
By the end of Early Stage 1, students ask questions and use known facts to explore mathematical problems and develop fluency with mathematical ideas. They use everyday language, concrete materials and informal recordings to demonstrate understanding and link mathematical ideas.
Students count to 30 and represent numbers to 20 with objects, pictures, numerals and words. They read and use ordinal numbers to at least ‘tenth’. Students use concrete materials to model addition, subtraction, multiplication and division. They use the language of money and recognise the coins and notes of the Australian monetary system. Students divide objects into two equal parts and describe them as halves. They recognise, describe and continue repeating patterns of objects and drawings.
Students identify length, area, volume, capacity and mass, and compare and arrange objects according to these attributes. They manipulate, sort and represent threedimensional objects and describe them using everyday language. Students manipulate, sort and describe representations of twodimensional shapes, identifying circles, squares, triangles and rectangles. They connect events and the days of the week and explain the order and duration of events, telling the time on the hour. Students give and follow simple directions and describe position using appropriate language.
Students answer simple questions to collect information. They use objects to create a data display and interpret data.
(Sourced from: http://syllabus.bos.nsw.edu.au/mathematics/mathematicsk10/stagestatements/)

By the end of Stage 1, students ask questions and use known facts, objects, diagrams and technology to explore mathematical problems and develop mathematical fluency. They link mathematical ideas and use appropriate language and diagrams to explain strategies used.
Students count, order, read and write two and threedigit numbers and use a range of strategies and recording methods. They use mental strategies and concrete materials to add, subtract, multiply and divide, and solve problems. Students model and describe objects and collections divided into halves, quarters and eighths. They associate collections of Australian coins with their value. They use place value to partition numbers. Students describe and continue a variety of number patterns and build number relationships. They relate addition and subtraction facts for sums to at least 20.
Students estimate, measure, compare and record using informal units for length, area, volume, capacity and mass. They recognise the need for formal units of length and use the metre and centimetre to measure length and distance. They use a calendar to identify the date and name and order the months and the seasons of the year. Students use informal units to compare and order the duration of events and tell the time on the half and quarterhour. They identify, describe, sort and model particular threedimensional objects and twodimensional shapes. Students represent and describe the position of objects and interpret simple maps.
Students collect, organise, display and interpret data using lists, tables and picture graphs. They recognise and describe the element of chance in everyday events.
(Sourced from: http://syllabus.bos.nsw.edu.au/mathematics/mathematicsk10/stagestatements/)

By the end of Stage 2, students ask questions and use efficient mental and written strategies with increasing fluency to solve problems. They use technology to investigate mathematical concepts and check their solutions. Students use appropriate terminology to describe and link mathematical ideas, check statements for accuracy and explain their reasoning.
Students count, order, read and record numbers of up to five digits. They use informal and formal mental and written strategies to solve addition and subtraction problems. Students use mental strategies to recall multiplication facts up to 10 × 10 and related division facts. They use informal written strategies for multiplication and division of twodigit numbers by onedigit numbers. Students represent, model and compare commonly used fractions, and model, compare and represent decimals of up to two decimal places. Students perform simple calculations with money and solve simple purchasing problems. They record, describe and complete number patterns and determine missing numbers in number sentences. Students recognise the properties of odd and even numbers.
Students estimate, measure, compare, convert and record length, area, volume, capacity and mass using formal units. They read and record time in hours and minutes, convert between units of time, and solve simple problems involving the duration of time. Students name, describe and sketch particular threedimensional objects and twodimensional shapes. They combine and split twodimensional shapes to create other shapes. They compare angles using informal means and classify angles according to their size. Students use a gridreference system to describe position, and compass points to give and follow directions. They make simple calculations using scales on maps and plans.
Students collect and organise data, and create and interpret tables and picture and column graphs. They list all possible outcomes of everyday events, and describe and compare chance events in social and experimental contexts.
(Sourced from: http://syllabus.bos.nsw.edu.au/mathematics/mathematicsk10/stagestatements/)

By the end of Stage 3, students ask questions and undertake investigations, selecting appropriate technological applications and problemsolving strategies to demonstrate fluency in mathematical techniques. They use mathematical terminology and some conventions, and they give valid reasons when comparing and selecting from possible solutions, making connections with existing knowledge and understanding.
Students select and apply appropriate mental, written or calculator strategies for the four operations and check the reasonableness of answers using estimation. They solve word problems and apply the order of operations to number sentences where required. Students identify factors and multiples and recognise the properties of prime, composite, square and triangular numbers. They connect fractions, decimals and percentages as different representations of the same value. Students compare, order and perform calculations with simple fractions, decimals and percentages and apply the four operations to money in reallife situations. Students record, describe and continue geometric and number patterns, and they find missing numbers in number sentences. They locate an ordered pair in any one of the four quadrants on the Cartesian plane.
Students select and use the appropriate unit to estimate, measure and calculate length, area, volume, capacity and mass. They make connections between capacity and volume, and solve problems involving length and area. Students use 24hour time in reallife situations, construct and interpret timelines and use timetables. They convert between units of length, units of capacity and units of mass. They construct and classify threedimensional objects and twodimensional shapes, and compare and describe their features, including line and rotational symmetries. Students measure and construct angles, and find unknown angles in diagrams using known angle results. They use a gridreference system to locate landmarks and describe routes using landmarks and directional language.
Students use appropriate data collection methods to interpret and analyse sets of data and construct a range of data displays. They assign probabilities as fractions, decimals or percentages in simple chance experiments.
(Sourced from: http://syllabus.bos.nsw.edu.au/mathematics/mathematicsk10/stagestatements/)