## Multiplication Methods

Last night I saw an intriguing tweet from @mr_chadwick . Mr Chadwick is a primary teacher and he was worried that his daughter who is in year 8 was still multiplying using the grid method. This caused a fascinating conversation regarding the different methods of completing multiplication tasks and the pros and cons of each and it got me thinking quite a lot about the subject.

There are many ways to complete multiplication problems, the main ones being Grid, Column (aka Standard or Long), and Chinese Grid (or Spagetti Method or Lattice Method). (Also, I have recently been shown this ancient method by an A Level pupil who grew up in the Democratic Republic of Congo).

I was wondering if any one was particularly faster than the other, so I tried some out:

Each method took me a little over a minute to compute the product of 2 three digit numbers. (Except the grid method which took about 15 seconds longer). From experience I know that people tend to prefer the method they were shown first, and I don’t see a problem using any of them as long as there is an understanding of the concepts and that the person in question is proficient at using the method they have chosen.

I did think my prefered method for teaching someone who didn’t know any methods would be the Lattice Method, as I see a much larger potential for silly errors in the other methods than i do for this, but last nights discussion has got me thinking a little differently. The discussion moved onto applications in algebra. I know a lot of people prefer to use the grid method to expand double brackets, I personally prefer crab claw method, but i teach both and allow my students to decide, and some much preefer the grid. It also works quite well for larger polynomials, as shown here (in a video which rather confusingly calls it the lattice method!). The grid method can also be applied to matrices, as I have written about previously.

I’m still unsure as to which i prefer. The Lattice method gives a far lower chance of making silly errors, and I think it is the best one fro ensuring the decimal point ends up in the correct place when multiplying decimals, but the grid does have the benefits of being applied to much higher levels! I’d welcome your views on the subject.

I feel that i should also include another multiplication method which I discovered a few years ago, I was introduced to it as Japanese multiplication, but I’ve recently heard of it referrred to Gorilla Multiplication. I think it may have its origins in india and if you want to know more then Alex Bellos has written about it in his book Alex’s Adventures in Numberland (Another on my christmas list… and a book who’s american title is the most amazing title for a maths book I’ve ever heard: “Here’s Looking at Euclid”!)

Great post concerning multiplication methods. This topic continues to fascinate me. I was a grade 8 & 9 math teacher, became a grade 4 & 5 teacher, and now I am teaching grade 6 math. It was natural for me to see the different multiplication methods based on their usefulness in Algebra. However, I have not found many colleagues who share this view. Many of the middle and high school teachers in my district HATE any method that is not the “standard” algorithm – but especially loathe lattice multiplication. I hear all the time that those other methods are o.k. for building the concept of multiplication, but that students should “grow out of it” and use the standard algorithm eventually. I actually believe that in reality when they “grow out of it” they will be use a calculator! But I can’t say that to my colleagues. I went back and looked at Here’s Looking at Euclid after reading your post. It is a great read, and I highly recommend it. Thanks for the link to gorilla multiplication – my students will love it!

Thanks for your comment. I agree entirely. There seems to be a strong feeling that the standard algorithm is the “grown up” method, but I don’t really see why.

Great post, but what is the crab claw method?

It’s where you draw curves showing which terms you are multiplying together. The curves form a claw.