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Year 5

Year 5 Programme of Study


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, including 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. 


Number – 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 multi-step problems in contexts, deciding which operations and methods to use and why. 


Number – 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

·         know and use the vocabulary of prime numbers, prime factors and composite (non- prime) 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 two-digit number using a formal written method, including long multiplication for two-digit numbers

·         multiply and divide numbers mentally drawing upon known facts

·         divide numbers up to 4 digits by a one-digit 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 multiplication and division including using their knowledge of factors and multiples, squares and cubes

·         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. 


 Number – 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 (for example,  ⅖  + ⅘  = 6/5 = 1 ⅕)

·         add and subtract fractions with the same denominator and denominators that are 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 (for example, 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 numbers up to three decimal places

·         recognise the percent symbol (%) and understand that percent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal

·         solve problems which require knowing percentage and decimal equivalents of ½, ¼, ⅕, ⅖, ⅘ and those fractions with a denominator of a multiple of 10 or 25. 



Pupils should be taught to:

·         convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)

·         understand and use approximate 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 rectangles (including squares), and including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes

·         estimate volume (for example, using 1 cm3 blocks to build cubes and cuboids) and capacity (for example, using water)

·         solve problems involving converting between units of time

·         use all four operations to solve problems involving measure (for example, 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 (°)

·         Identify angles at a point and one whole turn (total 360°); angles at a point on a straight line and ½ a  turn (total 180°); other multiples of 90°

·         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. 


Geometry – 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. 



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.