Year 5

Children will learn to:

• read, write, order and compare numbers to at least 10,000,000 and determine the value of each digits

• read Roman numerals to 1000 (M) and recognise years written in Roman numerals

• interpret negative numbers in context

• round any number to the nearest 10, 100, 1000, 10,000 and 100,000

• solve number problems and practical problems that involve all of the above.

Children will learn to:

• count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000

• count forwards and backwards with positive and negative whole numbers, including through zero

• use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy

• add and subtract whole numbers with more than 4 digits including using formal written methods

• add and subtract numbers mentally with increasingly large numbers

• solve addition and subtraction multi-step problems in context, deciding with operations and methods to use and why

• solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

• 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 numbers

• establish whether a number up to 100 is prime and recall prime numbers up to 19

• recognise and use square number and cube numbers, and the notation for squared and cubed

• mutiply numbers up to 4 digits by a one-digit or two-digit number using a formal written methods, 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

• solve problems involving multiplication and division including their knowledge of factors and mulitples, squares and cubes

• solve problems involving multiplication and division, including scaling bu simple fractions and problems involving simple rates.

Children will learn to:

• indentify, 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

• compare and order fractions whose denominators are all multiples of the same number

• 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

• 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 per cent symbol and understand that per cent relates to 'number of parts per hundred' and write percentages as a fraction with a denominator 100, and as a decimal

• solve probelms which require knowing percentage and decimal equivalents of a half, quarter, fifth, two-fifths, four-fifths and those fractions with a denominator of a multiple of 10 or 25.

Children will learn to:

• convert between different units of measure

• understand and use approximate equivalences between metric units and common imperial units

• use all four operations to solve problems involving measure using decimal notation, including scaling

• use all four operations to solve problems involving measure (for example, money)

• solve problems involving converting between units of time

• measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres

• calculate and compare the area of rectangles and including using standard units, square centimetres and square metres and estimate the area of irregular shapes

• estimate volume and capacity

Children will learn to:

• distinguish between regular and irregular polyhons based on reasoning about equal sides and angles

• use the properties of rectangles to deduce related facts and find missing lengths and angles

• 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

• identify:

  • angles at a point and one whole turn

  • angles at a point on a straight line and half a turn

  • other multiples of 90 degrees

• 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

Children will learn to:

• complete, read and interpret information in tables, including timetables

• solve comparison, sum and difference problems using information presented in a line graph.