The proficiency strands **understanding, fluency, problem-solving**
and **reasoning** are an integral part
of mathematics content across the three content strands: number and algebra,
measurement and geometry, and statistics and probability. The proficiencies
reinforce the significance of working mathematically within the content and
describe how the content is explored or developed. They provide the language to
build in the developmental aspects of the learning of mathematics. The
achievement standards reflect the content and encompass the proficiencies.

### Prep Year

At this year level:

·
**understanding**
includes connecting names, numerals and quantities.

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

·
**problem-solving**
includes using materials to model authentic problems, sorting objects, using
familiar counting sequences to solve unfamiliar problems and discussing the
reasonableness of the answer.

·
**reasoning**
includes explaining comparisons of quantities, creating patterns and explaining
processes for indirect comparison of length.

### Year 1

At this year level:

·
**understanding**
includes connecting names, numerals and quantities, and partitioning numbers in
various ways.

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

·
**problem-solving**
includes using materials to model authentic problems, giving and receiving
directions to unfamiliar places, using familiar counting sequences to solve
unfamiliar problems and discussing the reasonableness of the answer.

·
**reasoning**
includes explaining direct and indirect comparisons of length using uniform
informal units, justifying representations of data and explaining patterns that
have been created.

### Year 2

At this year level:

·
**understanding**
includes connecting number calculations with counting sequences, partitioning
and combining numbers flexibly and identifying and describing the relationship
between addition and subtraction and between multiplication and division.

·
**fluency**
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.

·
**problem-solving**
includes formulating problems from authentic situations, making models and
using number sentences that represent problem situations, and matching
transformations with their original shape.

·
**reasoning
**includes using known facts to derive strategies for unfamiliar
calculations, comparing and contrasting related models of operations and
creating and interpreting simple representations of data.

### Year 3

At this year level:

·
**understanding**
includes connecting number representations with number sequences, partitioning
and combining numbers flexibly, representing unit fractions, using appropriate
language to communicate times, and identifying environmental symmetry.

·
**fluency**
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.

·
**problem-solving**
includes formulating and modelling authentic situations involving planning
methods of data collection and representation, making models of
three-dimensional objects and using number properties to continue number
patterns.

·
**reasoning**
includes using generalising from number properties and results of calculations,
comparing angles and creating and interpreting variations in the results of
data collections and data displays.

### Year 4

At this year level:

·
**understanding**
includes making connections between representations of numbers, partitioning
and combining numbers flexibly, extending place value to decimals, using
appropriate language to communicate times and describing properties of
symmetrical shapes.

·
**fluency**
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.

·
**problem-solving**
includes formulating, modelling and recording authentic situations involving
operations, comparing large numbers with each other, comparing time durations
and using properties of numbers to continue patterns.

·
**reasoning
**includes using generalising from number properties and results of
calculations, deriving strategies for unfamiliar multiplication and division
tasks, comparing angles, communicating information using graphical displays and
evaluating the appropriateness of different displays.

### Year 5

At this year level:

·
**understanding**
includes making connections between representations of numbers, using fractions
to represent probabilities, comparing and ordering fractions and decimals and
representing them in various ways, describing transformations and identifying
line and rotational symmetry.

·
**fluency**
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.

·
**problem-solving**
includes formulating and solving authentic problems using whole numbers and
measurements and creating financial plans.

·
**reasoning**
includes investigating strategies to perform calculations efficiently,
continuing patterns involving fractions and decimals, interpreting results of
chance experiments, posing appropriate questions for data investigations and
interpreting data sets.

### Year 6

At this year level:

·
**understanding**
includes describing properties of different sets of numbers, using fractions
and decimals to describe probabilities, representing fractions and decimals in
various ways and describing connections between them, and making reasonable
estimations.

·
**fluency**
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.

·
**problem-solving**
includes formulating and solving authentic problems using fractions, decimals,
percentages and measurements, interpreting secondary data displays and finding
the size of unknown angles.

·
**reasoning**
includes explaining mental strategies for performing calculations, describing
results for continuing number sequences, explaining the transformation of one
shape into another and explaining why the actual results of chance experiments
may differ from expected results.