Selects from, and applies, an expanding range of mathematical and problem solving
strategies in a range of contexts

SUPPORT

CONTEXT

TEXT COMPLEXITY

TASK COMPLEXITY

Works independently and
initiates and uses support
from a range of established
resources

Range of contexts, including
some that are unfamiliar and/
or unpredictable

Some specialisation in less
familiar/known contexts

Complex texts
Embedded information
Includes specialised vocabulary

Includes abstraction and
symbolism

Complex task organisation
and analysis involving
application of a number of
steps

Processes include extracting,
extrapolating, inferencing,
reflecting, abstracting

FOCUS AREA:

PERFORMANCE FEATURES INCLUDE:

Problem solving processes
including estimating and
reflecting

- Draws on prior mathematical knowledge and experience, diagrammatic, symbolic and other
mathematical processes to:

represent the mathematical information in a form that is personally useful as an aid to
problem solving, e.g. table, summary or sketch

select appropriate strategies from an expanding range of mathematical processes

use estimation and other assessment skills to check the outcomes and decide on the
appropriate accuracy for the outcome

reflect on and evaluate the mathematics used and the outcomes obtained relative to
personal, contextual and real-world implications

Mathematical methods and
use of tools

– Flexibly uses both ‘in-the-head’ methods and formal pen and paper methods to calculate
and uses technological processes and tools, including a range of calculator or spreadsheet
functions, e.g. memory function on a calculator, formulae in a spreadsheet or software to
undertake a problem solving process

– Selects and flexibly uses a range of tools, hand-held devices, computers and technological
processes, e.g. enters a set of statistical data into a spreadsheet and uses it to calculate the
mean and to plot an appropriate graph

Mathematical knowledge
and skills: number and
algebra

– Uses and applies relevant ratio, rates and proportions, e.g. scales on maps and plans, in the
mixing of chemicals or ingredients, or calculating magnification factors

– Calculates with fractions, decimals and percentages and flexibly uses equivalent forms;
calculates with relevant positive and negative numbers; and uses numbers expressed as roots
and powers, e.g. 23 = 8, √4 = 2 or 3.6 x 103 = 3,600

– Develops, interprets and uses routine formulae and algebraic representations and conventions
that describe relationships between variables in relevant contexts, e.g. in sport, when
considering the cost of repairs, in calculating routine area and volume, using Pythagoras’s
theorem or in using workplace formulae

Mathematical knowledge
and skills: measurement
and geometry

– Uses knowledge about space and shape, including angle properties, symmetry and similarity to
describe, draw or construct relevant common 2D and 3D shapes, such as compound shapes

– Estimates, accurately measures and calculates quantities, including areas and volumes, using
relevant routine formulae

– Converts within the metric system and between metric and other relevant non-metric units

– Uses, calculates and interprets information based on maps and plans, including scales,
bearings, travel distances, speeds and times, and time zones

Mathematical knowledge
and skills: statistics and
probability

– Collects, represents, summarises and interprets a range of statistical data appropriately, e.g. in
tables, spreadsheets, graphs, plots, measures of central tendency (mean, median, mode) and
simple measures of spread

– Uses knowledge about chance and probability to estimate and interpret the outcomes of
common chance events in both numerical and qualitative terms