Mathematics

Year 5

Module 6

Volume

Pupils should be taught to:

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

use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling

Converting units

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
use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling.

Negative numbers

Pupils should be taught to:

interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero

Module 5

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.

Decimals

Pupils should be taught to:

read and write decimal numbers as fractions [for example, 0.71 = ]
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 of , , , , and those fractions with a denominator of a multiple of 10 or 25

Module 4

Shape

Pupils should be taught to:

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 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.

Statistics

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.

Perimeter and Area

Pupils should be taught to:

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

Module 3

NSPCC

Number Day 2025

Children explored the jobs of different parents and carers in the school and discovered how they use maths.

We were party planners for the day and had to plan a party and ensure we had a suitable venue, food drinks and decorations. We were given a particular budget to

Decimals and percentages

Pupils should be taught to:

read and write decimal numbers as fractions [for example, 0.71 = ]
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 of , , , , and those fractions with a denominator of a multiple of 10 or 25.

Fractions

Pupils should be taught to:

multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

Module 2

Multiplication and division

Pupils should be taught to:

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

Fractions

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, + = = 1]
add and subtract fractions with the same denominator and denominators that are multiples of the same number

Module 1

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.

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.

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 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

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