Number – number and place value 
Statutory requirements 
Pupils should be taught to:

Notes and guidance (nonstatutory) 
Pupils identify the place value in large whole numbers.
They continue to use number in context, including measurement. Pupils extend and apply their understanding of the number system to the decimal numbers and fractions that they have met so far. They should recognise and describe linear number sequences, including those involving fractions and decimals, and find the termtoterm rule. They should recognise and describe linear number sequences (for example, 3, 3½, 4, 4½…), including those involving fractions and decimals, and find the termtoterm rule in words (for example, add ½). 
Number – addition and subtraction 
Statutory requirements 
Pupils should be taught to:

Notes and guidance (nonstatutory) 
Pupils practise using the formal written methods of columnar addition and subtraction with increasingly large numbers to aid fluency (see Mathematics Appendix 1).
They practise mental calculations with increasingly large numbers to aid fluency (for example, 12 462 – 2300 = 10 162). 
Number – multiplication and division 
Statutory requirements 
Pupils should be taught to:

Notes and guidance (nonstatutory) 
Pupils practise and extend their use of the formal written methods of short multiplication and short division (see Mathematics Appendix 1). They apply all the multiplication tables and related division facts frequently, commit them to memory and use them confidently to make larger calculations.
They use and understand the terms factor, multiple and prime, square and cube numbers. Pupils interpret noninteger answers to division by expressing results in different ways according to the context, including with remainders, as fractions, as decimals or by rounding for example, 98 ÷ 4 = 98/4 = 24 remainder 2 = 24 = 24.5 ≈25 Pupils use multiplication and division as inverses to support the introduction of ratio in year 6, for example, by multiplying and dividing by powers of 10 in scale drawings or by multiplying and dividing by powers of a 1000 in converting between units such as kilometres and metres. Distributivity can be expressed as a(b + c) = ab + ac. They understand the terms factor, multiple and prime, square and cube numbers and use them to construct equivalence statements for example, 4 x 35 = 2 x 2 x 35 ; 3 x 270 = 3 x 3 x 9 x 10 = 9^{2} x 10 Pupils use and explain the equals sign to indicate equivalence, including in missing number problems for example, 13 + 24 = 12 + 25 ; 33 = 5 x n ).

Number – fractions (including decimals and percentages) 
Statutory requirements 
Pupils should be taught to:

Notes and guidance (nonstatutory) 
Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing proportions.
They extend their knowledge of fractions to thousandths and connect to decimals and measures. Pupils connect equivalent fractions > 1 that simplify to integers with division and other fractions > 1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractions. Pupils connect multiplication by a fraction to using fractions as operators (fractions of), and to division, building on work from previous years. This relates to scaling by simple fractions, including fractions > 1. Pupils practise adding and subtracting fractions to become fluent through a variety of increasingly complex problems. They extend their understanding of adding and subtracting fractions to calculations that exceed 1 as a mixed number. Pupils continue to practise counting forwards and backwards in simple fractions. Pupils continue to develop their understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities. Pupils extend counting from year 4, using decimals and fractions including bridging zero, for example on a number line. Pupils say, read and write decimal fractions and related tenths, hundredths and thousandths accurately and are confident in checking the reasonableness of their answers to problems. They mentally add and subtract tenths, and onedigit whole numbers and tenths. They practise adding and subtracting decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimal places, and complements of 1 (for example, 0.83 + 0.17 = 1). 
Measurement 
Statutory requirements 
Pupils should be taught to:

Notes and guidance (nonstatutory) 
Pupils use their knowledge of place value and multiplication and division to convert between standard units.
Pupils calculate the perimeter of rectangles and related composite shapes, including using the relations of perimeter or area to find unknown lengths. Missing measures questions such as these can be expressed algebraically, for example 4 + 2b = 20 for a rectangle of sides 2 cm and b cm and perimeter of 20cm. 
Geometry – properties of shapes 
Statutory requirements 
Pupils should be taught to:

Notes and guidance (nonstatutory) 
Pupils become accurate in drawing lines with a ruler to the nearest millimetre, and measuring with a protractor. They use conventional markings for parallel lines and right angles.
Pupils use the term diagonal and make conjectures about the angles formed between sides, and between diagonals and parallel sides, and other properties of quadrilaterals, for example using dynamic geometry ICT tools. Pupils use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems. 
Geometry – position and direction 
Statutory requirements 
Pupils should be taught to:

Notes and guidance (nonstatutory) 
Pupils recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2D grid and coordinates in the first quadrant. Reflection should be in lines that are parallel to the axes. 
Statistics 
Statutory requirements 
Pupils should be taught to:

Notes and guidance (nonstatutory) 
Pupils connect their work on coordinates and scales to their interpretation of time graphs.
They begin to decide which representations of data are most appropriate and why. 