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Below we list the academic material covered according to the CAPS system.

Number, Operations and Relations
  • Progression in Numbers, Operations and Relationships in the Senior Phase is achieved primarily by:
    • development of calculations using whole numbers to calculations using rational numbers, integers and numbers in exponential form
    • development of understanding of different number systems from natural and whole numbers to integers and rational numbers, as well as the recognition of irrational numbers
    • increasing use of properties of numbers to perform calculations
    • increasing complexity of contexts for solving problems
  • Numbers, Operations and Relationships in the Senior Phase consolidates work done in the Intermediate Phase and is geared towards making learners competent and efficient in performing calculations particularly with integers and rational numbers.
  • Recognising and using the properties of operations for different numbers provides a critical foundation for work in algebra when learners work with variables in place of numbers and manipulate algebraic expressions and solve algebraic equations.
Patterns, Functions and Algebra
  • Progression in Patterns, Functions and Algebra is achieved primarily by
    • increasing the range and complexity of:
      • relationships between numbers in given patterns
      • rules, formulae and equations for which input and output values can be found
      • equations that can be solved
    • developing more sophisticated skills and techniques for:
      • solving equations
      • expanding and simplifying algebraic expressions
      • drawing and interpreting graphs
    • developing the use of algebraic language and conventions.
  • In Patterns, Functions and Algebra, learners’ conceptual development progresses from:
    • an understanding of number to an understanding of variables, where the variables are numbers of a given type (e.g. natural numbers, integers, rational numbers) in generalized form
    • the recognition of patterns and relationships to the recognition of functions, where functions have unique outputs values for specified input values
    • a view of Mathematics as memorized facts and separate topics to seeing Mathematics as interrelated concepts and ideas represented in a variety of equivalent forms (e.g. a number pattern, an equation and a graph representing the same relationship)
  • While techniques for solving equations are developed in Patterns, Functions and Algebra, learners also practise solving equations in Measurement and Space and Shape, when they apply known formulae to solve problems.

Space and Shape (Geometry)
  • Progression in geometry in the Senior Phase is achieved primarily by:
    • investigating new properties of shapes and objects
    • developing from informal descriptions of geometric figures to more formal definitions and classification of shapes and objects
    • solving more complex geometric problems using known properties of geometric figures
    • developing from inductive reasoning to deductive reasoning.
  • The geometry topics are much more inter-related than in the Intermediate Phase, especially those relating to constructions and geometry of 2D shapes and straight lines, hence care has to be taken regarding sequencing of topics through the terms.
  • In the Senior Phase, transformation geometry develops from general descriptions of movement in space to more specific descriptions of movement in co-ordinate planes. This lays the foundation for analytic geometry in the FET phase.
  • Solving problems in geometry to find unknown angles or lengths provides a useful context to practise solving equations.
  • Progression in Measurement is achieved by the selection of shapes and objects in each grade for which the formulae for finding area, perimeter, surface area and volume become more complex.
  • The use of formulae in this phase provides a useful context to practise solving equations.
  • The introduction of the Theorem of Pythagoras is a way of introducing a formula to calculate the lengths of sides in right-angled triangles. Hence, the Theorem of Pythagoras becomes a useful tool when learners solve geometric problems involving right-angled triangles.
  • Measurement disappears as a separate topic in the FET phase, and becomes part of the study of Geometry and Trigonometry.
Data Handling
  • Progression in Data Handling is achieved primarily by:
    • increasing complexity of data sets and contexts
    • reading, interpreting and drawing new types of data graphs
    • becoming more efficient at organizing and summarizing data
    • becoming more critical and aware of bias and manipulation in representing, analysing and reporting data
  • Learners should work through at least 1 data cycle for the year – this involves collecting and organizing, representing, analysing, summarizing, interpreting and reporting data. The data cycle provides the opportunity for doing projects.
  • All of the above aspects of data handling should also be dealt with as discrete activities in order to consolidate concepts and practise skills. For example, learners need to practise summarizing data presented in different forms, and summaries should be used when reporting data.
  • Data handling contexts should be selected to build awareness of social, economic and environmental issues.
  • Learners should become sensitized to bias in the collection of data, as well as misrepresentation of data through the use of different scales and different measures of central tendency.
  • The following resources provide interesting contexts for data comparison and analysis that can be used in this phase:
    • Census at School – for school based surveys
    • national surveys from Statistics South Africa (StatsSA) – for household and population surveys.
    • international surveys from United Nations (UN Data) – for international social, demographic and environmental surveys. Many other websites may be consulted, especially for health and environmental data.