contents contents page · – step problem . s109 recognise numbers to the nearest tens. s207 add...

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CONTENTS

Contents Page

Acknowledgements 1

The Structure of the National Curriculum 1

Introduction 2

Rationale 3

Aims 4

General Objectives for Mathematics 5

Scope and Sequence of Topics 19

Terminal Objectives 24

Teaching/Learning strategies 36

Assessment 37

2

Acknowledgements

Mathematics in the National Curriculum was prepared by the Maths Unit of the Curriculum

Development Section and was modified by the members of Maths Section of the Maths,

Science & Environment Faculty of NIE: G. Kannangara, Jemmy Louange and U.M

Aboobucker.

Necessary support and background information were provided by the following members of

the following curriculum team.

Antonia Barbier

Bernard Songoire

Gerard Albert

Judy Padayachy

Raj Gopalan

Rose-Mary Ali

Soline Camille

This document was produced in accordance with the guidelines suggested by the Curriculum

Development Section of the Ministry of Education (1998)

The Structure of the National Curriculum

The National Curriculum applies to learners in Creche, Primary Schools and Secondary

School in Seychelles. It is organized on the basis of five cycles.

Cycle Learners’ Standard Year Level

1. Creche – P2 C – 2

2. P3 – P4 3 – 4

3. P5 – P5 5 – 6

4. S1 – S2 7 – 8

5. S3 – S5 9 – 11

3

Mathematics in the Seychelles National Curriculum

Introduction

Mathematics is the science of numerical and spatial relationships. It includes many topics of

study. The basic mathematics taught in schools involve the study of number, measurement,

shapes and relations.

The potential contribution of mathematics to the overall school curriculum is considerable.

There is in many topics and projects as well as in other subjects such as science, geography,

social sciences etc., a strong mathematical element which makes use, to varying degrees, of

the areas of study in mathematics. Consequently it has become an essential study to

understand human activities and events of the world and to communicate experiences

effectively.

The mathematics curriculum sets out to provide continuity in learners’ mathematical

development. It sets out a suitably balanced combination of knowledge, skills and attitudes

which will be developed through five continuous cycles. Application of the acquired

knowledge and skills in situations of solving mathematical problems as well as in other

aspects of every day life will help to enhance the confidence and the self-esteem of the

learner.

It adopts a spiral approach to ensure that topics are covered in increasing depths and

maintains the continuity and progression of the five cycle programme. The learning

outcomes for each cycle are outlined under the five strands; number, algebra, shape and

space, measure and handling data.

Problem solving is the central focus of the mathematics curriculum. It requires students to

use mathematical knowledge and skills to help them find solutions to problems in their daily

lives and to make decisions based on those solutions. It is the process by which students gain

pleasure and experience the power usefulness of mathematics around them and in the world.

Both primary and secondary level curricula are supported by learners’ textbooks/, workbooks

and teacher’s guides and variety of instructional materials. At upper secondary level learners

are exposed to a variety of supplementary booklets on problem solving and investigations.

Assessment of learners’ achievement is an integral part of the teaching/learning process.

Strategies are suggested to carry out continuous assessment of learners’ performance and

progress based on stated objectives.

4

Rationale

Mathematics is an essential element of communication, a powerful tool and a fascinating

study in its own right. Mathematical knowledge, skills and attitudes are all fundamental to

effective education. The whole spectrum of mathematical activity contributes to the overall

development of general skills of problem solving, reasoning and creativity. Thus in the

context of education for all, mathematics and mathematics education belong to the core of the

school curriculum.

The importance of teaching mathematics is not only because of its utilitarian purposed but

also because it helps to develop the aesthetic and cultural values and positive attitudes

necessary for the development of self–competence and self-fulfillment.

The study of mathematics helps to develop general skills, train the minds of learners and

assist them in the development of spatial awareness, provide learners a powerful means of

communication – to clarify, simplify and structure information in ways that help and extend

learning.

Since technology continues to dominate work and personal lives, competence in mathematics

will continue to be a growing demand in any society. The study of mathematics is

fundamental in meeting these demands and in helping young people to prepare for adult life.

Mathematics is an interrelated subject, It is derived from and used in many disciplines. Also,

knowledge and skills in mathematics can contribute to various specialities such as science,

Economics, Technology etc. Therefore the school curriculum allows learners to make

connections between mathematics and other learning areas avoiding the teaching and learning

of the subject to take place in isolation.

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Aims

The mathematics curriculum for primary and secondary school aims to enable pupils to:-

1. Acquire the necessary mathematical knowledge and skills in order to develop their

thinking processes and apply them in everyday life.

2. Develop positive attitudes and a sense of personal achievement in mathematics.

3. Use mathematics as a means of communication with emphasis on the use of clear

expressions.

4. Promote an appreciation of the place of mathematics in society and how it contributes

to the reasonable development of the world.

5. Stimulate interest to acquire skills to establish a firm foundation for an appropriate

further study of mathematics and of other disciplines.

General Objectives

For knowledge, the focus is on the understanding of concepts and relations the learners

should have in Number, Shape and Space, Measures, Algebra and Handling Data.

Skills refer to the manipulative skills, thinking and heuristic procedures and are structured

around the areas of computing, communicating, measuring, reasoning and problem solving.

The general objectives for Attitudes refer not only to the desirable behavior for learning but

also to the affective aspects of mathematics learning.

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GENERAL OBJECTIVES FOR MATHEMATICS

The table below sets out the knowledge, skills and attitudes which apply across the main areas of mathematics:

Number, Shape & Space, Measures, Algebra and Handling Data

KNOWLEDGE CYCLE 1

Students will

CYCLE 2

Students will

CYCLE 3

Students will

CYCLE 4

Students will

CYCLE 5

Students will

Algebra

Acquire facts and ideas

relevant to the

development of:

K107 grouping of numbers

and objects into

attribute sets.

Develop and

understanding of:

K208 recognising and

using patterns,

relationships and

sequences in numbers

and shapes.

Develop and demonstrate

an understanding of:

K308 identifying and

extending certain

common and

enrichment-oriented

patterns, relationships

and sequences, in

numbers and shapes.

K309 using letters for

numbers and variables.

