Year 5 maths · Key Stage 2 · Number – addition and subtraction
Year 5 adding and subtracting large numbers: a parent’s guide
In Year 5 the addition and subtraction children learned with four-digit numbers is extended to numbers with five digits and more. They use column methods accurately, calculate mentally when the numbers allow it, use rounding to check that an answer is sensible, and tackle multi-step word problems where they must decide which operations to use and why.
Adding and subtracting large numbers, explained
The column methods are the same as in earlier years, only with more columns, so the key is careful setting out. The digits are written so that ones are under ones, tens under tens, and so on, which matters when numbers have different numbers of digits. In column addition, the digits in each column are added, starting from the ones, and when a column totals 10 or more, the tens are exchanged into the next column to the left. In column subtraction, if the digit on top is smaller than the digit below, children exchange from the next column to the left of the top number: 1 ten is swapped for 10 ones, 1 hundred for 10 tens, and so on. Children are expected to be confident with this, even when the top number has zeros, as in 52,000 − 47,335.
Written methods are not always the best choice. Children also learn to add and subtract mentally with larger numbers, using what they know about place value. For 12,462 − 2,300 they can see that only the thousands and hundreds change, so the answer is 10,162. For 4,998 + 3,456 it is easier to add 5,000 and then take 2 off. Another useful method is counting up on a number line from the smaller number to the larger one, in jumps, to find the difference. Many schools encourage children to choose a method after looking at the numbers.
Rounding is used to check that an answer is sensible. Before calculating, children estimate by rounding each number: 34,586 + 12,749 is roughly 35,000 + 13,000 = 48,000. If the calculated answer is 47,335, the estimate shows it is in the right area. If the answer is 4,733 or 147,335, something has gone wrong. Rounding also helps children decide what level of accuracy a question needs. If you only need to know whether about 50,000 people could fit in a stadium, then rounding to the nearest thousand is enough. If a bank balance is being added up, every pound counts.
Finally, children solve multi-step problems in context. They must read the problem, decide what is being asked, pick an operation for each step, and explain their choices. The skill is as much in reading as in calculating. Words such as “altogether” suggest addition, “how many are left” or “how many more” suggest subtraction, but the best approach is always to picture what is happening or draw a bar model.
Words your child will hear
- Column addition
- A written method that adds digits in columns, starting from the ones.
- Column subtraction
- A written method that subtracts digits in columns, exchanging when needed.
- Exchange
- Swapping one ten for 10 ones, one hundred for 10 tens, and so on.
- Estimate
- A sensible rough answer found by rounding the numbers first.
- Inverse
- The opposite operation: subtraction undoes addition and the other way round.
- Difference
- How much bigger one number is than another, found by subtracting.
- Multi-step problem
- A problem that needs more than one calculation to solve.
What the National Curriculum says
In Year 5, pupils should be taught to:
- Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
- Add and subtract numbers mentally with increasingly large numbers
- Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
- Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.
A worked example
A library has 52,000 books. 34,586 are fiction and 12,749 are non-fiction. All the rest are reference books. How many reference books are there?
- Plan the steps. First add fiction and non-fiction to find how many books are not reference. Then subtract that total from 52,000. Estimate first: 35,000 + 13,000 = 48,000, and 52,000 − 48,000 = 4,000, so the answer should be close to 4,000.
- Add the fiction and non-fiction books, starting at the ones. 6 + 9 = 15, write 5 and exchange 10 ones. 8 + 4 + 1 = 13, write 3 and exchange. 5 + 7 + 1 = 13, write 3 and exchange. 4 + 2 + 1 = 7. 3 + 1 = 4.
3 4 5 8 6 + 1 2 7 4 9 ----------- 4 7 3 3 5 1 1 1 - Subtract 47,335 from 52,000. The top number has three zeros, so exchange from the left: 52,000 becomes 4 ten thousands, 11 thousands, 9 hundreds, 9 tens and 10 ones. Then subtract each column: 10 − 5 = 5, 9 − 3 = 6, 9 − 3 = 6, 11 − 7 = 4, 4 − 4 = 0.
4 11 9 9 10 5 2 0 0 0 - 4 7 3 3 5 ------------- 4 6 6 5 - Check using the inverse: add the answer to 47,335. 4,665 + 47,335 is 4,665 + 47,000 = 51,665, and 335 more makes 52,000. It also matches the estimate of about 4,000.
There are 4,665 reference books.
Common mistakes and how to help
Subtracting the smaller digit from the larger whatever its position
In 52,000 − 47,335, a child sees 0 − 5 in the ones and writes 5, since it feels wrong to take a bigger number from a smaller one. The result is a wrong answer without any warning.
What helps: Explain that the order matters, so the digits can’t be swapped round. If the digit on top is too small, exchange from the next column along. Adding the answer back on catches errors.
Getting stuck exchanging across zeros
A zero has nothing to give, so a child exchanges from the wrong column or forgets that the digit it exchanges from goes down by 1.
What helps: Start with the nearest non-zero digit and work back, or use counting up on a number line instead. Ask: how far is it from 47,335 to 52,000?
Misaligning numbers with different numbers of digits
When adding 3,458 and 12,749, the numbers are lined up from the left instead of the right, so thousands get added to ten thousands.
What helps: Always line up the ones first. Squared paper, or drawing faint column lines, makes the columns easy to see.
Accepting an answer without checking whether it is sensible
A missed exchange can change an answer by 10, 100 or 1,000, and the result still looks like a plausible number.
What helps: Make estimating a habit, rounding to the nearest thousand or ten thousand before starting. Then ask: is my answer close to my estimate?
How to help at home
- Estimate before you calculate. When you see two big numbers, such as the attendance at two matches or the populations of two towns, ask your child to round and estimate the total. Then compare with a calculation.
- Tell the story of a word problem. Ask your child to describe the problem in their own words and say which part is the whole and which are the parts. A simple bar drawn on paper often shows whether to add or subtract.
- Pick the best method. Give two or three calculations, such as 4,998 + 2,345, 30,000 − 4,000 and 63,215 + 28,876. Ask which could be done in the head and which need columns, and why.
- Use the inverse. After any addition or subtraction, check it with the opposite calculation. A habit of checking is more valuable than speed.
Related topics
Builds on
- Year 4: Column addition and subtraction
Leads on to
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