institute of adult education - iae of adult education ... syllabus uses competence based education...

INSTITUTE OF ADULT EDUCATION

ENHANCING ACCESS AND EQUITY TO SECONDARY EDUCATION THROUGH OPEN AND DISTANCE LEARNING (ODL)

MATHEMATICS SYLLABUS STAGE I AND II (FORM I-IV)

2015

Designed and prepared by;The Department of Distance EducationInstitute of Adult EducationDar es SalaamTanzania

© Institute of Adult Education, 2015

All rights reserved. No part of this publication may be reproduced, reported and stored in any system or transmitted in any form

or by any means; electronic, mechanical, photocopying, recording or otherwise without the permission of the copyright owner.

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Preamble

Education provision in Tanzania has been equipping learners with skills and knowledge for individual growth. Apparently,

researches show that some learners do not acquire adequate skills in the world of work. Secondary school graduates have been

over dependent and fail to engage in formal and informal employment. Consequently, learners are found losing national identity

and patriotism. This has resulted into incompetence in professionalism, as the syllabi do not carter for the learners’ immediate

needs, instead they them equipped mostly with theories. Hence, creating a gap between school life and the world of work.

Competence Based Education and Training (CBET) approach is being integrated into the syllabi. Different institutions including

the National Council for Technical Education (NACTE) in Tanzania advocate the CBET approach.

Competence is a process of integrating knowledge, skills and attitudes, which are associated with the ability to carry out some

occupational activities as, described in the syllabi. The competencies are applicable in wider attributes and evaluated by oral tests,

written and practical tasks.

Introduction

This Mathematics syllabus for Ordinary level Secondary school comprises of subject matter (topics) from form one to form four

and the topics are written in a modular format. It has integrated components that originate from the formal education syllabus and

the identified needs obtained from the baseline survey study conducted in 2008.

The integrated syllabus has been prepared to allow a learner to complete the course within the period of two years. It is intended

for learners outside the formal school system to enable them sit for Certificate for Secondary Education Examinations. The

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syllabus uses Competence Based Education and Training (CBET) approach which is result based indicating what a learner is

expected to do after completion of the ordinary level secondary school studies..

Objectives of Education in Tanzania

The education system in Tanzania has four objectives including:

1. To guide the development and improvement of the personalities of the citizens of Tanzania, their human resources and

effective utilization of their resources in bringing about individual and national development;

2. To promote the acquisition and appreciation of culture, customs and traditions of the people of Tanzania;

3. To promote the acquisition and appropriate use of literary, social, scientific, vocational, technological, professional and other

forms of knowledge, skills and understanding for the development and improvement of man and society; and

4. To develop and promote self-confidence and an inquiring mind; an understanding and respect for human dignity and human

rights and readiness to work hard for self advancement and national improvement (MoEVT, 2007).

Aims and Objectives of Secondary Education in Tanzania

The aims and objectives of Secondary Education in Tanzania are to:

1. consolidate and broaden the scope of baseline ideas, knowledge, skills and principles acquired and developed at primary

education level;

2. enhance further development and appreciation of national unity, identity and ethical personal integrity, respect for and

readiness to work, human rights, cultural and moral values, customs, traditions and civic responsibilities and obligations;

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3. promote the development of competency in linguistic ability and effective use of communication skills in Kiswahili and at

least one foreign language;

4. provide opportunities for the acquisition of knowledge, skills, attitudes and understanding in prescribed or selected fields of

study;

5. prepare students for tertiary and higher education; vocational, technical and professional training;

6. inculcate a sense and ability for self-study, self-reliance and self-advancement in new frontiers of science and technology,

academic and occupational knowledge and skills, and

7. prepare the student to join the world of work.

NON-FORMAL EDUCATION (NFE) IN TANZANIA

Non-Formal Education is any intentional and systematic education enterprise outside traditional schooling in which content,

media, time, units, admission criteria, staff, facilities and other system components are selected and/or adapted for particular

students, populations or situations in order to maximize attainment of the learning mission and minimize maintenance constraints

of the system.

Characteristics of Non-Formal Education

Non-Formal Education has many variations each with its unique characteristics. Those characteristics are:-

1. It occurs outside the schools and concerned with immediate and practical missions in any situation which affords

appropriate experiences may be employed as the learning site.

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2. It involves minimal but highly organized content, staff or structure and voluntary participation.

3. It is a part-time activity, sequential and seldom graded

4. It does not involve institutional on credentials and voluntary leaders are frequently involved.

5. It is not restricted to any particular organizational curricula or personnel classification and it has great promise for

renewing.

6. It has potential for multiplier effect economy and efficiency because of its openness to utilize appropriate personnel and

media.

General Objectives of Non-Formal Education

General objectives of Non Formal Education are:

1. To provide quality life through education that is functional, for example, occupational education aimed at developing

particular knowledge and skills associated with various economic activities and in making a living.

2. To solve the problems of equity and access to education and promotion of effective citizens’ participation in national

development (URT: 1995).

Specific Objectives of Non-Formal Education

Specific objectives of Non-Formal Education are:

1. To fulfil the realization of the basic human rights of education for all, and to complement formal education.

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2. To promote the acquisition and development of basic knowledge and functional skills relevant to personal development

and life in the community.

3. To mitigate illiteracy and sustain post literacy programmes.

4. To provide a second chance education, for those who are not reached by the formal school system and drop-outs (URT:

1995).

Objectives of Adult and Non-Formal Education Tanzania

Non–Formal Education (NFE) is any organized and systematic, educational activity carried outside the framework of the formal

education system to provide selected types of learning to particular sub groups in the population including adults, youth and

children. NFE is characterized by having flexible and diversified curriculum which is responsive to learner and environmental

needs. Its structure has flexible points of entry and exit, re-entry and re-exit. The evaluation is validated by learners’ experience of

success and the delivery is environmental based, community related, learner centred, resource serving, self governing and

democratic.

The objectives of Adult and Non-Formal Education in Tanzania are to:

1. provide alternative education to those who lack opportunity to acquire formal schooling;

2. extend formal schooling for those who need additional training or to become self employed;

3. update skills for those who are already employed;

4. counter balance some of the distortions created by formal education; and

5. Provide greater opportunity for innovation and creativity for self employment and entrepreneurship.

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General Competence for the Subject

By the end of this course the learner will demonstrate ability to:

1. Distinguish different types of numbers and sets to solve mathematical problems2. Assess and measure different quantities and make rational decisions3. apply coordinate Geometry and congruence.4. apply exponents, radicals and logarithms, functions in real life.5. use statistical concepts to other fields.6. Understanding Pythagoras theorem, trigonometrical ratios and transformations to solve Mathematical related problems in real

life situation and7. Understanding of algebraic operations to improve different processes in our daily activities.8. Apply sequence, series and rates in real life9. Understanding circles and earth as a sphere10. Use vectors, matrices and transformation of practical problems in daily life11. Understanding of three dimensional figures in real life12. Application of accounts in daily life.

Structure of the Syllabus

The syllabus for Mathematics for Ordinary level comprises the following:

ModuleImply set of separate units that can be joined together to form a part of a subject course of study

Principal learning outcomes

Principal learning outcomes imply what learners do after the completion of the subject course.

TopicImply area of interest of subject that is learned about.