Demonstrate a firm

understanding of:

K408 recognising and

using simple

functions, formulae,

equations and make

generalizations of

sequences.

K409 using letters for

numbers and

variables in resolving

mathematical

problem.

Demonstrate a firm

understanding of:

K510 algebraic

generalizations of

complex patterns and

using patterns to

model problems.

K511 symbolic and graphical

representation of

equations, inequations

and algebraic

functions.

Handling Data

Acquire facts and ideas

relevant to the

development of:

K108 ways of selecting

criteria for sorting

objects, record with

real object and

drawings and

Develop and

understanding of:

K209 basic methods of

collecting simple data and

record using tables to

communicate results.

Develop and

demonstrate an

understanding of:

K310 using a variety of

methods to gather,

analyse, display and

communicate

information.

Develop and

demonstrate an

understanding of:

K410 using a variety of

strategies to gather,

analyse, display,

interpret and evaluate

data.

Demonstrate a firm

understanding of:

K512 techniques of gathering

information from

various sources to

make decisions based

on the information and

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K109 ways of selecting

criteria for sorting and

classifying objects and

record using tables

and pictographs and


K210 communicate results

of simple data collected

through pictographs and

simple bar charts .

K311 using strategies to

interpret graphical

representations.

K411 using frequency

distribution on

histograms with

equal intervals.

communicate the

decisions using the

appropriate methods.

K513 application of

probability and

statistic in a variety of

investigations.

SKILLS CYCLE 1

Students will

CYCLE 2

Students will

CYCLE 3

Students will

CYCLE 4

Students will

CYCLE 5

Students will Computation

S101 add and subtract whole

numbers (2 digits) with

and without

decomposition.

S102 find halves and quarters

of a quantity.

S103 exchange money using

the names and values of

coins and notes.

S104 use repeated addition to

perform simple

multiplication.

S105 use repeated subtraction

to perform simple

S201 add and subtract whole

numbers (4 digits) with

and without

decomposition.

S202 order simple fractions

in magnitude and add

and subtract simple

fractions.

S203 exchange money using

the names and coins of

notes.

S204 multiply a whole

number by a whole

number within the

understanding of

multiplication tables up

to 12.

S205 divide a whole number

by a whole number

S301 use the four

operations with

whole numbers, and

decimals knowing the

order of operation.

S302 add and subtract

mixed umbers.

S303 solve money problems

involving profit, loss

and simple interest.

S304 recall the four

operations facts and

use them to perform

operations in other

bases less than 10.

S305 solve simple everyday

problem involving

S401 use the four operations

confidently with

whole numbers and

decimals.


with fractions.

S403 make use of currency

conversion graphs to

solve problems.


facts to manipulate

algebraic expressions.


with integers, indices

and numbers

expressed in standard

form.

S502 use their own strategies

to perform faster

calculations.

S503 calculate using money

and convert from one

currency to another.

S504 form and manipulate

equations or

inequations in order to

solve problems.

8

division.

S106 make a reasonable

estimation of a number

of objects up to 30.

within the

understanding of

multiplication tables up

to 12

S206 make estimations and

approximations to

check validity of

additions and

subtractions

calculations.

division.

S306 make estimations and

approximations to

check validity of

multiplication and

division problems

involving whole

numbers.

S405make estimations and

approximations to

check validity of any

calculations.

S505 make mental estimates

and approximate

solutions to numerical

calculations.

SKILLS CYCLE 1

Students will

CYCLE 2

Students will

CYCLE 3

Students will

CYCLE 4

Students will

CYCLE 5

Students will

Computation


mentally for numbers

0-20.

S108 use the operations

addition and

subtraction with whole

numbers to solve one

– step problem

.

S109 recognise numbers to

the nearest tens.


mentally for numbers

0 – 100.

S208 use the four basic

operations

appropriately to solve

simple word

problems.

S209 round numbers to

estimate sums and

differences.

S307 use mental

computational

strategies to solve

simple problems.

S308 select and use the

appropriate

operations to solve

problems.

S309 make estimation and

approximation to

check results.

S406 use mental

computational

strategies to formulate

their own problems.

S407 choose methods of

computation

appropriate to a

problem, adapt and

apply them accurately.

S408 check results by

different methods,

including repeating in

different order or

using inverses.

S506 approximate using a

specific number of

significance figures or

decimal places.

S507 use a variety of

checking strategies ad

apply them

appropriately to check

calculations.

S508 use estimate and

inverse operations to

confirm that results are

of the right order of

magnitude.

S509 understand and use the

facilities of a

calculator, including

9

the use of constant

function, memory and

brackets to plan

calculations and

evaluate expression.

SKILLS CYCLE 1

Students will

CYCLE 2

Students will

CYCLE 3

Students will

CYCLE 4

Students will

CYCLE 5

Students will

Measuring

S110 measure and compare

lengths and quantities

using non-standard

and standard units.

S111 make estimates based

on standard and non-

standard units.

S112 select appropriate

measurement tools for

length, mass and

capacity.

S113 use non-standard units

S210 use commonly used

standard units to

measure and compare

length, mass and

capacity.

S21 make estimate base on

familiar units.

S212 use larger and smaller

units to measure and

record results.

S213 use non-standard and

S310 use the relationships

between larger and

smaller units to

measure and record

results, and to

convert from one unit

to another.

S311 use measurements to

confirm estimation.

S312 make use of selected

appropriate units and

tools of measurement

required for the task.

S313 use standard units to

S409 solve involving

application of

knowledge of the

relationships between

larger and smaller

units to measure /

record results and to

convert from one unit

to another.

S410 make sensible estimate

related to everyday

objects.

S411 use a wide range of

measuring instruments

to measure with

reasonable accuracy.

S412 select and use the most

S510 use the relationships

between larger and

smaller units to

measure, record, make

conversions and to

apply appropriately in

solving problems.

S511 judge the

reasonableness in

estimates in measuring

activities.

S512 use a wide range of

measuring

instruments,

understanding the

degree of accuracy

that is possible or

appropriate for a given

problem.

S513 make conversions of

10

to measure area and

volume.

standard units to

measure area and

volume of non-

composite familiar

shapes and solids.

measure area and

volume of composite

familiar shapes and

solids.

relevant and

appropriate square and

cubic units and tools

for a given task.

square and cubic

measures as required.

