Click here for our other

The method traditionally used for multiplying two numbers of two or more digits is **long multiplication**, but this is quite an abstract process which is difficult to understand for many children. **Grid Multiplication** (also known as the **Grid Method**) is now taught in schools as an intermediate stage before long multiplication.

With**grid multiplication**, the two numbers to be multiplied are split (*partitioned*) up into their tens and units components - e.g. 34 = 30 + 4, or hundreds, tens, and units components - e.g. 345 = 300 + 40 + 5. (Click here for our 2-digit number partitioning worksheets and 3-digit number partitioning worksheets for partitioning practice)

The**grid method** enables a complex multiplication to be broken up into a collection of relatively simple multiplications followed by some column addition.

## Grid Method Example

54 x 12 can be *partitioned* to give us (50 + 4) x (10 + 2)

this can be expanded to four simple multiplications which when added together give the final answer: (50 x 10) + (50 x 2) + (10 x 4) + (4 x 2).

This is done with the use of a**grid** as shown below:

Total up the columns and write the totals in the row at the bottom of the grid. Then finally add together those totals for the final answer. Here 54 x 12 = 540 + 108 =__648__.

The Grid Method*can* be used to multiply very large numbers using a larger grid, but by the time a child is confident multiplying 3- and 4- digit numbers using grid multiplication, they are ready for long multiplication which is a faster method.

## TU x U Grid Multiplications - Pre-Partitioned

For this introduction to grid multiplication, numbers of type TU are multiplied by numbers of type U, for example **37x4**, **58x8**. The TU part is provided in the grid ready partitioned, so that the focus is on doing the multiplications and adding the results together for the final answer using the Grid Method.

Next move on to either Grid Multiplication TUxTU Partitioned for more complicated multiplications ready partitioned in the grid, or Grid Multiplication TUxU to try TUxU type multiplications where partitioning and grid set up need to be done by the child.

With

The

this can be expanded to four simple multiplications which when added together give the final answer: (50 x 10) + (50 x 2) + (10 x 4) + (4 x 2).

This is done with the use of a

x | 10 | 2 |

50 | 500 | 100 |

4 | 40 | 8 |

total | 540 | 108 |

Total up the columns and write the totals in the row at the bottom of the grid. Then finally add together those totals for the final answer. Here 54 x 12 = 540 + 108 =

The Grid Method

Next move on to either Grid Multiplication TUxTU Partitioned for more complicated multiplications ready partitioned in the grid, or Grid Multiplication TUxU to try TUxU type multiplications where partitioning and grid set up need to be done by the child.

All worksheets published online at

for non-commercial use by schools, children, parents, and care givers.

© 2010-2018 Mental-Arithmetic.co.uk - All Rights Reserved