Subtracting Four Digit Numbers: Free Printable Worksheet for Year 4

Subtracting Four Digit Numbers is a free printable worksheet for Year 4 (ages 8 to 9), in Key Stage 2. Exchange across the columns to subtract. It comes from the Mini Minds Hub, a growing library of free printables from Jaques of London, the British games and toy company that has been making games for families since 1795.

It is two A4 pages. Page 1 is the activity for children. Page 2 is for the grown-up: it has notes on how to use the sheet, help for children who find it hard, a stretch idea, and the answers. Print it at home or in the classroom. Black and white printing works well.

What is on the sheet

This worksheet includes numbered questions with space to answer.

A look at what children will meet:

• 7634 - 2451 =
• 5000 - 2736 =
• 8420 - 3185 =
• 6075 - 1938 =
• 9301 - 4567 =
• 4002 - 1789 =
• 7256 - 3489 =
• 6000 - 2345 =

Who this is for

Year 4 (ages 8 to 9) in Key Stage 2.

Key Stage 2 covers Years 3 to 6, ages 7 to 11. Children are widening what they know and getting better at explaining their thinking, so activities that ask them to reason, not only recall, are especially useful. Use it at home, in class, on a rainy afternoon or at a family gathering.

What children practise

• Subtraction
• Place value
• Exchanging

Children subtract four digit numbers and exchange tens, hundreds and thousands when needed.

Learning focus and curriculum link

Subject: Maths. Key stage: Key Stage 2. It supports the subject at this level through short, focused practice.

This sheet is a practice and play activity. It supports classroom learning and is not a replacement for it.

How to use it

1. Print both pages. Page 1 is for the child. Keep page 2 for the grown-up.
2. One child, about 15 minutes. Use scrap paper to set out the columns. Check each answer by adding it back.
3. Work through the activity together the first time. Talk about each choice.
4. Check against the notes on page 2 and the answers.
5. Come back to it another day. Repeating a familiar activity builds confidence.

If it feels too hard

Use place value counters or draw columns for thousands, hundreds, tens and ones.

To stretch confident children

Make up your own four digit subtractions that need two exchanges.

Make it a game

Roll dice to make two four digit numbers and subtract the smaller from the larger.

Tips for parents and teachers

• Print on plain A4 paper. Black and white printing works too.
• Work through it together the first time, then let children try alone.
• Praise effort and thinking, not only correct answers.

A screen-free maths activity for Year 4

Children spend a lot of time on screens. This is a screen-free maths activity that needs only paper and a pencil. It works as quiet time after school, a rainy day activity, a holiday boredom buster or a calm moment before bed. Screen-free learning gives eyes a rest and gets children talking, thinking and writing by hand.

Free maths resources for teachers

Teachers can use this worksheet as a starter, a plenary, an early finisher task, a supply teacher resource, a homework task or a table activity. It needs no preparation beyond printing. The learning focus and skills are listed above so you can match it to your planning, and page 2 gives support and stretch ideas for mixed ability groups.

Maths ideas for parents at home

You do not need to be a teacher to use this. Read the sheet through, sit with your child for the first go and let them lead. Short bursts of ten to fifteen minutes work better than long sessions. If you are looking for free maths worksheets for Year 4, or simple home learning for the weekend or school holidays, this is a good place to start.

Home education and tutoring

Home educators and tutors can print this as part of a wider maths plan. It pairs well with books, outdoor play and everyday talk. Because the sheet is free and printable, you can use it again for brothers and sisters or for revision a few weeks later.

Why it helps children learn

Hands-on, paper based activities slow learning down in a good way. Children read carefully, think before they answer and see their own progress on the page. Games and challenges add a reason to keep going. That mix of play and practice is why printable activities like this are popular with parents, teachers and home educators.

Curriculum links for teachers

This sheet supports the areas below. It is matched to the published England frameworks. Please check it against your own school plan.

What children will be able to do

• I can subtract four digit numbers.
• I can exchange tens, hundreds and thousands when I need to.
• I can check my answer by adding.

Check it worked

Ask these when the sheet is finished. Listen for the reasoning, not just the answer.