SKILLS CYCLE 1

Students will

CYCLE 2

Students will

CYCLE 3

Students will

CYCLE 4

Students will

CYCLE 5

Students will

Measuring

S114 compare shapes and

objects by size.

S115 sequence events e.g.

what happened first,

what happened last.

S116 use non-standard

methods to record the

passing of time.

S117 estimate and record

time in hours and

fraction of an hour.

S118 compare units of time

S214 compare shapes and

objects by measuring.

S215 relate specific times to

everyday activities

and routines.

S216 state and record time

to the nearest minute

using analogue and

digital clocks.


time in minutes and

hours.

S218 compare units of time

S314 record results of

measuring activities

using correct terms

and conventions.

S315 relate time intervals to

everyday activities.

S316 state and record time

on twelve and

twenty-four hour

clocks and make

conversions between

them.


time in seconds,

minutes and hours.

S318 compare the passing

S413 compare the passing of

S514 select and use

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in terms of days,

weeks and months.

S119 make comparisons with

real objects to develop

the concept of scale.

in days, weeks,

months and years.

S219 make comparisons

units of measures to

develop the concept

of scale.

of time in terms of

decades, centuries

and millenniums.

S319 read understand and

use scales given in

scales drawings.

time in terms of leap

years and regular

years.

S414 select and use

appropriate scale for

drawings.

appropriate scales for

scales drawings.

S515 read, interpret and use

scale with high degree

of accuracy.

SKILLS CYCLE 1

Students will

CYCLE 2

Students will

CYCLE 3

Students will

CYCLE 4

Students will

CYCLE 5

Students will

Communicating

S120 use the language of

number and

comparatives to

express ideas; e.g. next

to, one more than”.

S121 describe general

features of shapes and

objects using everyday

language.

S122 describe similarities

and differences of

shapes and objects

orally, using general

terms.

S220 use the languages of

number and

comparatives to

express properties of

numbers and

measures.

S221 describe general

features of shapes

and objects using

geometrical

language.

S222 communicate

solutions both orally

and in writing using

appropriate

mathematical

S320 use the mathematical

language and

notations to express

relationships.

S321 describe properties

and relationships of

shapes, solids and

movement using

geometrical language.

S322 discuss their work

responding to and

asking mathematical

questions centred

around problem


number, algebra and

geometry to explain

properties of number

and shapes and space.

S416 use mathematical

language in a precise

way to communicate

solutions.

S417 produce written records

of mathematical

activities.


number, algebra and

geometry to explain

properties of number,

shapes and spaces and

transformation.


language in a precise

way to explain their

work and


S518 give answers with a

complete explanation

of the steps used.

12

S123 use pictures and

symbols to show

numbers and results of

simple number

operations.

language.

S223 record information

using block / bar

graphs, charts and

tables.

solving and

investigations.

S323 communicate

solutions using basic

graphical methods.

S418 interpret mathematics

presented in a variety

of forms.

S519 describe the

explorations and

discussions involved

in investigations and

solving problems.

SKILLS CYCLE 1

Students will

CYCLE 2

Students will

CYCLE 3

Students will

CYCLE 4

Students will

CYCLE 5

Students will

Communicating

S124 explain their work and

solution to a problem

S125 present information

orally.

S126 record information

using tables and

pictographs.


responding to and

asking mathematical

questions centred

around problem

solving.

S225 present information

using picture and

diagram.


presented in tabular

and graphical forms.

S325 use a variety of forms

of mathematical

presentation.

S419 present information and

results clearly and

explain reasons for

their choice of

presentation.


presented in a variety

of terms and evaluate

forms of presentation.

S521 examine critically,

improve and justify

their choice of

mathematical

presentation.

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responding and asking

mathematical

questions.

SKILLS CYCLE 1

Students will

CYCLE 2

Students will

CYCLE 3

Students will

CYCLE 4

Students will

CYCLE 5

Students will

Reasoning

S128 recognise pattern in

skip counting in twos,

threes… starting at

any number up to

1000.

S129 sort, match, compare

and classify familiar

shapes and solids

according to given

criteria.

S130 define own criteria for

identifying given

objects.

S131 identify similarities and

differences in object.

S226 recognise simple number

patterns and make

simple generalizations

to predict other terms.

S227 discriminate between

different attributes of

shapes and solids in

their environment.

S228 verify general statements

e.g. all even numbers

divide by 2.

S229 make links between the

separate stages of

simple problems

S326 recognise and use

repeated pattern and

make predictions

about them.

S327 select relevant data

and procedures to

solve problems.

S328 investigate general

statement by trying

out a number of

examples.

S3329 make links between

the separate stages of

problems.

S420 recognise an d use

repeated patterns,

relationships and

sequences in numbers,

shapes and make

predictions about

them.

S421 give some justification

for solutions to

problems.

S422 make general

statements of their

own based on the

evidence they have

produced.

423 use examples to test

solutions, statements

and definitions.

.

S522 recognise and use

repeated patterns,

relationship sequences

in number, algebra and

geometry and make

predictions about

them.

S523 explain and justify in

depth how they arrived

at a conclusion or

solution to a problem.

S524 make general

statements based on

testing and

investigations.

S525 make conjectures and

hypotheses designing

methods to test them

and analyse results to

see whether they are

14

valid.

SKILLS CYCLE 1

Students will

CYCLE 2

Students will

CYCLE 3

Students will

CYCLE 4

Students will

CYCLE 5

Students will

Reasoning

S132 group given objects

according t basic

concepts.

S133 use their own logic to

decide given number

statements is true or

false.

S230 sequence events

according to their

natural or logic order.

S231 deal with logical

relations expressed

by statements.

S330 check results

considering whether

they are reasonable.

S331 make prediction based

on experience.

S424 search for patterns in

their solutions.

S425 use logical reasoning to

find resolutions to

mathematical

problems.

S526 appreciate and use

“if…then…” line of

argument in number,

algebra and geometry

and draw inferences

from statistics.


reasoning initially

when explaining and

then when following a

line of argument.

S528 justifying the solutions

to a problem involving

a number of features

or variables.

