Students who have achieved Early Stage 1 show a growing awareness of the many purposes of mathematical language in their daily lives both in and out of the classroom. They enjoy using objects, drawings, words, numerals and other symbols to ask and answer questions.

Students manipulate objects and materials and describe their size, shape, position and other features in everyday language. They explain their reasons for sorting objects into particular groupings and arranging them into certain patterns.

Students count, order and represent numbers in a variety of forms, using objects, words and numerals. They compare, combine and separate groups of objects, and describe their actions in everyday language. They are aware of the use of calculators in representing numbers.

Students who have achieved Stage 1 recognise the impact of the mathematical features of objects on their environment. They compare and describe objects in terms of their measurable attributes. They answer mathematical questions in relation to their own experiences and can give reasons for their responses.

They can visualise, recognise, name and describe the parts of two and three dimensional shapes and objects, using an increasing level of mathematical terminology in their descriptions. They describe the position of objects in relation to others. Students collect data for a specific purpose, represent it pictorially, and interpret results with teacher guidance.

Students demonstrate an awareness of the relationships between parts of a quantity and the whole, and recognise and extend patterns in both numerical and spatial aspects. They use the relationships between numbers to estimate and calculate and to solve simple number problems,
using a range of strategies including the recall of number facts for addition and subtraction, and gain some proficiency in the use of calculators. They are familiar with the range of coins currently in circulation and are aware of their relative monetary value.

Stage 2

Students who have achieved Stage 2 show their problem-solving skills in using a range of strategies to approach simple spatial, measurement and numerical problems. They can make comparisons between methods of solution, and check whether the solution is reasonable. Students can prepare and draw simple diagrams, using them to interpret mathematical situations. They demonstrate the confidence to apply mathematics and to seek and gain knowledge about the mathematics they need from a variety of sources.

They are able to classify and describe both two and three dimensional shapes and objects using appropriate mathematical terminology, and use geometric shapes in the creation and continuation of patterns and designs. They are aware of the nature and variety of angles in both the natural
and built environments, and can describe the relative positions of locations on a map or plan interms of simple grid references. Students can gather and organise information to answer a specific question which they have posed, presenting the information in simple column graphs and using them to interpret the data.

At this stage students know and can use the base units of measurement such as metres, kilograms and litres and can estimate and measure to the nearest unit. They are able to read the time on both digital and analogue clocks and are aware of the relationships between time units.
Students demonstrate an understanding of the groupings of ten in the symbolic representation of the base 10 number system. They can select and use the appropriate operation and related number facts, including the use of multiplication facts up to 10 X 10, to solve simple problems involving whole numbers.

Stage 3

Students who have achieved Stage 3 can extend mathematical investigations, using appropriate representations and problem solving strategies. They make informed choices about units of measurement and measuring devices, and select the appropriate number operations to solve problems of increasing demand. They appreciate that mathematics involves observing, generalising and representing patterns and relationships.

Students investigate and describe the properties of both regular and irregular two and three dimensional shapes, using accurate mathematical terminology. They draw and construct physical representations of shapes using strategies such as folding, tessellating, measuring angles and
lengths, using isometric paper and scale ratios.

Students are able to use grids, compass directions and larger or smaller units to describe the position and dimensions of the objects and locations with increasing levels of accuracy. They can develop, read and interpret displays of data in a variety of simple presentations and make
judgements based on such displays.

Their number skills enable them to solve a wide range of problems involving whole numbers, common and decimal fractions, and money. They recognise and use the relationships between common fractions, decimal fractions and percentages, and interpret their solution to problems in the context of the problem.