Revised National Curriculum Statement Grades R-9 (Schools) - Grade Nine

Learning Area: Mathematics

Learning Outcome 1:  Numbers, Operations and Relationships

The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment standards

We know this when the learner:

• Describes and illustrates the historical development of number systems in a variety of historical and cultural contexts (including local).
• Recognises, uses and represents rational numbers (including very small numbers written in scientific notation), moving flexibly between equivalent forms in appropriate contexts.
• Solves problems in context including contexts that may be used to build awareness of other Learning Areas, as well as human rights, social, economic and environmental issues such as:
  • financial (including profit and loss, budgets, accounts, loans, simple and compound interest, hire purchase, exchange rates, commission, rentals and banking);
  • measurements in Natural Sciences and Technology contexts.
• Solves problems that involve ratio, rate and proportion (direct and indirect).
• Estimates and calculates by selecting and using operations appropriate to solving problems and judging the reasonableness of results (including measurement problems that involve rational approximations of irrational numbers).
• Uses a range of techniques and tools (including technology) to perform calculations efficiently and to the required degree of accuracy, including the following laws and meanings of exponents (the expectation being that learners should be able to use these laws and meanings in calculations only):
  • xⁿ x x^m = x^{n + m}
  • xⁿ ÷ x^m = x^{n - m}
  • x⁰ = 1

           1

• x ^{- n} =  —
            x ⁿ

• Recognises, describes and uses the properties of rational numbers.

Learning Outcome 2:  Patterns, Functions and Algebra

The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment standards

We know this when the learner:

• Investigates, in different ways, a variety of numeric and geometric patterns and relationships by representing and generalising them, and by explaining and justifying the rules that generate them (including patterns found in natural and cultural forms and patterns of the learner’s own creation).
• Represents and uses relationships between variables in order to determine input and/or output values in a variety of ways using:
  • verbal descriptions;
  • flow diagrams;
  • tables;
  • formulae and equations.
• Constructs mathematical models that represent, describe and provide solutions to problem situations, showing responsibility toward the environment and the health of others (including problems within human rights, social, economic, cultural and environmental contexts).
• Solves equations by inspection, trial-and-improvement or algebraic processes (additive and multiplicative inverses, and factorisation), checking the solution by substitution.
• Draws graphs on the Cartesian plane for given equations (in two variables), or determines equations or formulae from given graphs using tables where necessary.
• Determines, analyses and interprets the equivalence of different descriptions of the same relationship or rule presented:
  • verbally;
  • in flow diagrams;
  • in tables;
  • by equations or expressions;
  • by graphs on the Cartesian plane

in order to select the most useful representation for a given situation.

• Uses the distributive law and manipulative skills developed in Grade 8 to:
  • find the product of two binomials;
  • factorise algebraic expressions (limited to common factors and difference of squares).
• Uses the laws of exponents to simplify expressions and solve equations.
• Uses factorisation to simplify algebraic expressions and solve equations.

Learning Outcome 3:  Space and Shape (Geometry)

The learner will be able to describe and represent characteristics and relationships between two-dimensional shapes and three-dimensional objects in a variety of orientations and positions.

Assessment standards

We know this when the learner:

• Recognises, visualises and names geometric figures and solids in natural and cultural forms and geometric settings, including:
  • regular and irregular polygons and polyhedra;
  • spheres;
  • cylinders.
• In contexts that include those that may be used to build awareness of social, cultural and environmental issues, describes the interrelationships of the properties of geometric figures and solids with justification, including:
  • congruence and straight line geometry;
  • transformations.
• Uses geometry of straight lines and triangles to solve problems and to justify relationships in geometric figures.
• Draws and/or constructs geometric figures and makes models of solids in order to investigate and compare their properties and model situations in the environment.
• Uses transformations, congruence and similarity to investigate, describe and justify (alone and/or as a member of a group or team) properties of geometric figures and solids, including tests for similarity and congruence of triangles.
• Recognises and describes geometric solids in terms of perspective, including simple perspective drawing.
• Uses various representational systems to describe position and movement between positions, including:
  • ordered grids;
  • Cartesian plane (4 quadrants);
  • compass directions in degrees;
  • angles of elevation and depression.

Learning Outcome 4:  Measurement

The learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts.

Assessment standards

We know this when the learner:

• Solves ratio and rate problems involving time, distance and speed.
• Solves problems - including problems in contexts that may be used to develop awareness of human rights, social, economic, cultural and environmental issues - involving known geometric figures and solids in a range of measurement contexts by:
  • measuring precisely and selecting measuring instruments appropriate to the problem;
  • estimating and calculating with precision;
  • selecting and using appropriate formulae and measurements.
• Describes and illustrates the development of measuring instruments and conventions in different cultures throughout history.
• Uses the Theorem of Pythagoras to solve problems involving missing lengths in known geometric figures and solids.

Learning Outcome 5:  Data Handling

The learner will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions, and to interpret and determine chance variation.

Assessment standards

We know this when the learner:

• Poses questions relating to human rights, social, economic, environmental and political issues in South Africa.
• Selects, justifies and uses appropriate methods for collecting data (alone and/or as a member of a group or team) which include questionnaires and interviews, experiments, and sources such as books, magazines and the Internet in order to answer questions and thereby draw conclusions and make predictions about the environment.
• Organises numerical data in different ways in order to summarise by determining:
  • measures of central tendency;
  • measures of dispersion.
• Draws a variety of graphs by hand/technology to display and interpret data including:
  • bar graphs and double bar graphs;
  • histograms with given and own intervals;
  • pie charts;
  • line and broken-line graphs;
  • scatter plots.
• Critically reads and interprets data with awareness of sources of error and manipulation to draw conclusions and make predictions about:
  • social, environmental and political issues (e.g. crime, national expenditure, conservation, HIV/AIDS);
  • characteristics of target groups (e.g. age, gender, race, socio-economic groups);
  • attitudes or opinions of people on issues (e.g. smoking, tourism, sport);
  • any other human rights and inclusivity issues.
• Considers situations with equally probable outcomes, and:
  • determines probabilities for compound events using two-way tables and tree diagrams;
  • determines the probabilities for outcomes of events and predicts their relative frequency in simple experiments;
  • discusses the differences between the probability of outcomes and their relative frequency.