Maths guide
Column addition and subtraction explained step by step
Written addition and subtraction in grades 3 and 4: place value, carrying, exchanging or counting on, typical mistakes and practice tips for parents.
Key points
- Written methods need secure place-value understanding.
- In addition the carry is written down; in subtraction, schools teach one of two common methods.
- Estimating and checking make answers verifiable.
- Children should practise the method their class uses.
In this guide
What children should know first
Written calculation is not a trick to replace mental maths. It is a method for numbers that get too big to hold in your head. For it to work, your child should know what ones, tens, hundreds and thousands are and solve simple sums up to 100 mentally. Without that place-value understanding the method becomes a routine they carry out but do not understand.
Column addition
Example: 468 + 375. Write the numbers one under the other so that ones sit under ones, tens under tens and hundreds under hundreds. Then work from right to left:
4 6 8
+ 3 7 5
-------- Ones: 8 + 5 = 13. Write the 3 and carry the 1 to the tens.
- Tens: 6 + 7 + 1 (carried) = 14. Write the 4 and carry the 1 to the hundreds.
- Hundreds: 4 + 3 + 1 = 8.
The answer is 843. A quick estimate confirms it: 470 + 380 is about 850.
Column subtraction: two common methods
One thing surprises many parents: there are several usual methods, and which one a class learns differs by school, region or country. The two most common are exchanging (also called decomposition or “borrowing”) and counting on (complementary addition). So look in your child’s exercise book and practise the same method. Mixing two methods tends to confuse rather than help.
Example: 623 − 275.
Exchanging: you cannot take 5 from 3, so exchange one ten: 13 − 5 = 8. The tens digit is now 1, and you cannot take 7 from 1, so exchange one hundred: 11 − 7 = 4. The hundreds digit is now 5: 5 − 2 = 3. Answer: 348.
Counting on: ask: 5 plus what makes 13? Answer: 8. The extra ten moves to the next digit of the lower number: 7 + 1 = 8. Then: 8 plus what makes 12? Answer: 4, again with an extra ten. In the hundreds: 2 + 1 = 3, and 3 plus 3 makes 6. Answer: 348.
Both routes give the same answer. The check shows it: 348 + 275 = 623.
Typical mistakes
- Digits drift out of their columns. Squared paper helps: one digit per square, places stay under each other.
- Taking the smaller digit from the larger. 3 − 5 becomes 5 − 3 in a hurry. Look at the place value and say “exchange” or “count on” out loud.
- Forgetting the carry. Write the carry small, in another colour.
- Zeros in the top number. For 500 − 237 you have to exchange across several places. Practise this separately.
Estimate and check: the safety net
Ask your child to round and estimate before calculating, and to check the answer with the inverse sum afterwards. The method is then not just carried out but checked. Children spot their own mistakes, and that builds confidence.
A sensible practice order
- Addition without carrying
- Addition with one carry
- Addition with several carries and bigger numbers
- Subtraction without exchanging, or counting on with one extra ten
- Subtraction over several places and with zeros
Three to five sums per session are enough. Written sums tire children faster than mental maths.
Where Recheneule can help
Recheneule also includes written calculations and is made for grades 1 to 4, with no ads and no account. For talking through the method, your child’s exercise book remains the main source; the app suits short revision rounds. More on the Recheneule page.
Try it now
- Estimate first: 468 + 375 is close to 470 + 380 = 850.
- Check addition: 843 − 375 must give 468 again.
- Check subtraction: 348 + 275 must give 623 again.
- Use squared paper: one digit per square keeps the columns straight.