The Grid Method for Multiplication

What is the grid method?

The grid method (sometimes called the box method) is a clear way to multiply bigger numbers. Instead of trying to do everything at once, you split the numbers into parts, multiply the parts separately, then add up the results.

It rests on something you may already know: how to partition a number into tens and ones, from Place Value to Thousands. It also helps to be quick with your Times Tables.

The big idea: partition, multiply, add

The grid method has three steps:

1. Partition each number into tens and ones (and hundreds if needed).
2. Multiply every part of one number by every part of the other, writing each answer in a box.
3. Add all the boxes together.

Why split them up? Multiplying 23 × 4 in one go is hard. But 20 × 4 and 3 × 4 are both easy. Place value lets us break the big job into small, friendly jobs.

Worked example 1: two-digit by one-digit

Work out 23 × 4.

Split 23 into 20 + 3. Make a grid with those across the top and 4 down the side.

×	20	3
4	80	12

1. 20 × 4 = 80 → write 80.
2. 3 × 4 = 12 → write 12.
3. Add the boxes: 80 + 12 = 92.

So 23 × 4 = 92.

Check the logic: 23 fours is the same as 20 fours (80) plus 3 fours (12). Splitting changed nothing about the total — it just made each piece easy.

Worked example 2: a bigger one-digit multiplier

Work out 137 × 6.

This time partition into hundreds, tens and ones: 100 + 30 + 7.

×	100	30	7
6	600	180	42

1. 100 × 6 = 600
2. 30 × 6 = 180
3. 7 × 6 = 42
4. Add: 600 + 180 + 42 = 822.

So 137 × 6 = 822. Add the boxes carefully: 600 + 180 = 780, then 780 + 42 = 822.

Worked example 3: two-digit by two-digit

Work out 24 × 13.

Now both numbers are split. 24 = 20 + 4 and 13 = 10 + 3. The grid has 2 columns and 2 rows = 4 boxes.

×	20	4
10	200	40
3	60	12

1. 20 × 10 = 200
2. 4 × 10 = 40
3. 20 × 3 = 60
4. 4 × 3 = 12
5. Add every box: 200 + 40 + 60 + 12 = 312.

So 24 × 13 = 312.

Why four boxes? Each part of 24 must meet each part of 13. The 20 must multiply both the 10 and the 3, and the 4 must do the same. Miss a box and you lose part of the total — that is the most common grid-method mistake, so always fill every box.

Adding the boxes neatly

When there are several boxes, line up the answers and add in steps. For 24 × 13:

Step	Running total
Start with 200	200
+ 40	240
+ 60	300
+ 12	312

A tip: add the biggest numbers first, then the smaller ones. It keeps the running total tidy.

Checking with an estimate

Round each number and multiply to see if your answer is sensible.

• 24 × 13 → about 20 × 13 = 260, or 24 × 10 = 240. The real answer 312 is a bit above these, which fits.
• 137 × 6 → about 140 × 6 = 840. Our answer 822 is close, so it looks right.

Try it yourself

Draw a grid for each and fill every box.

• 35 × 4 (Answer: 120 + 20 = 140)
• 216 × 3 (Answer: 600 + 30 + 18 = 648)
• 32 × 21 (Answer: 600 + 20 + 60 + 2 = 682)

For the last one, partition both numbers: 32 = 30 + 2 and 21 = 20 + 1.

Great job!

You can now multiply bigger numbers with the grid method by partitioning, multiplying each part, and adding. Best of all, you can see exactly where every number comes from.

When you are ready to fold the grid into a faster written method, move on to Long Multiplication, or sharpen the facts you need in your Times Tables.