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





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



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