Column Addition with Carrying

La méthode, étape par étape

1. 1

   Line the numbers up by column, not by edge

   487 + 356

   Ones under ones, tens under tens. Lining numbers up by their right-hand edge works only while both have the same number of digits, and fails silently the moment they do not. The columns are the method; the alignment is not presentation.

2. 2

   Add the ones column

   7 + 6 = 13 → write 3, carry 1

   Thirteen ones will not fit in a column that holds at most nine. Thirteen is one ten and three ones, so the three stays and the one ten moves to the tens column. That sentence is the entire justification for carrying, and a child who can say it will not misplace a carried digit.

3. 3

   Add the tens column, including what was carried

   8 + 5 + 1 = 14 → write 4, carry 1

   The carried 1 is added in with the column, not tacked on afterwards. Forgetting it is the single most common error in the method, which is why it is written down under the column rather than held in the head.

4. 4

   Add the hundreds column

   4 + 3 + 1 = 8 → write 8

   Nothing is carried out of this column because the total is under ten. If it had been over, the carry would create a new thousands column — which is how addition grows a number's digit count.

5. 5

   Check by estimating

   487 + 356 = 843. Check: 500 + 360 ≈ 860 ✓

   Rounding both numbers and adding mentally should land near the answer. It will not catch a small slip, but it reliably catches the big ones — a missed carry, a misaligned column, a digit in the wrong place — which are the errors that cost whole marks rather than one.

Carrying is exchange, not magic

The word "carry" hides what is happening. Nothing is being carried anywhere; something is being exchanged. Ten ones are swapped for one ten, because that is what ten ones are worth, and the exchanged ten is written where tens live. Children who are taught the words without the exchange can execute the method and cannot repair it when it goes wrong.

This matters because the same exchange runs backwards in subtraction, where a ten is broken into ten ones. A student who understands carrying as exchange meets borrowing as the same idea in reverse. A student who learned carrying as a rule meets borrowing as a second unrelated rule.

• Add right to left, ones first
• Ten or more in a column? Exchange for one of the next column up
• Write the carried digit down — do not hold it in your head
• Add the carry in with the column, not after it

Where the marks actually go

Three errors account for most lost marks. The carried digit is forgotten. The numbers are aligned by their left edge or by eye rather than by column. Or the carry is written above the column and then added twice. All three are bookkeeping failures rather than arithmetic failures, and all three are fixed by writing the carry in the same place every time.

There is a fourth that looks like carelessness and is not: a child who is insecure in number bonds spends so much working memory on 7 + 6 that there is none left for the carry. The addition is correct and the method still fails. Drilling the method harder does nothing; securing the bonds fixes it in a fortnight.

When not to use the column method

The written method is for numbers too big to hold in your head, and using it for numbers that are not is a habit worth breaking early. 199 + 47 is faster and safer done as 200 + 47 − 1. The national curriculum expects pupils to choose between mental and written approaches, not to default to one.

We ask students to glance at a calculation and decide before they start. It takes two seconds, and it separates the ones where the method earns its keep from the ones where it is slower and more error-prone than thinking.

How we teach column addition

We teach the exchange before the layout, using partitioning the student already knows: 487 + 356 becomes 400 + 300, 80 + 50, 7 + 6, and then the awkward totals get exchanged. Once a child has seen 130 tens become 1 hundred and 3 tens on their own terms, the compact column method reads as shorthand for something they understand rather than as an instruction to obey.

We also check number bonds first in any student whose column work is unreliable. It is the most common hidden cause, and it is much quicker to diagnose than to discover after a term of practice that has not helped.