Grid method multiplication

In mathematics education at the level of primary school or elementary school, the grid method (also known as the box method) of multiplication is an introductory approach to multi-digit multiplication calculations, i.e. multiplications involving numbers larger than ten.

Compared to traditional long multiplication, the grid method differs in clearly breaking the multiplication and addition into two steps, and in being less dependent on place value.

Whilst less efficient than the traditional method, grid multiplication is considered to be more reliable, in that children are less likely to make mistakes. Most pupils will go on to learn the traditional method, once they are comfortable with the grid method; but knowledge of the grid method remains a useful "fall back", in the event of confusion. It is also argued that since anyone doing a lot of multiplication would nowadays use a pocket calculator, efficiency for its own sake is less important; equally, since this means that most children will use the multiplication algorithm less often, it is useful for them to become familiar with a more explicit (and hence more memorable) method.

Use of the grid method has been standard in mathematics education in primary schools in England and Wales since the introduction of a National Numeracy Strategy with its "numeracy hour" in the 1990s. It can also be found included in various curricula elsewhere. Essentially the same calculation approach, but not necessarily with the explicit grid arrangement, is also known as the partial products algorithm or partial products method.

The grid method can be introduced by thinking about how to add up the number of points in a regular array, for example the number of squares of chocolate in a chocolate bar. As the size of the calculation becomes larger, it becomes easier to start counting in tens; and to represent the calculation as a box which can be sub-divided, rather than drawing lots and lots of dots.

At the simplest level, pupils might be asked to apply the method to a calculation like 3 × 17. Breaking up ("partitioning") the 17 as (10 + 7), this unfamiliar multiplication can be worked out as the sum of two simple multiplications:

so 3 × 17 = 30 + 21 = 51.

This is the "grid" or "boxes" structure which gives the multiplication method its name.

Faced with a slightly larger multiplication, such as 34 × 13, pupils may initially be encouraged to also break this into tens. So, expanding 34 as 10 + 10 + 10 + 4 and 13 as 10 + 3, the product 34 × 13 might be represented:

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