1. When do you need to exchange?
2. How can you check a subtraction with addition?
3. Which column was the trickiest?

More like this

• Adding Four Digit Numbers
• Adding Fractions: Same Bottoms
• Area of Rectangles
• Christmas Cracker Maths Cards

Same subject, one year up: Decimal Showdown Cards | Same subject, one year down: Shut the Box

Why subtracting four digit numbers matters

Our own view: four digit subtraction is where a child's written method gets a serious workout. Our own view: the numbers are big enough that many children will want to write the sum down. A method has to carry the load. That method is columnar subtraction: write the numbers one under the other, line up the thousands, hundreds, tens and ones, and work from the right.

Our own view: the exchange is a step where it is easy to slip. When the digit on top is smaller than the digit below it, a child takes one from the next column along and trades it for ten in this one. Our own view: zeros can make it harder, because there is nothing to take. On this sheet, 5000 minus 2736 and 6000 minus 2345 have zeros in three columns, so the exchange has to pass through them. The answers are 2264 and 3655.

The questions start with 7634 minus 2451, which needs one exchange, in the tens column, and move on to sums that need more exchanges. Our own advice: do not rush. The point is to see the same move several times.

What the research says children find hard

We did not find a study that counts the mistakes children make in four digit subtraction in England, so we have not made up any figures. What we can say comes from sources we opened and read.

• Subtraction has a partner. A review for the Nuffield Foundation by Terezinha Nunes and Peter Bryant at the University of Oxford says it is "absolutely essential" when adding and subtracting to understand that these are reversible actions. Our own view: that idea is what lets a child check a subtraction by adding the answer back.
• The inverse is hard to pin down. The same review reports that Piaget's theory says that children in the five to eight year range do not see that if 4 plus 8 is 12, then 12 minus 8 is 4. The review adds that Piaget never tested this claim directly, and it offers another explanation for the results of one of his later studies. So the research here is less settled than it sounds.
• Word problems. The review says two types of word problem cause difficulties for children: those involving the inverse relation between addition and subtraction, and those about relations. It does not say which year groups it means for this point, so we do not link it to Year 4 only.
• Working memory. The Ofsted mathematics research review, published on gov.uk, says pupils who cannot quickly recall maths facts struggle with calculations because their working memory is overloaded. Its example is addition and number bonds, not subtraction, but the same logic may apply. We have not seen a source that tests this for four digit subtraction.

Neither source tests this sheet or any worksheet. They describe why the underlying ideas matter.

What Year 4 children are expected to learn

The national curriculum for England, in its Year 4 programme of study for number, addition and subtraction, says pupils should be taught to:

• "add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate"
• "estimate and use inverse operations to check answers to a calculation"
• "solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why"

The non-statutory notes say pupils "continue to practise both mental methods and columnar addition and subtraction with increasingly large numbers to aid fluency".

The steps before and after are worth knowing. In Year 3 pupils are taught to "add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction". In Year 5 they are taught to "add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)". So Year 4 is the step from three digits to four, and the sheet sits right on it.

Why a short practice sheet and a game can help

We want to be straight about this. We did not find a study of a four digit subtraction worksheet, or of a dice game for subtraction, that we could open and quote. So we will not give you a number.

What we can point to is more modest. The Ofsted review says that evidence shows pupils can learn from worked examples, particularly if teachers help pupils make sense of them. The Year 4 notes talk about practising to aid fluency. A short sheet with eight questions gives a child several turns at the same method.

On games, the Ofsted review says that for younger pupils, rehearsal of number bonds and sequences can draw on games and songs involving dice, dominoes and counting sequences. That line is about younger pupils and number bonds. It is not about Year 4 subtraction. We mention it because the sheet's game idea uses dice, and we do not want to claim more than the review says.

The sheet is practice. It is not a lesson, and it does not replace one.