15

SKILLS CYCLE 1

Students will

CYCLE 2

Students will

CYCLE 3

Students will

CYCLE 4

Students will

CYCLE 5

Students will

Problem solving

S134 use concrete materials

to solve simple

problems.

S135 reset problems in their

own words.

S136 follow step by step

verbal instruction to

solve problems.

S137 learn to work in group

problem solving

activities.

S232 use diagrams,

drawings and charts

to solve problems.

S233 interpret and translate

problems to number

sentences and

solving.

S234 follow step by step

instructions to solve

problems.

S235 participate effectively

in group – problem

solving activities.

S332 make their own

diagrams, drawings

and charts to find

solutions to problems.

S333 translate problems to

number sentences and

equations and solve

them.

S334 follow steps in

standard method of

inquiry.

S335 work co-operatively to

identify and obtain

information necessary

to solve problem.

S426 select ad use

appropriate

mathematical

equipment and

materials.

S427 translate problems to

algebraic expressions

for solving problems.

S428 decide and develop on

appropriate strategies

of their own to solve

problems.

S429 probe into the problem

to find what kind of

information is given

and what are the

restrictions placed on

the solution.

S529 select and use

appropriate

mathematical

equipment and

materials.

S530 make and apply

problem-solving

models appropriate to

solve problems.

S531 develop sophisticated

strategies to solve

problem.

S532 identify and draw

resources within and

outside the group that

can be used to solve

problems.

16

SKILLS CYCLE 1

Students will

CYCLE 2

Students will

CYCLE 3

Students will

CYCLE 4

Students will

CYCLE 5

Students will Problem Solving

S236 apply the knowledge

and skills acquired to

construct and solve

simple problems.

S237 carry through a task

by breaking it down

into smaller

manageable tasks.


and skills acquired,

confidently to solve

problems.

S337 relate problems to

similar ones solved

earlier.


and skills acquired

with accuracy.

S431 show accuracy and

persistence in

investigating problem

to form strategies of

their own.

S432 probe into the problem

to find what kind of

information is given

and what are the

restrictions placed on

the solution.


and skills acquired

with accuracy,

thoroughness.

S534 examine different

explanations and

solutions to a problem,

determine their

validity and apply the

most appropriate

solution.

S535 pose questions of the

type “what-if-not” to

form strategies to

solve problems.

17

It is hoped that the stated below will be developed gradually through the study of Mathematics from Cycle 1 to Cycle 5.

ATTITUDES Cycle 1 to 3 (Primary)

Learners should:

Cycle 4 & 5 (Secondary)

Learners should:

TOWARDS SELF &

OTHERS

AP 1 have the capacity to identify, own and transmit their

thoughts, feelings and emotions;

AP 2 accept the efforts and show tolerance towards the feelings,

opinions and beliefs of others;

AP 3 be willing to develop and share their creative interests and

show appreciation for other forms of art and culture;

AP 4 understand their right of others and be committed to carry

out their responsibilities;

AS 1 want to find out more about themselves and their interdependent

relationship with other people and the world;

AS 2 appreciate the essential work of others and the commonality of

needs, rights, beliefs, aspirations, behavior and talents which

bind humankind;

AS 3 be willing to explore new patterns of interaction and be prepared

to utilize and value their capacities for creative and critical

thinking;

AS 4 have a commitment to defending their rights, respect the rights

of others and be committed to carry out their responsibilities;

TOWARDS THE

ENVIRONMENT

AP 5 have a respect and appreciation for all living things and their

place and functions in the overall environment;

AP 6 aware of and appreciate the relationship between the natural

and human-made environment and be willing to become

engaged and involved with environmental issues;

AS 5 appreciate, respect and value the different physical and human

environment and reflect positively upon their own place in it;

AS 6 appreciate that in an interdependent world system, consideration

for the overall good of humankind and the planet should

influence their decisions and actions.

TOWARDS

MATHEMATICS

AP 7 cultivate proper habits of study and power of concentration.

AP 8 enjoy playing mathematical games, solving mathematical

puzzles and doing investigations.

AP 9 aim to seek the ability to independent and original thinking.

AP 10 build self-confidence and reserve powers which constitute a

strong personality.

AP 11 be aware of the contribution and value of mathematics to

other subject areas.

AP 12 appreciate the significance of mathematics in everyday life.

AP 7 form the habit of systematically and logically pursuing a task to

completion

AP 8 train their minds in scientific thinking and reasoning logically.

AP 9 develop ability to identify problems, formulate hypotheses and

experiment to solve problems.

AP 10 develop a willingness to attain the power to clear and accurate

expression.

AP 11 enthusiastically seek knowledge with open mind for the sake of

its possible usefulness.

AP 12 acquire a foundation appropriate to their further study of

mathematics and of other disciplines.

Attitudes and values to be developed throughout the cycles to achieve the objectives.

Thrust, kindness, wisdom, honesty, open-mindness, courage, truthfulness, sense of humour, self riance, self esteem,

18

SCOPE AND SEQUENCE

Topics Cycle 1

Cycle 2

Cycle 3

Cycle 4

Cycle 5

Numbers (a) Whole Numbers

Numbers to 999

Place value (hundreds,

tens, units)

Addition and subtraction

Multiplication and division

by 2 and 3

Numbers to 99 999

Place value (thousands,

hundreds, tens, units)

Multiplication, 2/3/4/

digit numbers by 2 digit

numbers.

Division, 2,/3 digit

numbers by1 digit

numbers

Numbers million and

beyond.

