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 3 pupils need achieve by the end of the year, in order to
be ready to progress to year 4. There are accompanying materials which provide teaching
guidance for each ready-to-progress criterion, and example assessment questions.
We recommend that year 3 teachers should read the guidance for both year 2 and year 3, so
that they understand the starting point for year 3 pupils.
In Year 3 pupils need to know that 10 tens are equivalent to 100Ö
Öand use this fact to work out how many tens there are in other 3-digit multiples of 10.
Ten tens are 100 and 8 tens are 80, so 18 tens are equivalent to 180.
Pupils also need to understand the scaling model of place value and know that 100 is
10 times the size of 10, and 10 is one tenth the size of 100. 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 3 understanding these two different ways in which the unit
of 100 relates to the unit of 10: the grouping and exchange model and the scaling model.
Once they have understood multiple of 10s, pupils need to expand their understanding
to cover all 3-digit numbers. They should be able to decompose 3-digit numbers using
standard partitioningÖ
Öand also use non-standard partitioning to decompose 3-digit numbers in different ways.
This supports mental calculation, for example subtracting 2m from 342cm.
As well as understanding the quantity associated with numbers, pupils need to understand the
position of 3-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, for example the midpoint of
0 and 1000 is 500, and 342 sits roughly here relative to 0 and 500.
Positioning numbers in the number system prepares pupils for working with scales on measuring
instruments or charts, and helps pupils compare numbers and make estimations.
Pupils should have sufficient understanding of the number system to identify the previous
and next multiple of 100
And the previous and next multiple of 10.
And should be able to do this without a number line. This will prepare pupils for learning
to round numbers in year 4.
So, pupils will leave year 3 understanding these two models of 3-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 100 into 2, 4, 5, and 10 parts. 2 parts. 4
parts. 5 parts and 10 parts. This supports future fractions and measures work. Starting
to link 4 parts and 25 prepares children for understanding why º is equivalent to 0.25
when they meet decimals in year 5.
This decomposition of 100 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
In year 2, pupils learnt to add and subtract across 10, supported by tens frames and part-part-whole
models. In Year 3 pupils need to move beyond relying on models and jottings to solve these,
and need to become fluent in all of the addition facts shown here, and in corresponding subtraction
facts
During year 3, pupils need to start memorising their times tables up to 12 x 12 and be able
to derive corresponding division facts. This guidance suggests starting with the 10- and
5-times tables, then the 2, 4, 8 times tables so connections can be made between related
times tables.
As weíve seen, in Y3 children need to be able to work in units of 10 across the hundreds
boundary. Pupils need to be able to apply this knowledge to number facts by working
in units of 10. Pupils know that 8 + 6 = 14, so can reason that 8 tens add 6 tens is 14
tens, or 140.
And the same idea of applying known facts to units of 10 applies to multiplication.
3 x 5 = 15, so 3 x 5 tens is 15 tens or 150.
Pupils also need to learn to find complements to 100 in year 2. 62 + 8 ones makes 70, and
another 3 tens makes 100. This prepares pupils for finding change, for example, knowing that
if I have a £10 and spend £6.20, I will get £3.80 change and not £4.80.
Pupils should be taught the formal written methods of column addition, working with addends
with 2 or 3 digits and including regrouping. Dienes can be used to model the methods so
that children understand the significance of each digit in the recording of the formal
algorithms. Pupils should also be taught the formal written
methods of column subtraction.
Pupils have been taught about the additive relationship through Year 1 and 2. In Year
3 pupils need to develop flexibility in working with the relationship. They should be able
to write and understand the 8 equations that can represent an additive relationship and
know how each part of these equations relates to models showing the whole and two parts.
Pupils should use this understanding of the additive relationship to solve calculations
involving finding a missing addend, missing subtrahend, or missing minuend, and understand
what calculation they must use to find the missing number.
Pupils must be taught that multiplication is commutative. 4 groups of 5 and 5 groups
of 4, for example, give the same product (20). Knowing that 5 groups of 4 gives the same
total as 4 groups of 5 means that children do not need to learn 5 x 4 and 4 x 5 as separate
times table facts.
Pupils should be taught that the division facts they are learning can be applied to
two different division structures: quotative and partitive division. In quotitive division,
20 is divided into groups of 5 and there are 4 groups. In partitive division, 20 is distributed
equally between 5 with 4 in each part.
In year 3 pupils must be given a sold grounding in fractions. They must learn to use fraction
notation to represent a part of a whole that is divided into equal parts. Here the whole
is divided into 6 equal parts and one of those parts is shaded. One sixth of the whole is
shaded. Pupils should learn that a non-unit fraction is made up of a quantity of unit
fractions, for example, 5 sixths is 5 made up of 5 one-sixths. They should practise using
unitising language to emphasise this, interchanging the language of 5 sixths and 5 one-sixths.
Pupils should be taught to find a unit fraction of a small quantity and should link this to
partitive division ñ the equal distribution of a quantity into a defined number of parts.
Pupils know that 15 divided by 5 is 3, so 1/5 of 15 is 3. Pupils should only find fractions
of quantities which correspond to a known division fact so that the focus is on the
concept not the calculation.
Pupils must also understand that fractions are numbers. Pupils should become familiar
with seeing number lines labelled in fractions and practice counting in different unit fractions.
1/5, 2/5, 3/5, 4/5, 5/5 or 1. Pupils should also practice dual counting ñ one one fifths,
two one fifths ñ to reinforce that inside non unit fractions there are repeated unit
fractions. This will prepare pupils for addition and subtraction of fractions.
Pupils must be able to identify numbers on partially labelled number lines. Here, the
0 ñ 1 interval has been divided into 4 equal parts, so each of these parts is one quarter,
and the number indicated is æ. This will support pupils with ordering fractions, calculating
with fractions, and reading scales.
From all of this, pupils will understand that non-unit fractions are repeated additions
of unit fractions (for example ëinsideí three-eighths there are 3 one-eighths). Addition
and subtraction of fractions with the same denominator then follows logically: 3 one-eighths
plus 2 one-eighths is equal to 5 one-eighths. The same unitising principle applies to subtraction
of fractions. 5 one eighths minus 2 one eighths is 3 one eighths.
Pupils should be able to add and subtract fractions presented as equations and go beyond
needing images as a scaffold.
In Year 3 pupils should be taught about angles as a measure of turn and as a property of
shape. Pupils should be taught to recognise right angles presented in different orientations.
Pupils must have lots of opportunities to handle and manipulate shapes. They should
compose and decompose shapes to make other shapes, for example joining two identical
isosceles triangles to make a kite or a rhombus. Teaching pupils to see shapes within shapes
prepares them to decompose shapes for example when finding the area of compound shapes.
Pupils should be taught how to draw shapes. They must be taught how to mark vertices,
and how to position and hold a ruler to accurately join two marked points. They should draw shapes
on a variety of grids and papers to have plenty of opportunity to embed the precise drawing
skills that they will need going through KS2.