What Is The Column Method Of Addition And Subtraction? Explained For Primary School
The column method is one of the most common written methods pupils learn when adding and subtracting increasingly large numbers. Number and calculation is a large part of the primary maths curriculum and pupils are expected to use written methods to add and subtract by the end of Year 3.
What is the column method?
The column method is a mathematical way of carrying out calculation in which the numbers you are calculating are written with each digit in the correct place value column. This allows the children to use their knowledge of place value to understand addition and subtraction.
What is column addition?
Column addition is a formal method of adding two numbers. As above, the numbers are presented on top of one another, ensuring that each digit lines up correctly. This allows children to understand addition with regrouping when we cross the tens boundary.
What is column subtraction?
Column subtraction uses the same principles – presenting the digits one above the other and lining them up by place value. A benefit of using column subtraction as a method is that it allows the children to understand and visualise exchanging.
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How to arrange the column method
For the column method to work, it is essential that the children set it out correctly.
For this, they need to have a secure understanding of place value and partitioning numbers to show this so the digits are placed in the correct columns. This is where the standard practice of ‘one digit per square’ becomes about more than just presentation.
When teaching the column method, it is often a good idea to initially ask pupils to write column headings above their calculation (Th, H, T, O, etc.) and make a point of reminding them that there should be one digit in each square.
This advice avoids common problems pupils may face when setting their work out which therefore causes them to make mistakes in their calculation. Most of these mistakes involve pupils not using the correct columns when arranging their work.
In Year 3, when children add and subtract a three-digit and two-digit number, one way to ensure that they arrange their columns correctly is to use a zero as a place holder in the hundreds column for the 2-digit number.
There are also style considerations to be made regarding arrangement of the column method. In addition, we will sometimes need to regroup numbers between columns such as in the calculation 281 + 634.
At this point, 8 tens plus 3 tens equals 11 tens, equal to 110. We know we cannot put 11 into the tens column, so we need to exchange ten tens for one hundred. There are two options for how to arrange this:
I have found the option on the left to be the most effective in the classroom because pupils can see the one hundred when they come to adding the hundreds column. In my experience, pupils can forget that we have regrouped a hundred if it is below the working out as in the picture on the right.
Similarly, when exchanging in subtraction, we need to consider how we arrange it. The most common way to do this is as follows:
What is the expanded column method?
The expanded column method allows children to add numbers that require regrouping by adding each place value column individually. This is usually used as the first step to being able to use traditional columnar addition.
In the above example (taken from the Year 3 curriculum), we begin on the right as is necessary for column addition. We add the ones column (9+5) and write this answer following the correct place value columns.
The same method is followed for the tens column and the hundreds column. By writing the numbers they have added in brackets next to their work, children can see where their answer comes from.
This can also work for decimal numbers from Year 4 onwards:
Using the column method of addition here can help children to remember where the decimal point is in the number, since it always stays in the same place. In this example, we begin on the right again, adding the numbers in the same column together.
How to calculate using the column method
Step 1: Arrange the calculation using place value columns.
Step 2: Beginning on the right (in this case the ones column), complete the calculation (9-8) and write the answer underneath, in the same column.
Step 3: Calculate the next column to the left of this – here it is the tens column. When explaining this to the children, make sure they understand that it is 7 tens subtract 2 tens or 70-20, not 7-2.
Step 4: Move to the left again. In the example here, we need to exchange in the hundreds column. We cannot subtract 5 hundreds from 3 hundreds without exchanging 1 thousand. We need to exchange one of the thousands for ten hundreds, making the calculation thirteen hundreds subtract five hundreds.
Step 5: Complete the final column to the left – three thousands minus one thousand.
When do children learn about column methods in school?
The national curriculum specifies using ‘formal written methods of columnar addition and subtraction’ from Year 3. However, the guidance suggests in Year 2 that ‘recording addition and subtraction in columns supports place value and prepares for formal written methods with larger numbers’ so some schools may choose to introduce the column method with 2-digit numbers in Year 2, however this is not statutory in the KS1 maths curriculum.
From Year 5 as part of the fractions strand of the national curriculum, pupils will solve problems involving decimals. At this point, they also use the column method to add and subtract decimal numbers too.
What other methods of addition and subtraction are used in school?
While the column method is the main formal method mentioned in the national curriculum and therefore taught in school, children learn to add and subtract using a variety of different mental methods and resources during their time at primary school.
Knowledge of addition and subtraction begins in the early years and is focussed on using concrete materials to add more and take away from a group of objects. At this point they will be using the language ‘more than’ and ‘less than’ and then move onto ‘add’ and ‘subtract’ or synonyms of these.
Following the national curriculum, children need to use mental methods to find the answers to addition and subtraction calculations within twenty during Year 1. They use concrete and pictorial resources to help them become fluent with this as this is essential to producing confident mathematicians later on in their education.
Children use concrete maths resources such as counting blocks, numicon, dienes, bead strings, place value counters and number lines before working entirely with calculations to ensure that they develop a strong understanding of number value, number sense, addition and subtraction. They then move onto formal methods of calculation, primarily the columnar method, to be able to show their working out in more complex calculations and word problems.
The mathematics curriculum sees children repeat the same content with larger numbers in a spiral curriculum, so in Year 3 they will learn addition and subtraction with three-digit numbers, in Year 4 with four-digit numbers and in Year 5 with numbers up to one million.
How does the column method relate to other areas of mathematics?
The column method for addition and subtraction is set out in an exercise book in the same way as for the multiplication method. Therefore, a strong grounding in the column method in Year 4 will help pupils in Year 5 when they move onto multiplication and long division.
Column method worked examples
1. 3_4 + 615 = 989. Fill in the missing digit.
Here, the child has found the missing number by using the inverse. They know that 8 tens is the answer in the tens column and they already have one ten. Therefore, to work out the missing number they have used the inverse by subtracting 1 ten from 8 tens which is 7 tens.
2. A school has £5500 to spend on new resources. They buy 10 tablet computers for £3468 and then spend £956 on a charging unit. How much do they have left in the budget?
This question is a two part word problem. You could subtract each number from the original £5500, but here I have decided to add the two amounts that have been spent and then subtract this from the total budget. This shows an application of both column addition and subtraction to achieve the answer to the problem of £1076.
3. Is this calculation true or false? Prove it
8.7 + 0.4 = 8.11
This is false. As shown in the calculation is 9.1. The calculation serves as proof. You could stretch this by asking what they think has been done to get the answer 8.11.
Column method example questions
1. 3_57 + 4801 = 8058. Fill in the missing digit.
Answer: 2 hundreds
2. The highest mountain in the world is Mount Everest which is 29,029ft tall. The highest mountain in the UK is Ben Nevis which is 4411ft. How much higher is Mount Everest than Ben Nevis?
Answer: 29029ft – 4411ft = 24,618ft
3. Ali does a calculation:
Explain what Ali has done incorrectly.
The 24 needs to be moved along one place so the 2 is worth 2 tens and the 4 is worth 4 ones.
4. Charlie went to the shop and spent £24.56 on two items. She spent £6.78 on one item. How much did the second cost?
Answer: £24.56 – £6.78 = £17.78
5. What mistake has been made? How could it be corrected?
Answer: The tens column has not taken into account the ten regrouped from the ones column so should be 12 tens. This hasn’t been taken into account in the hundreds column either which should be 9 hundreds.
The column method is written by placing each number one above the other, ensuring that digits with the same place value are in the same column.
Column method is a written method to complete addition and subtraction calculations.
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