Compared to the grid method, traditional long multiplication may also be more abstract and less manifestly clear, so some pupils find it harder to remember what is to be done at each stage and why. The traditional method is ultimately faster and much more compact but it requires two significantly more difficult multiplications which pupils may at first struggle with. Traditional long multiplication can be related to a grid multiplication in which only one of the numbers is broken into tens and units parts to be multiplied separately: However, by this stage (at least in standard current UK teaching practice) pupils may be starting to be encouraged to set out such a calculation using the traditional long multiplication form without having to draw up a grid. The grid method extends straightforwardly to calculations involving larger numbers.įor example, to calculate 345 × 28, the student could construct the grid with six easy multiplications In countries such as the UK where teaching of the grid method is usual, pupils may spend a considerable period of time regularly setting out calculations like the above, until the method is entirely comfortable and familiar. This is the most usual form for a grid calculation. Once pupils have become comfortable with the idea of splitting the whole product into contributions from separate boxes, it is a natural step to group the tens together, so that the calculation 34 × 13 becomes Totalling the contents of each row, it is apparent that the final result of the calculation is (100 + 100 + 100 + 40) + (30 + 30 + 30 + 12) = 340 + 102 = 442. So, expanding 34 as 10 + 10 + 10 + 4 and 13 as 10 + 3, the product 34 × 13 might be represented: This is the "grid" or "boxes" structure which gives the multiplication method its name.įaced with a slightly larger multiplication, such as 34 × 13, pupils may initially be encouraged to also break this into tens. Breaking up ("partitioning") the 17 as (10 + 7), this unfamiliar multiplication can be worked out as the sum of two simple multiplications: Īt the simplest level, pupils might be asked to apply the method to a calculation like 3 × 17. 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 a multitude of dots. 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. Essentially the same calculation approach, but not with the explicit grid arrangement, is also known as the partial products algorithm or partial products method.Ĭalculations Introductory motivation It can also be found included in various curricula elsewhere. 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 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. 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. Whilst less efficient than the traditional method, grid multiplication is considered to be more reliable, in that children are less likely to make mistakes. Ĭompared 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. Because it is often taught in mathematics education at the level of primary school or elementary school, this algorithm is sometimes called the grammar school method. The grid method (also known as the box method) of multiplication is an introductory approach to multi-digit multiplication calculations that involve numbers larger than ten. ( February 2017) ( Learn how and when to remove this template message) You may improve this article, discuss the issue on the talk page, or create a new article, as appropriate. The examples and perspective in this article deal primarily with the United States and do not represent a worldwide view of the subject.
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