Selects from, and flexibly applies, a wide range of highly developed mathematical and
problem solving strategies and techniques in a broad range of contexts

SUPPORT

CONTEXT

TEXT COMPLEXITY

TASK COMPLEXITY

Autonomous learner who
accesses and evaluates
support from a broad range of
sources

Broad range of contexts

Adaptability within and across
contexts

Specialisation in one or more
contexts

Highly complex texts
Highly embedded information

Includes highly specialised
language and symbolism

Sophisticated task
conceptualisation,
organisation and analysis

Processes include synthesising,
critically reflecting, evaluating,
recommending

FOCUS AREA:

PERFORMANCE FEATURES INCLUDE:

Problem solving processes
including estimating and
reflecting

– Uses prior mathematical knowledge and experience, diagrammatic, symbolic and other
mathematical processes to:

organise and represent the mathematical information in an alternative, useful form as an aid
to problem solving, e.g. as a table, summary, algebraic representation or graph

select appropriate methods of solution from an expanded range of processes

use developed estimating and assessment skills to check the outcomes and decide on the

appropriate degree of accuracy required

critically review the mathematics used and the outcomes obtained to reflect on and question
the outcomes and real-world implications

Mathematical methods and
use of tools

– Uses a range of mathematical processes flexibly and interchangeably selecting from formal
pen and paper and mental and technologically assisted processes and tools, such as scientific,
graphics or CAS calculators for calculations, including using trigonometrical, statistical or
algebraic functions

– Selects and flexibly uses a range of specialised tools, hand-held devices, computers and
technological processes, e.g. uses a CAS calculator to solve a pair of simultaneous linear
equations

Mathematical knowledge
and skills: number and
algebra

– Calculates with rational and relevant irrational numbers

– Uses and solves a range of equations using a variety of algebraic techniques

– Applies graphical techniques to analyse and solve algebraic relationships and equations,
including the connections between formulae, their graphical representations and the situations
they represent, e.g. linear, quadratic, exponential or inverse relationships

Mathematical knowledge
and skills: measurement
and geometry

– Uses and applies knowledge about space and shape, including angle properties, symmetry
and similarity to describe, draw or construct accurate 2D and 3D shapes and scale plans and
drawings

– Estimates, accurately measures and calculates quantities, including for complex areas and
volumes using measurement formulae

– Converts between a range of metric and non-metric units

Mathematical knowledge
and skills: statistics and
probability

– Collects, organises and analyses data, including grouped data, using measures of central
tendency, percentiles and measures of spread, and interprets and draws conclusions about
trends and data reliability

– Uses and applies knowledge about probability to a range of relevant contexts (e.g. sporting
events), calculates theoretical probabilities and uses tree diagrams to investigate the probability
of outcomes in simple multiple event trials