Column addition
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 addition is the written method: the numbers stacked with ones over ones and tens over tens, each column added from the right, and a column that reaches ten sending 1 on to the next column — schools call this carrying, or exchanging. Set out this way, any two numbers can be added with the same small routine.
- Ones: 5 + 8 = 13. Write 3 and carry 1 into the tens.
- Tens: 4 + 7 = 11, and the carried 1 makes 12. Write 2 and carry 1 into the hundreds.
- Hundreds: 2 + 1 = 3, and the carried 1 makes 4. Write 4.
- 245 + 178 = 423.
The method is only as strong as the place value idea underneath it. Lining up the digits works because each column is worth ten of the one to its right; a child following the steps without that idea can produce an answer without noticing it is far too big or far too small.
When children learn it
Schools teach column addition with numbers up to 3 digits in Year 3, extending to 4 digits in Year 4. It follows the mental methods with 2-digit numbers taught in 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.
- The carry goes missing. 47 + 38 answered as 75. The ones column made 15, the 5 was written down, and the 1 that should move into the tens column never arrived. The answer comes out exactly ten short.
- Digits lined up from the left. 245 + 17 set out with the 1 under the 2, so tens are added to hundreds. The method has been learned as "stack and add" without the place-value rule that ones sit under ones. The same wrong idea shows in mental work, where a part gets added into the wrong place, and that is the skill this method is built on: if it is happening there too, the layout is not the thing to fix first.
- A column fact one out. The layout and carrying are right, but 8 + 7 comes out as 14, so the answer is one off. This is not a column-method problem — it is a number-facts gap showing through the method.
How to help at home
- Ask for an estimate before the working: 245 + 178 is about 250 + 180, so about 430. That one habit catches most lost-carry and misaligned answers.
- Use squared paper, one digit per square. Many wrong answers are layout errors, not arithmetic errors.
- When an answer is wrong, ask them to add it again aloud, column by column. Saying "4 tens add 3 tens and the 1 that came over" surfaces a missing carry.
- If single-digit facts are hesitant, practise those separately — the column method cannot be more reliable than the facts inside it.