Place value

Four operations

Rounding off

Order of operations

Integers


Multiples and factors

Prime numbers

Prime factors

Integers, indices

Four operations

Significant figures

Standard form

Rules of indices

Sets

Accuracy and

approximation

(b) Fractions

½, ¼ of a whole

½, ¼, 1/8

Ordering fractions

1/3, 1/5, 1/6, 1/10

Equivalence within

1/10 and ½

Improper fractions

Mixed numbers

Simplest form

Addition and

subtraction

Comparison of

fractions

Four operations

Fraction and

problem solving

(c) Decimals

2 places

Place values

Addition and

subtraction

4 places

Place value

Additional and

subtraction

Multiplication and

division by 1 digit

numbers

Division of a

decimal number by

a two digit decimal

number

Conversion to

fractions rounding

off

Significant figures

Standard form

19

d) Percentage Meaning of %

¼, ½ as %

% as fractions and

decimals

Discount

Simple interest

% of quantity

Percentage increase

and decrease

Profit and loss

Reverse percentage

e) Ratio and

proportion

Ratio in simplest

form

Proportion divisions

Enlarging and

reducing by a ratio

Direct proportion

Inverse proportion

Using formula for

direct and inverse

proportions

Measures

a) Money

Equivalence


up to R 10 000

Addition and subtraction of

any amount of money

Four operations

Profit and ;loss

Shopping bills

Earning, expenses and

saving

Household bills

Foreign currency

Wages and salaries

Piece work, hire, purchase

taxes

b) Time/

temperature

½ past, ¼ past,

minutes past

Calendar

24 hour clock time

a.m, / p.m

Minutes to an

hour

Time tables

Minutes and

seconds

Weather charts

12 and 24 clock time

Timetables, elapsed time

Measuring temperature

Temperature scale

Change temperature

c) Length

Measure to the

nearest m and ½

m

Estimation in km

Plans and scales

Addition and

subtraction

Measuring in cm,

mm

Relationships

between units

Multiplication and

divisions

Units of area and

volume

Conversion

Four operations

Relationship

between square and

cubic metre

Compound

measures

d) Mass

Balancing with grams/

kilogram’s

Estimation, in kg and

fractions of kg

Weighing in g


Four operations

Relationship between units

Conversions

Four operations

Kg and tonne

L in cm3

20

e) Capacity Measuring with 1L

Estimation and

comparison

Reading scales

Measuring in m

Equivalence

conversions

Conversions

Shape and Space

a) 2- D shapes

Square, rectangles,

triangles, circle

Basic properties

Area and perimeter of

square and rectangle

Perimeter of triangles

Radius, diameter and

circumference of

circles

Classification of triangles

by sides

Area of right angled

triangles

Classifications of triangles

by angles

Area of triangles

Mathematical properties of

square and rectangles

Circumferance and area of

circles

Drawing and constructing of

shapes I.

Pythagoras Theorem

Properties of regular and

irregular polygons

Similarities of rectangular

and irregular polygons

Similarity of 2-d and 3-D

shapes

Sin, cos, tan, ratios

Drawing and constructing

b) 3-D shapes

Cube, cuboid, cylinder,

sphere

Basic properties

Cone

Volume of cubes, cuboids

by counting cubes

Volume; cube cuboid

Mathematical properties of

cubes and cuboid

Nets and surface area of

cube and cuboid

Cylinder, volume; prism,

pyramid cone, sphere

Nets and surface area of

cylinder, triangular

prism and pyramid

c) Angles

Right, obtuse, acute,

straight

Perpendicular, vertical

horizontal

Angles at a point

Bearings

Constructing angles

Recognizing and naming

angles

Drawing angles

Angles formed with

intersecting and

parallel line.

Angle properties in a circle

Angles of elevation and

depression

Angle between tangent and

radius

d) Position and

movement

Position on a grid

Displacement on a

straight line

Four compass directions

Plot And read location on a

grid

2-D representation of 3-D

shapes

8 points of the comapss

Co-ordinates in the 1st

quadrant

Co-ordinates

Scale diagram and maps

Scales factor for enlargement

Vectors, Combining vectors

magnitude, directed

line segments

Translation, reflection,

rotation enlargement

21

Matrices

Travel graphs

e) Algebra

Compare numbers and

quantities

Picture Symbols to

represent numbers

Numbers patterns

Simple equations

Sequence of numbers

Simplification and

expressions

Using letters for numbers

Inequations and equations

Using brackets

Forming and using formulae

Straight line graphs

(y=mx+c)

Quadratic functions and

graphs

Parabolas: graph (y=x2)

Hyperbolas, grph (y=a) x

Handling Data

Picture graph

Calendar

Column graph

Tables

Plot co-ordinates

Block/bar graphs

Tallying and frequency

tables

Conversation tables and

graphs

Maps

Mean

Pictographs

Bar graphs

Pie charts

Line

Interpretation information

from different types of

graphs

Mean, mode, median

Histograms and frequency

tables with class

intervals

Cumulative frequency

distribution

probability

23

PRIMARY MATHEMATICS TERMINAL OBJECTIVES

Cycle 1

Whole Numbers and Algebra

Recognise and write numerals from 0 to 999

Link numbers 0 to 999 to various units of measurement e.g. time, money and weight.

Demonstrate understanding of place value of three-digit numbers by expanding

numbers between 10 and 999 into hundreds, tens and units, and state the value of the

digit within a three-digit numeral.

Demonstrate understanding of ordinal numbers 1 to 20 e.g. 1st, 2

nd, 3

rd, up to 100

th.

Read and write the numbers in words from 1 to 50.

Make estimates based on familiar measures, e.g. length(m), time(hr), money(R/ct.)

Compare numbers from 1 to 500 using the words more than, less than, same as.

Solve everyday problems involving numbers up to 500.

Use pictures or symbols to represent numbers.

Identify even and odd numbers from 1 to 100.

Addition, Subtraction, Multiplication and Division of the whole number

Add two or three 2-digit numbers with and without carrying (total not exceeding 500)

Subtract 2-digit numbers (with and without decomposition)

Add mentally 2, 3 single digit numbers.

Subtract mentally numbers up to 20 by a single digit number.

Demonstrate understanding of concept of multiplication by repeated addition with

2,3,4,5 and 10 as factors.

Interpret and use symbol to write multiplication facts.

Demonstrate knowledge of multiplication tables 2,3,4,5 and 10.

Demonstrate understanding of concept by division by repeated subtraction.

Solve everyday problems involving addition, subtraction, multiplication of numbers,

(not greater than 500).

Explore and generate patterns in multiplication facts.

24

Measurement of Length of Mass (Weight Capacity, Time, Angles and Money)

Recognise coins and currency notes of different denominations.

Make any value up to R1 by using various collections of coins, real or paper money.

Use real or paper money to solve everyday problems involving addition and

subtraction of money (without exceeding R50 and without conversion).

