Adding in columns
45271
+38156
83427
Addition and Subtraction
By Year 5, children add and subtract numbers with five and six digits, setting them out in neat columns and handling the trickier cases where they have to exchange across a zero. They learn that accuracy at this size comes from a careful layout and a clear sense of place value, not from speed.
Practise Addition and Subtraction
Have a guess, even if you're not sure. Get one wrong and we'll show you why, so every miss is a chance to learn.
Timed practice
The same practice, just with a gentle clock. Pick a length and see how many you can answer.
Good to know
Column method with big numbers
Two five-digit sums set out in columns: one that carries and one that exchanges across a zero.
Taking away in columns
60482
-13569
46913
For grown-ups
Year 5 also leans heavily on number sense: children add and subtract large numbers in their heads using rounding and adjusting, and they round to judge whether an answer looks sensible before trusting it. That habit of estimating to check, and of working through problems that take more than one step, is exactly the reasoning that keeps the bigger calculations and multi-step word problems of later years from feeling daunting.
What is in this topic
- Column addition and subtraction with 5- and 6-digit numbers
- Mental addition and subtraction of large numbers
- Using rounding to check answers
- Multi-step word problems
How to help at home
Accuracy at this size comes from a calm, tidy layout, not from speed. A handful of carefully lined-up sums each day, with every digit in its proper column, beats rushing through a long worksheet where one slipped place value spoils the lot.
- Insist on neat columns before any adding starts. Write 45271 above 38156 so the ones sit under ones and the ten-thousands under ten-thousands, then add right to left, carrying the small 1 underneath: 1 + 6 = 7, 7 + 5 = 12 (carry the 1), and so on up to 83427.
- Practise the tricky exchange across a zero on its own. In 60482 - 13569 the hundreds need 5 taken from 4, but the thousands column is a 0, so exchange from the ten-thousands first: the 6 becomes 5, the 0 becomes 10, then pass one of those thousands across to make the hundreds work, landing on 46913.
- Get them rounding to check the answer is sensible before trusting it. For 45271 + 38156, round to 45000 + 38000 = 83000, which sits right next to the real answer of 83427, so a slip like 8342 would jump out at once.
- For mental sums, split each number into its thousands and the rest, then work in two friendly steps. To add 38156, add 38000 and then the extra 156, and to take 13569 away, subtract 13000 then a further 569, rather than juggling it all at once.
Where children get stuck
The most common slip is losing track of the carried or exchanged digit, especially mid-column, so a sum that should reach 83427 comes out a hundred short. The fix is to write every carry clearly underneath the line and every exchange as a small crossing-out above it, never holding the number in their head. Ask them to point to and say each carry out loud as they go: 'carry the one' is a tiny habit that prevents most of these errors.
The other real wobble is exchanging across a zero, where children try to exchange from a column that has nothing to give. In 60482 - 13569 they cannot take from the 0 thousands directly, and many simply write the wrong digit and move on. The fix is to teach the two-step exchange explicitly: go past the zero to the next column that can give, turn the 0 into a 10, then pass one along to the column that actually needed it.