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# What Is Column Addition? Explained For Primary School Parents & Teachers

Here we explain what exactly column addition is, tell you how it is used and learnt in primary schools and provide some examples of questions involving this method!

Column addition is just one part of a child’s journey through addition. As with column subtraction it is also one part of the journey where teachers should not rush to get pupils to this point.

Our younger learners would be far better off with being exposed to, and having ample time to practice, mental methods of addition that have been carefully thought out and sequenced. It is not until Year 3 that the ‘formal’ method of column addition needs to be introduced.

Column addition is what the curriculum calls a ‘formal’ written method for solving questions and problems involving addition. Column addition is first introduced in Year 3 but will continue to be used by pupils up to Year 6 and beyond.

The column method of addition relies on pupils being able to correctly arrange a calculation, such as 789 – 642, into columns so that the operation of addition can take place. An example of this can be found in appendix 1 of the mathematics curriculum:

### What is the expanded column method for addition?

Before going straight to the column method above, a good intermediate way to get pupils ready for it is to use the expanded column method.

Expanded refers to writing out each digit into its corresponding value. For example, writing the 3-digit-number 456 in its expanded form would be 400, 50 and 6.

Place value counters are usually used to help show this connection, where 4 one hundred counters would be in the hundred’s column, 4 tens counters in the tens column and 6 ones placed in the one’s column.

In the context of column addition, for example 456 + 243, it would look like this:

400  50  6 +

200  40  3

When both numbers are added together, the answer 699 is obtained. This is shown by placing all the counters together.

There is, however, no requirement for teachers to teach the expanded addition method as it is not in the national curriculum. Join the Third Space Learning Maths Hub

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Children will first encounter column additionin Year 3. They will be expected to:

• add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction

In Year 4, this progresses to the following statement:

• add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate

When in Year 5, this progresses to:

• add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)

For Year 6, while there is no statutory statement for column method, the non-statutory notes and guidance stipulates the following:

• Pupils practise addition, subtraction, multiplication and division for larger numbers, using the formal written methods of columnar addition and subtraction, short and long multiplication, and short and long division

### How do you arrange and add columns?

When you rearrange a written addition calculation into columns, it is important to remember some crucial elements that need to be correct. Unlike with subtracting, the operation of addition benefits from the commutative law. This means that we can write 756 + 123 as the following:

756 +

123

Or as

123 +

756

The answer will be the same regardless.

However, like with column subtraction, an important part of the arrangement is to ensure the place values all align. This is especially true for when you need to add numbers that have a different number of digits. Getting this part of the process wrong will definitely result in the procedure delivering an incorrect answer. If the calculation was 1430 + 345, it is imperative that these are arranged correctly in the following way:

1,430 + and not as 1,430 +

345                         345

This is why having a real solid understanding of place value is imperative to being able to correctly use column addition.

### 2 digit addition with regrouping

In the early experiences of column addition, teachers need to be careful about not providing two digits that will cross over 10 as the procedure increases in complexity when this is the case. We will explore this through the calculation of 45 + 38.

The base system used in our number system is the base 10 number system, which means that the system creates an additional place value when the digits in the place value exceed 9. As can be seen in the ones column, the number represented by all the ones would exceed 9. Pupils who do not understand this aspect of the number system are likely to write the following answer:

45 +

38

713

The concept of exchanging is an important one and an idea that pupils need to master to be successful to perform column addition of this type.

Pupils need to know that they can group 10 ones and that these can be regrouped for 1 ten.

This 10, quite clearly, needs to be moved into the 10s place value.

We can see now how this regrouping has affected the representation. No longer are there 13 ones in the ones.  In terms of column addition, this now looks like this:

All that is left to do is add up all the 10s.

Pupils can now see that there are 9 tens counters so we can write this as:

Including the additional ‘1’ digit which was represented by the grouping of the additional 10 ones is also a crucial step that pupils can often miss out when performing the formal method. It is important to show this working out so that pupils can fully understand the method and what they are doing.

While I would advocate that pupils first learn the regrouping method of column addition with 2-digit by 2-digit calculations, this would be to show how the procedure works only and to make the maths more manageable.

