Mathematics

Proficiencies

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.

Achievement Standard

By the end of the year students are expected to:

• apply place value to partition, rearrange and regroup numbers in the tens of thousands to assist calculation and solve problems;
• choose appropriate mental and written strategies for calculations involving multiplication and division;
• solve practical and worded problems involving multiplication and division;
• convert mixed numbers to improper fractions and vice versa;
• count by quarters, halves and thirds, including with mixed numerals;
• recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two decimal places;
• solve simple purchasing problems;
• identify unknown quantities in number sentences;
• describe number patterns resulting from multiplication;
• recall multiplication facts to 10 x 10 and related division facts;
• use scaled instruments to measure, order and compare temperatures, lengths, perimeter, capacities and volume;
• compare areas of regular shapes using informal units;
• solve worded problems involving time duration;
• convert between units of time;
• recognise two-dimensional shapes that are the faces for three-dimensional objects such as prisms, pyramids and platonic solids;
• interpret and use information contained in maps, including the scale of cities and rural areas in Australia;
• create symmetrical pictures, shapes and patterns;
• classify angles as acute, obtuse, straight, reflex and revolution;
• identify dependent and independent events;
• list the probabilities of everyday events;
• describe different methods for data collection and representation, and evaluate their effectiveness;
• construct a variety of data displays from given or collected data;
• interpret data representations in the media and other forums in which symbols represent more than one data value.