Assessment standards

We know this when the learner:

• Describes and illustrates the historical and cultural development of numbers (e.g. irrational numbers).
• Recognises, classifies and represents the following numbers in order to describe and compare them:
  • integers;
  • decimals, fractions and percentages;
  • numbers written in exponential form including squares and cubes of natural numbers and their square and cube roots;
  • large numbers in scientific notation;
  • additive and multiplicative inverses;
  • multiples and factors;
  • irrational numbers in the context of measurement (e.g. and square and cube roots of non-perfect squares and cubes).
• Recognises and uses equivalent forms of the rational numbers listed above.
• 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 interest, hire purchase, exchange rates);
  • measurements in Natural Sciences and Technology contexts.
• Solves problems that involve ratio and rate.
• Estimates and calculates by selecting and using operations appropriate to solving problems that involve:
  • rounding off;
  • multiple operations with rational numbers (including division with fractions and decimals);
  • exponents.
• Uses a range of techniques to perform calculations including:
  • using the commutative, associative and distributive properties with rational numbers;
  • using a calculator.
• Uses a range of strategies to check solutions and judges the reasonableness of solutions.
• Recognises, describes and uses:
  • algorithms for finding equivalent fractions;
  • the commutative, associative and distributive properties with rational numbers (the expectation is that learners should be able to use these properties and not necessarily to know the names of the properties).

Assessment standards

We know this when the learner:

• Investigates and extends numeric and geometric patterns looking for a relationship or rules, including patterns:
  • represented in physical or diagrammatic form;
  • not limited to sequences involving constant difference or ratio;
  • found in natural and cultural contexts;
  • of the learner’s own creation;
  • represented in tables;
  • represented algebraically.
• Describes, explains and justifies observed relationships or rules in own words or in algebra.
• 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), checking the solution by substitution.
• Describes a situation by interpreting a graph of the situation, or draws a graph from a description of a situation, with special focus on trends and features such as:
  • linear or non-linear;
  • increasing or decreasing;
  • maximum/minimum;
  • discrete or continuous.
• 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;
in order to select the most useful representation for a given situation.
• Uses conventions of algebraic notation and the commutative, associative and distributive laws to:
  • classify terms as like or unlike, and to justify the classification;
  • collect like terms;
  • multiply or divide an algebraic expression with one, two or three terms by a monomial;
  • simplify algebraic expressions given in bracket notation, involving one or two sets of brackets and two kinds of operations;
  • compare different representations of algebraic expressions involving one or more operations, selecting those which are equivalent, and justifying own choice;
  • write algebraic expressions, formulae or equations in simpler or more useful equivalent forms in context.
• Interprets and uses the following basic algebraic vocabulary in context: term, expression, coefficient, exponent (or index), base, constant, variable, equation, formula (or rule).

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:
  • those previously dealt with;
  • the platonic solids (tetrahedron, cube, octahedron, dodecahedron, icosahedron).
• In contexts that include those that may be used to build awareness of social, cultural and environ-mental issues, describes and classifies geometric figures and solids in terms of properties, including:
  • sides, angles and diagonals and their interrelationships, with focus on triangles and quadrilaterals (e.g. types of triangles and quadrilaterals).
• Uses vocabulary to describe parallel lines cut by a transversal, perpendicular lines, intersecting lines and triangles in terms of angle relationships (e.g. vertically opposite, corresponding).
• Uses a pair of compasses, ruler and protractor to accurately construct geometric figures for investigation of own property and design of nets.
• Designs and uses nets to make a model of geometric solids studied up to and including this grade.
• Uses transformations (rotations, reflections and translations) and symmetry to investigate (alone and/or as a member of a group or team) properties of geometric figures.
• Uses proportion to describe the effect of enlargement and reduction on properties of geometric figures.
• Draws and interprets sketches of geometric solids from different perspectives with attention to the preservation of properties.
• Locates positions on co-ordinate systems (ordered grids), Cartesian plane (first quadrant) and maps, and describes how to move between positions using:
  • horizontal and vertical change;
  • ordered pairs;
  • compass directions.

Assessment standards

We know this when the learner:

• Solves more complex problems involving time, including relating time, distance and speed.
• Solves problems involving:
  • length;
  • perimeter and area of polygons and circles;
  • volume and surface area of rectangular prisms and cylinders.
• Solves problems using a range of strategies including:
  • estimating;
  • calculating to at least 2 decimal places;
  • using and converting between appropriate S.I. units.
• Describes the meaning of and uses in calculations involving circles and discusses its historical development in measurement.
• Calculates, by selecting and using appropriate formulae:
  • perimeter of polygons and circles;
  • area of triangles, rectangles, circles and polygons by decomposition into triangles and rectangles;
  • volume of triangular and rectangular-based prisms and cylinders.
• Converts between:
  • mm² cm² m² km²
  • mm³ cm³ m³
  • ml (cm³) l kl
• Estimates, compares, measures and draws angles accurate to one degree using protractors.
• Investigates (alone and/or as a member of a group or team) the relationship between the sides of a right-angled triangle to develop the Theorem of Pythagoras.
• Uses the Theorem of Pythagoras to calculate a missing length in a right-angled triangle leaving irrational answers in surd form ().
• Describes and illustrates ways of measuring in different cultures throughout history (e.g. determining right angles using knotted string, leading to the Theorem of Pythagoras).

Assessment standards

We know this when the learner:

• Poses questions relating to human rights, social, economic, environmental and political issues in own environment.
• Selects appropriate sources for the collection of data (including peers, family, newspapers, books, magazines, the Internet).
• Designs and uses questionnaires with a variety of possible responses in order to collect data (alone and/or as a member of a group or team) to answer questions.
• Performs simple experiments using random number generators, coins, spinners, dice and cards in order to collect data.
• Organises (including grouping where appropriate) and records data using tallies, tables and stem-and-leaf displays.
• Summarises grouped and ungrouped numerical data by determining mean, median and mode as measures of central tendency, and distinguishes between them.
• Determines measures of dispersion, including range and extremes.
• 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 presented in a variety of ways in order to draw conclusions and make predictions sensitive to the role of:
  • context (e.g. rural or urban, national or provincial);
  • categories within the data (e.g. age, gender, race);
  • data manipulation (e.g. grouping, scale, choice of summary statistics) for different purposes;
  • the role of outliers on data distribution;
  • any other human rights and inclusivity issues.
• Considers a simple situation (with equally likely outcomes) that can be described using probability and:
  • lists all the possible outcomes;
  • determines the probability of each possible outcome using the definition of probability (see Mathematics Learning Area Glossary);
  • finds the relative frequency of actual outcomes for a series of trials;
  • compares relative frequency with probability and explains possible differences;
  • predicts with reasons the relative frequency of the possible outcomes for a series of trials based on probability.