Year 5 programme of study (statutory requirements) 
NUMBER Number and place value
Pupils should be taught to:
 read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit
 count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000
 interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers through zero
 round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000
 solve number problems and practical problems that involve all of the above
 read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

Addition and subtraction
Pupils should be taught to:
 add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
 add and subtract numbers mentally with increasingly large numbers
 use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
 solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why.

Multiplication and division
Pupils should be taught to:
 identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.
 solve problems involving multiplication and division where larger numbers are used by decomposing them into their factors
 know and use the vocabulary of prime numbers, prime factors and composite (nonprime) numbers
 establish whether a number up to 100 is prime and recall prime numbers up to 19
 multiply numbers up to 4 digits by a one or twodigit number using a formal written method, including long multiplication for twodigit numbers
 multiply and divide numbers mentally drawing upon known facts
 divide numbers up to 4 digits by a onedigit number using the formal written method of short division and interpret remainders appropriately for the context
 multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
 recognise and use square numbers and cube numbers, and the notation for squared (^{2}) and cubed (^{3})
 solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
 solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

Fractions (including decimals and percentages)
Pupils should be taught to:
 compare and order fractions whose denominators are all multiples of the same number
 identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
 recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number (e.g. ^{2}/_{5} + ^{4}/_{5} = ^{6}/_{5} = 1^{1}/_{5})
 add and subtract fractions with the same denominator and multiples of the same number
 multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
 read and write decimal numbers as fractions (e.g. 0.71 = ^{71}/_{100})
 recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
 round decimals with two decimal places to the nearest whole number and to one decimal place
 read, write, order and compare numbers with up to three decimal places
 solve problems involving number up to three decimal places
 recognise the per cent symbol (%) and understand that per cent relates to “number of parts per hundred”, and write percentages as a fraction with denominator hundred, and as a decimal fraction
 solve problems which require knowing percentage and decimal equivalents of ^{1}/_{2}, ^{1}/_{4}, ^{1}/_{5}, ^{2}/_{5}, ^{4}/_{5} and those with a denominator of a multiple of 10 or 25.

MEASUREMENT
Pupils should be taught to:
 convert between different units of metric measure (e.g. kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)
 understand and use equivalences between metric units and common imperial units such as inches, pounds and pints
 measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
 calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm^{2}) and square metres (m^{2}) and estimate the area of irregular shapes
 estimate volume (e.g. using 1 cm^{3} blocks to build cubes and cuboids) and capacity (e.g. using water)
 solve problems involving converting between units of time
 use all four operations to solve problems involving measure (e.g. length, mass, volume, money) using decimal notation including scaling.

GEOMETRY Properties of shapes
Pupils should be taught to:
 identify 3D shapes, including cubes and other cuboids, from 2D representations
 know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
 draw given angles, and measure them in degrees (^{o})
 identify:
 angles at a point and one whole turn (total 360^{o})
 angles at a point on a straight line and ½ a turn (total 180^{o})
 other multiples of 90^{o}
 use the properties of rectangles to deduce related facts and find missing lengths and angles
 distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

Position and direction
Pupils should be taught to:
 identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed.

STATISTICS
Pupils should be taught to:
 solve comparison, sum and difference problems using information presented in a line graph
 complete, read and interpret information in tables, including timetables.
