Ross MackellUK-qualified primary teacher · 8 min read

Your child works out 403 − 178 and writes 375. The real answer is 225.

That isn't a careless slip. It's one specific habit, and once you know what it looks like, you'll spot it straight away. In this guide I'll show you how column addition and subtraction are taught in UK primary schools now, the three mistakes I see most often, and exactly what to say when they happen.

I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. By the end of this page, you'll be able to sit next to your child and actually help.

Why schools say "exchanging" instead of "borrowing"

If you learned to "borrow" at school, you weren't taught wrong. Your child just uses a different word, and there's a good reason for it.

• "Borrowing" suggests you take something and give it back later. You never give it back, which confuses children.
• "Exchanging" describes what really happens. You swap one ten for ten ones. The number stays exactly the same; it's just split up differently.

For example, 652 is 6 hundreds, 5 tens and 2 ones. Exchange one ten and it becomes 6 hundreds, 4 tens and 12 ones. It's still 652.

This is the big idea behind how maths is taught now. Children don't just learn the steps; they learn why the steps work, so they don't fall apart the moment a question looks a little different.

Tip: in school, your child will often use place value counters or base ten blocks first, then drawings, then the written method on its own. If they get stuck at home, drawing the tens and ones is never a step backwards.

Column addition, step by step

Subtraction builds on addition, so start here. Let's work out 347 + 285.

1. Line up the columns. Hundreds under hundreds, tens under tens, ones under ones. Say it out loud: "ones on the right."
2. Always start with the ones. 7 + 5 = 12. That's 1 ten and 2 ones, so write 2 in the ones column and carry 1 ten into the tens column. Write it small, under the line.
3. Tens next. 4 tens + 8 tens = 12 tens, plus the 1 ten we carried makes 13 tens. Write 3 in the tens and carry 1 hundred.
4. Hundreds. 3 + 2 = 5, plus the 1 we carried makes 6.
5. Read and check. The answer is 632. Does it make sense? Roughly 350 + 300 = 650, so 632 is about right.

Notice the language: "carry 1 ten", not just "carry 1". When your child carries, they should know what they're carrying. That's the difference between following steps and understanding them.

Column subtraction with exchanging

Now subtraction. Let's work out 652 − 237. Same rules: line up the columns and start with the ones.

1. Ones: 2 − 7. There aren't enough ones. This is the exact moment many children flip it and do 7 − 2. Instead, we exchange.
2. Exchange. Go next door to the tens. Cross out the 5 and write 4. That ten becomes ten ones, so the 2 becomes 12.
3. Ones again: 12 − 7 = 5.
4. Tens: 4 − 3 = 1. Use the 4, not the 5, because one of those tens has already been exchanged.
5. Hundreds: 6 − 2 = 4. The answer is 415.
6. Check with addition: 415 + 237 = 652. Get your child to do this every time. It turns one question into two.

Exchanging across a zero

This is the one that catches out children and adults. Back to 403 − 178.

1. Ones: 3 − 8. Not enough, so we go next door to the tens. But there are 0 tens, so there's nothing to give.
2. Go one further, to the hundreds. Cross out the 4 and write 3. That hundred becomes 10 tens.
3. Now exchange from the tens. Cross out the 10 and write 9. The ones become 13.
4. Work it out: ones 13 − 8 = 5, tens 9 − 7 = 2, hundreds 3 − 1 = 2.
5. The answer is 225, not 375.

The line to use at home: "If the top number is smaller, we don't flip it. We go next door and exchange." Say it the same way every time, and your child will start saying it to themselves.

The 3 column method mistakes you'll see at home

For each one, here's what it looks like and what to say. What you say matters more than the correction itself.

Mistake 1: Taking the smaller number from the bigger one

What it looks like: 403 − 178 = 375. In every column, your child took the smaller digit from the bigger one, whether it was on the top or the bottom.

Why it happens: they've learned "you can't take a bigger number from a smaller one", so they swap them.

What to say: "Which number is on top? We always start with the top number. If it's not enough, we go next door."

Mistake 2: Exchanging, then forgetting

What it looks like: 652 − 237 = 425. Your child did the hard part right and exchanged to get 5 in the ones, but then used the original 5 tens instead of 4.

Why it happens: they didn't cross out and rewrite, or they did it so small they ignored it.

What to say: "Show me what you crossed out. What's in the tens now?" Make crossing out and rewriting non-negotiable, every time.

Mistake 3: Columns that don't line up

What it looks like: 245 + 32 = 565. Look at how it's written: the 32 sits under the 24, so your child has really added 320.

Why it happens: children line numbers up on the left, like words.

What to say: "Where do the ones go?" Always on the right. Squared paper fixes this almost overnight: one digit per square.

None of these mean your child is "bad at maths". Each one is a specific habit with a specific fix.

A 10-minute routine to try tonight

Here's the routine I use. It has three steps: watch, copy, practise.

1. Watch (2 minutes). You do one question out loud while your child watches. Say every step, including "we go next door and exchange".
2. Copy (3 minutes). Your child does a very similar question, saying the steps out loud. You only speak if they get stuck.
3. Practise (5 minutes). Three questions on their own, then check each one with the inverse. Addition checks subtraction, and subtraction checks addition.

Three questions done well beats a whole worksheet done badly. Do this three or four times a week and you should see a difference within a fortnight.

If maths homework has turned into tears and "I hate maths", keep the sessions even shorter and always finish on a question they get right. I share the full small-wins plan in my child hates maths: what to do.

Practice questions to start with:

• 456 + 327
• 538 + 294
• 763 − 248
• 802 − 365

(Answers: 783, 832, 515, 437)

If your child's homework talks about "exchanging", part-whole models or bar models, and none of it looks like the maths you learned, my guide on why maths is taught differently now explains it all in plain English. And exchanging comes back again in division: here's how it works in the bus stop method.

Frequently asked questions

What is the difference between borrowing and exchanging?

They describe the same written step. "Exchanging" is the term UK schools use now because it's more accurate: you swap one ten for ten ones (or one hundred for ten tens), and the value of the number doesn't change.

What year do children learn column subtraction?

In England, children usually start formal column addition and subtraction in Year 3 (ages 7 to 8), with up to three digits. By Year 4 they work with four-digit numbers, and by Year 5 with numbers of more than four digits.

Why does my child keep getting column subtraction wrong?

Usually it's one of three habits: taking the smaller digit from the bigger one, forgetting to update a column after exchanging, or not lining up the columns. Find which one it is, then use the matching phrase above every time.