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SubtopicThese are sub area of interests of subject which if combined together they form a topic

Specific objectives

Specific objectives imply what learners have to do after completion of each module. Therefore it is assessed basing on the

outcomes.

Learning Activities

These are the observable tasks to be done by learners in realizing the specific learning objectives.

Learning/facilitation strategies

The column of facilitation and learning strategies indicates what the facilitator and learners are expected to do in the process of

facilitation and learning. This includes self conceptualization, self learning and face to face session.

Facilitation/learning Aids

Some learning/facilitation aids such as areal things and Braille machines for visual disabled students have been proposed.

However, the facilitator/learner can use other relevant/available aids.

Estimated time of study

Under this column self study and face-to-face facilitation, time has been proposed in hours. However, it is expected that in

self-study a total of one hour will be spent in a day for every subject.

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Number of modules

This syllabus contains twelve modules namely;

STAGE I

Module 1: Understanding different types of numbers and sets,

Module 2: Understanding approximations and measurement of different quantities,

Module 3: Understanding algebra,

Module 4: Working with geometry, congruence, similarity, perimeter and areas,

Module 5: Applications of exponents, radicals, transposition of formula and logarithms,

Module 6: Understanding of statistics,

Module 7: Understanding of Pythagoras theorem, trigonometrical ratios and transformations,

STAGE II

Module 8: Applying Algebra in Real life,

Module 9: Applications of sequence and series, Rates and variations in Real Life,

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Module 10: Understanding circles and the Earth as a sphere,

Module 11: Understanding vectors, matrices and transformations to solve practical problems,

Module 12: Understanding Three dimensional figures,

Modules 13: Understanding Trigonometry,

Modules 14: Applications of statistics and Probability in Real Life,

Modules 15: Applications of Accounts in Daily Life.

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STAGE I

OBJECTIVES:

After completing stage I the learner should be able to:

1. Perform computations on numbers,

2. Use approximations in solving simple problems,

3. Convert and do computations on basic units,

4. Construct and draw geometrical figures,

5. Derive and apply the laws of exponents, radicals and logarithms in mathematical manipulations

6. Do calculations using mathematical tables

7. Prove and apply congruence and similarity of figures

8. Represent reflections, rotations, translations and enlargements geometrically

9. Represent and interpret statistical data collected form real life situations such as road safety, HIV/AIDS, Environment and crimes

10. Perform operations on sets and apply stets to solve problems

11. Solve linear equations and in one or two unknowns,

12. Computer rations, profit and loss and simple interest

13. Find the angles in geometrical figures

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STAGE – I (FORM I AND II)

MODULE PRINCIPALLEARNINGOUTCOME

TOPIC SUBTOPIC SPECIFICOBJECTIVES

LEARNINGACTIVITIES

LEARNING/FACILITATING STRATEGIESFACILITATION/LEARNING

TIME HOURSSELF LEARNING FACE TO FACE

SESSIONSELF

LEARNING

FACE TOFACE

1. Understanding different types of numbersand sets

Upon completion ofthe module learners should be able to:Perform computation of numbers and sets

1.1 Number

1.1.1 Base ten numeration

The learners should be able to

i.Identity ii. Use the decimal

system of numeration

i.Write the place value of each digit in any givennumber

ii. Read numbers given in worlds and numerals

- Self conceptualization

- Library search- Internet search- Internet search- Field work- Resources centres- Rural information

centres- Take home

assignment

- Brainstorming- Discussion- Invited guest

speaker- Role play- Question and

answers- Case studies- lecture

- number cards

- number charts

- abacus

20hrs 2hrs

1.1.2 Natural andwhole numbers

The learners should be able to:i. identify whole

numbers, natural numbers, even, odd and prime numbers

ii.read and write numbers up to one billion

iii. perform operation with whole numbers

i.perform role play on numbers

ii. identify even, odd and prime numbers from other numbers

iii. practice on the identification of even, odd and prime numbers using a number line

iv. differentiate numbers

20hrs 4hrs

1.1.3 Real numbers


1. explain real numbers

2. perform operation with real numbers

3. find absolute value to real numbers

i.define and explain in real number

ii. solve practical problems based onreal numbers

iii. solve practical problems related to absolute value of real numbers

20hrs 4hrs

13



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

1.1.4 Integers

The learner should be able to:1. identify

integers2. perform basic

operations withintegers (+, -, x, ÷)

3. Use BODMAS4. Find factors of

numbers and multiples

i. represent integerson a number line

ii.perform basic operations with different operation by using BODMAS

iii. To find factors of number

- Manila paper

-Marker pens

-Abacus-Number line

-Factor chart

20hrs 6hrs

By the end of stage I the learners should be able to convert unit and fractions

1.2 Fraction

1.2.1 Identifications of Fraction

The learners should be able to identify

1. Proper fractions2. Improper

fraction3. Mixed numbers4. Equivalent

fraction

i.Discuss other familiar examples of fractions

ii.Generate mixed numbers form improper fractions

iii. Distinguish proper, improper fraction and mixednumber


- Library search- Resources

centres- Take home

assignment



answers

- Oranges- Paper- Cards- Knife- Manila

paper- Razor- Real other

objects

10hrs 3hrs

1.2.2 Operations with Fractions

1. Carry out the four basic operations with fraction (+, -, x, ÷)2. Perform mixed operations on fractions3. solve word problems involving fractions

i.In groups to perform basic operations with fraction

ii.Perform mixed operations on fraction in pair

iii. Translate word problems in to equations and solve them systematically



centres- Take home

assignment



answers

- Real objects - Manila

paper- Marker pen- Oranges- illustrations

10hrs 3hrs

14



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

1.2.3 Comparison of fractions

The student should be able to 1. simplify a

fraction to its lowest terms

2. arrange fraction in order of size

i.simplify a fraction to its lowest term

ii. use LCM to compare fractions

iii. arrange fractions in order of size

- number of line

- cuissen airrods

- manila paper

- marker pens

10hrs 2hrs1.3 Percentages, Ratio, Profit and Loss and simple interest

1.3.1 Percentage

1.3.2 Ratios1.3.3 Profit

and loss

1.3.4 Simple interest

The student should be able to

1. Compare different quantities of the same kind

2. Express ratios in simple form

3. Divide given quantity into given proportions

4. Define profit andloss and how to calculate them

5. Calculate percentage profit and percentage loss

6. Calculate simple interest

i.Compare different quantities of the same kind

ii. Write ratios in simple form

iii. Divide given quantity in to given proportions

iv. Explain profit and loss and perform calculation involve profit and loss

v. Calculate percentage profit and percentage loss

vi. Calculate simple interests

- Tactile charts

- Braille labelled container ofdifferent lengths areas

1.4 Decimals

1.4.1 Identification of terminatingand repeating decimals

The learner should be able to:1. Explain

meaning of decimals

2. Identify terminating and repeating

i.Define decimalsii. Identify

terminating and repeating decimals

iii. Convert decimal to percentage an fraction and vice versa



centres- Take home

assignment



answers- Lecture

- Print/Tactile charts

- Real shillings and cents

- Print/Braille labelled shillings 30hrs 4hrs

15



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

1.4.2 changing decimals into traction andvice versa

1.4.3 changing decimals into percentage and vice versa1.4.4 Applicationof basic operations in decimals

decimals3. Changing

decimal in to fraction and vice versa

4. Convert decimal to percentage and vice versa

5. Carry basic operations with decimals(+, -, x, ÷)

iv. Convert decimal to percentage and vice versa

v. Solve questions with decimals

vi. Enough exercise

- Field work- Rural formation

centres

- Group discussion

- Think pair and share

and cents

1.5 Rational and irrational numbers

1.5.1 identification of irrational and rationalnumbers

1.5.2 conversion of irrationalnumber in to fraction.

