The aims of this guidance are firstly to bring greater coherence to the National Curriculum
by exposing core concepts and demonstrating their progression from year 1 to year 6, and
secondly to summarise the most important knowledge and understanding within each year group and
important connections between them.
This video guide summarises the knowledge and understanding that year 6 pupils need
achieve by the end of the year, in order to be ready to progress to year 7. There are
accompanying materials which provide teaching guidance for each ready-to-progress criterion,
and example assessment questions.
We recommend that year 6 teachers should read the guidance for both year 5 and year 6, so
that they understand the starting point for year 6 pupils.
By the end of year 6, pupils should have a cohesive understanding of the whole place-value
system, from decimal fractions through to 7-digit numbers. Pupils need to be able to
read and write numbers from 1 hundredth to 10 million, written in digits, beginning with
the powers or 10, as shown here, and should understand the relationships between these
powers of 10.
Pupils should know that each power of 10 is equal to 1 group of 10 of the next smallest
power of 10, for example 100,000 is equal to 10 ten thousands.
And 1 million is ten hundred thousands
Pupils should extend this knowledge to write multiples of these powers of 10, for example
knowing how to write 18 hundred thousands in digits. Pupils should be able to restate
the quantity in the appropriate power of 10, for example 18 hundred thousands is equal
to 1 million 8 hundred thousand.
Once pupils understand the relationships between powers of ten, they should extend this to
other numbers in the Gattegno chart. They must be able to identify the number that is
10, 100, 1,000, 1 tenth, 1 hundredth or 1 thousandth times the size of a given number,
and associate this with multiplying or dividing by 10, 100 and 1,000.
50,000 is 100 times the size of 500. Multiplying by 100
500 is one-hundredth times the size of 50,000. Dividing by 100
This will prepare pupils for multiplying by decimals in key stage 3, when they will learn,
for example, that dividing by 100 is equivalent to multiplying by 0.01.
So, pupils will leave year 6 understanding these two different ways in which place value
units relate to one another: the grouping and exchange model and the scaling model.
These models show the relationship between tenths and hundredths, but pupils should be
able to extend this understanding through the place value system.
Pupils must be able to combine units from millions to hundredths to compose numbers,
and partition numbers into these units, and solve related addition and subtraction calculations.
They should be able to decompose numbers into place value numeration units like this using
standard partitioning
Öor using non-standard partitioning to decompose decimal numbers in different ways. This supports
mental calculation, for example subtracting 30 centimetres from 3.42m.
As well as understanding the quantity associated with numbers, pupils need to understand the
position of numbers in the linear number system. They should be able to place them on partially
marked number lines at a range of scales, for example placing 7-digit numbers on a number
line labelled in millionsÖ
Or on a number line marked in hundred thousands.
Pupils should also be able to make a reasonable estimation about the position of numbers on
unmarked number lines. Teach pupils to mark midpoints to support them with this. 75,000
is here, so 65,000 is about here relative to 50,000 and 75,000.
And as for partitioning numbers, pupils should be able to extend this understanding through
the number system, for example estimating the position of 3.42 in relation to 3 and
4. The midpoint is 3.5, so 3.42 is about here.
Pupils should also be able to identify previous and next multiples of powers of 10, which
will allow them to round numbers to a reasonable degree of accuracy. For example, for a 7-digit
number of pupils should be able to identify the previous and next multiple of 1 million
and 1 hundred thousand, and round to the nearer of these without relying on a number line.
Pupils should understand that the purpose of rounding numbers is to give an approximate
value.
So, pupils will leave year 6 understanding these two different models of number: number
as enumeration and number as measure and will be able to understand numbers through the
number system, including decimal numbers, in both of these ways.
Pupils need to be able to decompose powers of 10 into 2, 4, 5 and 10 parts. This shows
decomposition of 1 million.
However, pupils need to be able to decompose any integer power of 10 up to 10 million in
this way.
This relates to number as measure because it allows pupils to use common graphing units.
They should be able to complete and read scales for integer powers of 10 up to 1 million,
marked in 2 parts, 4 parts, 5 parts and 10 parts.
And pupils should be able to identify numbers marked on continuations of those scales such
as these. 2 parts, 4 parts, 5 parts and 10 parts.
Throughout key stage 2, pupils have learnt about and used 2 types of mathematical relationship
between numbers: additive relationships and multiplicative relationships. In year 6, pupils
should learn to identify the additive relationship between 2 given numbers or the multiplicative
relationship. In year 6 this should be restricted to integer multipliers, but this will prepare
pupils for scaling numbers by fractions in key stage 3.
