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 NUMERACY LEVEL 5 5.10 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