EYFSChildren are taught that addition is the combining of two or more amounts. They begin by counting all of the items in the groups, then move on to counting on from the largest amount. Children are encouraged to develop a mental image of the size of numbers. They learn to think about addition as combining amounts in practical, real life situations. They begin to record addition number sentences such as 2+4=6 and 8=3+5.

Progression in written addition

Stage 1Children move on to using Base 10 equipment to support their understanding of addition.12 + 6 = 18

12 cubes are lined up (1 ten and 2 ones.)

If possible, use two different colours of base 10 equipment so that the initial amounts can still be seen.Calculations should also be expressed as 18 = 12 + 6.Number lines mayalso be used to calculate or record.

Stage 2Children continue to use the Base 10 to support their calculations, including exchanging 10 units/ones for 1 ten when the total of the ones is 10 or more. They will record their own drawing of the Base 10 equipment, using lines for 10 rods and dots for the units/ones. 43 + 24 = ? The ones are addedfirst 3 + 4 = 7The tens are added next40 + 20 = 60Both answers are put together60 + 7 = 67

38 + 26 = ?As the units add to make a number higher than 10 an exchange will take place before adding the tens.

This can be shown in their recording with exchanged ones crossed out, a ten added in and any ones not exchanged have a ring put around them. They should also calculate additions where more than 2 numbers are involved, where the answer is less than 100.

32 + 24 + 14 = ?Place value arrows can be used to support understanding as children move towards stage 3 and expanded methods.

Stage 3Children continue to use Base 10 and/or notation taught in Stage 2.65 + 27

Children may need to record using expanded methods to begin with (use place value arrows to support this) , quickly moving on to a standard written method.

The first example below would be said as follows 5 + 8 = 13, put down 3 carry the 1020 + 40 + 10 carried over = 70 ( 7 written in tens column)600 + 0 = 600 ( 6 written in hundreds column).

Stage 4Children will be expected to use the method taught in Stage 3 to add numbers with • More than 3 digits• Numbers involving decimals• And adding any numbers of amounts togetherThis can be scaffolded with the use of Base Ten, place value counters, coins ( £1, 10p, 1p)

Children should be able to revert to expanded methods if experiencing any difficulty.

Progression in written additionStage 5Children should be encouraged to choose and use practical manipulatives, or pictorial representations to support their calculations if needed. This should especially be encouraged when the type or amount of numbers in calculations changes e.g. additions of different types or amounts of measures.

They will be using a formal written method but may need to briefly use expanded methods in certain situations.

Children will be introduced to calculating additions with more than 4 digits:

and calculations where units are not exactly the samee.g.. 342cm + 9·5m

Stage 6At this stage children should be using formal columnar addition to calculate answers of problems with • large numbers,• decimals • more than 2 figures• multi-step problems which involve

addition,They should know when to use addition in problems with context. They should be able to decide whether to use manipulatives and representations to support their calculation but be encourage to move to the formal written method as soon as possible.

Column addition with support Traditional column addition

Addition

12 = 10 + 2

12 + 6 = 18

Base 10 equipment used

0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2

Counting and count on

65 + 27 Group the ones first

Regroup = 92

Different units of measure:3·4m + 127 cm