When given a sequence of numbers, pupils should be able to identify whether the terms are
all related additively or multiplicatively, identify the specific difference or multiplier,
and use this to continue a sequence either forwards or backwards
In previous year groups in key stage 2 pupils have learnt about and used the commutative
and associative properties of addition and the commutative, associative, and distributive
properties of multiplication. In year 6 pupils should learn the compensation property
Pupils should be able to use the compensation property to simplify calculations such as
3 tenths times 320. They should use their knowledge that multiplying one factor by a
number and dividing the other factor by the same number means the product remains the
same. Here, this simplifies the calculation to 3
times 32.
Pupils should be able to combine their understanding of these properties or arithmetic, with their
understanding of inverse relationships and place value in both additive and multiplicative
contexts, to derive related equations.
For example, pupils should be able to explain how they would use the first equation to complete
the second equation. Here pupils first need to apply their understanding
of place value to make the sum and addends 1 tenth times the size to give this equation.
Then they need to apply the compensation property of addition to solve the equation: add 10
to the first addend and subtract 10 from the second addend.
Pupils should also be taught to solve problems involving ratio relationships. They should
be taught to describe one to many, or many to one correspondence, using sentences such
as for every 1 red bead there are 3 blue beads. Pupils should be able to represent
these correspondences in tables and should understand that the generalisation "for every
1 red bead there are 3 blue beads" applies to all of these instances equally. Pupils
should be able to solve problems involving ratio relationships, for example working out
how many red and blue beads there would be if there were 20 beads in total. Pupils should
be able to extend correspondence tables, and identity the multiplicative relationship from
a single unit to other values in the table.
Pupils should also extend this to many-to-many correspondences. These 4 examples can all
be described by the generalisation for every two yellow beads there are 3 green beads.
Pupils should be able to represent many-to-many correspondences in tables as well.
Pupils should be comfortable working with and solving equations with two unknown values
and should recognise that an equation like the one here has an infinite number of solutions.
Pupils must also be able to solve problems with two unknowns with only one value, for
example finding two numbers such that their sum is 48, and one number is one-fifth of
the other number. Here pupils are given on piece of additive
information and one piece of multiplicative information. Pupils should be able to draw
models to help them solve this type of problem. Here the model exposes the 6 equal parts,
meaning each part must have a value of 8. One number is 8 and the other number is 40.
Building on their understanding of equivalent fractions from year 5, pupils should be taught
to simplify fractions which are not in their simplest form by identifying a common factor
of the numerator and denominator. As they did in year 5, pupils should recognise that
equivalent fractions have the same value and sit at the same place on a number line.
Pupils should be able to identify whether a fraction is in its simplest form or not
without being prompted to check for this.
By the end of year 6, pupils should be able to compare two fractions and identify which
is larger.
Where the fractions are close in value, pupils should be able to identify a common denominator,
and use this to compare the fractions.
Pupils should be taught to identify where they compare fractions by reasoning, rather
than conversion to a common denominator. They should be able to compare fractions with the
same numerator.
They should reason that, because 1/5 is greater than 1/6, then 2 one fifths must be greater
than 2 one sixths, and should be able to generalise that, when fractions have the same numerator,
then the larger the denominator the smaller the fraction.
In previous year groups, pupils have learnt to estimate the position of numbers including
fractions in the linear number system and make judgements about the relative size of
the numerator and denominator in fractions.
They should be able to use this to identify that 5 is a relatively large part of 6, and
so 5/6 sits roughly here in the linear number system, but that 7 is a smaller part of 11
so sits about here in the linear number system, and should be able to use this reasoning to
compare fractions like these. Before they move to year 7, pupils must be able to understand
that the value of 5/6 is greater than that of 7/11, despite both the numerator and denominator
in 7/11 being greater than those in 5/6.
Through key stage 2, pupils have learnt to measure perimeters, angles, and areas of shapes,
and have learnt to draw polygons by joining marked points and draw angles of a given size.
By the end of year 6, pupils must be able to draw, compose and decompose shapes defined
by specific measurements, for example drawing a rectangle, on squared-centimetre
paper, with a perimeter of 14cm or drawing a pentagon with an area of 10cm2.
Pupils should also be able to reason with compound shapes, for example using the given
length of 7cm on the rectangle on the left to find the perimeter of the compound shape
on the right. Composing and decomposing shapes prepares pupils for solving geometry problems
at key stage 3, for example, finding the area of a trapezium by decomposing it to a rectangle
and 2 triangles.