Column Addition and Subtraction — Why 23 + 4 Goes Wrong
Ask your child to write 23 + 4 in column form, and they write the 4 under the tens digit — the answer comes out 63. This is a new stumble that shows up in grade 2, right after a child has learned addition with carrying in grade 1.
Column form works because lining up place value turns a calculation on a big number into a set of single-digit calculations. If the digits aren't lined up, this mechanism doesn't work at all. When I looked into it, the commentary places the point where a child becomes able to understand column form right when their sense of carrying becomes clear. Once I knew that, I ordered diglabo's worksheets in stages — no carrying, one carry, two carries.
The root cause: what lining up place value means hasn't landed
Japan's Ministry of Education, in its commentary on the national curriculum guidelines for elementary mathematics (2017), lists this as something a child should be able to do by the end of grade 2: "understand that calculating 2-digit addition and its inverse, subtraction, builds on basic calculations with 1-digit numbers and the like, and be able to carry these calculations out reliably. Also, understand how to write these as column calculations." (Grade 2, Numbers and Calculation)
The same commentary also explains the mechanism of column form itself: "When each place's calculation is written with the places lined up like this, a 2-digit calculation is reduced to a calculation on the digits in each place, and can be handled with 1-digit addition and its inverse, subtraction, and so on. Column form is what makes this easy to process in a fixed way." Lining up place value isn't a matter of appearance — it is the very mechanism that breaks a big-number calculation down into single-digit calculations.
When a 2-digit-plus-1-digit column addition has the 1-digit number written under the tens digit, that's a sign this idea of "lining up place value" hasn't landed yet. If 23 + 4 comes out as 63, suspect this pattern.
The carried "1" disappears
In column additions with two carries in a row, a common error is forgetting to add the small carried 1 into the next place, so the answer comes out exactly 10 too small. The same commentary states: "once a child's sense of carrying becomes clear, they become able to understand the column form ordinarily used." Without understanding what carrying means, a child can't treat the 1 they wrote as something to be added in the next step. Moving on to 3-digit column calculations brings a two-step borrow — borrowing from the hundreds place when the tens digit is 0 — and that's where more children get stuck.
How to teach it at home
Step 1: Line up place value on grid paper
Use dedicated column-calculation paper or a grid notebook, and start by practising lining up the ones and tens digits in vertical columns. Plain ruled paper makes it easy for the digits to slip out of line. If a child keeps calculating with the digits already out of line, there's no chance left to check that the writing is correct.
Step 2: Decide where the carried "1" goes
Decide on one fixed spot for the carried 1 in each place being calculated — small above the digit, off to the side, wherever — and use the same spot every time. If the spot keeps changing, the carried 1 gets missed once the calculation moves on to the next place.
Step 3: Say "borrow" out loud for borrowing
When borrowing from the place above in subtraction, say it out loud while writing: "borrow 1 from the tens place, 13 minus 7." Saying it out loud turns a step that was only happening in their head into something visible.
What to avoid
When you spot a mistake in column form, don't just have your child fix the answer — check first whether the digits are lined up. Doing more problems doesn't automatically make a child more accurate. Some children end up learning exactly how their digits slipped or exactly which carry they skipped, and that wrong method is what sticks. Taking the time to check, problem by problem, where it went wrong works better.
How to practise
- 2-Digit Addition runs from no carrying up to two carries, repeating the same steps across column form, calculation, fill-in-the-blank, and word-problem formats
- 3-Digit Addition and Subtraction confirms that lining up place value works the same way even as the number of digits grows
- By grade 3, Column Addition and Column Subtraction extend this to 3 and 4 digits. If the habit of lining up place value is in place by the end of grade 2, the steps stay the same as the digits increase
Even as the number of digits grows, the idea of breaking practice into stages by the number of carries stays the same. Grade 3 worksheets carry this same ordering forward.
Mark the work against the answer sheet, check which pattern it is — a place-value slip or a missed carry — and then have your child redo only the problems they got wrong.
Frequently asked questions
Q. My child can do it mentally — is there still a need to make them write it in column form?
A. Yes. Column form is a way of writing for when the numbers get bigger, and the habit of lining up place value that a child builds in grade 2 is used again for 3- and 4-digit addition and subtraction later on, and again for column multiplication and division. Getting the way of writing settled now saves confusion later.
Q. My child isn't writing the carried digit and seems to be adding it in their head
A. If they're handling it correctly in their head, there's no need to force them to write it down. But if mistakes start increasing, try going back to writing it out for a while. Writing it in a visible form gives a child a way to spot their own mistakes, and it's also something to fall back on once the numbers get too big to hold in their head.
Whether the digits are lined up is easy to see just by looking at the answer. There's no need to rush — take the time to check it one digit at a time.
This article is written by a parent who builds diglabo. I am not a teacher or an education specialist. The general guidance here is based on how the topic is taught in Japanese primary schools, checked against Japan's national curriculum guidelines.
diglabo's worksheets follow the Japanese curriculum. What that means if you are outside Japan