The learner should be able to:1. Identify the

rational and irrational numbers

2. Convert an irrational number in to fraction

i.Identify the rational and irrational number

ii. Changing irrational numberto fraction


- Library search- Take home

assignment- Field work

- Discussion- Question and

answers- Lecture

- Rulers- Geometrical

instruments

20hrs 2hrs

1.6 Sets 1.6.1 Definition

The learner should be able to:

i.Identify and explain the

- Sets of different

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LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

and description of sets

1.6.2 Typesof sets

1.6.3 operation with sets

1.6.4 Venn diagram

1. Define a set2. Explain

meaning of set and universal set

3. State and distinguish types of sets

4. Make operations with sets

5. Use venn diagram in solving a sets problem

meaning of setii. Differentiate

finite and infinitesets

iii. Distinguish between equivalent and equal sets

iv. Define subsets and list subsets for the given sets

v. Find the union oftwo sets

vi. Find the compliment and intersection between sets

vii.Draw venn diagram and to read answers from the venn diagram

viii. Solve problems on sets

items- Pencils- Charts of

venn diagram

- Pictures- Playing

cards30hrs 4hrs

2 UNDERSTANDING MEASUREMENT AND APPROXIMATIONS

Upon completion ofthe module learners should be able to:Estimate, compute numbers and measure quantities.

2.1 Length and Mass

2.1.1 units of length and mass

2.1.2 operations with units of length and mass


1. Define length and mass and explain units of the same

2. Perform operations with mass and length

i.To give meaning ofmass and length and differentiate their units

ii. To perform conversion of different units of mass and length



centres- Take home

assignment- Field work- Rural in

formation centres



answers- Lecture

-Tape measure, rulers, balances, charts of units of mass and length

12hrs 4hrs

17



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

2.1 Lengthand mass

2.1.3 Units of capacity

The learner should be able to:1. State the

standard unit of measuring capacity

2. Use litre in daily life

i.Describe meaning of capacity and relate it with volume of quantities

ii. Relate litre with other units of volume

iii. Solve problems related to unit of capacity



centres- Take home

assignment- Field work- Rural formation

centres



answers- Lecture

-Containers with capacities in litres

12hrs 4hrs

2.2Time 2.2.1 Conversionof unit of time

2.2.2 Conversionof times of 12 hour clock to 24 hour clock

2.2.3 Operations with time

The learner should be able to:1. Convert one

unit of time to another

2. Read and concert times of 12 hour clock to 24 hour clock and vice-versa

3. Solve problems about time

i. Convert one unit of time to another ii. Read time using 12 hour clock and 24 hour clockiii. Convert time on12 hour clock and vice-versa

iv. Solve problems related to time



centres- Take home

assignment- Field work- Rural in

formation centres



answers- Lecture

-Clock faces-Time tables-12 hour clock

-24 hour clock

-Talking calculator

-Braille Abacus

-Braille tapemeasure

-Cell phones

12hrs 4hrs

2.3 Approximations and significant figures

2.3.1 Approximations

2.3.2


1. Make proper higher or lower approximations

i. Perform proper approximations in either higher or lower approximations




speaker- Role play

-Number charts

-Manila papers

-Marker

18



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

significant figures

2. Write a number in a required significant figure(S)

3. Determine decimal places

ii.Round off whole numbers to givenplace values

iii. Round off decimal to a given number of decimal places

iv. Write a number to a given number of significant figures

v. Make approximation in calculations

centres- Take home


centres

- Question and answers

- Lecture

pens 12hrs 2hrs

3 UnderstandingAlgebra

Upon completion ofthe module learners should be able to simplify algebraic expressions, solve algebraicequations and draw graphs

3.1 Algebraand Algebraic expressions

3.1.1 Formation of algebraicexpression

3.1.2 Operations withalgebraic expressions

3.1.3 Binary operations

The learner should be able to;

1. Use letters to form algebraic expressions

2. Perform basic operations with algebraic expressions

3. Compute problems on binary operations

i.Formulate algebraic expressions

ii. Perform basic operations with algebraic expressions (+, -,x, ÷)

iii. Use real life examples of salesof fruits (or else) to obtain prices for unknown quantities

iv. Solve problems with binary notations (stars)



centres- Take home


centres



answers- Lecture

-Real objects

-Coloured chalks

-Manila papers

-Marker pens 30hrs 4hrs

3.2 Algebraic Equations

3.2.1 Linear equations in one unknown


1. Read a word problem and form algebraic

i.Formulate linear equations form a given word problem

ii.Solve linear




speaker- Role play

-Beam balance

-Manila paper

-Coloured

19



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

3.2.2 Linear equations into two unknowns

equations2. Solve linear

equations in one unknown

3. Solve linear simultaneous equations in two unknowns

equations in one unknown

iii. Solve linear simultaneous equations

centres- Take home


centres


- Lecture

chalk-Marked pen-Chart -Printed/chart tactile

-Work sheet

3.3 Coordinate geometry

3.3.1 Coordinates of a point

3.3.2 Gradient ofa line


1.Read coordinate axes and locate points and read coordinates of located points

2.Plot given coordinates

3.Calculate the gradient of a line given two points

4.

i.Draw coordinate axes and locate points and read coordinates of located points

ii. Determine the gradient (slope) of a line drawn through given points



centres- Take home


centres



answers- Lecture

-Graph paper

-Rural-Manila paper

-Marker pen-Garboard-Rubber band

-Graph board

30hrs 4hrs

3.3.2 Equation ofa straight line


1. Find the equationof a line given the coordinates of two points

2. Draw graphs of linear equations

3. Solve inequalities in one unknown

i. Determine equation of line putting in the form: y = mx+c where M = slopeC = y - intercept

ii.Find slope and y – intercept from a given equation

iii. Find x – and y –intercepts of a given equation

iv. Draw table of values for a given equation

v. Plot the graph of



centres- Take home


centres



answers- Lecture

-Graph paper

-Rural-Manila paper


-Graph board

30hrs 8hrs

20



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

a given equationvi. Solve problems

of linear inequalities.

