Grade 8

Meet the natural numbers, whole numbers, integers and rational numbers as nested sets, discover irrational numbers for the first time, and practise classifying given numbers into the correct set or sets.

Establish and apply the five laws of exponents, write large numbers in scientific notation, and calculate squares, cubes, square roots and cube roots of integers and rational numbers.

Multiply and divide integers using sign rules, apply commutative, associative and distributive properties, identify additive and multiplicative inverses, and calculate with squares, cubes and roots of integers.

Divide whole numbers and fractions by common fractions using the reciprocal method, calculate squares, cubes, square roots and cube roots of common fractions, and solve grouping and sharing problems with mixed numbers.

Multiply and divide decimal fractions by other decimal fractions, calculate squares, cubes, square roots and cube roots of decimal fractions, and solve real-world problems involving decimal operations.

Find original amounts after percentage increases and decreases by working backwards, calculate new amounts from given percentage changes, and solve multi-step real-life problems involving successive percentage changes.

Investigate and extend numeric and geometric patterns, find and test general rules using algebraic notation, and justify rules for both linear and quadratic sequences.

Determine input and output values using equations, interpret equivalent forms of a relationship expressed verbally, in tables and as equations, and generate tables of ordered pairs using substitution.

Learn conventions for writing expressions, classify like and unlike terms, identify coefficients and exponents, add, subtract, multiply and divide expressions, and evaluate expressions by substitution.

Set up and solve equations by inspection, use additive and multiplicative inverses to solve equations, apply laws of exponents, and use substitution to generate tables of ordered pairs.

Interpret and draw global graphs of problem situations, plot points on the Cartesian plane, and sketch graphs from real-life descriptions identifying increasing, decreasing, constant, maximum and minimum features.

Write formal definitions of triangles and quadrilaterals, identify congruent and similar shapes, and solve geometric problems using known properties of sides and angles.

Explore the 5 Platonic solids and their properties, build 3D models from nets including pyramids, and compare and classify 3D objects using faces, vertices and edges, verifying Euler's formula.

Revise angle relationships formed by intersecting and perpendicular lines, explore corresponding, alternate and co-interior angles with parallel lines cut by a transversal, and solve multi-step geometric problems using angle relationships.

Reflect and translate points and triangles on a coordinate plane, rotate shapes around the origin using coordinate rules, and use proportion to describe the effect of enlargements and reductions on perimeter and area.

Use a compass, ruler and protractor to bisect line segments and angles, construct perpendicular lines, build triangles and quadrilaterals, construct angles of 30°, 45° and 60° without a protractor, and bisect the angles of a triangle to find the incentre.

Calculate the circumference and area of circles using π ≈ 3.14, decompose complex polygons into rectangles and triangles to find their areas, solve real-life perimeter and area problems to at least 2 decimal places, and convert between SI area units (mm², cm², m², km²).

Find the volume and surface area of triangular prisms, solve real-life capacity and volume problems with SI unit conversions (mm³↔cm³↔m³, ml↔l↔kl), and explore how surface area and volume change at different rates when dimensions are scaled.

Investigate the relationship between the sides of a right-angled triangle, apply the theorem to find unknown sides, determine whether a triangle is right-angled, and solve real-life problems involving missing lengths and surd form answers.

Organise data using tally marks, tables and stem-and-leaf displays, calculate range and identify extremes, draw and interpret histograms and broken-line graphs, and critically analyse data for bias, misleading scales and valid conclusions.

List all possible outcomes, calculate probability using favourable outcomes divided by total outcomes, predict and compare relative frequency with theoretical probability, and solve multi-step probability problems in context.