Mathematics - Curriculum Development

National Curriculum Statement
Grades 10 – 12 (General)
Subject Information
Mathematics
June 2004
Western Cape
E d u c a t i o n
Department
Directorate
Curriculum
Development
http://curriculum.wcape.school.za

Wes-Kaap Ondewysdepartement
Western Cape Education Department
ISebe leMfundo leNtshona Koloni
Subject Information
Mathematics
Table of Contents
FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
THE NATIONAL CURRICULUM STATEMENT (NCS) . . . . . . . . . . . . . . . . . . . . . . . 1
LEARNING FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
RULES OF COMBINATION FOR FETC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
SUBJECT OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
WHAT IS MATHEMATICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
PURPOSE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
EDUCATIONAL AND CAREER LINKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
LEARNING OUTCOMES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
ASSESSMENT STANDARDS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
CONTENT AND CONTEXTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
ICT LINKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Foreword
The National Curriculum Statement Grades 10 – 12 (General) represents a policy statement for learning
and teaching in schools in the Further Education and Training Band. It aims to provide a transformational
curriculum that focuses on high knowledge and skills.
This guideline provides a quick overview of the National Curriculum Statement.
It offers cross-referencing to the Further Education and Training Policy For Grades 10 – 12 (General) Overview
and the Qualifications and Assessment Policy Framework Grades 10 – 12 (General) (see Overview and subject
statement links with FET NCS policy, on page 4 of this guide)
Teachers should use this guideline as a tool to navigate the subject policy statement.The various sections
in the subject policy statement are cross-referenced by providing the relevant page numbers from the
related policy document(s).
The infusion of ICT into the implementation of the NCS is focussed at both teacher development and
classroom practice.These guidelines therefore provide a brief overview of this exciting medium in terms
of curriculum delivery, including teaching, learning and assessment.
To conclude it must be noted that this subject statement guide serves as a first step in the preparation of
teachers for the implementation the NCS in their own classrooms.Teachers are encouraged to study this
guide as well as the Subject Policy Statement in preparation for the training events of 2005.
THE NATIONAL CURRICULUM STATEMENT (NCS)
The NCS Grades 10 – 12 (General) consist of three policy documents, which should be read
together.These documents are:
1. Overview
This document provides an overall introduction to the NCS. It describes the philosophical underpinnings
of the curriculum and explains the reasons for change. It also summarises the main issues related to
inclusive education and assessment.
2. Qualification and Assessment Policy Framework
This document aims to provide a mechanism through which you assess the attainment of the learning
outcomes. It outlines the requirements and the rules for the award of the Further Education and Training
Certificate (FETC).
3. Subject Statement
The third pillar of the NCS comprises subject statements. Each containing:
• Definition
• Purpose
• Scope
• Education and Career Links
• Learning Outcomes
• Assessment Standards
• Competence Descriptions per grade
• Content and Contexts for attaining the assessment standards
• A generic section on assessment.
It is important that teachers realise that these documents are interrelated and should be read in
conjunction.
National Curriculum Statement 1 Mathematics
Grades 10 – 12 (General)

Learning Fields
Six Learning Fields
(See NCS Overview, page 12)
(See Qualifications & Assessment Policy Framework, page 13 – 14)
• Languages (Fundamental)
• Arts & Culture
• Human and Social Studies and Languages
• Physical, Mathematical, Computer, Life and Agricultural Sciences
• Business, Commerce, Management and Service studies
• Manufacturing, Engineering and Technology
Rules of Combination for FETC
(Refer to Qualifications and Assessment Policy Framework pp 15 – 17)
Fundamental Core Elective
Home Language (20)
(4,5 hours per week)
Home Language /
1st Add Language (20)
(4,5 hours per week)
Mathematics/
Maths Literacy (20)
(5 hours per week)
Life Orientation (10)
(2 hours per week)
2 subjects from
one Field
(2 x 20)
(2 x 4,5 hours per week)
1 subject from the same
or a different Field
(1x 20)
(1 x 4,5 hours per week)
70 credits 40 credits 20 credits
SUBJECT OVERVIEW
WHAT IS MATHEMATICS
See Subject Statement, page 9
We will not define mathematics but describe what informs our view of the subject. It is a human activity
practised by all cultures. Knowledge in the subject is constructed as a result of observing patterns and
formulating theories using rigorous logical thinking.This is done through the establishment of descriptive,
numerical and symbolic relationships. Mathematics is developed and contested over time through both
language and symbols and by social interaction and is thus open to change.
Purpose
See Subject Statement page 9
Mathematics enables creative and logical reasoning about problems in the physical and social world as
well as in the context of the subject itself. Mathematical problem solving enables us to understand the
world and make use of that understanding in our daily lives. It also provides access to further study in
various fields such as the sciences and engineering as well as a variety of career paths.
Mathematics 2 National Curriculum Statement
Grades 10 – 12 (General)

