Why Kids Who Know Their Times Tables Still Trip Up — The Steps of Column Multiplication
Just because a child can say their times tables doesn't mean column multiplication comes easily. Plenty of children get the times-table part right and still stumble on the steps of writing it in column form.
A mistake in column multiplication tends to get blamed on the times tables. Usually, though, it's a different step that's the problem.
Knowing your times tables isn't enough — column form takes a separate skill
Japan's Ministry of Education, in its commentary on the national curriculum guidelines for elementary mathematics (2017), states: "When the multiplier is a 1-digit number, calculate by paying attention to groupings of numbers." (Grade 3, Numbers and Calculation) It adds: "This is a way of thinking that connects to how column form works." So knowing single-digit times tables is the foundation of column multiplication, but only once a child can apply that knowledge to the right grouping of digits.
In other words, a child who stumbles at column multiplication hasn't forgotten the times tables — they're stuck at the step of assembling the times-table facts into the right place value. This is easy to miss while a child is still doing 2-digit by 1-digit multiplication, where the times tables can be used almost directly. It only surfaces once a child moves on to 3-digit by 1-digit, or 2-digit by 2-digit, multiplication — where not tracking place value properly finally shows.
Cause 1: forgetting to shift the second row one place left
In 2-digit by 2-digit column multiplication, the answer from multiplying by the tens digit (the second row) has to be shifted one place to the left before it's written down. Skip that shift and write it straight underneath instead, and the answer comes out far too small. If the left edges of the two rows line up, suspect this pattern.
Cause 2: adding the carry too early
For 23 × 4, the correct order is: 3 × 4 = 12, write the 2 and carry the 1; then 2 × 4 = 8, add the carried 1 to get 9. Some children add the carried 1 to the 2 first, and multiply that by 3 instead. A stubborn mistake like turning 23 × 4 into 122 comes from exactly this — the order of multiplying and adding has been swapped.
How to teach it at home
I assumed at first that these two skills were the same. Once I learned that the times-table facts and the steps for assembling place value are entirely separate skills that can be practised separately, I started treating them as two distinct things to pay attention to.
Step 1: Confirm each times-table fact out loud before writing
Before starting the column calculation, check each fact one at a time out loud — "what's 3 times 4?" — and confirm the answer is right before writing it down. If the times tables are still shaky when a child starts learning the column steps, you lose the ability to tell the two apart later. When the answer is wrong, you won't be able to tell whether it's a times-table mistake or a mistake in the shift or the add order. Confirming the building blocks first ends up being the faster route.
Step 2: Say "shift one place left" out loud for the second row
When you get to the row for the tens digit, build the habit of saying "shift one place left and write it" out loud. Using a grid notebook lets a child see with their own eyes that the first and second rows are offset by one square. This settles in faster than a spoken reminder on its own.
Step 3: Fix the order to "multiply, then add the carry"
Confirm the order — "multiply, then add the carry" — the same way, every time. The mistake of adding first happens because this order isn't fixed yet.
What to avoid
Don't look at a mistake in column form and decide "back to the times tables." The times-table facts themselves are usually correct. Get the cause wrong, and you end up making a child doubt the part they were already getting right. Ask to see one column multiplication problem they got wrong. Checking the three spots in order — the times-table answer, the shift, and the order of multiplying and carrying — usually narrows down the cause.
How to practise
- Multiplication (2-Digit, 3-Digit) runs through calculation, column form, and word problems in that order. Calculation confirms the times-table groupings first, then column form practises the steps of writing it down
- Column form progresses in stages, from 2-digit by 1-digit up to 3-digit by 2-digit. When a particular mistake pattern shows up, repeat it with variants of the same structure
- Working through to the word problems connects both the times tables and column form to "what situation do you use this in"
The same commentary also states, about this stage of learning: "The competencies developed here feed into the grade 4 study of division with many digits and the grade 5 consideration of multiplication and division of decimals." Practising attention to place value in column multiplication carries straight through to Division (÷ 1-Digit Number) in grade 4. I didn't know it reached that far across grade levels until I looked into it.
Frequently asked questions
Q. Is it okay to start practising column form while the times tables are still shaky?
A. I'd rather not recommend it. Column form is a set of steps that uses the times tables as building blocks. If the building blocks themselves are unreliable, you can't tell a step mistake from a times-table mistake. Moving on to column form once a child can answer a fact from Times Tables: 6 to 9 and 1 in about 2 seconds makes it much easier to isolate the cause.
Q. Is it okay to let them check their answers with a calculator?
A. It works for confirming whether the answer is right. But when a problem is wrong, don't just leave it at the calculator's answer — go through it together to find which step it went wrong at. Checking the answer and finding the cause are two different jobs, and a calculator can only do the first one.
Column multiplication is a unit where the steps for lining up place value get built on top of the foundation of the times tables. When the foundation is solid, a slip in the steps can be fixed one 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