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