The grid method for multiplication, step by step

How do you do grid method multiplication?

To do grid method multiplication, partition the bigger number into its place value parts, write the parts along the top of a grid and the other number down the side, multiply to fill each box, then add the boxes together. Here is 47 × 6.

47 × 6 with the grid method

×	40	7
6	240	42

1. Partition 47 into 40 and 7.
2. 40 × 6 = 240.
3. 7 × 6 = 42.
4. Add the answers in the grid: 240 + 42 = 282.

The hard part is never the grid itself. It's the times tables facts inside it and multiplying by multiples of 10. For 40 × 6, your child uses 4 × 6 = 24 and then makes it 10 times bigger: 240. If the 6 times table isn't secure yet, the grid gets slow and the mistakes creep in.

Why the grid method works

The grid method works because of partitioning. 47 is 40 and 7, so 47 lots of 6 is 40 lots of 6 plus 7 lots of 6. Our guide to partitioning shows how children learn to split numbers like this from Year 2.

In Year 4 the national curriculum calls this the distributive law, and gives the example 39 × 7 = 30 × 7 + 9 × 7. Government guidance for teachers shows it with an array: 14 rows of 3 dots, split into 10 rows and 4 rows, so 14 × 3 is 30 + 12. The grid method is that array drawn as boxes, with the dots left out.

Is the grid method in the national curriculum?

No, not by name. The national curriculum asks Year 3 children to multiply two-digit numbers by one-digit numbers "using mental and progressing to formal written methods", and to develop reliable written methods before short multiplication. The grid method is one of the written methods many schools use for that step, in Year 3 and Year 4.

The KS2 maths test framework does mention the grid method. In the arithmetic paper, a child who uses a formal written method can get a mark for correct working even if the final answer is wrong. That mark isn't given when the grid method is used for long multiplication. So the grid method is a way into the formal methods, not where children stop.

The grid method with a three-digit number

With a three-digit number, the grid just gets one more box: hundreds, tens and ones. Here is 253 × 4.

253 × 4 with the grid method

×	200	50	3
4	800	200	12

1. Partition 253 into 200 and 50 and 3.
2. 200 × 4 = 800.
3. 50 × 4 = 200.
4. 3 × 4 = 12.
5. Add the answers in the grid: 800 + 200 + 12 = 1,012.

Adding the boxes is where three-digit grids go wrong, so encourage your child to add them in a column or tick each box as it's added. A child who knows column addition can set the three answers out one above the other.

If a number has a zero in it, there's no box for that place. 305 × 4 has a box for 300 and a box for 5, and nothing for the tens.

Long multiplication with the grid method

The grid method also works for two-digit numbers multiplied by two-digit numbers. Partition both numbers, so the grid has two columns and two rows and four boxes to fill. Here is 36 × 24.

36 × 24 with the grid method

×	30	6
20	600	120
4	120	24

1. Partition 36 into 30 and 6, and 24 into 20 and 4.
2. 30 × 20 = 600.
3. 6 × 20 = 120.
4. 30 × 4 = 120.
5. 6 × 4 = 24.
6. Add the answers in the grid: 600 + 120 + 120 + 24 = 864.

Each box uses a times tables fact and some tens. For 30 × 20, your child works out 3 × 2 = 6, then makes it 100 times bigger, because both numbers are multiples of 10: 600. Children meet multiplying by a two-digit number in Year 5, when they learn long multiplication, the formal written method. The grid shows them where each part of a long multiplication comes from.

Why many schools teach the grid method first

Many schools teach the grid method first because every step can be seen. Each box is one small multiplication, and nothing is carried or hidden. Once children understand why 47 × 6 is 240 + 42, the column method makes sense instead of being a set of rules to remember.

Short multiplication, the column method, does the same multiplications in the same order. It starts with the ones (7 × 6 = 42), writes the 2 and carries the 4 tens, then works out 4 tens × 6 and adds the 4 tens carried. That's the grid method squashed into one line, with the adding done as you go.

Moving from one to the other works best side by side. Do the same calculation both ways and ask your child to find the 42 and the 240 in the column method.

Common mistakes with the grid method

• Losing the zero. Writing 40 × 6 as 24 instead of 240. Ask "is it 4 sixes or 40 sixes?"
• Partitioning by digit. Splitting 47 into 4 and 7 rather than 40 and 7. A place value chart helps.
• Missing a box when adding. This is most common with four boxes. Tick each one off.
• A times tables slip. One wrong fact, like thinking seven sixes are 48, spoils the whole answer. Practise the facts on their own, away from the grid.
• Not checking. 47 × 6 is close to 50 × 6 = 300, so an answer of 2,820 or 28 can't be right.

How to help at home

• Practise multiplying by 10 and 100 first. If your child knows 3 × 7 = 21, ask for 30 × 7 and 300 × 7.
• Keep the times tables going. A few minutes a day on the times tables makes every grid quicker. The times table grid is handy to have on the fridge while facts are still being learned.
• Use squared paper. It keeps the boxes and the adding neat.
• Ask how school does it. Schools set the grid out in slightly different ways, so follow the layout your child brings home.

Grid method questions to try

1. 27 × 4
2. 53 × 6
3. 68 × 5
4. 214 × 3
5. 23 × 14
6. 45 × 32

Answers

1. 108 (80 + 28)
2. 318 (300 + 18)
3. 340 (300 + 40)
4. 642 (600 + 30 + 12)
5. 322 (200 + 30 + 80 + 12)
6. 1,440 (1,200 + 150 + 80 + 10)

For everything else in these years, see the Year 3 maths and Year 4 maths guides.