Scope
See Subject Statement page 10
Learners exiting the FET band will develop competence in the use of mathematical process skills in the
context of Numbers and Algebra, Geometry (including the techniques of trigonometry and co-ordinate
and transformational geometry), and Measurement, Data Handling and Probability.This includes:
• Critically investigate and monitor the financial aspects of personal and community life
• Produce useful equivalents for algebraic expressions and mathematical models
• Describe, represent and analyse shape and space in two and three dimensions
• Collect and use data to establish statistical and probability models
• Use and understand the principles of differential calculus and solve simple optimisation problems
• Investigate the historical aspects of the development o and use of Mathematics in various cultures
• Use available technology in calculations and in the development of mathematical models
Educational and Career Links
See Subject Statement page 11
Mathematics is vital for any learner who wishes to pursue a career in the Physical, mathematical,
Computer, life, earth, Space and environmental sciences. Mathematics also supports careers in the
economic, management and social sciences. Mathematics in the FET band will provide a basis for further
Mathematical studies at tertiary institutions. Mathematical habits of mind is also an essential component
for success in the workplace
NOTE: If a learner does not perceive mathematics to be essential for their chooses career path or
further study he/she may choose Mathematical Literacy.
Learning Outcomes
See Subject Statement page 12 – 14
LO 1: Number and Number Relationships
When solving problems the learner is able to recognise, describe, represent and work confidently with
numbers and their relationships to estimate, calculate and check solutions.
LO 2: Functions and Algebra
The learner is able to investigate, analyse, describe and represent a wide range of functions and solve
related problems.
LO 3: Space, Shape and Measurement
The learner is able to describe, represent, analyse and explain properties of shapes in 2-dimensional and
3-dimensional space with justification.
LO 4: Data Handling and Probability
The learner is able to collect, organise, analyse and interpret data to establish statistical and probability
models and to solve related problems.
Assessment Standards
See Subject Statement page 16 – 38
Assessment standards are written per grade for each learning outcome, thus indicating conceptual
progression from grade to grade.They embody knowledge, skills and values required to achieve the LOs.
In this sense they provide criteria of what the learners should know and demonstrate at a specific grade.
National Curriculum Statement 3 Mathematics
Grades 10 – 12 (General)

CONTENT AND CONTEXTS
See Subject Statement, page 44 – 62
Summary of content for Mathematics
GRADE 10 GRADE 11 GRADE 12
LO 1 • Recurring and terminating decimals
• Laws of exponents (integral exp.)
• Rational approximation of surds
• Number patterns (linear)
• Simple and compound growth
• Foreign exchange rates
LO 2 • Study of different functions
• Conversion between numerical,
graphical, verbal and symbolic
representations
• Investigating the effect of different
parameters
• Sketchgraphs using properties of
functions
• Algebraic manipulations
• Solution of equations and
inequalities
• Average rate of change
LO 3 • Effect on volume and surface area
when changing linear dimensions
• Investigation of polygons
• Co-ordinate geometry (points)
• Transformation Geometry
• Trigonometry
• Historical development of geometry
and trigonometry (research)
LO 4 • Data Handling (calculations):
• Measures of central tendency
• Measures of dispersion
• Errors in measurement
• Data Handling(Representations):
• Bar and compound bar graphs
• Histograms and frequency polygons
• Pie charts
• Line and broken-line graphs
• Probability:
• Definition
• Relative frequency
• Venn diagrams
• Mutually exclusive events
• Complementary events
• Potential uses and misuses of
statistics and charts
• Recognition of non-real numbers
• Laws of exponents (rational exp.)
• Operations with simple surds
• Error margins
• Number patterns (quadratic)
• Simple and compound decay
• Different periods of compounding
growth and decay
• Study of different functions
• Conversion between numerical,
graphical, verbal and symbolic
representations
• Investigating the effect of different
parameters
• Sketchgraphs using properties of
functions Algebraic manipulations
• Solution of equations and
inequalities
• Average rate of change
• Linear Programming
• Formulae for the surface area of
prisms, cones and spheres and
combinations of these shapes
• Euclidean geometry (triangles)
• Co-ordinate geometry (str. Lines)
• Transformation Geometry
• Trigonometry
• Historical development of geometry
and trigonometry
• Calculations and representations of
data:
• Measures of central tendency and
dispersion of univariate data
• five number summary
• box and whisker diagrams
• ogives
• variance and standard deviation
• Scatter plots of bivariate data and
intuitive choice of function of best fit
• Symmetric and skewed data
• Probability:
• dependent and independent
events
• two-way contingency tables
• product rule for independent
events
• Venn diagrams and other
techniques to solve probability
problems
• Logarithms
• Calculation of n in compound growth
and decay formulae
• Number patterns including APs and
GPs
• Sigma notation
• Proof and applications of formulae for
summating different series
• Recursive formulae
• Annuities, bond repayments and
sinking funds
• Loan options
• Study of different functions and
inverses of functions
• Sketchgraphs of inverses of functions
• Factorising 3rd degree polynomials
including the use of the factor
theorem
• Differential calculus
• Linear programming
• Euclidean Geometry (circles)
• Co-ordinate geometry (circles)
• Transformation Geometry
• Trigonometry
• Research: historical development and
one or more of: spherical geometry,
taxi cab geometry, fractals
• Content from previous grades as used
in statistical investigations
• Sampling
• Intuitive understanding of linear
regression (least squares method)
• Regression functions and correlation
for bivariate data
• Identification of normal distributions
of data
• Probability problems using the
fundamental counting principle
Note:
Content must serve the LOs and not and end in itself. Contexts are central to the development of
Mathematical Literacy in learners.Awareness of and use of local contexts will enable the content to be
embedded in situations that are meaningful to the learner.
Mathematics 4 National Curriculum Statement
Grades 10 – 12 (General)

