Y5 Mathematics

Number and Place Value
  • read, write, order and compare numbers to at least 1000 000 and determine the value of each digit
  • count forwards or backwards in steps of powers of 10 for any given number up to 1000 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 and 100
  • solve number problems and practical problems that involve all of the above.
Addition and Subtraction
  • add and subtract whole numbers with more than 4 digits, including using informal written methods (Any Order Addition and number lines)
  • 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.
Multiplication and Division
  • 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 and prime factors
  • 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
  • multiply and divide numbers mentally drawing upon known facts
  • divide numbers up to 4 digits by a one-digit number using a formal written method (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.
Fractions
  • 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, 2/5 + 4/5 = 6/5 = 11/5]
  • 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 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 100, and as a decimal
  • solve problems which require knowing percentage and decimal equivalents ofof 1/2, 1/4, 1/5, 2/5 , 4/5 and those fractions with a denominator of a multiple of 10 or 25.
Ratio and Proportion
  • use ratio to compare quantities and find missing values using multiplication.
Algebra
  • use simple formulae
  • Measurement
  • 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 cuboids (including cubes)] 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.
  • Properties of Shapes
  • 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 anda 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.
  • Position and Direction
  • 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
  • solve comparison, sum and difference problems using information presented in a line graph
  • complete, read and interpret information in tables, including timetables.