Progression in Teaching Addition
EYFS and KS1
It is essential that children learn Maths through a progression of
concepts through concrete methods, pictorial methods and finally
abstract methods.
EYFS
N
Progression of skills and Methods
Counting in order with
objects and actions also
in a random arrangement
EYFS
N
Counting objects from a
larger group
EYFS
N
Matching numbers 0-10
with objects and actions
EYFS
N
Understand numbers change
in quantity when adding
(more than)
EYFS
N
Count in ones from any given
number up to 10
EYFS
Relate addition by combining
two groups of objects
EYFS
Rec
Reconsining numbers 0-20
and ordering numbers
EYFS
Rec
Use familiar stories and
rhymes to count on in
ones, twos, fives and tens
EYFS
Rec
Count in ones from any given
number up to 20
Can you count
me out 4
coats?
+
3, 4, 5, 6 …
15, 16, 17, 18…
EYFS
Rec
EYFS
Rec
1
Using objects and a number line
to add one more and to add
together 2 one-digit
numbers.
Know doubles of numbers
Read, write and interpret mathematical
Statements involving addition (+),
Subtraction (-) and equals (=) signs
1
Represent and use number bonds
and related addition and
subtraction facts within 20
1
Add and subtract one-digit and
two-digit numbers to 20,
including zero
2
Show that addition can be
done in any order (commutative)
and subtraction cannot
2
Derive and use related number facts
up to 100
3 + 7 = 10
3 + 7 = 10
15 + 5 = 20
2
Add 1 or multiples of 10
from any two-digit number
30 + 70 =100
85 + 5 = 100
2
Begin to partition numbers
in order to add
2
Counting in fractions up to 10, starting from any numbers and using the ½ and
2/4 equivalence on the number line
KS2
By the end of KS2, children will be taught to calculate at an abstract level using concrete and pictorial methods for
support where needed. The following explains how children can make progress using number lines, partitioning, the
column methods of addition and adding fractions
Using a number line

Count on by partitioning the second number only then recombining
53 + 36 =
53 + 30 = 83
83 + 6 = 89
+ 30
When pupils begin using the
number line they may initially
add with different amounts.
They may need to add in ones,
two, five or tens e.g. 10 + 10
+10
+6

Count on, bridging through tens boundary, partitioning the second number then recombining

Add the nearest multiple of 10, then adjust
+ 10
68 + 19 =
68 + 20 = 88
88 – 1 = 87
68
+10
78
88
Partitioning
It is important that children have a good understanding of place value and partitioning using pictorial and concrete resources to support
calculations. This method allows children to see what happens to numbers in the standard written method.
T
Expanded Column Method
U
40
+
30
70
+
+
Children should use apparatus
to support them when they
first begin to use this method.
When they have shown an
understanding of the process,
apparatus may not be
necessary.
8
6
14 = 84
TU
48
+36
14
70
84
Children continue to use
apparatus to support them
if required, in particular
use of place value coins.
Standard Column Method
The previous method reinforces what happens to the numbers when they are added together. This method can be applied to adding
increasingly larger number. However pupils must understand the place value of each digit e.g. 45378 = 40000 + 5000 + 300 + 70 + 8
Appendix New National Curriculum
Fractions
Addition of fractions with the same denominator within one whole.
Addition of fractions with the same denominator and denominators that are multiples of the same number to become fluent
through a variety of increasingly complex problems beyond one whole .Counting using simple fractions and decimals, both
forwards and backwards .
Add fractions with different denominators and mixed numbers, using the concept of equivalent fractions
 Start with fractions where the denominator of one fraction is a multiple of the other (e.g. 1/2 + 1/8 = 5/8) and
progress to varied and increasingly complex problems
 Practise calculations with simple fractions and decimal equivalents to aid fluency