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# mathematics programmes of study

## Number - number and place value

Pupils should be taught to:

#### Notes and guidance (non-statutory)

Using materials and a range of representations, pupils practise counting, reading, writing and comparing numbers to at least 100 and solving a variety of related problems to develop fluency. They count in multiples of 3 to support their later understanding of a third.
As they become more confident with numbers up to 100, pupils are introduced to larger numbers to develop further their recognition of patterns within the number system and represent them in different ways, including spatial representations.
Pupils should partition numbers in different ways (for example, 23 = 20 + 3 and 23 = 10 + 13) to support subtraction. They become fluent and apply their knowledge of numbers to reason with, discuss and solve problems that emphasise the value of each digit in two-digit numbers. They begin to understand 0 as a place holder.

## Number - addition and subtraction

Pupils should be taught to:

• ## recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems

Notes and guidance (non-statutory)

## Number - multiplication and division

Pupils should be taught to:

• ## solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts

Notes and guidance (non-statutory)

## Number - fractions

Pupils should be taught to:

## Notes and guidance (non-statutory)

Pupils use fractions as ‘fractions of’ discrete and continuous quantities by solving problems using shapes, objects and quantities. They connect unit fractions to equal sharing and grouping, to numbers when they can be calculated, and to measures, finding fractions of lengths, quantities, sets of objects or shapes. They meet as the first example of a non-unit fraction.
Pupils should count in fractions up to 10, starting from any number and using the and equivalence on the number line (for example, 1 , 1 (or 1 ), 1 , 2). This reinforces the concept of fractions as numbers and that they can add up to more than 1.

## Measurement

Pupils should be taught to:

## Notes and guidance (non-statutory)

Pupils use standard units of measurement with increasing accuracy, using their knowledge of the number system. They use the appropriate language and record using standard abbreviations.
Comparing measures includes simple multiples such as ‘half as high’; ‘twice as wide’.
Pupils become fluent in telling the time on analogue clocks and recording it.
They become fluent in counting and recognising coins. They read and say amounts of money confidently and use the symbols £ and p accurately, recording pounds and pence separately.

## Geometry - properties of shapes

Pupils should be taught to:

## Notes and guidance (non-statutory)

Pupils handle and name a wide variety of common 2-D and 3-D shapes including: quadrilaterals and polygons and cuboids, prisms and cones, and identify the properties of each shape (for example, number of sides, number of faces). Pupils identify, compare and sort shapes on the basis of their properties and use vocabulary precisely, such as sides, edges, vertices and faces.
Pupils read and write names for shapes that are appropriate for their word reading and spelling.
Pupils draw lines and shapes using a straight edge.

## Geometry - position and direction

Pupils should be taught to:

## Notes and guidance (non-statutory)

Pupils should work with patterns of shapes, including those in different orientations.
Pupils use the concept and language of angles to describe ‘turn’ by applying rotations, including in practical contexts (for example, pupils themselves moving in turns, giving instructions to other pupils to do so, and programming robots using instructions given in right angles).

## Statistics

Pupils should be taught to: