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 2 pupils need achieve by the end of the year, in order to
be ready to progress to year 3. There are accompanying materials which provide teaching
guidance for each ready-to-progress criterion, and example assessment questions.
We recommend that year 2 teachers should read the guidance for both year 1 and year 2, so
that they understand the starting point for year 2 pupils.
In year 2, pupils must be taught to connect the way two-digit numbers are written in numerals
to their value. ìThis is the number 23. The 2 shows we have 2 groups of ten. The 3 shows
we have 3 extra ones.î They must be able to do this also when the position of tens
and one manipulatives is reversedÖ
Öor when tens and ones are presented randomly.
Pupils must understand that 23, for example, can be composed of 23 onesÖ
Öor of 2 tens and 3 ones. Pupils should know that they can group objects into 10s, and
count the number of 10s and number of ones, to enumerate the objects in large set.
Once pupils have understood the composition of a number in terms of number of tens and
number of ones, they should be able to apply this understanding to solve addition and subtraction
calculations which involve standard partitioning.
Pupils should become familiar with seeing 0 ñ 100 number lines and placing the numbers
0 ñ 100 in the linear numbers system. They should be able to identify numbers on partially
labelled number lines using strategies other than counting forward in 1s, for example identifying
that this number is 36 because it sits one more than the halfway point between 30 and
40, or that this is 79 because it is one less than 80. Pupils should also be taught to estimate
the position of numbers to 100 on unmarked number lines. Teach pupils to mark the midpoint
of number lines to help estimate the position of numbers, for example 60 sits roughly here
relative to 50 and 100. 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. So, pupils will leave year 2 understanding
these two models of 2-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.
Slide 10 In year 1, pupils learnt addition and subtraction facts within 10. Pupils must
continue to practice these facts in year 2 so that they are able to recall facts fluently
and apply them to 2-digit calculation. Slide 11 Year 2 pupils should also learn to
add and subtract across 10. They should use tens frames and partitioning diagrams to understand
how to do this. To add 7 and 5, we partition the 5 into two
parts. 7 and 3 make 10, and 2 more make 12.
To subtract across 10, pupils should use one of two alternative strategies. In the ësubtracting
through 10í strategy, we subtract the subtrahend, in this case 9 in two steps, first subtracting
5 to give 10, and then we still have 4 more to subtract which leaves 6.
In the ësubtracting from 10í strategy we partition the minuend into 10 and 5. Subtract
the 9 from the 10 to leave 1, and then put the remaining 1 and 5 together to make 6.
Here are the two strategies for subtracting across 10 side by side. Subtracting through
10 and subtracting from 10. Both show that 15 ñ 9 is equal to 6.
In year 1 pupils met the additive structures of aggregation and partitioning, and augmentation
and reduction. To be ready to progress from year 2 pupils also need to be able to solve
questions such as: There are 5 red cars. There are 3 blue cars. How many more red cars are
there than blue cars? This is the difference structure, where two quantities or measures
are being compared. Pupils should be able to solve difference problems phrased as ëfind
the differenceí, ëhow many moreí and ëhow many fewerí. They should relate them to either
a missing addend equation or to subtraction, applying known facts and strategies.
In year 2 pupils must learn to apply addition and subtraction facts within 10 to units of
10. Because 4 ones + 3 ones is 7 ones, 4 tens + 3 tens = 7 tens. And equally we can subtract
either of those parts using known facts, so 7 tens minus 4 tens is equal to 3 tens, and
7 tens minus 3 tens is equal to 4 tens. Working in a unit of 10 in this way is called unitising.
Pupils must learn to use this knowledge to solve addition and subtraction of 2-digit
numbers. Pupils can use the knowledge that 4 + 3 = 7 to solve calculations like 40 +
30 = 70,
And pupils can use their knowledge of number facts within 10 to solve calculations involving
the subtraction of a multiple of 10. 7 minus 3 is equal to 4, so 75 ñ 30 = 45
because we are subtracting 3 tens from 7 tens.
The range of calculations that pupils should be able to apply their knowledge of 4 + 3
= 7 is shown here. Adding or subtracting multiples of 10, adding a multiple of 10 to, or subtracting
a multiple of 10 from another 2-digit number, and adding a single digit number to or subtracting
a single digit number from a 2-digit number.
Pupils must also be able to subtract a single digit number from a multiple of ten, by using
complements to 10 ì10 minus 3 is equal to 7, so 30 minus 3
is equal to 27.î
Pupils also need to be able to add both multiples of ten and single digit numbers. They need
to be able to identify the multiples of 10 and add these, and then add the single digit
numbers.
They then have the requisite understanding to add two 2-digit numbers by partitioning
into tens and ones parts.
Place value manipulatives, such as Dienes, expose this structure for pupils, and pupils
should be able to use place value equipment to explain how to add two 2-digit numbers.
To be ready to progress to year 3 pupils need to be able to use their own jottings to solve
calculations such as these, without relying on manipulatives to help them get an answer.
Pupils also need to be able to subtract from a 2-digit number. Pupils should be able to
partition the subtrahend, and then subtract both these parts in turn. 45 minus 20 is equal
to 25. 25 minus 3 is equal to 22.
In year 2, pupils should be taught to relate equal group contexts to multiplication and
division. Pupils can already write repeated addition expressions. In year 2 they must
be taught to write multiplication expressions to represent the same context and relate the
terms to the context 3 times 5.
The 3 represents the number of groups. The 5 represents the number of eggs in each
group.
Pupils must be able to understand equivalence between a repeated addition expression and
a multiplication expression and write and complete similar equations.
Pupils should also learn to calculate the total the product of repeated groups of 2,
5 or 10s, initially by skip counting: 5, 10, 15.
3 times 5 is equal to 15
Pupils should be able to relate multiplication to situations where the total number of items
cannot be seen, for example by representing 3 x 5 with 3 five-value counters.
Pupils should also be able to solve multiplication equations presented without a visual prompt.
They may skip count on their fingers or may draw their own simple groups of 5 picture
to help calculate this. 5, 10, 15
Pupils need to be able to find the number of groups needed to give a particular total
to solve multiplication equations with missing factors. For example, ìThere are 15 biscuits.
If I put them into bags of 5, how many bags will I need?íí can be represented by the
equation shown. Pupils can use skip counting or their emerging
2, 5 and 10 multiplication table fluency to calculate the missing factor. 1 group of 5,
2 groups of 5, 3 groups of 5 is equal to 15.
Pupils also need to be taught that dividing a total into equal groups can be represented
with a division equation. 15 divided into groups of 5 is 1 group of
5, 2 groups of 5, 3 groups of 5. 15 biscuits divided into groups of 5 is 3
groups.
Pupils also need to be able to solve division calculations that are not set in contexts.
They should recognise that they need to skip count in the divisor (2, 5 or 10), or use
the associated multiplication fact, to find the quotient. To calculate 15 div 5, they
can skip count in five (5, 10, 15) to see there are 3 groups or apply the fact that
3 x 5 = 15
To gain sufficient experience of shapes, pupils need to handle a wide variety of common 2D
and 3D shapes including quadrilaterals and polygons, and cuboids, prisms and cones.
Teach pupils to identify the faces, edges and vertices in 3D shapes, and the sides and
vertices in 2D shapes. Pupils must know that a polygon is defined
by its number of sides, rather than whether it looks like an image of a particular shape.
For example, although pupils may informally describe this as being like a square with
two corners cut off, they should recognise that it is in fact a hexagon because it has
6 straight sides.
As well as identifying and counting sides and vertices, which are precursors to perimeter
and angles, pupils should also reason about the space inside a 2D shape as a precursor
to area. They should reason about the shape and size of polygons relative to each other.
As children do not have techniques measure this space yet, their descriptions will necessarily
involve informal language, for example they may describe shape F as being like shape A
stretched out so that it is longer than A and therefore is larger.