.xYh - irNfhs;
Compass - ud,sudj - jpirawpfUtp
Clock wise - olaIK
s dj¾; - tyQ;Rop

127
Teacher’s Guide - Grade 9 Mathematics

Instructions to plan the lesson:

Given below is a specimen lesson with a practical activity designed

to achieve learning outcome 4 with the aim of giving practical
experience to students of locating a place after a developing in
them the learning outcomes 1, 2 and 3 under the competency
level 13.1.
Time: 80 minutes

Quality inputs:
• Protractors with the calibration 0 - 3600 and fixed on thick 20 cm × 20 cm
polystyrene sheets with a tube (annex 1) - one for each group
• Compasses- one for each group
• Measuring tapes (10 m/ 20 m)- one for each group
• Copies of the activity sheets

Instructions for the teacher:

Approach:
• Recalling that the direction north can be obtain in relation to east on which the
sun rises or using a compass, draw a diagram to show the eight directions in
the board.
• Explain that north is used as the base to describe the location of a place using
the bearing.
• Let the students do the following activity to inquire into the method of finding
the location by rotating the angle clockwise from north.

Development of the lesson:

• Divide the class into groups of five.
• Let each group go out carrying a desk with a flat top. (If it is difficult to do the
activity outdoor, select suitable places inside the classroom.)
• Give each group an activity sheet , a compass, a protractor and measuring
tape.
• Assign a place for each group and instruct to align 00 in the protractor on the
table along the direction of north identified by the compass.
• Assign four points A, B, C and D for the students to observe. (Position one of
these along one of the other three main directions.)
• Ask students to observe the place marked and to measure and record the
relevant angle and the distance to the place from the point from which the
measurement is made.
• After the completion of the activity make a review in the light of the sketches
made by groups to highlight that the location of a place can be indicated by the
angle measured clockwise from the north and the distance.

128
Teacher’s Guide - Grade 9 Mathematics

Activity sheet for the students:

• Keep the desk at the place assigned to you, keep the compass on it and
identify north. Place the protractor steadily on the desk so that its 00 points
north.
• Observe each place shown to you by the teacher through the drinking straw
fixed to the protractor. Measure clockwise from north the angle corresponding
to the location of each place and record it.
• Measure the distance from the protractor to the place you were asked to
observe by the teacher with the measuring tape and record as follows.
P  0400  12m
(This means that P is located at an angle of 400 clockwise from north at a
distance of 12 m)
• Indicate the measurements made in a table such as the one shown below.

Observation point (place) Angle Distance (m)

A
B
C
D
• Present the above information on a rough chart.
• Present your work to the whole class.

Assessment and evaluation:

• Assessment criteria:
• Measures correctly clockwise from the north the angle along which a given
point is located from another given point.
• Accepts that in order to locate a place distance is also essential in addition
to the bearing.
• Measures correctly the distance from a given point to another given point.
• Indicate in a rough sketch the location of a place relative to another place
using angle and distance.
• Accepts the convenience of working as a group.
• Direct the students to do the relevant exercises in lesson 27 of the textbook.

Practical applications:
• This section is very important for giving the location of a certain point definitely
and to take measurements required to sketch a plan of a small plot.

For further reference:

129
Teacher’s Guide - Grade 9 Mathematics

28. Data Representation and Interpretation

Competency 28 : Facilitates daily work by investigating the various methods of
representing data.

Competency 29 : Makes predictions after analyzing data by various methods, to

facilitate daily activities.

Competency Level 28.1: Represents data such that comparison is facilitated.

Competency Level 29.1: Investigates frequency distributions using representative values

Number of Periods: 10

Introduction:
A given group of data can represent in a frequency distribution without class
interval and interpret. Such a distribution is known as an ungrouped fre-
quency distribution. When there is a large amount of data with regard to an
experiment use of ungrouped frequency is not an easy or meaningful task. In
such a case we can make the task manageable by taking data as groups and
indicating the frequency rather than giving the frequency for each piece of
data. Such a table in which frequencies are given for grouped sets of data is
known as a grouped frequency distribution. Generally a grouped frequency
distribution has two columns. One is the groups of the data known as class
intervals and the other is the number of the pieces of data within those class
intervals or frequency. This aims to study how a given group of data is rep-
resented in a frequency distribution with class intervals.

