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# What is the grid method?

We explain what the grid method is, how it is taught in primary-school maths and how it is used to multiply a two-digit number by a one-, two- or three-digit numbers, when multiplying amounts of money and when multiplying decimals.

## What is the grid method (or box method of multiplication)?

The grid method is a written method used to teach children multiplication. It involves partitioning numbers into tens and units before they are multiplied.

In some schools the grid method is referred to as the box method of multiplication because children learn to partition numbers into a grid of boxes.

## Multiplying a one-digit number by a two-digit number with the grid method

Teachers often start teaching the grid method in Year 3 when showing children how to multiply a two-digit number by a one-digit number.  For example: they would demonstrate how to work out 37 x 5 by partitioning the numbers and putting them in a grid, then multiplying each one in turn:

The answers of each multiplication calculation (150 and 35) then need to be added, to find the answer, which is 185.

## Multiplying a two-digit number by a two-digit number with the grid method

Children need to have the following skills before moving onto this next stage of the grid method:

• Good knowledge of times tables
• Able to multiply any number by 10
• Able to multiply a one-digit number by a multiple of ten (for example: 5 x 70, 2 x 30, 4 x 80 etc.)
• Able to multiply two multiples of ten (for example: 50 x 20, 80 x 30, 60 x 40 etc.)
• A reliable written method for adding four numbers (some three-digit)

In Years 4 and 5 children move onto multiplying a two-digit number by another two-digit number.

Look at the following number sentence38 x 62 =
Each number would be partitioned into tens and units and placed in the grid. The numbers in the left-hand column would then be multiplied by each of the numbers in the top row and the answers written in the blank squares as follows:

The four numbers would then be added, using whichever method the child is familiar with.

## Multiplying a three-digit number by a one-digit number with the grid method

In Years 4 and 5, children are expected to be able to multiply a three-digit number by a one-digit number. This can also be done using the grid method:

482 x 6 =
Again, the numbers need to be partitioned up and put in a grid. Then the 6 is multiplied by each of the three numbers to make the answers. The numbers then need to be added to produce the answer.

## Multiplying amounts of money with the grid method

This method can be useful to children in Year 3 and 4 who are having to work out, for example, the cost of 3 books, each costing £2.63:

It is very important when using the grid method to multiply amounts of money that children remember to keep writing £ or p next to the numbers so that they do not get confused about which unit of money they are dealing with.

## Multiplying a decimal by a one-digit number with the grid method

Children in Year 6 are also expected to multiply decimals by one-digit numbers. Before moving onto this, children should be able to multiply decimals such as 0.5, 0.3, 0.8 etc. by a single-digit number mentally. This is a good way to teach this:

0.4 x 7 =

• First work out 4 x 7 = 28
• Then, because the 4 was actually 0.4, the answer needs to be divided by ten, so the answer is 2.8.

If a child was asked to multiply 5.9 x 3, they could do this using the grid method in the following way:

## Multiplying a three- or four-digit number by a two-digit number with the grid method

In Year 6, children are expected to multiply numbers of up to four digits by two-digit numbers. If they used the grid method to do this, they would do it as follows:

However usually, at this stage, a child would use long multiplication (also called column multiplication) as a quicker method for these larger numbers.

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