ICT LINKS
Information and Communication Technologies supporting the National Curriculum
Statement through e-Learning
The national Department of Education has indicated that ICT will support the introduction of the NCS
by distributing official documentation, delivering OBE orientation for educators, introducing new subject
content to teachers, assisting in the development of learning programmes, delivering exemplar material
for NCS subjects, giving access to learning and teaching support materials, and providing opportunities
for educators to communicate and share experiences and expertise.The national education portal,
Thutong, is dedicated to electronic teaching and learning support: (http://www.thutong.org).
The Western Cape
In the Western Cape, the provincial education portal (WCED Online) is at http://wced.wcape.gov.za.This
will contains a great deal of information about the WCED and its services to schools.The Curriculum
website can be accessed from WCED Online, or directly at http://curriculum.wcape.school.za. Schools in
the Khanya Project will have visited http://www.khanya.co.za.All these websites and others provide
information and resources for schools, and will be extended in due course.
Computers in schools
Many high schools in the Western Cape already have computers for the use of their teachers and
learners.Those without computers will be assisted to acquire them over the next few years.Access to
computers means that teachers and learners can obtain access to world class resources. Learners are
able to do research, calculate, write, save and organize their assignments logically. School Management
Teams will be responsible for planning and organizing school timetables so that teachers, classes and
learners have equitable access to available ICT resources.Teachers will be provided with opportunities to
acquire the skills necessary for integrating ICT into their planning and teaching.
ICT and the FET Subjects
The NSC documents clearly specify the use of computers for some of the FET subjects, and advocate
their use in many others. Each school will take this into account when planning the learning fields and
subjects it offers. In planning their lessons, teachers will select the medium for each specific learning
activity which will best achieve the learning outcomes required. In this way teachers and learners will
engage with a variety of media.
The culminating benefit to learners who learn through the use of computers will be the development of
a mindset for the twenty-first century. E-Learning encourages them to become citizens with the logic,
creative thinking and problem solving skills to contribute meaningfully to South African and global society.
National Curriculum Statement 5 Mathematics
Grades 10 – 12 (General)

REFERENCES
1. Legislation: Government Gazette 25545, Notice 1407 of 6 October 2003
2. Software: MS Word Applications e.g. Draw, Equations Editor; Spreadsheets e.g. Excel.
Customised software: Dynamic geometry e.g. Geometer's Sketchpad, Graphing software, e.g.
Autograph, Statistical software
3. Web Sites: See links on the WCED Curriculum, FET Mathematics page:
http://curriculum.wcape.school.za
4. Other resources:
• EDULIS: 15 Kruskal Avenue, Bellville.Tel. 021 – 957 9600
Textbooks and Reference books and Subject journals: Many titles available from EDULIS for
new content, Current textbooks used in schools for content that remained unchanged.
• DataBase may be searched at http://edupals.wcape.gov.za
Mathematics 6 National Curriculum Statement
Grades 10 – 12 (General)