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;
• recognise, model, represent, order, rearrange and regroup numbers beyond 1 million;
• write correct number sentences using brackets and order of operations;
• select and apply efficient mental and written strategies to solve addition and subtraction problems;
• 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;
• solve practical problems using knowledge of volume length, perimeter, area, volume and capacity using appropriate formal units of measurement;
• interpret a variety of everyday timetables for a specific purpose;
• add, subtract, multiply and divide decimals where the results are terminating decimals;
• calculate common percentage discounts on sale items;
• draw and construct simple prisms and pyramids;
• locate an ordered pair in any one of the four quadrants on the Cartesian plane;
• describe combinations of transformations;
• solve problems using the properties of angles;
• construct, interpret and compare a variety of data displays including those displays for two categorical variables;
• identify potentially misleading data representations;
• analyse and evaluate data from secondary sources, including digital media and elsewhere;
• specify, list and communicate probabilities using simple fractions, decimals and percentages;
• compare observed and expected frequencies of events, with expected frequencies;
• conduct repeated trials of chance experiments, identifying the variation between trials.