Carrying and Borrowing: Why Column Sums Go Wrong, and What Helps

15 September 2026 · by Larry

She knows 7 + 5 without thinking. She can take 3 away from 9 in her sleep. Then the homework has two-digit numbers set out in columns, and 52 − 27 comes back as 35. The next one, 48 + 35, comes back as 713.

Both answers were worked out carefully. Neither is a guess. And both are wrong in a way that tells you something quite specific, if you know what to look for.

Carrying (in addition) and borrowing (in subtraction) are often called regrouping. StudyLab's level-by-level guide puts adding and subtracting within 1000 in Primary 2, and that is where regrouping arrives; her workbook will show exactly when. It is also one of the places a child who was doing well can suddenly start losing marks.

What regrouping actually is

The whole idea fits in one sentence: ten ones make one ten, and one ten can be broken back into ten ones.

In 48 + 35, the ones column gives 8 + 5 = 13. Thirteen ones is one ten and three ones. The three stays in the ones column; the ten moves across to join the tens. That is "carrying one" — and the one being carried is a ten, not a one.

In 52 − 27, there are 2 ones and she needs to take away 7. She cannot. So one of the five tens is broken into ten ones, leaving 4 tens and 12 ones. Now 12 − 7 = 5, and 4 − 2 = 2. The answer is 25.

A child who sees 52 as "a 5 and a 2" rather than "five tens and two ones" has nothing to hang any of this on. The steps become a ritual to remember, and rituals break under pressure. Nearly every slip below comes back to that one idea.

The five ways it goes wrong

1. Smaller from larger, in every column. 52 − 27 = 35. She looked at the ones column, saw a 2 and a 7, and took the smaller from the larger: 7 − 2 = 5. Then 5 − 2 = 3 in the tens. It feels right to her, because until now subtraction has always meant the big number take away the small one.

2. Borrowed, but forgot to pay it back. She knew she needed more ones, made the 2 into 12, and 12 − 7 = 5. But she left the tens as 5 instead of 4, so 5 − 2 = 3. The answer is 35 again.

That is worth pausing on. Slips 1 and 2 give exactly the same wrong answer for completely different reasons. One child does not know she has to borrow. The other knows and missed a step. You cannot tell them apart from the answer. You can only tell from the working — which is the same point made in careless mistakes in maths: look at the working, not the answer.

3. The whole total written in the ones column. 48 + 35 = 713. The ones gave 13, and she wrote down 13. Then 4 + 3 = 7 went in front. She has not carried at all, because she has not seen that the 1 in 13 is a ten.

4. The carry forgotten. 48 + 35 = 73. She wrote the 3, meant to carry the 1, and did not add it to the tens. This one really can be a slip, especially when the carried digit is not written down anywhere.

5. Borrowing across a zero. 304 − 128. There are 4 ones and she needs to take away 8. She goes next door to borrow a ten — and there are no tens. This is where children who had regrouping sorted come unstuck all over again.

The right way: one of the 3 hundreds is broken into 10 tens, leaving 2 hundreds. Then one of those 10 tens is broken into 10 ones, leaving 9 tens and 14 ones. Now 14 − 8 = 6, 9 − 2 = 7, 2 − 1 = 1. The answer is 176.

The common wrong answers are 224 (smaller from larger, all the way along) and 186 (she turned the 0 into 10 but forgot that it then gave one ten to the ones, so it should have been 9). If her answer to a zero question is off by exactly 10, this is the first thing to look for.

There is a sixth, simpler one that sits underneath all of them: digits not lined up. 305 + 42, with the 42 written under the 30 instead of under the 05, comes out as 725 instead of 347. The columns only work if ones sit under ones.

A two-minute check tonight

Give her these three, on paper, and do not help. Just watch where the pencil goes.

• 63 − 28. The answer is 35. If she writes 45, see whether she crossed anything out. Nothing crossed out means slip 1: she does not yet know she has to borrow. Something crossed out but the tens left at 6 means slip 2.
• 46 + 38. The answer is 84. 714 is slip 3. 74 is slip 4.
• 402 − 157. The answer is 245. 355 is smaller from larger. 255 is the zero that should have become a 9.

