What maths is taught in Year 5?

In the Year 5 maths mastery curriculum, the main focus is for children to extend their understanding of the number system and place value to include larger integers.  Also to develop the connection of multiplication and division with fractions, decimals, percentages and ratio.

This video has been created by the Department for Education and the NCETM.  Although it is primarily for teachers and schools, we believe parents/carers will also find it helpful and informative in providing an overview to the maths mastery curriculum in Year 5.    It summarises the most important knowledge and understanding children need to master in order to be ready for Year 6.   

The following is a more detailed list of all the maths that is learnt in Year 5.  This has been taken from the National Curriculum in England: Mathematics Programmes of Study for Pupils in Year 5 (updated 28th September 2021).

 Year 5 objectives that can be supported with our plavalmat® place value mats, counters and base ten have been highlighted. 

COMING SOON!
We are in the process of creating a series of video tutorials that demonstrate how to use our plavalmat® resources with the White Rose Maths schemes of learning to help children to master these areas of the mathematics curriculum. 

If there is any mathematical terminology that you are unsure of, you may find the explanations on the Maths Vocabulary section of our website helpful. 

• 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 0

• round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000

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

• read Roman numerals to 1,000 (M) and recognise years written in Roman numerals

• 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

• identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 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 1,000

• 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

• 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 = 1  1/5]

• 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 2 decimal places to the nearest whole number and to 1 decimal place

• read, write, order and compare numbers with up to 3 decimal places

• solve problems involving number up to 3 decimal places

• recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per 100’, and write percentages as a fraction with denominator 100, 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 fractions with a denominator of a multiple of 10 or 25

• 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), 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

• 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 1 whole turn (total 360°)
  • angles at a point on a straight line and half 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

• 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

5NPV–1 

Know that 10 tenths are equivalent to 1 one, and that 1 is 10 times the size of 0.1. Know that 100 hundredths are equivalent to 1 one, and that 1 is 100 times the size of 0.01. Know that 10 hundredths are equivalent to 1 tenth, and that 0.1 is 10 times the size of 0.01. 

5NPV–2 

Recognise the place value of each digit in numbers with up to 2 decimal places, and compose and decompose numbers with up to 2 decimal places using standard and nonstandard partitioning.

5NPV–3 

Reason about the location of any number with up to 2 decimals places in the linear number system, including identifying the previous and next multiple of 1 and 0.1 and rounding to the nearest of each. 

5NPV–4 

Divide 1 into 2, 4, 5 and 10 equal parts, and read scales/number lines marked in units of 1 with 2, 4, 5 and 10 equal parts.

5NPV–5 

Convert between units of measure, including using common decimals and fractions.

There are no Ready-to-Progress Criteria for Addition and Subtraction in Year 5.

5F–1 

Find non-unit fractions of quantities.

5F–2 

Find equivalent fractions and understand that they have the same value and the same position in the linear number system.

5F–3 

Recall decimal fraction equivalents for 1/2 , 1/4 , 1/5 and 1/10, and for multiples of these proper fractions. 

5NF–1 

Secure fluency in multiplication table facts, and corresponding division facts, through continued practice.

5NF–2 

Apply place-value knowledge to known additive and multiplicative number facts (scaling facts by 1 tenth or 1 hundredth).

5MD–1 

Multiply and divide numbers by 10 and 100; understand this as equivalent to making a number 10 or 100 times the size, or 1 tenth or 1 hundredth times the size.

5MD–2 

Find factors and multiples of positive whole numbers, including common factors and common multiples, and express a given number as a product of 2 or 3 factors.

5MD–3 

Multiply any whole number with up to 4 digits by any one-digit number using a formal written method.

5MD–4 

Divide a number with up to 4 digits by a one-digit number using a formal written method, and interpret remainders appropriately for the context.

5G–1  

Compare angles, estimate and measure angles in degrees (°) and draw angles of a given size.   

5G–2  

Compare areas and calculate the area of rectangles (including squares) using standard units.