Column multiplication is the written method for calculating the product of multi-digit numbers, by stacking one number under the other and solving digit by digit. It's taught around 3rd and 4th grade (ages 8-10), once a child already knows the multiplication tables from 1 to 10 by heart. This guide explains the procedure step by step, with worked examples of increasing difficulty.
If your child doesn't yet know the multiplication tables well, it's worth reviewing them first: without them, every step of column multiplication becomes much slower. You can check what multiplication tables are before moving on with this guide.
What does the column multiplication method involve?
The method places the longer number on top and the shorter one below, aligned to the right. Then each digit of the bottom number is multiplied by every digit of the top number, from right to left, writing one partial result row per digit of the multiplier. At the end, those partial rows are added together, each one shifted one place to the left according to the position of the digit that generated it.
It's an orderly method: instead of multiplying everything at once, it breaks the problem into small steps any child can follow with paper and pencil.
