# Grid Method for multiplication - are your pupils weaned off it by end of year five?

Discussion in 'Mathematics' started by mounthood, Sep 10, 2011.

1. ### mounthood

But it is a method that can be taught understanding of. Although it doesn't look at all like the grid method it is essentially the same. Don't assume they won't understand because if you teach it properly with understanding of why (use decimal equipment- unit cubes, ten sticks, 100 blocks etc) then they probably will (most of them anyway!) understand it. By the way there is also a "half-way" method which looks just like long multiplication but with 4 rows of answers to add up, not 2, which are actually the same answers as in the grid method. This might help. And after mastery and understanding of this "half-way" (my description) method they can go one step further and do full long multiplication with 2 rows only.

Excuse me! I do know how to teach properly you know, and can quite easily teach the "long multiplication method" should I wish ( including the half way method-both of which I taught to my top group this week!) I don't assume anything, please do me the courtesy of doing the same!

3. ### mounthood

Sorry sorry sorry. The my advice is, seeing how many students

Really sorry. I didn't mean to assume anything about you, except if I think anything at all it would be that you are an excellent teacher. I meant it as a generalisation more than anything. Perhaps because so many people give the reason for not teaching long multiplication as one of non-understanding (they understand the method but they say their students can't). My apologies

4. ### mounthood

Delete first line!

5. ### PaulDGOccasional commenter

Back in the golden days, no one ever understood long multiplication.
They just got very good at doing it (because of lots and lots of repitition).
Yes.
Or, to put it another way, it leads to errors because they don't practice it enough.
That would be nice, but there's an element here of reaching for that top block on the pyramid without putting all the foundation stones in.
Today's primary kids come to secondary generally able to do grid method.
But, outside the top sets there's:
1. No evidence that they understand what they're doing.
and;
2. No evidence they can spot mistakes.

It's not really about the method (though I believe grid does not scale as the opportunities for transcription and order of magnitude errors are far greater than long multiplication), it's about practice.
Yesterday's kids - the grandparents, perhaps, of those we see in class today got lots and lots of practice.
In the rush for "deep learning" and "understanding", and frankly behaviour issues, today's kids don't do the practice.
Without the foundation stones, that pyramid falls down.

6. ### mr_paul_mchugh

Well, multiplying numbers with decimals always seems to cause a problem for those who can only use grid method.
Ask any grid user to calculate 2.35 x 1.23 and they flounder.Trying to figure out 0.05 x 0.03 as part of the grid is beyond them.
Wheras a long multiplication user can easily compute the correct answer, by ignoring the decimal points until the last stage, then just counting up all the digits to the right of the decimal point, and ensuring there are an equal number in the answer.
But my original point remains, GRID is a stepping stone to LONG, not an alternative. If Primary only teach grid, then why does secondary not move them on. If all pupils have seen both, they will all win.
And yes, a sound knowledge of times tables would also help.
And how many primary teachers are even aware that they are supposed to be progressing to long multiply? Judging by the responses here, most don't even realise it is their remit. If in doubt, why not ask your maths advisor.

There is a difference between an adult saying they don't understand long multiplication-which probably means it takes a bit of thinking about-and an 8 or 9 year old saying the same thing, what they mean is they don't! Yes, the brighter ones do and so they are taught it, but the less able ( and there are many of them!) do find the concepts, even with the use of modelling, concrete resources and repetition, difficult and DO NOT grasp the understanding behind the methodology, even if they can follow it step by step.
I wouldn't by any means say I'm an excellent teacher ( although a third of my year 6's achieved level 6 last year if that is any measure!) but I do teach year 5 and year 6 children maths day in, day out and have a good understanding of their level of conceptual understanding and for many at this stage in their mathematical education long multiplication is just a step too far!

8. ### DMNew commenter

Avatar hoody?

You have spoken to ONE primary maths advisor, speak to a second and they will give you a completely different response!

But why practice a method they don't understand, when they can practice a method they do!

