Year 4 maths · Key Stage 2 · Number – addition and subtraction
Year 4 column addition and subtraction: a guide for parents
In Year 4 children add and subtract numbers with up to four digits using written column methods, exchanging between columns when they need to. They estimate first, check answers using the inverse operation, and solve two-step problems in which they must decide which calculations to do and why.
Column addition and subtraction, explained
In column addition the numbers are written one under the other so that ones are under ones, tens under tens, hundreds under hundreds and thousands under thousands. Children add from the right. When a column adds up to 10 or more, they exchange: 10 ones become 1 ten, which is written as a small 1 in the tens column (many schools put it below the answer line), and so on across the number. Using four digits just means one more column than in Year 3, but there can be more exchanges to keep track of.
Column subtraction works the same way but in reverse. When a digit on top is smaller than the digit underneath, children exchange from the next column along: 1 ten becomes 10 ones, or 1 hundred becomes 10 tens. Schools now say “exchange”, not “borrow”. Place value counters or base 10 equipment are used until children understand why the exchange doesn’t change the value of the number. The hardest case is a zero in the column next door, as in 6,205 − 2,478, where the exchange has to go across two columns.
The curriculum says to use columns “where appropriate”. Not every calculation needs them. 5,000 − 1 or 3,400 + 600 can be done in your head, and 4,002 − 3,998 is easier by counting on from 3,998 to 4,002, a jump of 4. Choosing a clever method is a skill children keep practising, and part of the reason for learning to estimate first.
Estimating means rounding the numbers to make a quick, rough answer, for example 6,205 − 2,478 is roughly 6,200 − 2,500 = 3,700. If the written answer is nowhere near the estimate, something has gone wrong. Children also check using the inverse operation, which is the opposite calculation: after finding 6,205 − 2,478 = 3,727, they add 3,727 + 2,478 and should get back to 6,205. Addition is checked by subtracting one of the numbers from the total.
Children then use these methods to solve two-step problems, where one answer is needed to find another. For example: a school raises £2,350 at a fair and £1,875 at a sponsored walk, then spends £1,260 on books. How much is left? They decide which operation each step needs, often with a bar model, and give their reasons: add to find the total, £2,350 + £1,875 = £4,225, then subtract the spending, £4,225 − £1,260 = £2,965.
Words your child will hear
- Column method
- A written method where the digits of each number are lined up in columns by place value.
- Exchange
- Swap 10 of one place for 1 of the next place up, or 1 for 10 of the place below. Older books say “carry” and “borrow”.
- Inverse operation
- The opposite calculation, used to check: subtraction undoes addition and the other way round.
- Estimate
- A rough answer found by rounding the numbers first.
- Digit
- One of the symbols 0 to 9. The number 6,205 has four digits.
- Difference
- How far apart two numbers are, found by subtracting the smaller from the larger.
- Two-step problem
- A problem that needs two calculations to reach the answer.
What the National Curriculum says
In Year 4, pupils should be taught to:
- Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
- Estimate and use inverse operations to check answers to a calculation
- Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why
Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.
A worked example
Work out 6,205 − 2,478 using column subtraction, then check it.
- Estimate first: 6,205 is about 6,200 and 2,478 is about 2,500. 6,200 − 2,500 = 3,700, so the answer should be close to 3,700.
- Write the numbers in columns. In the ones, 5 − 8 can’t be done. There are 0 tens to exchange, so first exchange 1 hundred for 10 tens (hundreds 2 becomes 1, tens 0 becomes 10).
- Now exchange 1 of those tens for 10 ones. Tens go from 10 to 9 and ones from 5 to 15. Ones: 15 − 8 = 7. Tens: 9 − 7 = 2.
- Hundreds: 1 − 4 can’t be done, so exchange 1 thousand for 10 hundreds. Thousands go from 6 to 5 and hundreds from 1 to 11. Hundreds: 11 − 4 = 7. Thousands: 5 − 2 = 3.
Th H T O 5 11 9 15 6 2 0 5 - 2 4 7 8 ------------------------ 3 7 2 7 - Check with the estimate: 3,727 is close to 3,700. Check with the inverse: 3,727 + 2,478 = 6,205, which is the number we started with.
6,205 − 2,478 = 3,727
Common mistakes and how to help
Subtracting the smaller digit from the larger in each column
In the ones column of 6,205 − 2,478, 5 − 8 can’t be done, so a child turns it round to 8 − 5 = 3. This gives a wrong answer.
What helps: Return to counters. You can’t take 8 ones from 5 ones, so a ten has to be exchanged. Estimating first will show an answer that is clearly out.
Getting stuck when there is a zero to exchange from
To exchange from the tens, a child needs a ten, but there are none. Some children write 10 in the tens column without taking a hundred from the hundreds column.
What helps: Show 6,205 with place value counters (6 thousands, 2 hundreds, 0 tens and 5 ones): swap a hundred for ten tens, then a ten for ten ones. Say the steps aloud in order.
Lining up numbers from the left instead of by place value
Adding 3,482 + 95, a child lines the 95 up on the left, so the 9 sits under the 3 thousands and the 5 under the 4 hundreds.
What helps: Put the ones digits in a line first, using squared paper or a place value grid with Th, H, T and O headings.
Choosing the operation from a key word
A child sees “left” or “more” and picks a calculation without reading the whole problem. Many children also stop after the first step of a two-step problem.
What helps: Ask them to retell the story in their own words and draw a bar model. Then ask what the question actually wants to know, and whether they have found it yet.
How to help at home
- Make estimating a habit. Before any calculation, ask “About what should the answer be?” Rounding to the nearest hundred or thousand takes seconds and catches most mistakes.
- Use real four-digit numbers. Mountain heights make good practice. Ben Nevis is 1,345 m high and Snowdon (Yr Wyddfa) is 1,085 m. How much higher is Ben Nevis, and how high are they added together?
- Check with the inverse. After any sum, ask your child to undo it. 4,361 + 2,785 = 7,146, so does 7,146 − 2,785 get back to 4,361? The habit of checking is a skill they will use for the rest of school.
- Spot the mistake. Write a column sum with one deliberate error, such as a missed exchange, and ask your child to find it. Explaining someone else’s error is a good way to understand exchanges.
- Exchange with coins. Use £1 coins, 10p coins and 1p coins as hundreds, tens and ones, and swap ten 10p coins for a pound. It shows why the exchange doesn’t change the amount.
Related topics
Builds on
- Year 3: Column addition and subtraction
Leads on to
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