Teaching the grid method for multiplying

[mystery]

How is it generally taught these days?

Let's say we were calculating 23 x 46. The grid method splits it into four simple multiplications. 20 x 40, 20 x 6, 3 x 40, 3 x6.

Is it taught by illustrating this with arrays e.g. A 23 x 46 array which is then split down into those 4 sub-arrays.

Which situations are children taught that the grid method is good for? For numbers beyond a certain size it seems to become very unwieldy and I make too many errors as it's hard to have any alignment in the adding needed to reach the answer.

E.gl. 12, 345 x 678. - I can't seem to get this right by the grid method.

When are children judged ready to be taught column multiplication by the most compact method?
.

[SleepyHead]

Dd was taught to partition the Numbers for grid method

So in your example

345 becomes 300 | 40 | 5 horizontally making 3 columns


678 as 600
70
8

As 3 rows . And you need to draw this up as a grid

The sums are
600 * 300 , 600 * 40, 600 * 5
70 * 300, 70 * 40, 70 * 5
8 * 300, 8 * 40, 8 * 5

Add up all the results and hopefully it works
Basically you have a 3 by 3 grid

Hope it helps
Sleepy

[Jean.Brodie]

Our daughter was taught this method at her primary school, using grids.

We then taught her old fashioned long multiplication at home. She was resistant and hesitant for a while. But she kept trying, learned to do it mechanically at first and eventually the penny dropped. She saw for herself that both methods were mathematically the same, with long multiplication having a leaner layout.

I mention this because this recognition of patterns is fundamental to Maths and builds confidence. We too were unsure about the mechanics of the grid method so wedecided to learn it and encourage the use of both methods. Most primary schools seem not to take the next step and link one method to the other. Long multiplication is also very useful for 11 plus exams.

[SleepyHead]

We then taught her old fashioned long multiplication at home. She was resistant and hesitant for a while. But she kept trying, learned to do it mechanically at first and eventually the penny dropped. She saw for herself that both methods were mathematically the same, with long multiplication having a leaner layout.

Ditto here, DD now does Long multiplication instead, it took sometime to convince her that it was worth the effort!

[russet]

This may help them understand the grid method.

[Yamin151]

Search for it on youtube, there are some fantastic vids explaining it.

[mystery]

Ah, sorry my question was not clear enough. I can do the grid method myself but I find that for large numbers e.g. 12 345 x 678 it is very error prone as there are so many big numbers to add which are not neatly columnized. Also the volume of writing is huge.

Are children taught not to use this method for numbers over a certain size, or given some tricks to avoid the problems? Try my example by the grid method to see what I mean.

Also I was wondering how children are taught the understanding which lies behind this method?

E.g. 54 x 63

Draw an array 54 by 63. - could use squared paper - and then show that is can be spit into four sectors - 50 x 60, 4 x3, 4 x60 and 3 x 50 . The grid is just one way of displaying the four calculations needed in this explanation.

I have not seen the grid method taught but my children just show me a grid they were given to fill in. I don't know why this would promote the understanding that I thought the grid method was designed to promulgate as people felt the column method was being taught and carried out without understanding.

So how is the grid method taught in schools these days - where best practice is employed?

And when do they normally then make the links to long multiplication in columns and move to that method for appropriate calculations?

I think that the old maths curriculum did not require this to take place at primary school but the new one does?

[yoyo123]

I either add the numbers in the grid vertically or write them to the side then add.

Grid method is good for finding any errors. Long multiplication with large numbers can be tricky as well as the "carrying" can get in the way and get added in ( I do this even though I have been using long multiplication for nearly 50 years ( before calculators in school)

Interestingly, we tried to teach long multiplication in year 5 and all but the 2 brightest found it very difficult. A year on and with far more experience using grid method they nearly all got it and were very quick. They were ready to learn it I suppose.

[mystery]

Do you find it easy for 12,345 x 678 ?

What do teachers do to teach the understanding necessary behind the grid method?

Were children losing their place a lot with the traditional method or were they not understanding what each part of the calculation was doing? Was it not possible to teach them this methodically just as other primary arithmetic is taught, step by step both the method and the meaning?

[Guest55]

mystery - children would never be asked to do that calculation anyway other than by using a calculator!

The benefit of grid its its extension to algebra, completing the square and polynomial factorisation - none of which are helped by long multiplication.