3.3.3 Graphical solutions oflinear simultaneous equations

The learner should be able to determine the graphical solutions of linearsimultaneous equations

i. Draw table of values of the linear simultaneous equations

ii.Draw the equations on the same set of exes

iii. Determine the point of intersection of the linear equations

iv. Determine the solution of the equations



centres- Take home


centres



answers- Lecture

-Graph paper

-Rural-Manila paper


-Graph board

30hrs 4hrs

3.4 Quadratic equations

3.4.Ququadratic expressions


1. Form quadratic expression form two linear factors

2. Write the generalform of quadraticexpression

3. Factorized quadratic expressions

i.Multiply two linearfactors to form quadratic expressions

ii. Identify terms and coefficients of quadratic expressions

iii. Identify quadratic expressions formnon-quadratic expressions

iv. Factorize the quadratic expressions

v. Discuss the



centres- Take home


centres



answers- Lecture

-Multiplication charts

-Factor tree-Colored chalks

-Manila papers

20hrs 2hrs

21



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

perfect squares and difference of two squares

3.4.2 Solutions of quadratic equations

3.4.3 General solution of quadratic equations

3.4.4 Graphical solutions of quadratic equations


1. Identify quadratic equations

2. Find a solutions of quadratic equations by factorization and completing the square

3. Solve quadratic equations by general formula

4. Find solutions of quadratic equations by graphs

i.Define terms of a quadratic equation

ii. Solve quadratic equations by factorization and completing the square

iii. Derive the general quadraticformula from: ax2 + bx + c = 0

iv. Solve quadratic equations by the general quadraticequations graphically

v. Solve word problems involving quadratic equations

vi. Solve system of simultaneous equations involving one linear and one quadratic equation



centres- Take home


centres



answers- Lecture

-Graph papers

-Manila papers

-Rulers-pencils

30hrs 6hrs

22



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

4. Working with Geometry, Congruence, Similarity, Perimeter and Areas

Upon completion ofthe muddle learners will be able to solve Geometrical problems, compare angles and find perimeter andareas of the different geometrical figures

4.1 introduction to geometry

4.1.1. Pointand lines

The learner should be able to 1. Define and explain the concept of a point 2. Extend the concept of a point to draw a line3. distinguish point and line4. Draw different types of lines

i. Define pointsii. Draw a linesiii Differentiate point and a lineiv. Distinguish between a line, linesegment and a ray

- Library search- Self

conceptualization

- Internet search- Resources

centres- Take home

assignments

- Group discussion


- Lecturate- brainstorming

-mathematicsets

-chalk boardruler

-manila paper

-marker pen

20hrs 4hrs

4.1.2 Polygons regions andAngles

The learners should be able to:1. describe a

polygon and regions

2. draw angles \measure angles of different size using protractor

3. name different types of angles

4. name different types of angles

i. describe a polygon and regions

ii.construct different types oftriangle

iii. construct different quadrilaterals

iv. draw different angles in different size byusing protractor and name them


conceptualization


centres- Take home

assignments

- Group discussion



-mathematicinstruments

-protract or chalk boardruler

20hrs 4hrs

4.1.3 Constructions


1. construct a perpendicular bisector to a

i. construct perpendicular bisector to a line segment

ii.construct an


conceptualization

- Internet search

- Group discussion


- Lecturate

-mathematical instruments

-manila papers

23



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

line segment2. construct an

angle of 60º using a pair of compasses

3. bisect a given angles

4. copy a given angle by construction

5. construct parallel lines and identify different types of angles formed by parallel lines and a transversal.

angle of 6º using compasses

iii. based angles using compasses

iv. copy different angles by construction

v.construct different parallel lines

vi. find the sizes of different angles formed by parallel lines and a transversal

- Resources centres

- Take home assignments

- brainstorming -braille’s-typewriters-thermal form machines

-braillon papers

10hrs 2hrs

4.1.4 Circles

The student should be ale to1. draw circle.

i. draw a circles and label its parts

- - -Circular objects

-Ropes 10hrs 2hrs

4.2 Postulates Theorems and congruenceof Triangles

4.2.1 Postulate and theorem

4.2.2 Congruence of triangles

The learners should be able to:1. distinguish

between postulates and theorem

2. define congruence

3. determine theconditions forcongruence of triangles

i. identify the theorem, postulates and congruence of triangle

ii.state and write the properties of congruent triangles

iii. prove the theorem based on cases of SSS,


conceptualization


centres- Take home

assignments

- Group discussion



-Manila papers

-Geometric figures

-Paper cutting

-Marker pens

-Photographs

-Table -diagrams

20hrs 5hrs

24



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

4. prove theorems based on congruence of triangles

5. solve problems on congruent triangles

AAs and SASiv. prove theorem

based on isosceles triangles

4.3. Similarfigures

4.3.1 similar figures and problem solving

Students should be able to:1. state

conditions forsimilarity of polygons

2. prove theorems on similarity of polygons

3. solve problems on similarity

i. Identify the similar figuresii. state AAA property iii AA and corresponding sides proportionaliv. A and side aboutthe angle are propositionalv.Write the

conditions for similar triangle

vi. Solve problems using similar triangle theorem


conceptualization


centres- Take home

assignments

- Group discussion



-graph papers

-mathematical sets

10hrs 4hrs

4.4 Perimeters

4.4.1 Triangles and Quadrilaterals

The learners should be able to:1. derive the

formulae for perimeters of triangle and specific quadrilaterals

i. identify triangle and quadrateral

ii.define perimetersiii. determine

perimeters of triangles and quadrilateral by using derived formulae


conceptualization


centres- Take home

assignments

- Group discussion



-photographs

-similar planes

-similar objects

10hrs 3hrs

4.4.2 Circumference of a

The learners should be able to:1. find

i. to define circumference

ii.identify the


conceptualizatio

- Group discussion

- Question and

-circular objects

-rope

25



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

circle circumference of a circle

2. estimate the value of Pi (π)

formula for finding circumference of a circle

iii. calculate the circumference of a circle

iv. identify the relationship between π = Pi

r =RadiusD = Diameter for the formula of circumference of a circle

n- Internet search- Resources

centres- Take home

assignments

answers- Lecturate- brainstorming

-thread-ruler

10hrs 3hrs

4.5 Areas 4.5.1 Triangle and quadrilaterals

The learners should be able to:1.define and 2. describe the

formulae for areas of triangles and quardrilateral

i. find area of triangle

ii.find area of rectangles

iii. find area of trapezium

iv. find area of parallelogram


conceptualization


centres- Take home

assignments.

- Group discussion



-circular objects

-rope-thread-ruler

10hrs 3hrs

4.5.2 Circle The learners should be able to:1. find areas of

circles

i. write areas of circle

ii.calculi areas of circle


conceptualization


centres- Take home

assignments

- Group discussion



-circular objects

-rope-thread-ruler

10hrs 3hrs

5. Applicationsof Exponents, Radicals,

Upon the completion ofthe module

5.1 Exponents, radicals

5.1.1 Exponents and

The learner should be able to:1. List laws of

i. Define exponentsii.Derive laws of

exponents


conceptualizatio

- Group discussion

- Question and

-mathematical tables

-manila

26



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

Transposition of Formula and Logarithms In Real Life

learners should be able to:Find relationships among exponents, radicals and logarithms and organize different formulae

and transposition of formulae

radicals exponents 2. Verify laws f

exponents 3. Apply laws of

exponents in computation

4. Simplify radicals

5. Perform basicradical operations

6. Rationalize the denominator

7. Read square root and cuberoot form mathematical tables

iii. Apply laws of exponents in computations

iv. Define radicalsv.Simplify radicalsvi. Perform basic

operations with radicals

vii. Rationalize denominators

viii. Find square root from mathematical tables

n- Internet search- Resources

centres- Take home

assignments

answers- Lecturate- Brainstorming- Invite guest

speaker- Case studies- lecture

papers-maker pens-rulers-calculators

20 hr 4hrs

5.1.2 Transposition of formulae

The learner should be able to:Transpose different formulae

i. re-arrange letters so that one letter is the subject of the formula

ii.transpose formulae with square roots and squares


conceptualization


centres

- Group discussion


- Lecturate- Brainstorming- Invite guest

speaker

-Mathematical formula

20hrs 4hrs

27



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE


- Case studies- Lecture

5.2 Logarithms

5.2.1 Standard form

5.5.5 Laws of logarithms

5.2.3 Table of logarithms

The learner should be able to:1.Write number in

standard form2.Compute

number involving multiplication and division expressing themin standard form

3.State laws of logarithms

4.Verify laws of logarithms using knowledge of exponents

5.Simplify logarithms expression

i. Define the standard form

ii.Write numbers instandard form

iii. Multiply and divide numbers and expressing solutions in standard form

iv. Derive laws of logarithms

v.Apply laws of logarithms in computations

vi. Solve logarithms equations

vii. Solve problems by logarithms tables

- Mathematical tables

- Charts- Graph

papers

20hrs 4hrs

6 UnderstandingStatistics in Daily Life

After completion ofthis muddle in stage I learners should be able to apply statistics in daily life