11. ### PaulDGOccasional commenter

We've told you why.
We can get our boxes ticked with grid method.
If we waste/invest time in teaching them long multiplication, that's time we're not spending getting them other easy marks around the GCSE paper.
Which may mean we don't hit our target A*-Cs or even A*-Gs.
Our primary colleagues are in the same boat. They need to demonstrate the proper number of levels of improvement. Grid will get them there.
That it doesn't deliver what you feel you want, nor what employers seem to be saying they want is, to be harsh, "not our problem".
Knowing about long multiplication is not one of the benchmarks we have to hit. And as there is no shortage of other benchmarks we have to hit, teaching long multiplication is a sub-optimal use of our time.

12. ### PaulDGOccasional commenter

Agreed.
But they don't practice it, do they?
I went to primary in the 1960s. A maths lesson for us was often doing dozens of long multiplications. I'd guess I did well over a thousand (maybe several thousand) in primary school and that would have been the norm.
If today's kids did well over a thousand grid method calculations, perhaps they'd be as good at it as we were at long multiplication?
And, as it is easier to understand, perhaps they'd be even better.
Do you think it's an experiment that will ever be tried?
(Or perhaps I should add "in the public sector?")

Well, if the Government let us just concentrate on ensuring primary children could add, subtract, multiply and divide we would have much more time for practice, but whilst I have to teach children the rest of the maths curriculum and squeeze them through the restrictions of the SATs papers at the same time there is little hope of that!

14. ### DMNew commenter

Well you are likely to welcome the new Primary NC then (if they ever share it with us).

And ( since the OP sets so much store by the words of one primary adviser) the last one we had in explained in all seriousness that a lesson would be graded as unsatisfactory if children completed more than 5 examples of a method before moving on as 5 correct calculations would "show" that the child had grasped the concept and thus must then be "stretched further" or progression would not be seen.

I thought I'd missed it
Don't get me wrong, I LOVE teaching maths, especially top set and we have great fun exploring algebra, factors and geometry, translations, tesselations and trigonometry. But for the vast majority of our children they need the basics and they need more of it!

17. ### AnonymousNew commenter

Meanwhile in the real world, that's why we have calculators.
In the real world - how would you do 2.35 x 1.23?
Much better to get them to understand the answer is approx 2.4 x 1 .
Even better if they recognise the last number will be a 5.

18. ### trinity0097New commenter

I teach the grid method, and if theya re doing decimal calculations I get them to multiply by whatever powers of 10 needed to get each number a whole number, then use the grid method, then divide byt he same powers of 10.
i.e. I teach understanding of what is happening rather than take out the decimal points and then put back in as the OP seems to be suggesting.
I have found over the last 8 years or so when I have taught in KS2 and 3 that pupils who use the grid method to multiply can move on far better with expanding brackets than more able pupils who use the trad long mult method who I need to explain the grid method to first!

19. ### mounthood

To DM
Well done DM for finding this, and thanks for taking the time also.
Is it a sports team badge? A speed limit sign? It is very distinctive isn't it and I like it. I wonder if it comes in different numbers? I don't know how other people choose their user names but I was struggling to think of something good which didn't sound silly. I therefore have to admit I have no connection at all with Mount Hood except that I flew over it on a commercial flight this summer.
About multiplication method. Despite everything I have said, and I did definitely mean it all and I like long multiplication and do not like grid, I teach grid method almost exclusively in lesson,only because before me (primary or before they have me at secondary school) they have been taught it and if they have a teacher after me, they will learn it,and so on, and I think it is best that one method is kept throughout secondary school. However with division - different story. I always teach "traditional" even if they have only done "chunking". I can't tell you enough about my experience of marking division questions at GCSE and the "mess" produced with "chunking" methods.

20. ### BillyBobJoeEstablished commenter

I have to hold my hands up at this point and admit to having never learned long multiplication. I learned a method not unlike the grid method but just listing the components rather than using a grid to ensure they are all present. Given a free choice these days I'll use Napier's method for long multiplication (even more so for decimals), and encourage any students who can reliably draw the grid to do the same. I can't see any benefit to long multplication that can't be gained from other methods. For the record, never being taught long multiplication (or division for that matter) was no impediment to my A* GCSE, 2 A grade A-Levels and half a masters degree in maths.