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 4 pupils need achieve by the end of the year, in order to
be ready to progress to year 5. There are accompanying materials which provide teaching
guidance for each ready-to-progress criterion, and example assessment questions.
We recommend that year 4 teachers should read the guidance for both year 3 and year 4, so
that they understand the starting point for year 4 pupils.
In Year 4 pupils need to know that 10 hundreds are equivalent to 1,000Ö
Öand use this fact to work out how many hundreds in other 4-digit multiples of 100. Ten hundreds
are 1,000 and 8 hundreds are 8 hundred, so 18 hundreds is equivalent to 1,800.
Pupils also need to understand the scaling model of place value and know that 1000 is
10 times the size of 100, and 100 is one tenth the size of 1000. Itís important that pupils
have a sense of a movement through the place value units as a scaling of a unit, rather
than just as grouping and exchange, as it will prepare them to multiply and divide by
10 and 100, particularly as they move into decimals in Year 5.
So, pupils will leave year 4 understanding these two different ways in which the unit
of 1000 relates to the unit of 100: the grouping and exchange model and the scaling model.
Once they have understood multiples of 100, pupils need to expand their understanding
to cover all 4-digit numbers. They should be able to decompose 4-digit numbers using
standard partitioningÖ
Öand also use non-standard partitioning to decompose 4-digit numbers in different ways.
This supports mental calculation, for example subtracting 4kg from 5,342g.
As well as understanding the quantity associated with numbers, pupils need to understand the
position of 4-digit numbers in the linear number system. They should be able to place
them on partially labelled number lines
And also make a reasonable estimation about the position of numbers on unmarked number
lines. Teach pupils to mark midpoints to support them with this.
Positioning numbers in the number system prepares pupils for working with scales on measuring
instruments or charts, and helps children compare numbers and make estimations.
Pupils should use their knowledge of where 4-digit numbers sit in the number system to
identify the previous and next multiple of 1000, and round to the nearer of these.
And identify the previous and next multiple of 100 and round to the nearer of these. It
is important that children understand that the point of rounding is to give an approximate
value.
Pupils should be able to round 4-digit numbers to the nearest 1000 and nearest 100 without
a number line.
So, pupils will leave year 4 understanding these two models of 4-digit numbers: number
as enumeration, which is the cardinality of a number, and number as measure, which is
its place in the linear number system.
Pupils need to be able to decompose the unit 1,000 into 2, 4, 5, and 10 parts. This supports
future fractions and measures work. For example, linking 4 parts and 250 prepares children
for understanding why º is equivalent to 0.25 when they meet decimals in year 5.
This decomposition of 1,000 allows pupils to use common graphing units. They should
be able to complete and read scales marked in 2 parts, 4 parts, 5 parts and 10 parts.
Pupils should be able to read values such as these on partially marked scales. 2 parts,
4 parts, 5 parts and 10 parts
As weíve seen, in Y4 children need to be able to work in units of 100 across the thousandís
boundary. Pupils need to be able to apply this knowledge to their number facts by working
in units of 100. Pupils know that 8 + 6 = 14, so can reason that 8 hundreds add 6 hundreds
is 1400, or 1400.
And the same idea of applying known facts to units of 100 applies to multiplication.
4 x 3 = 12 So, 4 x 3 hundreds = 12 hundreds, or 1,200
By the time they leave year 4, pupils need to have memorised their times tables up to
12 x 12. Several of the year 5 ready to progress criteria are dependent on fluency in times
table facts. It is essential that sufficient time is given to these.
Particularly important are the times tables up to 9 x 9, because these forms the within
column calculations in short multiplication and short division, which children must master
in year 5.
When children apply their knowledge of the commutative property of multiplication, this
leaves 36 facts which are essential for progression into year 5.
From memorised multiplication facts, pupils must be able to quickly derive related division
facts. In year 3 pupils learnt to find unit fractions of quantities using multiplication
facts they already knew. They should extend this to multiplication facts learnt in year
4.
It is essential that pupils are also able to calculate division facts with remainders
by the end of year 4. They will use these for division in year 5. 21 divided by 8 is
2 groups of 8, remainder 5.
Pupils also need to be able to interpret remainders in context, knowing when to round up and down.
A rounding down context would include working out how many packs of 8 buns can be made out
of 21 buns on a tray. 1 pack of 8 buns, 2 packs of 8 buns can be made. A rounding up
context would include working out how many tents are needed for 21 scouts on scout camp,
if 8 scouts fit in one tent. We need one tent, two tents, and a third tent for the remaining
5 scouts.
In year 4, the focus of addition and subtraction is extending concepts and methods taught in
year 3 to 4-digit numbers. See year 3 for guidance on what children are expected to
master in y3 to be ready to progress to year 4.
So now we move onto multiplication and division. Firstly, pupils need to multiply single digit
numbers by 10. Pupils have learnt their ten times table in year 3, but pupils also need
to be taught to think of multiplying by 10 as making 10 times the size. Pupils have already
met this scaling language when they looked at the relationship between 100 and 1000 in
number and place value. And although pupils can already divide two-digit multiples of
10 by 10 from their times table work, we need them to link dividing a number by 10 to making
a number one tenth of the size. This will prepare pupils for decimals in year 5.
And the same applies to multiplying and dividing by 100.
Making 100 times the size Making 100th of the size.
This includes multiplying and dividing numbers to complete calculations such as these.