6.1 Presentation of data

6.1.1 Pictograms,Bar charts, line graphs tables and pie-charts and Histograms

The learners should b able to:1. Represent given

information by graphs, pictograms, Bar charts tables and pie-charts and Histograms

i. Draw pictogramsii.Draw bar chartsiii. Draw pie-chartsiv. Draw tablesv.Draw Histogramsvi. Line graphs


conceptualization


- Group discussion


- Brainstorming

- Charts- Graph

paper- Tactile

charts- Graphs

form papers and journals

10hrs 6hrs

6.1.2 Frequency distribution

The learners should be able to 1.Make frequency

distribution table form grouped and

i. Define frequencyii.Collect

informationiii. Make frequency

distribution tables


conceptualization


- Group discussion


- Brainstorming

- Charts- Graph

paper- Tactile

charts- Graphs

28



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

ungrouped data2. Interpret

frequency form a table

iv. Group data and get grouped data

v.Interpret the frequencies


10hrs 3hrs

6.1.3 Frequency polygon

The learners should be able to 1.Identify

cumulative frequency

2.Draw and read cumulative frequency curve

3.Interpret cumulative frequency curve

i. Construct cumulative frequency distribution

ii.Draw and read a cumulative frequency curve(o-give)

iii. Interpret the graph


conceptualization- Take home

assignments

- Group discussion


- Brainstorming

- Charts- Graph

paper- Tactile

charts- Graphs


5hrs 3hrs

7. UnderstandingPythagoras Theorme, Trigonometric Ratios and Transformations

Upon completion ofthe module learners should be able to do scale drawingand geometrical trans-formations

7.1 Pythagoras theorem

7.1.1 Proof of Pythagoras theorem

7.1.2 Applicationof Pythagoras theorem

The learners should be able to:1. State and prove

the Pythagoras theorem

2.Apply the Pythagoras theorem to find lengths of sides of given right angled triangle

i. Investigate the illustrations of Pythagoras theorem

ii.Rove the theoremiii. Solve problems

related to right angled triangles

iv. Solve real life problems using Pythagoras theorem


conceptualization- Take home

assignments- Library search- Resource centres- Rural information

centres

- Group discussion


- Brainstorming- lectures

- garboard- square

cuttings - right

angled triangles

- square root tables

- square tables

9hrs 3hrs

29



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

7.2 Trigonometric ratios

7.2.1 Sine, cosine and tangent of an angle

The learner should be able to:1. define sine,

cosine and tangent of angle

2. find sine, cosine, and tangent of angle withoutusing tables

i. measure the fidesof the triangles drawn and compotation of sides to establish sine, cosine and tangents

ii.compute sines, cosines and tangents of rightsangled triangles without table

4hrs 2hrs

7.2.2 Special angles

The learners should be able to:1. Determine

the sine, cosine and tangent angle of 30, 45, and60 without using mathematical tables

2. Solving problems involving trigonometricrations

i. Use Pythagoras theorem to determine sine, cosine and tangent of 30, 45,and 60 without using trigonometric tables

ii.Do calculation involving sine, cosine and tangent of 30, 45 and 60

iii. Solve problems involving trigonometric ratios


conceptualization


- Library search- Resource

centres- Rural

information centres

- Group discussion


- Brainstorming- lectures

- trigonometric tables

- Braille- Mathem

atical sets

- Rulers- Manila

papers- Marker

pens

10hrs 4hrs

7.2.3 Angles of Depression and Elevation

The learners should be able to:1.Demonstrate

angles of depression and elevation

2. Solve

i. Explain angle of elevation and depression

ii.Measure angle ofelevation and depression using clinometers


conceptualization


centres

- Group discussion


- Lecturate- Brainstorming- Invite guest

- trigonometric tales

- clinometers

- rope- string- wood glue 10hrs 6hrs

30



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

problems involving angle of depression andelevation

iii. Find angle of depression and elevation of distant objects

iv. Solve problems usingtrigonometric ratios and formula


speaker- Case studies- lecture

- trundle wheel

- braille

7.3 Transformations

7.3.1 Reflection

The learners should be able to:1.describe the

characteristic ofreflection in a plane

2.represent different reflections by drawing

i. investigate and write the properties of reflection

ii.draw different reflection in a plane

iii. solve problemsrelated with reflection


conceptualization


centres- Take home

assignments

- Group discussion


- Brainstorming- Think pair and

share- Lecture

- Plane mirrors

- Geo-boards manila sheets

- Game, graphs, papers andidentical pictures

- Rubber bands

- Mathematical sets.

5hrs 3hrs

31



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

7.3.2 Rotation

The learners should be able to:1.Describe

characteristics of a rotation on a plane

2.Represent different rotation on a plane by drawings

i. Identify and write the properties of rotation in a plane

ii.Draw rotation of a points, lines and polygons using Mathematical sets

iii. Solve problems using propertiesof rotation

10hrs 2hrs

7.3.3Translation

7.3.4 Enlargement

By the end of this subtopic learners should be able to:1. Explain

translation and enlargement

2. Show translation and enlargement in drawing

3. Identify the properties of translation and enlargement

i. State properties of translation

ii.Draw translationsof a points, linesand polygons in a plane

iii. Apply the properties of translation to solve problems

iv. Develop scale of enlargement

v.Identify properties of enlargement

vi. Draw figures to scale

vii. Solve problems related with translation and enlargement


conceptualization


centres- Take home

assignments

- Group discussion


- Brainstorming- Think pair and

share- Lecture

- Plane mirrors

- Geo-boards manila sheets

- Game, graphs, papers andidentical pictures

- Rubber bands

- Mathematical sets

10hrs 4hrs

7.3.5 The learner should i. Combine reflection - - -

32



LEARNINGACTIVITIES



SESSIONSELF

LEARNING

FACE TOFACE

Combined Transformation

be able to:1. Draw combined

transformation2. Solve problems

on combined transformation

and translationii.Combine reflection

and rotationiii. Draw combined

transformation in a plane

iv. Solve problems on combined transformations

10hrs 2hrs

33

STAGE II

OBJECTIVES

After completing stage ii the learner should be able to:

