Carrying and borrowing: the slips to look for

When column sums come back wrong, the cause is often one of four slips: a carry that was dropped, a carry added twice, the smaller digit taken from the larger, or a borrow that went wrong at a zero. Each leaves a recognizable answer, and each has one question that helps.

9 minute read · Updated October 5, 2026

You may recognize this. The worksheet has twelve sums on it and five are marked wrong. Your child insists they did them properly. The numbers are lined up and there are little digits above the columns. The answers are still wrong.

Before you reach for "be more careful", look at how the answers are wrong. In column work the wrong answer is a clue. Read it and you know which step went missing.

Are carrying, borrowing, regrouping and exchanging the same thing?

Yes. They are four words for one idea: ten of one unit can be swapped for one of the next unit up, and back again. Carrying moves ten ones into the tens column as one ten. Borrowing breaks one ten into ten ones. You will hear regrouping in US schools and exchanging in England.

Use your child's word, whatever you grew up with. And notice that nothing is really borrowed and given back: a ten is swapped for ten ones. A child who sees that can check their own working.

Why do the same wrong answers keep coming back?

Because many wrong answers in column work are not random. They come from one small fault in the method, repeated faithfully every time that step comes up. If your child's mistakes look alike across a page, you are probably looking at a faulty step and not at carelessness.

One classic study of children's column subtraction found that errors often come from small, consistent faults in the procedure that produce the same kind of wrong answer each time. Guidance for teachers from England's Education Endowment Foundation makes the practical point: a misconception leads to a "systematic pattern of errors", and it is important that misconceptions are "uncovered and addressed rather than side-stepped or ignored".

For a parent that is good news: a pattern can be found, named and fixed. Here are the four to look for first, described from what the working looks like on the page.

Slip one: the carry is written but never added

The dropped carry is the first slip to look for in addition. Your child adds the ones, writes the small 1 above the tens exactly as taught, and then adds the tens column without it. The answer comes out exactly ten too small.

Wrong         Right
    1             1
    4 7           4 7
  + 3 8         + 3 8
  -----         -----
    7 5           8 5

The question to ask: "What is the little 1 for, and where did you use it?" A child who answers "it is a ten" will usually spot the gap unprompted. If the slip keeps returning, have them add the carried digit first in each column for a week.

Slip two: the carry is added twice

Here the carried 1 is counted once in the head and once more from the page. The child says "5 and 2 is 7, and one more is 8", then sees the small 1 still sitting there and adds it again. The answer comes out exactly ten too big.

Wrong         Right
    1             1
    5 6           5 6
  + 2 7         + 2 7
  -----         -----
    9 3           8 3

The question to ask: "Say the tens column out loud for me, one number at a time." Hearing themselves add a fourth number is usually enough. A tidy habit helps: cross out the small 1 the moment it has been used.

Slip three: the smaller digit is taken from the larger

This is the first slip to look for in subtraction. In each column the child takes the smaller digit from the larger one, whichever row it is in, so no borrowing is ever needed. For 52 − 27 they see a 2 and a 7, say "7 take away 2 is 5" and move on.

Wrong         Right
                  4 12
    5 2           5  2
  - 2 7         - 2  7
  -----         ------
    3 5           2  5

It is a sensible mistake. Your child was once told you cannot take a bigger number from a smaller one, so they turn the column over and carry on. The giveaway is an answer that is too big: here, 35 added back to 27 makes 62, not 52.

The question to ask: "Which number are we taking away from? Can you take 7 from 2?" Then leave a silence. If the answer is "no", follow with "so where can we get more ones?"

Slip four: borrowing across a zero

Zeros are where borrowing gets hard. The child needs more ones, looks to the tens, and finds nothing there to take. The right move is to go on to the hundreds and exchange twice. The common slip is to turn the zero into a 9 and forget to pay for it.

Wrong           Right
       9 12         3  9 12
    4  0  2         4  0  2
  - 1  5  8       - 1  5  8
  ---------       ---------
    3  4  4         2  4  4

A second version of the same slip takes the ten for the ones straight from the hundreds and leaves the tens at zero, then does 5 − 0 in the tens column. That gives 254.

With two or three zeros the idea is the same, done more times. Each zero becomes a 9 on the way through, and the last column gets the 10:

    3  9  9 10
    4  0  0  0
  - 1  2  6  7
  ------------
    2  7  3  3

The question to ask: "You needed more ones. Where did they come from, and what is left there now?" Every column that gave something away should have a crossed-out digit and a new one above it.

What else should I check on the page?

Check the layout before the arithmetic. Some wrong answers come from working that is right but written in the wrong place, and no practice on carrying will fix digits that are not lined up. Three things are worth a glance on any page of column work.

• Columns not lined up. 345 + 27 with the 27 written under the 3 and the 4. Squared paper, one digit per square, settles this quickly.
• Both digits written in one column. 47 + 38 answered as 715, because the 15 was written whole under the ones.
• The wrong sign. A subtraction on a page of additions, added like the rest. Have your child circle the sign before starting each sum.

How do I fix a slip once I have found it?

Name the one step that went wrong, show why it matters with tens and ones your child can see, then practice that step alone on small numbers before going back to the homework. Three or four sums where the step comes up will tell you more than a full page.

When is this expected? England's national curriculum has columnar addition and subtraction with up to 3 digits in Year 3 and up to 4 digits in Year 4. In the US, the Common Core standards expect fluent multi-digit addition and subtraction with the standard algorithm by the end of Grade 4. A child of 7 or 8 who still makes these slips has not fallen behind either list. See math by grade.

Where Plusy fits

Plusy sets these sums out in columns as they are written on paper, with carry and borrow boxes for your child's own working. When an answer worked in the boxes is wrong, Plusy reads the working and says what happened, such as "You forgot to add the carried 1" or "You forgot to borrow. Borrow 1 from the tens".

Your child's own digits stay on the grid, marked right or wrong, and Walk me through it goes through the sum step by step, followed by one new question with the same trap in it. If the same kind of mistake turns up three times in a week, a short practice set for it appears on Home. See column questions and what Plusy does after a wrong answer.

The carrying and borrowing worlds are free, like every other world. Start free, or keep going with pencil and squared paper: the four questions above work on any worksheet.

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