Solve daily life problems involving rupees up to R100, and involving cents in

multiples of 5 and 10 up to R1.

Estimate measurement of length, weight, capacity and use non-standard unit to check

the measurement.

Read clocks, show and record time in hour, half-hour, and quarter-hour.

Demonstrate an understanding of area and perimeter of rectangle and square.

Shapes in terms of non-standard units of measurement.

Simple Fraction, Decimal and Percentages

Recognise ½ as a number symbol.

Demonstrate understanding of a quarter as part of a whole, a quarter of a number, the

equivalent of fraction, e.g. two quarters is equivalent to a half. (Use language but not

symbols).

Shape and Space

Recognise and name 3-D shapes, cuboid, cube, cylinder and sphere.

Use language to describe properties of 2-D and 3-D shapes, cuboid, cylinder and

sphere.

Identify objects with straight edges and curved edges.

Construct cuboids, cylinders, cubes and spheres.

Describe the position and place of objects on a grid.

Statistics

Order events and use appropriate language to justify the order.

Collect and record data leading to frequency tables.

Construct and interpret frequency tables and pictorial graph or block graph.

Distinguish outcomes of some events as 6.6.04.

25

Cycle 2

Whole Number and Algebra

Recognise and write numerals from 1,000 to 100,000.

Read and write numbers in words up to 10,000.

1.4.03 Demonstrate understanding of place value of 4-digit numbers by expanding.

Numbers between 1,000 to 9,999 into thousands, hundreds, tens, units and state the:

Value of the digits within 4-digits numerals.

Identify numeral(s) before, after and in between any numeral(s) from 1,000 to 10,000.

And arrange numbers in ascending and descending order.

Compare numbers from 1,000 to 10,000 using <,>,=.

Make estimates based on familiar units.

Demonstrate understanding of multiples and factors of a number.

Demonstrate understanding of square numbers up to 50.

Recognise numbers up to the nearest hundreds.

Solve everyday problems involving numbers up to 10,000.

Recognise patterns, which arise in various situations, e.g. multiples, factors etc.

Understand the effect of multiplying a number by 10 or 100.

Addition, Subtraction, Multiplication and Division of Whole Number

Add two or three, 4-digit numbers with carrying of tens and hundreds.

Subtract 4-digit numbers with decomposition of tens and hundreds.

Multiply 2 and 3-digit numbers by a 2-digit number with product not exceeding

10,000.

Divide a 3-digit number by a single digit number (with decomposition hundred, tens

and remainder).

Demonstrate understanding and use the effect of multiplying and dividing whole

numbers by 10 and 100.

Recognise relationship between multiplication and division.

Use a variety of strategies to perform mental calculations.

Estimate and approximate to check the validity of additional and subtraction

calculations.

Use language associated to addition, subtraction, multiplication and division.

Solve everyday problems involving any of the four basic operations.

26

Measurement of Length of Mass (Weight), Capacity, Time, Angles and Money.

Interpret numbers on a range of measuring instruments.

Solve simple money problems with conversion using any of the four operations of

addition, subtraction, multiplication and division.

Solve daily life problems mentally involving rupees or cents where the sum does not

exceed R100.

Demonstrate understanding of the concept of profit and loss.

Demonstrate understanding of the relationship between different units of

measurement, e.g. kilometers and meters, kilograms and grams etc.

Convert different units e.g. meters to centimeters and vice versa.

Estimate and use different measuring instruments such as ruler, weighing scale, etc. to

check the measurement of various objects in the environment (meters only or

centimeters).

Use non-standard and standard units of measurement to find perimeter of rectangular

and square surfaces.

3.4.09 Apply the formula to calculate the perimeter of rectangular and square shapes.

3.4.10 Find the area of rectangular and square surfaces in square units.

Demonstrate understanding of the relationship between area of rectangle and area of:

Composite shapes made up of rectangles.

Interpret a calendar.

Read, record and show the time in hours and minutes.

Calculate the duration of an activity or event in the hour and half the hour only.

Find the volume of cuboid and cube by counting cubes.


Demonstrate understanding of mixed numbers involving fractions ½, ¼ and 1/8.

Convert mixed numbers into improper fractions and vice versa.

Demonstrate understanding of equivalent fractions of given fractions (e.g.

½=2/4=3/5)

Add and subtract simple fractions up to eights.

Calculate fractions of a number.

Calculate fractions of a unit of measurement.

Arrange fractions in ascending and descending order.

Solve everyday problems involving addition and subtraction of fractions with same

denominator.

Recognise the effect of dividing a unit number by 10.

Read and write decimal fractions (one decimal place) on a place value chart number

line.

27

Shape and Space

Use a ruler to measure and construct 2-D and 3-D shapes.

Recognise right, obtuse and acute angles in pictures and objects in the environment.

Use a protractor to measure and check right, obtuse and acute angles.

Reflect simple shapes in a mirror line.

Use grid reference to read and plot location on grids.

Give and understand instruction for turning through right angles.

Find area and perimeter of 2-D shapes (as measurement).

Statistics

Extract information/data from tables.

Construct and interpret informative bar graphs.

Place events in order of “likelihood” and use appropriate words to identify the change

e.g. likely, very likely, certain.

Cycle 3

Whole Number and Algebra

Read, write and order large numerals and number work.

Use with understanding the relationship between lace values in whole numbers.

Understand the effect of multiplying a number by 10, 100, 1000 or 10,000.

Recognise negative whole numbers in familiar contexts e.g. temperature shown on a

thermometer.

Recognise negative numbers on a number line.

Calculate Lowest Common Multiples (LCM), and Highest Common Factor (HCF).

Write numbers to the nearest 100, and 10,000.

Use odd, even, prime and square numbers in problem solving.

Use large numbers to solve everyday problems.

Use patterns in numbers to generate sequences.

Understand and use simple formulae expressing in words.

Relate numbers to units of measurement (length, mass, capacity, money, time).

Write the numerals 1 to 1,000 in base 2 to 10.

Convert from base 10 to any base lower than it and vice versa.

28

Measurement of Length of Mass (Weight) Capacity, Time, Angles and Money

Add and subtract large numbers.

Add and subtract mentally single digit numbers, two-digit numbers.