4. Draw graphs of relations and functions and identify their properties

5. Apply computations on sequences and series to discover mathematical patterns and solve problems on compound interest

6. Apply the knowledge on rates and variation in real life situations

7. Locate places on the Earth’s surface and find the distance between any two places

8. Represent data statistically and draw conclusions from numerical statistical information (mean, mode and median)

9. Prove and apply circle theorems

10. Solve real life problems involving double entry and trail balance

11. Apply mathematical knowledge and skills to form lines, calculate distance between two points and do problems on parallel and

perpendicular lines in two – dimensional geometry,

12. Find the sum, difference and scalar multiplication of vectors and hence use the knowledge to solve practical problems

13. Use 2 x 2 matrices to solve simultaneous equations and solve problems on transformations

14. Calculate the probability of an event and perform simple combination of probabilities

15. Draw graphs of sine and cosine functions and apply sine and cosine rules to solve problems

16. Use oblique projections to draw three dimensional figures and find angle between a line and a plane and angle between two planes

34

STAGE II: (FORM III AND IV)



LEARNINGACTIVITIES

LEARNING/FACILITATINGSTRATEGIES FACILITATION/

LEARNING

TIME HOURS

SELF LEARNING FACE TO FACESESSION

SELFLEARNING

FACETO

FACE

8. Applying Algebra in Real Life

Upon completion ofthe module learners should be able to:use mathematical knowledge, skills and concepts in solving real life related problems

1.8 Relations

8.1.1 relations, concepts

8.1.2 Domain and range

8.1.3 Graphs of relations

8.1.4 Inverse of relations


iii. Explain conceptof relation

iv. Represent relations

v. Determine domain and range

vi. Draw graphs of relations

vii.Determine the inverse of a relation

iii. Define therelations

iv. Identify types of relations

v. Explain representation of relations pictorially

vi. Find domain range of the relations\

vii. Draw the graph of a relation

viii. Find the inverse of a relation

ix. Find the domainand range of inverse of a relation

x. Draw the graph of inverse of relation


- Library search- Internet search- Internet search- Field work- Resources

centres- Rural

information centres

- Take home assignment



answers- Case studies- lecture

- colored chalks- red objects- manila papers- maker pen- graph papers- Geo-board- Rubber bands- Graph boards

30hrs 8hrs

35



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

8.2 Functions

8.2.1 Definition and representation of a function

8.2.2 Domain and Range

8.2.3 Graphic function

8.2.4 Inverse of afunction

The learners should be able to:

iv. Define and represent function pictorially

v.Identify functions among relations

vi. State domain and range of thefunctions

vii.Draw the graphsof functions

viii. Explain inverse of a function

ix. Draw the graph of inverse function

x. Domain and range inverse function

v. Define functionvi. Represent

function pictorially

vii.Distinguish one to one mapping, one to many mapping, many to one mapping

viii. Find domain and range of a function

ix. Draw the graphs of step function

x. Draw the graph of polynomial functions up to third degree

xi. State the behaviour of graphs of functions

xii.Find inverse its domain and range and graphs

30hrs 8hrs

8.3 Coordinate Geometry

8.3.1 Equation oflines


4. Derive the general equation of a straight line

iv. Derive a linear equation in the general form ax + by + c = 0

v. Rewrite linear equations in the general form


- Library search


speaker- Role play

-graph papers-squared paper-geo-board-rubber band-graph board

10hrs 3hrs

36



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

- Internet search- Internet search- Field work- Resources

centres- Rural

information centres



- Case studies- lecture

-Mathematical instruments

-Mathematic tales

-Graph papers-Rubber bands-Geo-board

8.3.2 Midpoint of line segment

The learner should be able to:5. Determine the

coordinates of the midpoint ofa line segment

iv. Formulatethe formala midpoint of a line segment

v.Find the midpoint of a given line segment

8.3.3 Distance between two points on a plane


5. Calculate the distance between points on a plane

iv. Use Pythagoras theorem to form a distance between two points on a plane

10hrs 3hrs

37



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

8.3.4 Parallel andperpendicular lines


1. Compute gradients in order to determine the conditions for any two lines beparallel

2. Compute gradient in order to determine the conditions on for any two lines to be perpendicular

3. Solve problems on parallel and perpendicular lines

iv. Calculate the gradients of different lines

v. Discuss the resultsof gradients for the parallel lines

vi. Generalize condition for two lines to be parallel

vii.Discuss the results of the gradients for the perpendicular lines

viii. Generalize the condition forthe lines to be perpendicular

ix. Solve problems on perpendicular lines

x. Solve parallel and perpendicular lines problems

xi. Apply the knowledge of parallel and perpendicular lines in daily life


- Library search

- Resources centres




answers

- Real objects - Manila paper- Marker pen- Oranges- illustrations

20hrs 5hrs

38



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

8.4 Linear programming

8.4.1 the objective function

8.4.2 Maximum and minimum value

The learner should be able to 3. form objective

function form a word problem

4. locate corner points on feasible region

5. find maximum and minimum values using objective function

iv. form simultaneous equations form word problems

v. solve simultaneous equations graphically

vi. form linear inequalities in two unknowns from word problem

vii.find solution set of simultaneous linear inequalities graphically

viii. form an objective function

ix. locate corner points on the feasible region

x. find the max and min values using objective function

- manila papers

- graph papers- rulers- geo-board- coloured

chalks- marker pens- squared

papers- rubber bands

30hrs 10hrs

9. Applications of Sequence and Series, Rates and Variations in Real Life

Upon completion ofthe module learners should be able to:use knowledge

9.1 Sequence

i.Arithmetic progressionii.Geometirc progressioniii.Compound interest

The learner should be able to:6. Distinguish

between sequence and series

7. Find terms of a sequence

vii. Explain the concept of sequence and series

viii. Discuss types of sequence and series

ix. Identify an A.P


- Library search

- Resources centres

- Take home



answers- Lecture

- Number cards

- Number patterns

- Mathematic tables

- Scientific calculators 30hrs 8 hrs

39



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

and skills on the study to solve real lifesituations

8. Identify finiteseries

9. Find the nth term, the sumand the arithmetic mean of A.P

10. Find the general term of an A.P

11. Find the nth term, sum and geometric mean of G.P

12. Find the general term of a G.P

13. Find the compound interest

x. Find the general term of an A.P andG.P

xi. Derive a formula for nth term of A.P and G.P

xii.Derive compound interestformula

xiii. Apply compound interestformula in solvingproblems

assignment- Field work- Rural

formation centres

- Group discussion

- Think pair and share

- Colored chalks

- Manila paper- Marker pens- Different

currencies- News papers- T.V- Magazines- Radio

9.2 Rates and Variations

9.2.1 Rates

9.2.2 Variations

The learner should be able to:3. Relate

quantities of thesame kind and of different kinds

4. Convert Tanzanian currencies into other currenciesand vice-versa

5. Solve problems on direct and inverse

iii. Define the term rate

iv. Find the relationship between quantities of the same and different kinds

v. Solve problems related to rates

vi. Define the terms direct proportion,inverse proportion and joint variations


- Library search

- Resources centres


- Field work- Rural

information centres



answers- Lecture- Group

discussion- Think pair and

share

- Number cards

- Number patterns

- Mathematicaltables

- Scientific calculators

- Colored chalks

- Manila paper- Marker pens- Different

currencies- News papers

30hrs 4hrs

40



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

proportions6. Draw graphs of

direct and inverse proportions

7. Use joint variations to solve problems

vii.Solve different problems on direct, inverse and joint variation

- T.V- Magazines- Radio

10.Understanding Circles andthe Earth as a Sphere

Upon completion ofthe module learners should be able to:prove circles theorems and describe the earth as a sphere

