I decided to investigate the grid method of multiplication because my son, in his first year of secondary school (Year 7), came home with his first bit of maths homework. The homework included the following multiplication:
7.23 x 6.3
My son is ok at Maths, in fact he’s quite good, he was one of only a few at his primary school that achieved “Level 6″. However, he was really struggling with this question. He was using the grid method of multiplication. The grid method was never used when I was at school but now it’s commonly used as a stepping stone to the traditional method of long multiplication.
The Grid Method of Multiplication
The grid method can only really be explained by using an example.
So let’s use:
16 x 23
First you draw up a grid. In this example, which is multiplying a two digit by a two digit number, we need 2 columns and two rows. Next we split the numbers into tens and digits. So 16 becomes 10 and 6 and 23 becomes 20 and 3 and enter as below.
Then multiply out (refer the grid below) 20 x 10 = 200, 20 x 6 = 120, 3 x 10 = 30 and 3 x 6 =18.
Then add up each column 200 + 30 = 230 and 120 + 18 = 138.
Finally (see the sum beneath the grid) just add 230 +138 = 368.
Here’s a video that takes you through this example, step-by-step:
I can see the advantages of using the grid method. It is highly visual, contrast how difficult it was to follow my written explanation compared to how easy it was to just look at the actual grid! The other advantage is that it clearly separates tens and units (and hundreds and thousands etc. for larger numbers). In my view this helps children to understand how it works.
Multiplying Decimals Using The Grid Method
As my son now realizes, you have to be careful when you use the grid method to multiply decimals. As I mentioned above he had to solve this multiplication question:-
7.23 x 6.3
This was roughly how he set out his grid to answer this question (THIS IS AN EXAMPLE OF HOW NOT TO DO IT!):
The cells in the grid above are correct. My son, using pen and paper and the typically less than neat presentation skills of an eleven year old, managed to get the decimal point in the wrong place in more than one of the cells. The trick here is to eliminate the decimal point when you use the grid and use a simple rule to introduce it back after you’ve used the grid.
So we have:
7.23 x 6.3
Step 1: Eliminate the decimal points
7.23 x 6.3 becomes 723 x 63
Step 2: Use the grid method
Step 3: Reintroduce the decimal point using this simple method.
Count the number of digits in the original question that are after the decimal point and then alter the answer from the grid so that there are that number of digits after the decimal place.
Hmmm… that’s not easy to put into words!
Best look at our example:
The original question was 7.23 (2 digits after the decimal place) x 6.3 (1 digit after the decimal place), so in this case there are 3 digits after the decimal place.
So we need to take our answer from the grid: 45549 and alter it so that there are 3 digits after the decimal place = 45.549
Final Answer 7.23 x 6.3 = 45.549