How to Teach Long Multiplication: Area Method, Then Column Method
Long multiplication is how we multiply bigger numbers on paper, such as 34 × 26 or 156 × 23. Many parents learnt it as a set of steps to follow without being told why. Children today usually learn it in two stages: first the area method (also called the box or grid method), which shows exactly what is going on, and then the faster column method. Teaching it in that order means your child understands the steps instead of just copying them.
What your child needs first
Long multiplication combines several smaller skills. Check these are secure before you start, because most mistakes come from one of them rather than from the method itself:
- Times tables to 10 × 10. Every step relies on quick facts. If these are shaky, see our guide on how to learn times tables fast.
- Multiplying by 10 and 100. Knowing that 30 × 20 = 600 because 3 × 2 = 6, then × 10 and × 10 again.
- Partitioning. Splitting 34 into 30 + 4. Our guide on teaching place value covers this.
- Adding in columns, including carrying (sometimes called regrouping).
Step 1: Multiply a 2-digit number by a 1-digit number
Start small with something like 23 × 4. Split 23 into 20 and 3, multiply each part by 4, then add:
| × | 20 | 3 |
|---|---|---|
| 4 | 80 | 12 |
80 + 12 = 92, so 23 × 4 = 92. Ask your child to say what each box means: “20 times 4 is 80, 3 times 4 is 12.” The printable 2-digit by 1-digit multiplication worksheet gives plenty of practice at this stage.
Step 2: The area (box) method for 2-digit × 2-digit
Now try 34 × 26. Draw a rectangle and split both numbers by place value: 34 becomes 30 and 4, and 26 becomes 20 and 6. That makes four boxes, and each one is a simple multiplication:
| × | 30 | 4 |
|---|---|---|
| 20 | 600 | 80 |
| 6 | 180 | 24 |
Add the four answers: 600 + 80 + 180 + 24 = 884. So 34 × 26 = 884.
Why does this work? Imagine a rectangle 34 squares long and 26 squares wide. Its area is 34 × 26. Cutting it into four smaller rectangles doesn't change the total area, and each small rectangle is easy to work out. Drawing it on squared paper once makes this click for many children.
Step 3: Short multiplication (column method with one digit)
Before tackling two-digit multipliers in columns, practise the column method with a single digit. Here is 347 × 6:
- Ones: 7 × 6 = 42. Write 2 in the ones column and carry the 4 tens.
- Tens: 4 × 6 = 24, plus the 4 carried = 28. Write 8 and carry the 2 hundreds.
- Hundreds: 3 × 6 = 18, plus the 2 carried = 20. Write 20.
So 347 × 6 = 2,082. Always multiply first, then add the carried digit. The 3-digit by 1-digit multiplication worksheet is ideal practice here.
Step 4: The column method for long multiplication
Use the same example, 34 × 26, so your child can see it is the area method in a tidier form. We multiply 34 by the 6, then by the 20, and add the two rows:
| Step | H | T | O |
|---|---|---|---|
| 3 | 4 | ||
| × | 2 | 6 | |
| 34 × 6 | 2 | 0 | 4 |
| 34 × 20 | 6 | 8 | 0 |
| Add | 8 | 8 | 4 |
- Multiply by the ones digit (6): 4 × 6 = 24, write 4, carry 2. Then 3 × 6 = 18, plus 2 = 20. The first row is 204.
- Multiply by the tens digit (2, which is really 20): write a 0 in the ones column first as a placeholder, because we are multiplying by tens. Then 4 × 2 = 8 and 3 × 2 = 6. The second row is 680.
- Add the rows: 204 + 680 = 884.
Point out that 204 is the same as 180 + 24 from the bottom row of the box, and 680 is 600 + 80 from the top row. Same parts, fewer boxes.
Step 5: Bigger numbers (3-digit × 2-digit)
Once 2-digit × 2-digit is comfortable, the method stretches easily. For 156 × 23:
- 156 × 3 = 468
- 156 × 20 = 3,120 (placeholder 0, then 156 × 2 = 312)
- 468 + 3,120 = 3,588
So 156 × 23 = 3,588. The long multiplication worksheet has fresh questions every time you print it.
Always estimate first
A quick estimate catches most big mistakes. Round each number and multiply in your head:
- 34 × 26 is about 30 × 30 = 900, so 884 is sensible.
- 156 × 23 is about 150 × 20 = 3,000, so 3,588 is sensible, but 35,880 or 468 would not be.
Common mistakes and how to fix them
| Mistake | What it looks like | Fix |
|---|---|---|
| Forgetting the placeholder zero | 34 × 26 worked out as 204 + 68 = 272 | Ask “are we multiplying by 2 or by 20?” Go back to the box method to show it. |
| Adding the carry before multiplying | (3 + 2) × 6 instead of 3 × 6 + 2 | Say the order aloud: “multiply, then add the carry”. |
| Digits drifting out of their columns | Rows don't line up, so the addition goes wrong | Use squared paper, one digit per square. |
| Muddled carried digits | Carries from the first row get used in the second | Write carries small and cross them out once used. |
| Slow times tables | Long pauses and counting on fingers | Short daily fact practice alongside the written method. |
Which method should my child use?
| Method | Best for | Watch out for |
|---|---|---|
| Area (box or grid) method | Understanding why it works; children who like to see every part | Takes more space and lots of adding at the end |
| Column method | Speed and bigger numbers once the idea is understood | Easy to forget the placeholder zero without understanding |
Both are correct. Check which method your child's school teaches, start with the area method if they are unsure, and move to the column method when they can explain each step. For mental strategies that work alongside written methods, see how to improve mental maths.
When do children learn long multiplication?
Children usually multiply 2-digit and 3-digit numbers by a single digit around Grade 4, and move on to long multiplication with 2-digit multipliers around Grade 5 to Grade 6. If multiplication itself still feels new, start with our guide on how to teach multiplication.
Frequently asked questions
What is the easiest way to teach long multiplication?
Start with the area or box method: split both numbers into tens and ones, multiply each pair in a grid, then add the parts. Once your child understands why it works, move on to the faster column method.
Why do you put a zero in long multiplication?
When you multiply by the tens digit you are really multiplying by a multiple of ten, such as 20 rather than 2. The zero in the ones column is a placeholder that keeps every digit in the right place value column.
What is the difference between short and long multiplication?
Short multiplication multiplies by a single digit, such as 347 × 6, in one row. Long multiplication multiplies by a number with two or more digits, such as 34 × 26, using one row for each digit and then adding the rows.
How can my child check a long multiplication answer?
Estimate first by rounding, for example 34 × 26 is about 30 × 30 = 900, and see if the answer is close. They can also swap the numbers around or use the area method as a second check.