10.1 Circles

10.1.1 definitions of terms

i. Angle propertiesii. Tangent propertiesiii. Radian measure

The learner should be able to:14. Define circle,

radius, chord diameter, arc centre, sectors secant, tagent

15. Derive the formula for the length of an arc

3. Calculate central angles

4. Explain the concept of radian measure

5. Prove circle theorems

6. Applying circletheorems in solving related problems

7. Identify chord properties

8. Prove the theorem on the perpendicular

iii. Give the meaningof a circle, centre, radius, chord, secant, tangent, sector etc

iv. Define an arcv. Define central

anglevi. Derive the

formula of arc length

vii.Solve problems related with arc length

viii. Define theradian measure

ix. Convert radian measures to degrees and vice-verse

x. Define an inscribed angle

xi. Prove the angle at the centre theorem

xii.Prove the angle


- Library search

- Resources centres


- Field work- Rural

formation centres

- Case studies



answers- Lecture- Case studies

-Compass-Coloured chalks

-Manila papers-Marker pens-Set square -Mathematical instruments

10hrs 20hrs

41



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

bisector to a chord

9. Prove the theorem on parallel chords

10. Apply the chord theoremsin solving related problem

11. Describe tangent to a circle

12. Identify tangent properties of a circle

13. Prove tangent theorem

14. Apply tangent theorems in solving related problems

in a semicircle theorem

xiii. State chord properties of a circle

xiv. Prove the theorem on the perpendicular bisector of a chord

xv. Solve problems on perpendicular bisector of a chord problems

xvi. Draw different tangents to a circle

xvii. List tangent properties of a circle

xviii. Prove theorems relatingtangents to a circle

xix. Solve problems related to tangentto a circle

10.3. The Earth as a sphere

10.3.1 Longitude and Latitude

10.2.2 Distance along great

The learner should be able to:7. Describe

the equator, great and smallcircles latitude

8. Describe

v. Define longitude and latitude

vi. Define meridian

vii.Define small circle

viii. Define


- Library search

- Resources centres

- Take home



answers- Lecture

-Globe -Spherical objects

-Oranges-Mathematical tables

-Chalk -Graph papers

12hrs 4hrs

42



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

and small circles

meridian and longitude

9. Locate places on a map or globe

10. Calculatethe distances along great andsmall circles

great circleix. Identify

great circle and small circle

x. Locate places along meridians and longitudes

xi. Find distances along the great and small circles

assignment- Field work- Rural

formation centres

- Case studies

- Case studies

11.Understanding Vectors, Matrices and Transformation to solve practical problems

Upon completion ofthe module learners should be able to perform computations on matrices vectors and transformation

11.1 Vectors

11.1.1 displacement and position vectors

The learner should be able to;

4. Define and resolve vector into i and j components

5. Find the magnitude and direction of a vector

6. Find unit vector7. Differentiate

vectors and scalar quantity.

v. Explain meaning of vector and resolve it in its i and j components

vi. Find magnitude and direction of avector

vii.Find unit vector viii. Distinguis

h between vector quantity and scalar quantity


- Library search

- Resources centres


- Field work- Rural

formation centres



answers- Lecture

-Graph board-Rulers-Graph papers-Set squares-Coloured chalks

-Geo-board-Rubber band -Mathematical table

10hrs 4hrs

43



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

11.2.1 operations with vectors

The learner should be able to:1. Sum and

difference of two or more vectors

2. Multiply vector by scalar

3. Solve linear simultaneous equations in two unknowns.

i. Find the sum of the vectors without using diagramii. Find the

differences between vectors without using diagramiii Find the product

of vector by scalar

11.2.2 Applicationof vectors

The learners should be able to:1. Apply vectors in solving real lifeproblems

i. Solve simple problems on velocities, displacement and forces

ii. Find bearings by drawing and measuring

iii. Uses of vectors

44



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

11.2 Matrices

11.2.1 Basic definitions and terminologies in matrices

11.2.2 operations on matrices


5. Define and represent information in matrix

6. Add matrices oforder up to 2 x 2

7. Multiply matrices of order 2 x 2 by scalar

8. Multiply two matrices of order 2 x 2

iii. Explain the concept of matrix

iv. Explain the meaning of matrix

v. Add and subtract matrices of order up to 2 x 2

vi. Multiply a matrixof order 2 x 2 by a scalar

vii.Multiply two matrices of order 2 x 2


- Library search

- Internet search


- Group discussion


- Lecture

-Coloured chalks

-Prices of items-Charts of matrices

20hrs 4hrs

11.2.3 Inverse of amatrix


4. Calculate the determinant of a matrix of 2 x 2

5. Find the inverse of a 2 x 2 matrix

vii. Define determinant and calculate the determinant of a 2 x 2 matrix

viii. Find the inverse of given matrix


- Library search

- Internet search


- Group discussion


- Lecture

-Charts of determinant ofmatrices

-Charts of inverses of matrices

20hrs 4hrs

11.2.4 Applicationof matrices

The learner should be able to: 1. Use matrices insolving simultaneous equations

v. Apply 2 x 2 matrices in solving simultaneous equation

10hrs 4hrs

45



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

11.3 Transformations

11.3.1 Translation of a point


4. Transform any point p(x,y) into p’(x’,y’) by pre-multiplying (x) y with a transformation matrix T= a b c d

vi. Translate the given points by using different transformation matrices

vii. Solve problems related with translation


- Library search

- Internet search


- Group discussion


- Lecture

-Colored chalks

-Graph board-Mathematical table

-Rulers-Geo-board-Rubber band-Graph papers-Square papers

30hrs

40hrs

8hrs

2hrs

11.3.2 Reflectionsof a point

11.3.3 Rotation ofa point


5. Apply matrixX 1 0 to 0 -1 reflect a point p(x,y) in the x and y-axisThe learners should be able to:

1. Use matrix operator to rotate any point P(x,y) through 90º, 180º, 270º and 360º about the origin

vii.Reflect a point p(x,y) in the x-axis using matrix1 00 -1

viii. Reflect a point P(x,y) in the y-axis

i.Rotate various points through 90º, 180º, 270º and 360º about the origin using the appropriate transformation matrix

T= cosө sinө Sinө cosө

46



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

11.3.4. In Enlargament matrix

The learner should be able to 1. Enlarging figures suing matrix K OE = O K2. solve different problems involving enlargement of a matrix

i.Enlarge given figures using enlargement matrix

K OE = O Kii. solve problems involving enlargement of a matrix


- Library search

- Internet search


- Group discussion


- Lecture

-Colored chalks

-Graph board-Mathematical table

-Rulers-Geo-board-Rubber band-Graph papersSquare papers

47



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

12.Understanding Three Dimensional Figures

Upon completion ofthe module learners should be able to: construct and calculate the three dimensional figures

