Column Multiplication and Short Division: Step by Step Practice for Years 4 to 6

Children meet column multiplication and short division in Years 4 to 6, and they keep needing them: on the KS2 SATs arithmetic paper, in 11+ maths, and for any calculation too big to do in their head. Most of the mistakes I see happen at the same few points. A carried digit gets forgotten or added in the wrong place, the second row of a long multiplication starts in the wrong column, or a zero goes missing from the middle of a division answer.

Below, each method is set out the way most primary schools teach it, with the point where children tend to go wrong and a question to ask your child at that point. There is free step by step practice for both in our Maths Skills Lab.

When each method is taught

The national curriculum brings the written methods in gradually.

• Year 4: multiplying 2-digit and 3-digit numbers by a 1-digit number, set out in columns.
• Year 5: multiplying numbers up to 4 digits by a 1-digit or 2-digit number, and short division of numbers up to 4 digits by a 1-digit number, with remainders.
• Year 6: long multiplication up to 4 digits by 2 digits, long division of numbers up to 4 digits by a 2-digit number, and giving remainders as whole numbers, fractions or rounded, depending on the question.

The SATs arithmetic paper has 36 questions in 30 minutes, worth 40 marks. It does not ask for a particular method, but a child who is unsure how to set out a multiplication or a division will spend too long on those questions.

Schools set these methods out in slightly different ways. Ask your child to show you how they do it at school and practise in that layout, so you are not teaching them a second version.

Start with the grid method

Many schools teach the grid method first, and it is worth starting there at home if your child is not confident. To work out 46 × 7, split 46 into 40 and 6, multiply each part by 7, then add: 280 + 42 = 322.

The grid shows what each digit is worth. That is useful later, because the column method is the same calculation with fewer steps written down.

Column multiplication

Here is 46 × 7 in columns.

1. Multiply the ones. 6 × 7 = 42. Write 2 in the ones column and carry the 4 into the tens column.
2. Multiply the tens. 4 × 7 = 28, plus the carried 4 makes 32.
3. Finish the answer. Write the 32 to the left of the 2, giving 322.

At step 1, point at the carried 4 and ask your child, "Four what?" The answer you want is four tens. If they say four, or four ones, go back to the grid for a while.

To multiply by a 2-digit number there is a second row. For 46 × 23, the first row is 46 × 3 = 138. The second row is 46 × 20, so your child writes a 0 in the ones column first and then works out 46 × 2 = 92 next to it, giving 920. Adding the rows gives 1,058.

If that zero is missing, ask your child to point at the 2 in 23 and say what it is worth. Once they say twenty, they can see why the second row starts one column to the left.

An estimate shows whether the answer is in the right range. 46 × 23 is close to 50 × 20, which is 1,000, so an answer of 1,058 is about right. An answer like 230 or 10,580 is not.

Short division

Short division is often called the bus stop method. Here is 745 ÷ 4.

1. Hundreds. 4 goes into 7 once, with 3 left over. Write 1 above the 7. The 3 left over is 3 hundreds, which is 30 tens, so it joins the 4 tens to make 34.
2. Tens. 4 goes into 34 eight times, with 2 left over. Write 8 above the 4. The 2 tens left over join the 5 ones to make 25.
3. Ones. 4 goes into 25 six times, with 1 left over. The answer is 186 remainder 1.

In Year 6 your child also learns to write the remainder in other ways. 1 left over when dividing by 4 is a quarter, so the answer is 186¼. To get a decimal, they put a decimal point after 745, write a 0 after it and keep dividing: 10 tenths divided by 4 is 2 tenths with 2 left, then 20 hundredths divided by 4 is 5 hundredths. That gives 186.25.

The mistake to watch for is a zero in the middle of the answer. In 624 ÷ 6, 6 goes into 6 once. Then 6 goes into 2 zero times, so your child must write 0 above the 2 before carrying the 2 to make 24. 24 ÷ 6 = 4, giving 104. Leave out that 0 and the answer comes out as 14, which a quick estimate shows is far too small.

Practising at home

Ten minutes on one method, three or four times a week, is easier to keep going than a long session when your child is tired after school.

In the Skills Lab, open the method and choose Teach first. It works through one question a step at a time, with a short note on each step. Pause before each new step and ask your child what they think comes next. Then switch to Practise for ten questions at the same level, worked out on paper and checked one at a time.

Column multiplication has 8 levels, from 2-digit × 1-digit with no carrying up to 3-digit × 3-digit. Level 5 is the one with the second row and the zero. Short division has 9 levels, finishing with remainders as fractions and division past the decimal point. The Lab counts a level as secure at 8 out of 10, so move up when your child gets there and can tell you what went wrong in the others.

Times tables make both methods much easier. If your child has to stop and count up to find 7 × 8, they often lose track of the carried digit while they do it. The Lab has times tables practice too, along with multiplying and dividing decimals.

If arithmetic mistakes keep coming back, our post on why children get stuck on 11+ arithmetic looks at the usual causes. For a full course, the Complete KS2 SATs Maths Course is 64 interactive lessons for £160, and the Complete 11+ Maths Course is 80 lessons for £200.

Questions parents ask

What is the difference between short division and long division?

They use the same idea. In short division the remainders are carried as small digits in front of the next number. In long division each subtraction is written out underneath, which makes it easier to keep track when dividing by a 2-digit number.

Should my child use the grid method or the column method?

Both have a place. The grid shows where each part of the answer comes from, and the column method is quicker once that makes sense. Most children move on to columns during Year 4 or Year 5.

Why does my child keep forgetting the zero in long multiplication?

Usually because they learned it as a rule without the reason. The second row multiplies by the tens digit, so everything in it is ten times bigger. Ask them what the 2 in 23 is worth. Once they can explain the zero, they stop forgetting it.

Is the Skills Lab free?

It is free to use with no account. It works best on a laptop or desktop, where the working has room to show clearly.