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Column Addition and Subtraction at Home: Carrying, Exchanging and Practice Sets
Short answer
Write the numbers one above the other with ones under ones and tens under tens. Start with the ones column. In addition, if a column totals 10 or more, write the ones and carry the ten. In subtraction, if the top digit is smaller, exchange one ten for ten ones first. Always check with the inverse.
Column addition and subtraction work by lining up digits by place value and working from the ones column to the left, carrying a ten when a column totals 10 or more and exchanging a ten for ten ones when the top digit is too small to subtract from. Once a child understands why each step happens, the method works for any size of number.
Schools use different words for the same steps. Carrying is also called regrouping; exchanging is also called borrowing or regrouping. In England, the national curriculum introduces formal columnar addition and subtraction in Year 3 for numbers with up to three digits. In the US, Common Core asks Grade 2 children to add and subtract within 100 using place-value strategies, with the standard written method expected to be fluent by Grade 4.
Key points
- Line digits up by place value; misaligned columns cause many wrong answers.
- Always start with the ones column and move left.
- Carrying (regrouping) moves a ten into the next column; exchanging (borrowing) breaks a ten into ten ones.
- Teach without regrouping first, then with regrouping, then zeros in the top number.
- Check every answer with the inverse: add back the answer to the number you subtracted.
How do you do column addition with carrying?
Take 47 + 28. Write 47 on top and 28 underneath, with 7 above 8 and 4 above 2. Draw a line underneath for the answer.
- Ones: 7 + 8 = 15. Write 5 in the ones column and carry the 1 ten, written small under the tens column.
- Tens: 4 + 2 = 6, plus the carried 1 makes 7. Write 7.
- Answer: 75. Say it aloud: “seven tens and five ones.”
- Three digits: 245 + 178 works the same way. 5 + 8 = 13 (write 3, carry 1); 4 + 7 + 1 = 12 (write 2, carry 1); 2 + 1 + 1 = 4. Answer: 423.
How do you do column subtraction with exchanging?
Take 52 − 27. In the ones column, 2 − 7 is not possible with whole numbers, so exchange one of the 5 tens for ten ones. Cross out the 5 and write 4; the 2 ones become 12.
Now 12 − 7 = 5 in the ones and 4 − 2 = 2 in the tens. The answer is 25. Always subtract the bottom digit from the top digit, never the other way round.
- Ask first: “Is the top digit big enough?” If not, exchange before subtracting.
- Use the phrase “one ten becomes ten ones” so the step has meaning, not just a crossing-out ritual.
- Check by adding: 25 + 27 = 52, so the answer is right.
How do you subtract when the top number has a zero?
Numbers like 403 − 156 are the hardest step, because there are no tens to exchange. Go to the hundreds instead: 4 hundreds become 3 hundreds and 10 tens. Then exchange one of those tens: 10 tens become 9 tens, and the 3 ones become 13 ones.
Now subtract: 13 − 6 = 7, 9 − 5 = 4, 3 − 1 = 2. The answer is 247, and 247 + 156 = 403 confirms it. Practise this only after exchanging across one column is secure.
What are the most common column method mistakes?
Most errors fall into a handful of patterns. Spotting the pattern tells you exactly what to reteach.
| Mistake | Example of wrong work | What to do |
|---|---|---|
| Subtracting the smaller digit from the larger | 52 − 27 = 35 (did 7 − 2) | Ask “Is the top digit big enough?” before every column |
| Forgetting the carried ten | 47 + 28 = 65 | Write the carried 1 clearly and tick it once added |
| Writing the whole column total | 47 + 28 = 615 | Only one digit goes in each column; the ten moves left |
| Misaligned columns | 125 + 34 written as 125 + 340 = 465 | Use squared paper, one digit per square, ones on the right |
| Starting from the left | Carries land in the wrong place | Draw an arrow from right to left above the sum |
Practise this with a 12-week pack
Grade 2 (Year 3): 60 dated sheets with your child’s name, levelled by a quick check, with weekly answer keys. €19 once.
Should children use objects before the written method?
Yes, briefly. Show 52 − 27 with 5 bundles of ten straws and 2 loose straws, or with base-ten blocks. When you cannot take 7 loose straws away, unbundle one ten. Doing this physically a few times makes the written exchange obvious.
Move to the written method once your child can explain the step in words. If errors return later, go back to the objects for one session rather than repeating the rule louder.
What practice sets work best at home?
Practise in short daily sessions of 10-15 minutes, about 10 to 16 problems, moving to the next stage only when your child gets most of a set right without help. Mix in a few problems from earlier stages so they stay sharp; our guide to spiral review maths practice explains why.
| Stage | Skill | Example | Answer |
|---|---|---|---|
| 1 | 2-digit addition, no carrying | 34 + 25 | 59 |
| 2 | 2-digit subtraction, no exchanging | 63 − 21 | 42 |
| 3 | 2-digit addition with carrying | 47 + 28 | 75 |
| 4 | 2-digit subtraction with exchanging | 52 − 27 | 25 |
| 5 | 3-digit addition with two carries | 245 + 178 | 423 |
| 6 | 3-digit subtraction across a zero | 403 − 156 | 247 |
How long does it take to learn column addition and subtraction?
It varies, but most children need several weeks per stage rather than days, and subtraction with exchanging usually takes longest. Stages 1 to 4 match the Grade 2 skills of adding and subtracting within 100; stages 5 and 6 belong with Grade 3 work within 1,000. Pencilpace’s Grade 2 maths worksheets follow the same order: without regrouping first, then with it.
Questions
What is the difference between carrying and regrouping?
None in practice. Carrying is the traditional word in addition; regrouping is the term many US schools use for both addition and subtraction, because ten ones are regrouped as one ten or the reverse. In England, teachers usually say exchanging for subtraction. Use whichever word your child’s teacher uses, so home and school match.
Is borrowing the same as exchanging?
Yes. Both describe breaking one ten into ten ones, or one hundred into ten tens, so that a column can be subtracted. Many teachers prefer exchanging because nothing is paid back: the number keeps its value, it is simply written differently. For example, 52 becomes 4 tens and 12 ones.
When should a child learn column addition?
In England, the national curriculum introduces formal columnar addition and subtraction in Year 3, with numbers up to three digits. Many US schools teach place-value methods in Grade 2 and expect fluency with the standard written method by Grade 4. Before that, children should be secure with facts to 20 and with tens and ones.
Should my child still do mental maths if they know the column method?
Yes. Sums like 40 + 30 or 99 + 15 are quicker in the head, and choosing between mental and written methods is a skill in itself. A useful rule: if your child can do it in their head in a few seconds, there is no need to write it in columns. Keep columns for harder numbers.
How can I check my child’s column work quickly?
Use the inverse. For subtraction, add the answer to the number subtracted and you should get the top number. For addition, subtract one of the numbers from the total. Teach your child to do this check too, so they catch their own errors. The free sample sheet is a quick way to try this routine.
My child gets the right answer but cannot explain the method. Is that a problem?
It can be later, when numbers grow and zeros appear. Ask them to explain one sum a session in words, using “ones”, “tens” and “one ten becomes ten ones”. If they cannot, spend a few minutes with straws or base-ten blocks. Understanding the exchange step prevents most errors with three-digit numbers.
Sources
Try it at home
Print a free Grade 2 (Year 3) sheet with the answers on page 2, no email needed. If it suits your child, a 12-week pack gives you 60 dated sheets, one for every school day (€19, full refund within 14 days).