How to get the most out of Subtracting Four Digit Numbers

1. Do the first question together. Our own advice: start with 7634 minus 2451. There is one exchange, in the tens column, because 3 is smaller than 5. Say each column out loud: "4 take away 1 is 3."
2. Talk through an exchange. Our own advice: take 8420 minus 3185. The ones column has 0 on top and 5 below. Say: "I cannot take 5 from 0, so I take one ten and turn it into ten ones."
3. Use something to hold. Our own advice: place value counters can help, and so can a drawing of columns headed thousands, hundreds, tens and ones. Let your child move the counters, not you.
4. Estimate first. Our own advice: round both numbers and guess the answer before starting. For 5000 minus 2736, think 5000 minus 2700. That is about 2300.
5. Check by adding. The curriculum asks pupils to use inverse operations to check. Add the answer to the number taken away. You should get the number you started with.
6. Mark page 2 together. Our own advice: ask your child to explain any wrong answer, rather than just telling them the right one.
7. Come back another day. Our own advice: ten minutes a few days later is better than one long session.

Common mistakes, and what to say

• Taking the smaller digit from the larger in a column. Our own advice: when you mark, look for a column where the bottom digit has been taken from the top the wrong way round. Say: "Which number is the start? That one goes on top, and it stays on top."
• Forgetting to reduce the next column. If you take ten from the tens column, the tens digit goes down by one. Our own advice: cross out and rewrite the digit in small writing so it is visible.
• Zeros in the middle. In 4002 minus 1789, the tens and hundreds are both zero. Our own suggestion: exchange from the thousands, and pass a ten down through each column. 4002 minus 1789 is 2213.
• Misaligned columns. Our own suggestion: use squared paper, or turn lined paper sideways so the lines become columns.
• Skipping the check. Our own advice: add the answer back. If it does not match, the sum needs another look.

Why teachers matter to us

We are a games company, and we have been making games for families since 1795. We do not think a printable replaces a teacher. A 2011 interim report for the Sutton Trust looked at how much teachers affect pupil achievement. It found that in one year with a very effective maths teacher, pupils gain 40% more learning than with a poorly performing maths teacher. That is a finding about maths teachers, and it is a good reason to use a sheet like this next to a lesson, not instead of one.

The same report found that for poor pupils the difference between a good teacher and a bad teacher is a whole year's learning. It also found that paper credentials explain less than 8% of teacher quality. A University of Bristol working paper (CMPO 09/212) found considerable variability in teacher effectiveness, using a UK dataset that linked over 7000 pupils to their teachers. Our own view: exchanging across columns is best explained live, by a person who can see the child's working.

A caution on the Sutton Trust figures: the report draws on US studies as well as English ones. The 40% compares a very effective teacher (at the 84th percentile) with a poorly performing one (at the 16th percentile). The figure that paper credentials explain less than 8% of teacher quality comes from US research. We use them as pointers, not as a promise about any one child.

Why education matters to us

Our own view: numbers sit under so much of everyday life, from shopping and saving to scores and score sheets. We want children to meet big numbers without worry. Jaques of London has made things for children to hold and play with for generations. The Mini Minds Hub is our way of carrying that on: free, screen-free, and simple enough for a parent at a kitchen table to use next to a teacher in a classroom.

Subtracting Four Digit Numbers: 20 questions and answers

1. What is an "exchange" in subtraction?

It is when you trade one from the next column along for ten in the column you are working on. It lets you subtract a bigger digit from a smaller one. This sheet uses the word "exchange".

2. Why do the answers need an exchange at all?

Because a digit on top is sometimes smaller than the digit below it. In 8420 minus 3185, the ones column asks for 0 minus 5. Taking one ten from the tens column makes that possible.

3. What happens when the digit I need to take from is zero?

You go one column further. In 5000 minus 2736, the hundreds, tens and ones are all zero. Take one thousand and trade it down through each column. The answer is 2264.

4. What is the easiest way to check an answer?

Add it back. The Year 4 curriculum asks pupils to use inverse operations to check. For 7634 minus 2451, the answer is 5183. Add 5183 and 2451 and you should get 7634.

5. Why does adding check a subtraction?

Addition and subtraction undo each other. A Nuffield Foundation review calls it essential to understand that they are reversible actions.

6. Should we estimate first?

Yes. The curriculum says "estimate and use inverse operations to check answers". For 9301 minus 4567, think 9300 minus 4600. That is about 4700. The real answer is 4734.