12.1 Three dimensional figures

12.2 Surface area of three dimensional figures

12.3 Volumes ofthree dimensional figures

1. Prisms2. Cones and sphere3. pyramids

The learners should be able to:5. classify three

dimensional figures

6. list the characteristic of each class of three dimensional figures

7. construction three dimensional figures

8. sketch three dimensional figures

9. identify properties of three dimensional figures

10. find the anglebetween a line and place

11. calculate the angle between planes

12. derive the formulae of surface area of prisms, cylinders, pyramids and cones

v.define three dimensional figures

vi. collect various three dimensional objects and classify them into cones, pyramids, prismsand cylinders

vii.sketches of three dimensional figures

viii. use simplematerials to construct three dimensional figures e.g paper, manila cards etc

ix. sketch three dimensional figures using oblique projections

x.discuss intersecting planes of three dimensional figures

xi. calculate angles between two intersecting planes

xii. calculate

- internet search

- library search

- rural information centres

- Resources centres


- Group discussion


- Lectures

-Manila cards-Cones-Pyramids-Cylinders-Three dimensional models

-Papers-Stress-Glue-Mathematical instruments

-Marker pens

40hrs 16hrs

48



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE13. UnderstandingTrigonometry

Upon completion ofthe module learners should be able to: perform practical of trigonometry

13.1 Trigonometric ratios

13.1.1 Applicationof Trigonometric ratios

The learners should be able to1. Determine

sine, cosine and tangent of an angle clockwise (negative angleand anti clockwise positive angles)

2. Use sine cosine and tangent to solvereal life problems

vii. Determinesine, cosine and tangent of an angle

viii. Use sine, cosine and tangent to solve real life problems

- Library search


- Internet search

- Field work- Take home

assignments

- Group discussion


- Lecture- Brainstorming- Case studies

-mathematical tables

-Braille’s-tactile diagrams

-magnifiers-geometrical instrument

10hrs 4hrs

49



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

13.1.2 Sineand cosine functions

The student should be ale to1. find sins and

cosines of angles such that -720º≤ ө ≤ 720º

2. draw graphs of sine and cosine

3. interpret the graphs of sine and cosine functions

i. read values of sine and cosine for angles

-720º≤ ө ≤ 720º

ii.Prepare table of values of sine and cosine of angle ө such that

-720º≤ ө ≤ 720ºiii. draw the graph of sine and cosine functions using table of valuesiii. identify even

or odd functions and periodic or non periodic function

- Library search


- Internet search

- Field work- Take home

assignments

- Group discussion


- Lecture- Brainstorming- Case studies

-mathematic tables

-braillers-tactile diagrams

-magnifiers-geometrical instrument

13.1.3 Sineand Cosine rules

The learners should be able to:1. Derive sine rule

and cosine rule 2. Use sine rule

and cosine rule to solve problems

vii. Draw the graph fine and cosine functions using table of values

viii. Solve problems by using the formulaof sine rule and cosine rule

4hrs

50



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

13.1.4 Compound Angles

Students should be able to:1. Apply

compound angle formulae for sine, cosine and tangent in solving trigonometric problems

2. Derive compound angle formulae for sine, cosine and tangent

i. Explain the compound angles of sine and cosineii. use compound angle formulation solving and simplify trigonometric problems using compound angle formulae

- Library search


- Internet search

- Resources centres


- Group discussion



-graph papers-mathematical sets

10hrs 4hrs

14. Applicationof Statistics and Probability in Real Life

Upon completion ofthe module learners should be able to: Use statistical andprobability concepts to solve real lifeproblems

14.1 Measures of central tendancy

14.1.1 Mean

14.1.2 Mode

14.1.3 Median

The learners should be able to:1. Find the mean,

mode and median of a given data either in: -Grouped data, ungrouped data

2. Calculate median form o-give

3. Calculate modefrom the histogram

i. Define mean, median and mode

ii. Calculate mean, mode and median of ungrouped data

iii. Calculate mean,mode and mediaum of grouped data

iv.Draw cumulative frequency curve (ogive)

v. Estimate the median value form the ogive

vi.Draw the histogram

vii. Estimate the


conceptualization


centres- Take home

assignments- Information

resource centres- Field work

- Group discussion

- Invited guest speaker

- Lecture- Brainstorming- Case study

-Graph papers-Squared papers

-Geo-board-Rubber bands-Calculators-Chart with statistical reposition HIV/AIDS

10hrs 4hrs

51



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

value of mode form histogram

14.2 Probability

14.2.1 Probability of an event

14.2.2 Combined events

The learners should be able to:1. Determine

probability of an event through experiments

2. Interpret experimental results in real life situation

3. Write the formula for finding the probability of an event

4. Do experiment of two combined events

5. Draw tree diagrams

6. Find probability of combined events

i. Define terms event, outcome, experiment and sample space

ii. Define the term probability

iv.Calculate the probability of mutually

v. Calculate the probability of combined events

vi.Do as many exercise as he/she can.

- Library search


- Internet search

- Resources centres


- Group discussion



-circular objects

-rope-thread-ruler -coin-die-coloured objects

-cloth -cards-games-playing cards-charts-ruler-population records

10hrs 3hrs

15.Application of Accounts In Daily Life

15.1 Accounts

15.1.1 Double entry

The learners should be able to:1. Explain the

meaning of double entry

2. Identify incomeand expenditure

i. Discuss the principles of double entry system

ii. Identifying Debit side and Credit side

iii. Explain the

- Library search


- Internet search

- Resources

- Group discussion


- Lecture- Brainstorming- Case study- Role play

-Ruler-Different ledger books

-Coloured chalks

-Samples of vouchers

10hrs 4hrs

52



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

(debit and credit)

3. Explain different types of ledger

4. Construct a ledger

5. Post entries in the ledger

6. Close the simple accounts

meaning of ledger

iv. Explain different types of ledgers suchas cash accounts, capital, purchases, scales, expenses and stock

v. Label credit and debit side

vi. Post entries in the ledger

vii.Close accounts

centres- Take home

assignments- Information

resource centres

- Field work

15.1.2 TrialBalance

The learners should be able to:1. Explain the

concept of trial balance

2. Construct trial balance

3. Post debit balances and credit balances

4. Check the balances

i. Define the termtrial balance

ii. Construct and qualify a trail balance

iii. Do exercises on posting debit balance and credit balance

iv. Do exercises on checking the balances

- Library search


- Internet search

- Resources centres


- Group discussion


- Lecture- Brainstorming- Case study- Role play

-Ruler-Different ledger books

-Coloured chalks

-Samples of vouchers

20hrs 3hrs

53



LEARNINGACTIVITIES


LEARNING

TIME HOURS


SELFLEARNING

FACETO

FACE

- Information resource centres

- Field work

15.1.3 Trading profit and loss

The learner should be able to:1. Ascertain gross

profit/loss using trading account

2. Ascertained profit/loss accounts

i. Identify how to ascertain gross profit/loss using trading account

ii. Ascertaining net profit/loss accounts in trading accounts

-Ruler -Ledge books-Calculators-Balance sheets

10hr 3hrs

15.1.4 Balance sheet


1. Construct a balance sheet

2. Post entries in balance sheets

3. Interpret information from the balance sheet

i. Explain the meaning of balance sheet

ii. Construct a balance sheet

iii. Identify how to post entries in the balance sheet

iv.Interpret information form the balancesheets

v. Do exercise on interpreting balance sheets

-Various Balance sheets

-Ruler-Manila sheet -marker pens-Principles of account manual

-Calculators-Coloured chalks

20hrs 4hrs

54

institute of adult education - iae of adult education ... syllabus uses competence based education...

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