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Year Five Mathematics

Numbers & the number system


  • 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 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.

Calculation - addition & subtraction


  • Add and subtract whole numbers with more than 4 digits, including using formal methods (columnar + & -)
  • Add and subtract numbers mentally with increasingly large numbers.
  • Use rounding to check answers 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 & why.


Calculation - multiplication & division


  • Identify multiples & factors; find all factor pairs of a number & common factors of 2 numbers.
  • Know & use the vocabulary of prime numbers, prime factors & composite non-prime numbers.
  • Establish whether a number up to 100 is prime; recall primes up to 19.
  • Multiply numbers up to 4 digits by a one or two-digit number using a formal 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; interpret remainders appropriately for the context
  • Multiply and divide whole numbers and those involving decimals by 10, 100 & 1000.
  • Recognise and use square numbers & cube numbers and notation for squared 2, cubed 3
  • Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes
  •  Solve problems involving    + - x ÷  and a combination of these, including understanding meaning of = sign
  • Solve problems involving x and ÷ including scaling by simple fractions & problems involving simple rates.


Calculation - Fractions, Decimals & Percentages


  • Compare & order fractions whose denominators are all multiples of the same number
  • Identify, name & write equivalent fractions of a given fraction, represented visually, inc. 1/10 & 1/100 
  • Recognise mixed numbers & improper fractions; convert from one form to the other; write mathematical statements > 1 as a mixed number [e.g. 2/5 + 4/= 6/= 11/5]
  • Add & subtract fractions with the same denominator & denominators that are multiples of the same number.
  • Multiply proper fractions & mixed numbers by whole numbers, supported by materials & diagrams.
  • Read and write decimal numbers as fractions [e.g. 0.71 = 71/100 ]
  • Recognise and use 1/1000  and relate them to 1/10, 1/100  & 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 with number to three decimal places.
  • Recognise the per cent symbol (%) and understand that per cent relates to ‘the number of parts per 100’ 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/and those with a denominator of a multiple of 10 or 25.




  • 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 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) & square metres (m2) and estimate the area of irregular shapes
  • Estimate volume [eg. using 1 cm3 blocks to build cuboids including cubes] and capacity [e.g. 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.


Shape & Space


  • Identify 3-D shapes, including cubes and other cuboids, from 2-D 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 360o); angles at a point on a straight line and ½  a turn (total 180o); other multiples of 90o
  • 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.
  • 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.




  • Solve comparison sum and difference problems using information presented in a line graph.
  • Complete, read and interpret information in tables, including timetables.