# 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:

- recognise the properties of prime, composite, square and triangular numbers;
- describe the use of integers in everyday contexts;
- solve problems involving all four operations with whole numbers;
- connect fractions, decimals and percentages as different representations of the same number;
- solve problems involving the addition and subtraction of related fractions;
- make connections between the powers of 10 and the multiplication and division of decimals;
- describe rules used in sequences involving whole numbers, fractions and decimals;
- connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation;
- make connections between capacity and volume;
- solve problems involving length and area. They interpret timetables;
- describe combinations of transformations;
- solve problems using the properties of angles;
- compare observed and expected frequencies;
- interpret and compare a variety of data displays including those displays for two categorical variables;
- evaluate secondary data displayed in the media;
- locate fractions and integers on a number line;
- calculate a simple fraction of a quantity;
- add, subtract and multiply decimals and divide decimals where the result is rational;
- calculate common percentage discounts on sale items;
- write correct number sentences using brackets and order of operations;
- locate an ordered pair in any one of the four quadrants on the Cartesian plane;
- construct simple prisms and pyramids;
- list and communicate probabilities using simple fractions, decimals and percentages.