So, pupils will leave year 4 understanding that 18 x 100 for example corresponds
to both these structures.
Pupils should arrive in year 4 knowing that multiplication is commutative and 2 groups
of 7 is equivalent to 7 groups of 2. In year 4 pupils should master an understanding of
the different structures that can be represented by multiplication and division equations.
This will give them the conceptual understanding to work flexibly with multiplicative structures
as they move into year 5.
Letís take this structure of 2 groups of 7. It can be represented by both of these
multiplication equations. Reading the first as 2 groups of 7 and the second as 7 multiplied
by 2 or 7 two times.
Now letís look at this structure, 7 groups of 2. That can equally be represented by the
same two multiplication equations, this time reading the first as 2 multiplied by 7, 2
seven times, and the second as 7 groups of 2.
So, the equation 2 ◊ 7 = 14 can represent either 2 groups of 7 or 7 groups of 2. And
equally the equation 7 ◊ 2 = 14 can represent either 2 groups of 7 or 7 groups of 2.
Pupils should also be able to relate both of these division equations to the same structures.
Here 14 is divided into groups of 7, and there are 2 of them. This is quotitive division.
But the same equation can also represent this structure. Here 14 is shared between 7, giving
2 in each share. This is partitive division. If we take the corresponding division sentence,
we find it can represent the same 2 structures. 14 shared between 2 is 7 in each part. Partitive
division. 14 divided into groups of 2 is 7 groups of 2 - Quotitive division. MAKE SURE
THIS HAS SOME POINTING OR ANIMATION TO MAKE IT CLEAR WHICH YOU ARE TALKING ABOUT
As well as learning the new times tables facts referenced in the number facts section, pupils
need to learn about patterns within times tables and the underlying structures. They
should be able to describe the relationship between adjacent multiples in their known
times tables. In the 6 times table for example, every time we add an additional group of 6
the product increases by 6. 4 groups of 6, plus another 6, gives 5 groups of 6. Expressions
such as this also teach children to construct expressions with mixed operations ñ in this
case both multiplication and addition. Understanding this will prepare children for
multiplicative reasoning in upper KS2 and beyond.
This extends to the distributive law. Just as 3 + 2 = 5, 3 groups of 6 plus 2 groups
of 6 is 5 groups of 6.
In Year 4, pupils must understand fractions beyond the 0 ñ 1 interval. Pupils should
become familiar with seeing number lines labelled in fractions and mixed numbers and understand
how the patterns and structures they have learnt about in fractions within 1 are extended.
Pupils must be able to identify numbers on partially labelled number lines. Here, the
interval between integers has been divided into 4 equal parts, so each of these parts
is one quarter, so the number indicated is 2 æ. This will support them with ordering
fractions, calculating with fractions and reading scales.
Pupils must also be able to convert between mixed numbers and improper fractions in year
4. Pupils know that there are five fifths in one whole, so in 2 3/5 there must be two
groups of 5 fifths, which is 10 fifths, and 3 more fifths, which is 13 fifths. In the
National Curriculum this is in Y5, but this guidance suggests it is taught in year 4 to
aid coherence. Children will best be able to add and subtract fractions across 1 when
they can work with both improper fractions and mixed numbers.
And working the other way, pupils must also convert from improper fractions to mixed numbers.
So, in 21 eighths there are 1 group of 8 eighths, 2 groups of 8 eighths, and 5 more eighths,
2 and 5 eighths.
Pupils should understand how improper fraction number lines correspond to mixed number lines
and understand that an improper fraction and an equivalent mixed number share the same
numerical value. They should also recognise that improper fractions in which the numerator
is a multiple of the denominator are equivalent to an integer in value.
TO add and subtract fractions with the same denominators over 1 whole, pupils must extend
their knowledge of adding and subtracting fractions with the same denominators within
1 whole from year 3. 7 one fifths + 4 one fifths is 11 one fifths, because 7 + 4 is
11. Here we are working with units of one fifth. Weíve seen in many cases in Year 4
we are applying our understanding of arithmetic to different units. The PV section showed
how children must work with units of 100. The MD section showed how children must work
with units of 6 for example, and other numbers they are learning times tables for, and here
the pupils must work with unit fractions.
Pupils must also be able to extend their adding and subtracting of fractions within 1 whole
to mixed numbers. 7 eighths ñ 2 eighths is 5 eighths so 3 and 7 eighths minus 2 eights
is 3 and 5 eighths.
In year 4 pupils are introduced to the first quadrant of the coordinate grid. Pupils must
be able to draw polygons specified by coordinates in the first quadrant. They should work accurately
with a ruler to join marked points accurately, developing drawing skills they learnt in year
3 geometry.
Pupils must also be able to translate shapes within the first quadrant, for example drawing
a translation of this kite in which point A has moved to point B.
Pupils should be able to identify line symmetry in different orientations in 2D shapes.
Pupils should also draw reflections of polygons in a line of symmetry.
This should include drawing reflections of shapes which are not in the same orientation
as the original shape.
Pupils must know that regular polygons are polygons in which all the sides are the same
length and all the angles are the same size. They should be familiar with a wide range
of examples of irregular polygons, including polygons in which all the sides are the same
length, or all of the angles are the same size.
Pupils should be able to calculate the perimeter of shapes drawn on cm grid by counting the
units.
Öor by calculating the perimeter from individual side lengths.