I would still want to encourage mental methods of solving these types of questions in the first instance. Pupils should know that the formal written method should be a fall back strategy when they cannot perform the calculation mentally, not the default.

### Addition of three digit numbers

Thankfully, when pupils have understood the concept behind the place value system, there is nothing new to learn, as such. Rather, there are just more times where it needs to be applied. Take 537 + 572. First, we can add the ones.

The total of 3 + 7 = 10 and so we can group those 10 tens and group them into 1 hundreds. It is important that 0 is written as a place value holder. The 1 hundred can be written above or below the 100 column.

Finally, we can add the digits in the hundreds together. This will include the additional ‘1’ hundred and give a total of 11. As there are no more columns to add together the 11 may be written without having to place a digit above the next place value.

It is important for pupils to realise however that this is not 11 but represents a 1 in the thousands place and a 1 in the hundreds. This is demonstrated pictorially below.

When pupils increase their understanding of decimal place value, they will be expected to use their knowledge of this and of column addition to solve problems involving decimals. This is usually done in the context of measurements.

It is important that pupils understand that the principles of place value that they should know and how column addition works does not change, it is only the context (decimals) that changes.

### What other methods of addition are used in schools?

As mentioned in the introduction, column addition should not be the go-to strategy that pupils are taught immediately. There are many other mental strategies that pupils need to learn first which they do in the early stages of schooling.

Common strategies include:

• Partitioning: This is where numbers are partitioned (broken apart) into its place value. This is then used for the pupils to perform two separate additions.

For example. 36 + 22 =

36 + 20 + 2. From here pupils could perform 2 + 6 and 30 + 2 and before adding the sum of both questions together to get 58.

• Bridging to ten: This is linked to partitioning, but the number is not broken up into its expanded form but partitioned in such a way that a bond to 10 can be created.  For example, in 67 + 25, the 25 could be partitioned into 20 + 3 + 2. This would allow the 3 to be added to the 67 to get 70 and then 20 could be added to the 70 to get 90 before finally adding the 2 to get a total of 92. Number lines are a useful tool to aid pupils in doing this.

As has already been warned previously, but I feel it important to state again, when pupils go on to learn the formal method of addition, they fall into the habit of using this method to solve every addition question they come across.

Teachers, however, should encourage the use of the formal written method as a fall back or checking strategy and prioritise the mental strategies in Key Stage 2.

1. 356 + 567 =

This question should prove straight forward and require little explanation at this stage as to what the steps are. It is crucial that pupils remember to write the digit that they are ‘carrying’ over to the next place value for the answer to be accurate.

2. 4,783 + 2,349

As with the question above, this question is no more complicated but just contains more steps to reach the conclusion. Pupils will need to add 9 and 3 to get 12. The ones will need to be written in the ones column and the 1 ten written underneath the tens.

Next is to add 80, 40 and 10. The tens are written down in the tens place and the hundred is carried over. This is repeated until all the digits have been added together.

3. 2,354.43 + 1,789.52 =

As in the examples above, once pupils have that understanding of place value, the concept of column addition remains the same.

1. Harry had £476 in his bank account.  His brother, Ron, had £874 in his. How much money did they have altogether?

This is an example of the addition structure of aggregation. There are two separate quantities, and we want to see what the combined total is. However, the two amounts remain quite distinct.

Together, they would have £1,350.

2. A bike costs £1899. The price increases by £279. What is the new price?

This is the augmentation structure of addition where there is a clear increase in quantity and not a combination of two separate quantities. The process of solving the problem is the same as all other column addition problems.

1. 345 + 237 =

2. 6,473 + 4,287 =

3. 795.32 + 452.12 =

4. Harry had £734 in his bank account.  His brother, Ron, had £609 in his. How much money did they have altogether?

5. Bill wrote 2,378 words on Saturday morning and then wrote another 1,789 words in the afternoon.  How many words did he write altogether?

6. A bike costs £1699. The price increases by £579. What is the new price?

Wondering about how to explain other key maths vocabulary to your children? Check out our Primary Maths Dictionary, or try these:

You can find plenty of worksheets for primary school pupils on the Third Space Learning Maths Hub.

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