# Mathematics proficiencies

## Fluency

### Portfolio summary

In F–2, students become fluent as they develop skills in choosing appropriate procedures; and recalling factual knowledge and concepts readily.

In Years 3–6, students become fluent as they develop skills in choosing appropriate procedures; carrying out procedures flexibly and accurately; and recalling factual knowledge and concepts readily. Students are fluent when they calculate answers efficiently, when they recognise robust ways of answering questions, and when they recall definitions and regularly use facts.

In Years 7–8, students develop skills in choosing appropriate procedures; carrying out procedures flexibly, accurately, efficiently and appropriately; and recalling factual knowledge and concepts readily. Students are fluent when they calculate answers efficiently, when they recognise robust ways of answering questions, when they choose appropriate methods and approximations, and when they recall definitions and regularly use facts.

In Years 9–10, students develop skills in choosing appropriate procedures; carrying out procedures flexibly, accurately, efficiently and appropriately; and recalling factual knowledge and concepts readily. Students are fluent when they calculate answers efficiently, when they recognise robust ways of answering questions, when they choose appropriate methods and approximations, when they recall definitions and regularly use facts, and when they can manipulate expressions and equations to find solutions.

### View the proficiencies across F–10

Foundation includes readily counting numbers in sequences, continuing patterns and comparing the lengths of objects.

Year 1 includes readily counting number in sequences forwards and backwards, locating numbers on a line and naming the days of the week.

Year 2 includes readily counting numbers in sequences, using informal units iteratively to compare measurements, using the language of chance to describe outcomes of familiar chance events and describing and comparing time durations.

Year 3 includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and communicating positions.

Year 4 includes recalling multiplication tables, communicating sequences of simple fractions, using instruments to measure accurately, creating patterns with shapes and their transformations and collecting and recording data.

Year 5 includes choosing appropriate units of measurement for calculation of perimeter and area, using estimation to check the reasonableness of answers to calculations and using instruments to measure angles.

Year 6 includes representing integers on a number line; calculating simple percentages; using brackets appropriately; converting between fractions and decimals; using operations with fractions, decimals and percentages; measuring using metric units; and interpreting timetables.

Year 7 includes calculating accurately with integers, representing fractions and decimals in various ways, investigating best buys, finding measures of central tendency and calculating areas of shapes and volumes of prisms.

Year 8 includes calculating accurately with simple decimals, indices and integers; recognising equivalence of common decimals and fractions including recurring decimals; factorising and simplifying basic algebraic expressions; and evaluating perimeters and areas of common shapes and volumes of three-dimensional objects.

Year 9 includes applying the index laws to expressions with integer indices, expressing numbers in scientific notation, listing outcomes for experiments, developing familiarity with calculations involving the Cartesian plane and calculating areas of shapes and surface areas of prisms.

Year 10 includes factorising and expanding algebraic expressions, using a range of strategies to solve equations and using calculations to investigate the shape of data sets.