Then one last question, with no numbers written down: "In 63, what does the 6 stand for?" If the answer is "six" rather than "sixty" or "six tens", that is where to start — before any more column sums.

What actually helps at home

Use money. $10 notes and $1 coins are regrouping you can hold, and play money works just as well. Put out $52: five $10 notes and two $1 coins. Now pay someone $27. She cannot hand over seven $1 coins when she has two, so she has to change a $10 note for ten $1 coins. That swap is borrowing. Do the same for 48 + 35: once she has 13 coins, swap ten of them for a note. Two or three evenings of this does more than a page of sums, because she can see why the tens go down by one.

Say the value, not the digit. "Five tens take away two tens", not "five take away two". "Carry one ten", not "carry one". It feels fussy for a week. It is the thing that stops slips 1 and 3, because the sentence itself reminds her what the digits mean.

Check subtraction by adding back. 52 − 27 = 35? Add 35 and 27. That makes 62, not 52, so something went wrong. This is a check she can do alone, in a test, without anyone telling her the answer was wrong — and it catches all of the subtraction slips above.

Check addition by rounding first. 48 + 35 is about 50 + 35, so about 85. An answer of 713 cannot be right. One second of estimating before writing the answer catches slip 3.

Write the small digits down. The carried ten, the crossed-out tens, the new ones. Follow the way her workbook sets it out, even if it is not how you learned it — when the school's method is not the one you learned explains why that matters. Slips 2 and 4 are mostly steps kept in her head that belonged on the paper.

Practise zeros on their own. Once ordinary borrowing is steady, give her a few with a zero in the middle — 305 − 117, 603 − 248 — and nothing else. Mixed in with ordinary ones, the zero questions are too rare to learn from.

What does not help

• A rhyme or a rule with no picture behind it. "If the bottom is bigger, go next door" works until next door is a zero. The money swap is what carries across to 304 − 128.
• Another page of the same sums. If she is doing smaller from larger, twenty more questions is twenty more rehearsals of it. Find the slip first, then practise.
• Mental shortcuts too early. Adding 48 + 35 in your head by jumping to 50 is a lovely skill, and it can come later. If the column method is what her class is being taught, showing her a shortcut instead of fixing the columns tends to leave both half-learned.
• Calling it careless. Smaller from larger is not carelessness. It is a sensible habit from last year applied to a sum where it no longer works. The same thing happens again later with time, where children borrow 100 minutes instead of 60 — covered in telling the time.

Why it matters beyond Primary 2

Regrouping does not stay in one chapter. It is inside long multiplication, long division, adding money, subtracting lengths, and later adding decimals, where lining up ones under ones becomes lining up the decimal point — see decimals: the four slips. When the questions become two-step word problems in Primary 3, a child still unsure about borrowing loses marks in a question that looks as if it was about something else entirely.

So a few weeks spent getting this steady is not falling behind. It is laying the part everything else stands on.

Where a screen fits, honestly

StudyLab's maths practice has Primary 2 topics called Add within 1000 and Subtract within 1000. Every sum is set out in columns, one digit per box, with ones under ones and tens under tens, so the layout on screen is the layout she should use on paper. The numbers are chosen at random, so some questions need regrouping and some do not.

Two honest limits. The answer is typed in as one number, so there is nowhere to write the carried or borrowed digits — and a wrong answer on a screen does not show which of the five slips caused it. For finding the slip, paper and a pencil you can watch are the tool. And no screen replaces the $10 note being changed into coins; that is the part that makes it make sense.

Borrowing across a zero is also the example in one of my Forum posts, more practice questions won't help my child, about what a pile of extra questions cannot notice.

The short version

• Ten ones make a ten, and a ten can be broken into ten ones. Every column-sum slip comes back to that.
• 52 − 27 = 35 can be two different problems. Look at the working to see which.
• An answer like 713 means the 13 was never seen as a ten and three ones.
• Zeros are their own skill: the 0 becomes 10, then 9.
• Use $10 notes and $1 coins. Changing a note is borrowing she can see.
• Say "five tens", not "five".
• Check subtraction by adding back. Check addition by rounding first.