7. Which question is a good warm-up?

Our own view: the first one, 7634 minus 2451, because it needs only one exchange, in the tens column. The answer is 5183.

8. Which question is hardest?

Our own view is 4002 minus 1789 and 6075 minus 1938. Both ask for more than one exchange, and 4002 has zeros in the middle. The answers are 2213 and 4137.

9. Is columnar subtraction the only method?

No. The curriculum says "using the formal written methods of columnar addition and subtraction where appropriate" and also that pupils keep practising mental methods. Our own suggestion: for 6000 minus 2345, try counting up from 2345 to 6000.

10. What is "counting up" or "finding the difference"?

It means starting at the smaller number and working up to the bigger one. From 2345 to 2400 is 55. From 2400 to 3000 is 600. From 3000 to 6000 is 3000. Add 55, 600 and 3000 to get 3655.

11. What should my child already know from Year 3?

Year 3 pupils are taught to add and subtract numbers with up to three digits using columnar methods. Our suggestion: if three digit sums are shaky, go back to those first.

12. What comes next in Year 5?

Year 5 pupils are taught to add and subtract whole numbers with more than four digits, including with columnar methods. Our own view: a secure Year 4 method is a good base for that.

13. What is a "two-step" problem?

It is a word problem that needs two calculations. The Year 4 curriculum says pupils should decide which operations and methods to use and why.

14. Does knowing number bonds help?

The Ofsted mathematics review says pupils who cannot recall maths facts quickly struggle because working memory is overloaded. Its example is addition. Our own advice: if exchanging is slow, check that number facts are quick.

15. How should we set out the sum on paper?

Our own suggestion: write the bigger number on top and the smaller below. Line up the ones under the ones. Squared paper helps. Write the exchanged digits small and clear.

16. What are place value counters?

Our own description: they are counters for ones, tens, hundreds and thousands. You show the top number with counters, then take away the lower number. When you run short in a column, trade one counter from the next column for ten in this one. If you have none, use paper squares.

17. Can the dice game work for subtraction?

Our own suggestion: roll a die four times for each of two numbers. Put the smaller number below the larger. Subtract. We have not found a study of this exact game, so treat it as practice and play, not proof of anything.

18. How many questions should we do in one go?

Our own advice: four, then a break.

19. What if my child gets an answer bigger than the number they started with?

That is a signal to check. Our own view: subtracting makes a number smaller. Estimating first catches this quickly.

20. Do teachers do it the same way?

Our own advice: ask your child's teacher which layout they use and copy it at home.

Sources

1. Department for Education, National curriculum in England: mathematics programmes of study: gov.uk.
2. Nunes, T. and Bryant, P., Key understandings in mathematics learning, Paper 2: Understanding whole numbers, Nuffield Foundation, University of Oxford: nuffieldfoundation.org.
3. Ofsted, Research review series: mathematics (2021): gov.uk.
4. Sutton Trust, Improving the impact of teachers on pupil achievement in the UK, interim findings (2011): dera.ioe.ac.uk.
5. Slater, Davies and Burgess, University of Bristol CMPO Working Paper 09/212 (2009): bristol.ac.uk.

Frequently asked questions

What age is Subtracting Four Digit Numbers for?

It is written for Year 4 (ages 8 to 9), in Key Stage 2.

What will children practise?

Children subtract four digit numbers and exchange tens, hundreds and thousands when needed.

How do I use it?

One child, about 15 minutes. Use scrap paper to set out the columns. Check each answer by adding it back.

What if it feels too hard?

Use place value counters or draw columns for thousands, hundreds, tens and ones.

Is it free?

Yes. It is free to print for home and classroom use.

Is Subtracting Four Digit Numbers suitable for teachers to use in class?

Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing.

Is this a screen-free activity?

Yes. It is a screen-free printable that needs only paper and a pencil, so it works well for quiet time, rainy days and school holidays.

Can I use it for home education?

Yes. Home educators and tutors can use it on its own or as part of a wider plan. It is free to print again for brothers, sisters or revision.

How long does it take?

Most children finish page 1 in 10 to 20 minutes. The notes on page 2 suggest ways to make it shorter or longer.

Do I need to print in colour?

No. It prints well in black and white on plain A4 paper.

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