Column subtraction
National Curriculum: this is in the Year 3 programme of study, part of key stage 2 (Years 3 to 6). Schools have to teach the key stage 2 programme by the end of Year 6, and can introduce content earlier or later within it.
Children in Year 3 are 7 or 8, and turn 8 during the school year.
What it is
Column subtraction is the written method for taking one number from another: digits lined up by place value, each column subtracted from the right, and a column whose top digit is too small borrowing — exchanging — one from the column to its left, which turns into ten.
- Ones: 2 is too small to subtract from, and the column to its left is a 0, so the exchange starts in the hundreds: the hundreds digit drops by one, the columns it passes are left as 9, and the ones become 12. 12 − 7 = 5.
- Tens: 9 − 3 = 6.
- Hundreds: 3 − 1 = 2.
- 402 − 137 = 265.
Errors are more common here than in column addition, because two things must be held at once: the subtraction inside each column, and what the exchange did to the column next door.
When children learn it
Schools teach column subtraction with numbers up to 3 digits in Year 3, extending to 4 digits in Year 4, alongside column addition and after the mental 2-digit methods of Year 2.
What it looks like when it goes wrong
These patterns come up again and again in children's answers on this skill. Each one points at a specific missing idea, not carelessness.
- Smaller from larger, whatever the order. 42 − 17 answered as 35. In the ones column 2 − 7 cannot be done, so they quietly do 7 − 2 instead. Every column still produces a tidy digit, so the wrong answer looks plausible and often goes unnoticed.
- The exchange is not paid for. The ten is borrowed and 12 − 7 = 5 is done correctly, but the tens digit it came from is never reduced. The answer comes out exactly ten too big.
- A zero stops everything. 402 − 137 falls apart at the tens column: there is nothing to borrow from, and the extra step — exchange from the hundreds first — is missing. Numbers with a zero in the middle are the standard test of whether the method is understood or memorised. Exchanging is met first in Year 2, subtracting two-digit numbers, and that is where to go back to if the exchange is the part that keeps failing.
How to help at home
- Check by adding back: if 42 − 17 = 35, then 35 + 17 should give 42. It gives 52, so something went wrong. This inverse check is the habit schools teach.
- Estimate first: 402 − 137 is about 400 − 140, so about 260. An answer of 335 — the smaller-from-larger result — cannot be right.
- Act out one exchange with coins: swap a 10p for ten 1ps and watch the tens pile shrink. The crossing-out on paper is a record of exactly that.
- Watch one calculation and listen at "you can't do 2 take away 7". What they say next shows whether the method is understood or improvised.