# Mathematics

## Proficiencies

**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, explaining why the actual results of chance experiments may differ from expected results.

## Achievement Standard

By the end of the year students are expected to:

**Number and Algebra**

- recognise the properties of prime, composite, square and triangular numbers and determine sets of these numbers;
- solve problems that involve all four operations with whole numbers and describe the use of integers in everyday contexts;
- locate fractions and integers on a number line and connect fractions, decimals and percentages as different representations of the same number;
- solve problems involving the addition and subtraction of related fractions. Students calculate a simple fraction of a quantity and calculate common percentage discounts on sale items, with and without the use of digital technology;
- make connections between the powers of 10 and the multiplication and division of decimals;
- add, subtract and multiply decimals and divide decimals where the result is rational;
- write number sentences using brackets and order of operations, and specify rules used to generate sequences involving whole numbers, fractions and decimals;
- use ordered pairs of integers to represent coordinates of points and locate a point in any one of the four quadrants on the Cartesian plane.

**Measurement and Geometry**

- relate decimals to the metric system and choose appropriate units of measurement to perform a calculation;
- solve problems involving length and area, and make connections between capacity and volume;
- interpret a variety of everyday timetables;
- solve problems using the properties of angles and investigate simple combinations of transformations in the plane, with and without the use of digital technology;
- construct simple prisms and pyramids.

**Statistics and Probability**

- interpret and compare a variety of data displays, including displays for two categorical variables;
- analyse and evaluate data from secondary sources;
- compare observed and expected frequencies of events, including those where outcomes of trials are generated with the use of digital technology;
- specify, list and communicate probabilities of events using simple ratios, fractions, decimals and percentages.