Year 3 maths · Key Stage 2 · Number – addition and subtraction

Year 3 column addition and subtraction: a guide for parents

In Year 3 children add and subtract three-digit numbers in two ways. They do simple calculations mentally by working with hundreds, tens and ones, and they learn the formal column methods for larger numbers, including exchanging between columns. They also learn to estimate an answer first and use the inverse operation to check it.

Column addition and subtraction, explained

Mental methods come first. Children add and subtract ones, tens and hundreds to and from three-digit numbers without writing anything: 346 + 5 = 351, 346 + 30 = 376, 346 + 200 = 546, and 346 − 20 = 326. The tricky ones cross a boundary, such as 398 + 5, where bridging to 400 first (398 + 2, then 3 more) gives 403. Mental questions with two-digit numbers can also have answers over 100, such as 68 + 57 = 125, so children can’t rely on staying below 100 any more.

For harder calculations children learn the formal column methods. The numbers are written one beneath the other with the ones, tens and hundreds lined up, and the calculation begins with the ones. In addition, if a column adds to ten or more, an exchange is made: 10 ones become 1 ten, or 10 tens become 1 hundred. Most schools record this as a small 1 in the next column, often just below the answer line. The method is introduced with base 10 blocks or place value counters, so children understand what is happening to the digits and don’t treat it as a trick.

Subtraction is harder because it often needs an exchange the other way. In 534 − 178, there are not enough ones to take 8 from 4, so 1 ten is exchanged for 10 ones. If a column has a zero, as in 502 − 237, the exchange passes along: one hundred is exchanged for ten tens, and then one of those tens for ten ones. Many children find this the hardest part of the year, and it improves with practice using equipment before moving to digits alone.

Two habits matter as much as the method. The first is estimating: before calculating 534 − 178, a child thinks “about 530 − 180, so about 350”, and afterwards checks that the answer is close. The second is checking using the inverse: add the answer back to the number taken away, or subtract one part from the total. Children also solve word problems that need them to decide what to do, and missing number problems such as □ + 148 = 523, where the inverse gives the answer: 523 − 148 = 375.

Words your child will hear

Column method: A written way to add or subtract, with digits lined up in ones, tens and hundreds columns.
Exchange: Swapping 1 ten for 10 ones, or 1 hundred for 10 tens (or the other way round). Older books call it carrying or borrowing.
Estimate: A rough answer worked out first, to see whether the final answer is sensible.
Inverse: The opposite operation. Addition and subtraction undo each other, so they can be used to check answers.
Partition: Split a number into hundreds, tens and ones, such as 346 = 300 + 40 + 6.
Difference: How far apart two numbers are, found by subtracting the smaller from the larger.
Missing number problem: A calculation with a gap, such as □ + 148 = 523, where the child finds the number that fits.

What the National Curriculum says

In Year 3, pupils should be taught to:

Add and subtract numbers mentally, including: a three-digit number and 1s; a three-digit number and 10s; and a three-digit number and 100s
Add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction
Estimate the answer to a calculation and use inverse operations to check answers
Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Work out 534 − 178 using column subtraction, and check the answer.

Estimate first. 534 is close to 530 and 178 is close to 180, so the answer should be around 350. Then set the numbers out in columns, lining up the ones.
```
    H  T  O
    5  3  4
  − 1  7  8
  ---------
```
Ones: 4 is smaller than 8, so exchange 1 ten for 10 ones. The 3 tens become 2 tens and the 4 ones become 14 ones. Now 14 − 8 = 6.
```
    H  T  O
    5  2 14
  − 1  7  8
  ---------
           6
```
Tens: 2 is smaller than 7, so exchange 1 hundred for 10 tens. The 5 hundreds become 4 hundreds and the 2 tens become 12 tens. Now 12 − 7 = 5.
```
    H  T  O
    4 12 14
  − 1  7  8
  ---------
        5  6
```

Hundreds: 4 − 1 = 3.

    H  T  O
    4 12 14
  − 1  7  8
  ---------
    3  5  6

Check with the inverse by adding the answer to the number taken away: 356 + 178 = 534. It matches, and 356 is close to the estimate of 350.

534 − 178 = 356

Common mistakes and how to help

Always taking the smaller digit from the larger one: 534 − 178 = 444

In each column the child avoids the awkward exchange by subtracting the smaller digit from the larger one: 5 − 1 = 4, 7 − 3 = 4 and 8 − 4 = 4.

What helps: Estimate first: 444 is far from 350, so something is wrong. Use blocks to show that 4 ones cannot give 8 away, and that a ten must be exchanged.

Exchanging but forgetting to reduce the column it came from

The child turns 4 ones into 14 but leaves the 3 tens as 3, so the same ten has been counted twice.

What helps: Cross out and rewrite both digits every time: the 3 tens become 2, and the 4 ones become 14. Check by adding the answer back to the number taken away.

Misaligning the digits when numbers have different lengths

In 346 + 52, a child writes the 52 under the 3 and 4, so the 5 is added to hundreds instead of tens.

What helps: Write H, T and O above the columns, or use squared paper, so each digit has its own square. Read the number aloud as hundreds, tens and ones as you write it.

Writing both digits of a two-digit column total in one place

In 348 + 267, the child gets 8 + 7 = 15 and writes 15 under the ones column. The 10 should have been exchanged to the tens column, and the answer has too many digits.

What helps: Say it as ones and tens: “15 ones is 1 ten and 5 ones.” Write the 5 in the ones column and the 1 small in the tens column. The answer is 615.

How to help at home

Practise adding 10 and 100 mentally. Take a three-digit number from a bus ticket, a page number or a receipt and ask for 10 more, 100 more, 10 less and 100 less. Include numbers like 395 or 902 that cross a boundary.
Estimate before you work it out. When your child is about to add or subtract, ask “About how much do you think it will be?” Estimating using nearby tens or hundreds becomes a habit that spots most mistakes.
Use coins to understand exchange. Show 134p as a £1 coin, three 10p coins and four 1p coins. To take away 48p there are not enough pennies, so a 10p coin is swapped for ten 1p coins. Then there are not enough 10p coins to take away four, so the £1 coin is swapped for ten 10p coins. Doing it with real coins shows what an exchange means (the answer is 86p).
Check by working backwards. After a column calculation, ask your child to check it using the opposite operation. Make a few missing number puzzles, such as 245 + □ = 612, and swap with a sibling or parent.

Builds on

Year 2: Adding and subtracting to 100

Leads on to

Year 4: Column addition and subtraction

Everything in Year 3 maths

Updated 20 October 2026.