Recall multiplication facts to 10 times 10 and use them in multiplication and division

problems.

Calculate the average of a set of numbers.

Estimate and approximate to check the validity of calculations.

Use the knowledge of inverse operations to check calculations.

Use a variety of strategies to perform mental calculations.

Apply the four basic operations to solve everyday problems.

Add and subtract two 2- to 4-digit numbers, of the same base, in bases lower than 10.

Addition, Subtraction, Multiplication and Division of Whole Number

Solve money problems involving profit and loss and simple interest.

Solve everyday problems relating to standard units of length, weight and capacity.

Apply standard units in mental calculations.

Estimate and approximate measurements in different units.

Apply formulae to calculate area and perimeter of rectangles, squares and triangles.

Apply formulae to calculate circumference of a circle, volume of cuboid and cubes in

given measures.

Solve everyday problems involving area, perimeter and volume of familiar shapes.

Use time measuring instruments.

Solve problems involving calendar, 24 hour clock time.

Interpret dates in numerals.

Use protractor to measure angles.

Calculate angles in degrees.


Find equivalent of simple fractions.

Convert mixed numbers to improper fractions and vice versa.

Add and subtract mixed numbers.

Multiply simple fractions.

Calculate fractions of a number or units of measurements e.g. ¼ of 2kg.

Use with understanding the relationship between place values in decimal number up

to 3 places.

Convert simple fractions to decimal.

Perform basic operations involving decimal numbers.

Convert fractions and decimals into percentages and vice versa.

Solve problems involving simple fractions decimals and percentages.

29

Shape and Space

Use instrument, such as protractor or compass to draw and construct 2-D and 3-D

shapes (cube, cuboid, and cylinder).

Construct polygons from 2-D shapes.

Use appropriate language to describe the properties of the above prisms, triangles and

quadrilaterals.

Recognise the relationship between angles and shapes which tessellate.

Identify reflective symmetry in various shapes.

Use grid references to read and plot locations on grids (coordinate in the first

quadrant).

Use network to solve problems.

Use knowledge of area, perimeter, and circumference of 2-D shapes to solve

problems.

Understand eight points of the compass using clockwise and anti-clockwise.

Statistics

Collect, group and order discrete data using tallying methods and create frequency

table for grouped data.

Understand, calculate and use the mean and range of a set of discrete data.

Construct and interpret pictograms, pie charts and line graphs.

Give and justify estimates of probabilities in a variety of situations.

30

TERMINAL OBJECTIVES- MATHEMATICS

Number Cycle 4

NUMBER

Make estimates of numbers and quantities.

Choose methods of computation appropriate to a problem.

Use methods of computation with arithmetical accuracy.

Apply multiples, factors, prime numbers and prime factors appropriately in solving

problems.

Use directed numbers in context including ordering, addition and subtraction.

Fractions Decimals

Use with confidence the four operations on fractions.

Demonstrate and understanding of place value and of the four operations on decimals.

Use decimal notation confidently in the context of measurement.

Percentage

Appreciate, discuss and express ideas about the use of percentage in the outside

world.

Work out fractional and percentage changes and related calculations in a variety of

context.

Ratio and Proportion

Demonstrate the understanding of the elementary idea of and notation of ratio.

Apply ratio to maps, plans and models in the form of scale and in enlarging and

reducing.

Solve problems involving proportional divisions.

Distinguish between direct and inverse proportions and use them appropriately in

problem solving.

MEASURES

Decimal Measures

Know the commonly used units of measurement and their relationships.

Make estimates based upon familiar units.

Choose the most appropriate units of measurement for given everyday objects.

Express quantities in terms of larger and smaller units.

Use measuring instruments to measure to a reasonable degree of accuracy.

31

Money, Time and Temperature

Solve problems involving, earnings, expenses and savings.

Solve problems involving the days, weeks and months of a calendar year.

Use the 24 hour clock time and 12 hour clock time in a variety of context.

Compare temperatures in a geographical context and calculate changes in

temperature.

SHAPE AND SPACE

2-D and 3-D Shapes

Demonstrate the understanding of units of length, area and volume.

Distinguish between formulae for area and volume.

Use formulae to calculate area and volume.

Understand and use the specific properties of quadrilaterals, triangles and circles.

Use mathematical instruments to construct 2-D shapes.

Use the language associated with 2-D and 3-D shapes appropriately.

Angles

Recognise and name angles

Draw and measure and angles to the nearest degree.

Understand and use the notation of angles.

Use the language associated with angles.

Identify different types of angles.

Understand and use the properties of angles at a point.

Understand and use the bearing as an application of turning.

Use the concept of angles in practical situations.

Position, Movement and Transformation

Use the coordinate system to specify locations.

Select and use appropriate scales for scale drawings.

Read and interpret scale diagrams, maps and plans.

Construct plane figures from given data.

ALGEBRA

Form algebraic expressions for given situations.

Determine possible rules for generating sequences.

Construct and solve simple equations.

Use the notational convention of multiples and indices.

Develop formulae and use them in calculations.

32

HANDLING DATA

Draw and use pictographs and bar graphs as simple and effective ways of presenting

statistical data.

Draw and interpret pie charts and line graphs.

Be aware of different methods of collecting data and use them in statistical

representations.

NUMBER Cycle 5

Number

Demonstrate the understanding of integers, powers (indices) and use them in a variety

of practical applications including problem solving.

Use index notation to express powers and roots.

Express and use numbers in standard form.

Approximate numbers using significant figures.

Use the language, notation and Venn diagrams to describe and represent relationships

between sets.

Fractions

Use the knowledge skills and understanding attained at lower levels in a wider range

of contexts.

Decimals

Approximate decimal numbers to specified places of decimals and significant figures.

Express and use decimal numbers in standard form.

Use the knowledge, skills and understanding attained at lower classes in a wider range

of contexts.

Percentage

Demonstrate a firm understanding of percentage and use the knowledge to calculate

percentage increase, decrease and reverse percentages.

Use the knowledge and understanding of percentage to make comparisons,

evaluations and to solve everyday problems.

33

Ratio and Proportion

Demonstrate the understanding of the ideas and notation of common measures of rate

and use them in solving problems.