Learning outcomes relevant to Competency Level 28.1:

1. Identifies a frequency distribution.
2. Presents a given group of data in a frequency distribution without class
intervals.
3. Identifies what a class interval is.
4. Identifies presenting data in class intervals as grouping data.
5. Represents a given group of data in a frequency distribution with class
intervals.

Glossary of terms:
Data - o;a; - juT
Frequency distribution - ixLHd; jHdma;sh - kPbwd; guk;gy;
Grouping - iuQykh - $l;lkhf;fy;
Class intervals ;- mka;s m%dka;r - tFg;ghapilfs

130
Teacher’s Guide - Grade 9 Mathematics

Instructions to plan the lesson:

This lesson aims to develop the subject concepts relating to the

learning outcomes 5 after the reinforcement of subject concepts
relating to the learning outcomes 1, 2, 3 and 4 in students under the
competency level 28.1. A specimen lesson designed for this adopting
the lecture discussion method coupled with an individual activity is
presented below.

Time: 40 minutes

Quality inputs:
• Copies of the activity sheet
• A slot panel
• A flip chart with the grouped frequency table
• Cards with data
• Felt pens
• A4 sheets

Instructions for the teacher:

Approach:
• Start a discussion asking how a given group of data is represented in a
frequency distribution without class intervals.
• Discuss about the class interval and the way the data are grouped.
• Approach the lesson asking how a grouped frequency table is prepared by
grouping data when the amount of data is large.

Development of the lesson:

• Say that when preparing a grouped frequency distribution, first the range of
data should be found.
• Describe that range means the difference between the highest and lowest
values of given data.
• Say that afterwards, separation into suitable class intervals can be done in two
ways. One is, first deciding on the number of class intervals and then the class
size accordingly. The other is first deciding on the class size and then finding
the number of class intervals.
• Explain that when finding the class size, the range should be divided by the
number of classes while when finding the number of class intervals the range
should be divided by the class size. Say that here the answer should be
obtained to the nearest whole number.

131
Teacher’s Guide - Grade 9 Mathematics

• Describe that after separation of class intervals, the grouped frequency distri-
bution is prepares by tallying all the data and writing the respective numbers
opposite each class interval
• Then group the students as appropriate and distribute a copy of the activity
sheet and a paper to each.
• Engage the students in the activity.
• Let the students present their findings.
• Following the presentation of findings remove the data presented in the slot
panel and fill the grouped frequency table drawn in the flop chart. Build up the
whole of the lesson.

Activity sheet for the students:

• Engage individually in the activity according to the instruction given to you.

Given below is the information regarding the s.m.s. received by an amateur
singer at a reality show to make him the winner.

5 21 12 32 45 32

23 6 24 18 40 35

26 13 15 7 38 49

24 13 24 19 35 28

27 38 28 25 40 15

(i) What is the minimum value in this group of data?

(ii) What is the maximum value in this group of data?
(iii) Taking the number of class interval as 5, find the width of a class by
dividing the range of the group of data by 5.
(iv) Using that class width, prepare the relevant class intervals starting with the
minimum value in the group of data.
(v) Prepare a grouped frequency distribution using tally marks and inserting
data relevant to each interval.
(vi) Get ready to present the frequency distribution prepared.

Assessment and evaluation:

• Assessment criteria:
• Describes how the range of a group of data is found.
• Decides the number of class intervals, finds the class width and prepares
class intervals.
• Groups the data and prepares a frequency distribution.

132
Teacher’s Guide - Grade 9 Mathematics

• Accepts that it is easy to retrieve data by grouping data when the amount of
data is large.
• Works in the group respecting the ideas of the others.
• Direct the students to do the relevant exercises in lesson 28 of the textbook.

For your attention...

Development of the lesson:
• Plan and implement a suitable method to develop in students the subject
concepts related to the learning outcomes in the competency level 29.1

For further reference:

•

133