Column addition and subtraction, estimating and checking
By Year 6, children should be fluent with column addition and subtraction for large numbers and decimals. The marks that get lost are rarely about the method; they're about alignment, exchanging across zeros and not checking whether an answer makes sense.
The column method
Column addition and subtraction line numbers up by place value, ones under ones and tens under tens, and work from right to left. In addition, a column total of 10 or more is carried into the next column. In subtraction, when the top digit is too small, one is exchanged from the next column to the left.
The method itself is usually secure by Year 6. What changes is the size of the numbers (five digits and more) and the appearance of decimals, where lining up the decimal points is the whole battle.
Exchanging across zeros
Subtractions like 4,005 − 1,238 are where most errors happen, because there's nothing to exchange from in the tens and hundreds columns. Children have to go all the way to the thousands, then work back:
- 4,005 → 3 thousands, 9 hundreds, 9 tens, 15 onesOne thousand is exchanged and passed down the columns.
- 4,005 − 1,238 = 2,767Check: 2,767 + 1,238 = 4,005.
Showing the exchange with place value counters or base 10 equipment first, then the written method alongside, helps children see why the zeros become nines.
Decimals in columns
When numbers have different numbers of decimal places, the decimal points must line up. Filling empty places with zeros makes this foolproof:
- 12.25 + 3.50 = 15.753.5 written as 3.50 so the columns match.
- 12.25 + 3.5 lined up on the right = 12.60Misaligned: the 5 has been added to the hundredths.
Estimating and checking
Estimating means rounding the numbers to make a quick mental calculation, so that children know roughly what the answer should be. Checking means using the inverse operation to confirm it. The Year 6 curriculum asks pupils to use both routinely, and they are the cheapest way to catch errors in the SATs.
- Estimate first: 6,892 + 3,105 is about 7,000 + 3,000 = 10,000.
- Calculate: 6,892 + 3,105 = 9,997.
- Compare: 9,997 is close to 10,000, so the answer is sensible.
- Check with the inverse: 9,997 − 3,105 = 6,892.
Word problems
Year 6 problems are usually multi-step and include information that must be selected carefully. The biggest errors come from reacting to keywords (“more”, “left”) without reading the whole question, or answering only the first step. A bar model shows the structure of the problem before any calculating happens, and makes it clear whether to add or subtract.
Number puzzles
Missing-digit calculations, number pyramids and “find two numbers with a sum of… and a difference of…” problems test reasoning rather than calculation. They reward working systematically: start where the puzzle is most constrained, try a value, check it with the inverse operation, and keep a record of what's been tried.
In the SATs
Column addition and subtraction appear on the arithmetic paper, including large whole numbers and decimals. On the reasoning papers, they appear inside word problems, missing-digit puzzles and questions that ask children to check or explain a calculation. Calculators aren't allowed in any paper, so accuracy with written methods matters.
Common mistakes
- Misaligned columns, especially with numbers of different lengths or decimals.
- Forgetting to add the carried digit.
- Subtracting the smaller digit from the larger regardless of which is on top.
- Mishandling exchanges across zeros.
- Accepting an answer without an estimate, even when it is wildly wrong.
Teaching ideas
Squared paper, always
One digit per square keeps columns straight. For decimals, draw the decimal point on a grid line so it can't drift.
Estimate, then race
Give a calculation and 10 seconds to write an estimate before anyone calculates. Then compare answers with estimates. Pupils start to see estimating as a tool, not an extra job.
Spot the error
Show worked calculations with one mistake each: a missed carry, a wrong exchange, a misaligned decimal. Children find and explain the error. This builds the checking habit better than more practice questions.
Bar model first
For word problems, make drawing a bar model the first step for a few weeks, even for easy questions. When the problems get harder, the habit is already there.
Try it: five quick questions
SATs-style questions to use as a starter or a quick check. Tap to see each answer.
Calculate 7,003 − 2,456.
Show answer
4,547
Calculate 23.4 + 8.75.
Show answer
32.15
Estimate 4,912 + 2,086 to the nearest thousand.
Show answer
About 7,000.
Check 5,630 − 1,975 = 3,655 using the inverse.
Show answer
3,655 + 1,975 = 5,630, so it's correct.
A shop had 1,250 books, sold 368, then received 500 more. How many now?
Show answer
1,382
Free worksheets for this topic
Printable A4 PDFs with answers. Free to use in class or at home.