Express direct and inverse variation in algebraic terms and use them to find unknown

quantities.

Select and use scales to draw graphs to show the relation between average speed,

distance and time.

MEASURES

Decimal Measures

Use the knowledge, skills and understanding attained at lower classes in a wider range

of contexts.

Use the current units of length, mass, capacity, area and volume in practical situations

and in solving problems.

Make estimates, give approximations to specified numbers of significant figures and

decimal places and round off answers to reasonable accuracy in the context of a given

problem.

Understand and use compound measures.

Money

Convert one currency to another.

Draw and use currency conversion graphs.

SHAPE AND SPACE

2-D and 3-D Shapes

Understand and use specific properties of polygons and circles.

Apply the knowledge and skills in area to solve problems.

Demonstrate the understanding of properties of similar shapes.

Demonstrate the understanding of Pythagoras Theorem and apply to problem solving.

Use sine, cosine and tangent ratios in right-angled triangles.

Use the appropriate formulae to calculate the volume of prisms, pyramids, cones and

spheres.

Calculate the surface area of the above mentioned solids.

Understand and use the relationships between the volumes of similar 3-D solids.

Solve simple trigonometrical problems involving elevation and depression.

34

Angles

Understand and use the properties of angles formed by intersecting and parallel lines.

Understand and use the properties of the sum of angles of regular/irregular polygons.

Understand and use properties of angles in a circle.

Position, Movement and Transformations

Recognise and visualize the transformations of translation, reflection, simple rotation

and enlargement.

Use the properties of transformations to create and analyse patterns and to investigate

the properties of a shape.

Enlarge a shape by a whole number scale factor.

Understand and use vector notation to describe translation.

Understand and perform vector addition, subtraction and multiplication by a scalar.

Find the magnitude of a vector using its components.

ALGEBRA

Appreciate and use letters to represent variables.

Explore number patterns arising from a variety of situations.

Interpret, generalize and use simple relationships and generate rules for sequences.

Interpret graphs that represent real life situations.

Manipulate a range of algebraic expressions as needed in a variety of contexts.

Transform simple formulae and use them in calculations.

Solve a variety of linear inequalities and use the straight line graphs to locate regions

given by linear inequalities (problems in linear programming is not included).

Solve simultaneous linear equations with two unknowns.

Solve quadratic equations using factorization.

Draw, interpret and use straight line graphs.

Identify and draw the graphs of quadratic functions of the form “y=ax2+bx+c”.

Use the rules of indices for rational values.

Display information in the form of a matrix of any order and calculate the sum and

differences of matrices and product of a matrix and a whole number.

35

HANDLING DATA

Construct and interpret frequency diagrams choosing suitable class intervals covering

the range for a continuous variable.

Construct and interpret histograms with understanding of the connection between area

and frequency.

Understand and use the vocabulary of probability.

Understand and use the probability scale from 0 to 1.

Draw tree diagrams or use a tabulation to define all the possible outcomes of 3 events

where each event has 2 outcomes.

Find the mean, median, mode and range of frequent distribution of given sets of data

and interpret results.

TEACHING AND LEARNING STRATEGIES

This Mathematics curriculum calls for balance in using a variety of teaching methods which

take into consideration that students like action, talking in groups, making things, being

creative, doing things and playing. Many teachers develop one or two teaching methods and

stick to them. This is a mistake. A variety of methods as well as increasing student attention

and interest gives you flexibility to deal with the problems teachers inevitably encounter. It

also helps you deal with the increasing demands of the ever changing teacher’s role.

Paragraph 243 of the Cockroft report states that:

Mathematics teaching at all levels should include opportunities for-

Exposition by teacher.

Discussion between teacher and pupils and between pupils themselves.

Appropriate practical work.

Consolidation and practice of fundamental skills and routines.

Problem solving including the application of mathematics to everyday situations.

Investigational work.

The teaching methods being advocated will need to incorporate the project, laboratory

heuristic, generic, drill, question-answer, directed study, developmental and lecture. The

latter to be used sparingly at S4/S5 level. These calls for the teacher to select from and

combine teacher talk, explanation, demonstration, supervised student practice, questioning,

discussion, group work and student talk, games, simulations, role play: active learning

methods, seminars by students, projects, assignments and essays. This will include research

work through enrichment activities. The emphasis will be on learning for remembering

through free plays, structured activities and guided discovery methods so as to promote

creativity, the ability to design and a thirst for invention. Hence, the teacher will encourage

pupils to learn from experience through classroom activities, private study and homework.

36

ASSESSMENT AND EVALUATION

Teachers are expected to build up a close-working and successful relationship with students.

The former to function in such a learning environment, they need to take into consideration

the following basic tenets which have guided the development of this curriculum:

Teachers need to know where the child is academically and attitudinally.

Children need to be provided with opportunities to experience success.

Children need the opportunity to strive for an objective in a variety of ways.

Children need “real world” situations in which to operate, devoid of abstraction symbolism

their operant facilities.

Teachers need to be sensitive to the variances in children’s learning modes.

The teacher is a facilitator rather than a director.

Mathematics should be a pleasant and interesting experience for both students and teachers.

This calls for different assessment instruments to be used. These fall into three main

categories which are: Performance and Experience Tests; Written Tests; Objective-based

Tests.

Hence, the teacher will be called upon to employ a variety of methods of analysis and

recording the class room. Such a call requires the teacher to plan carefully;

a) How he/she is going to diagnose the child’s needs.

b) How he/she intends to assess the child’s progress.

c) How he/she is going to record the child’s progress.

It is expected that students will be pre and post-tested so that the teacher will have a better

picture of how the pupil is learning and whether to progress to a new topic or re-teach

him/her whatever concepts he/she has not mastered yet. In the past, too much attention had

been placed on summative assessment at the expense of formative assessment. This

curriculum allowed more diagnostic assessment tools to be used. Although the teacher is

expected to give attention to the affective, psychomotor and cognitive aspects of the student’s

learning development, the understanding that is focused upon is one based mainly on the

knowledge level and intellectual level of cognition. Students should be tested as to whether

they can make connections as per the components of the interaction rhombus illustrated

below.

Mathematical Language

Pictures Symbols

Concrete Situations (Actual or Described)

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