# What is the grid method?

### 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 sentence: *38 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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