Division made simple

Villagedad · Post by **Villagedad** » Tue Nov 10, 2009 10:47 am

Hi all

My DS is doing division having just started KS2 / yr3. This is not long division yet just the first stage concept of division.

Please could someone point me towards a worksheet that explains division in a really simple and easy to understand way that I can give to my DS to have a read of, possibly with some examples etc..

Many thanks everyone
Villagedad

Tracy · Post by **Tracy** » Tue Nov 10, 2009 11:08 am

Get a large packet of sweets and ask your child to 'share' them out amongst the family.

You can then introduce the words 'divide' ie meaning the same as 'share' and 'remainder' for the sweets left over.

You will need to do this several times with various sized bags of sweets and different friends/family.

The sweets method always works!!!

Nathair · Post by **Nathair** » Tue Nov 10, 2009 11:23 am

I have just been going over division basics with my DD, she seemed to have a bit of a mental block. We went through the bit on the BBC bitesize website http://www.bbc.co.uk/schools/ks2bitesize/maths/number/ I think it helped.

Milla · Post by **Milla** » Tue Nov 10, 2009 12:21 pm

you've hit on a personal bugbear of mine, Villagedad. For instilling the initial concept of division, yes, keep it physical, sweets (it was always dried pasta our school told us to use) - similarly with fractions, it's always imagining a cake or a pizza since visualising fractions is important I think.

But, moving on, I really have "issues" with the way that they are taught both multiplication and long division, for one they use "gridding" and the other "chunking." Gridding involves, for say 36 x 45 creating a grid and doing 30 x 40, 30 x 5, 40 x 6, and 5 x 6 and then adding them together. I suppose, grudgingly, if it shows them that that is how the sum is composed, then all well and good, but they're still doing it in Year SIX!!

For the grammar tests, we don't have Maths as a separate paper, but there is a maths element in the VR, so I said to my boys that for school, yes, ok do it their way but for 11+ they had to do it my way. Just the speed of the thing, the fewer opportunities to make mistakes meant that I could not countenance him being vulnerable to making errors by gridding. Although to be fair, my second son, at least, can do quite complex multiplications in his head. I will draw a veil over my older son!

As for chunking, well, give me strength. Chunking works by chipping away at the big number with smaller mulitples of the dividing number, so if you had, say 658 divided by 7, you'd start by taking away chunks of 70 and recording tens somewhere. As far as I'm concerned, again, there are so many places where things can go wrong, that taking away 70s is not that easy for a child.

Whereas saying, OK 7 into 6 doesn't go
7 into 65 is 9 R2
7 into 28 is 4
answer 94.
Easy peasy

As for your actual question (!), no, I can't help! I'm just warning you that it might get worse before it gets better and if you're of any age at all it won't correlate with any way you were taught. I'd ask the teacher if there is any way they would recommend help being given since you don't want to conflict (yet!) with their teaching methods which will only confuse the child. However much better I see "my way" I was careful to introduce it late-ish and explain that it was for the tests since I didn't want fisticuffs at school.

It might be different in private schools.

Certainly, I do think it madness to continue this method of teaching so late into primaries (and it might not be at all schools) since Y7 maths came as a HUGE shock to my DS1 and he hadn't been served at all well by this primitive approach.

Rant over.

First-timer · Post by **First-timer** » Tue Nov 10, 2009 1:19 pm

I agree about the chunking and gridding - it is beyond belief that children are expected to use these methods in year 6. Same goes for number lines being used beyond infant school! The thing these modern methods are supposed to promote is understanding but they are simply more time consuming and more likely to lead to errors. The able maths students will come to an understanding of the various manipulations whichever method is used. Those with little mathematical aptitude may never quite get their heads around why a particular method works. Isn't it more important that all children are able to calculate long multiplication/division whether or not they understand exactly what's going on? The understanding can follow in due course. I remember learning to use various mathematical formulae years before learning their proofs from first principles.

I too instructed my DS to use traditional methods at home and to follow the convoluted method at school. At parents' evening DS's teacher said he was allowing DS to use these traditional methods in class as they "seemed to be quicker and more accurate". No kidding!

Schools seem to have their hands tied and a lot of the changes are not for the better. Don't even get me started on the so-called rainbow reading "schemes" and the demise of comprehension.

It would be interesting to see what proportion of successful 11+ candidates use the traditional methods. I suspect it is fairly significant.

Milla · Post by **Milla** » Tue Nov 10, 2009 1:52 pm

First-timer wrote: Isn't it more important that all children are able to calculate long multiplication/division whether or not they understand exactly what's going on? The understanding can follow in due course. I remember learning to use various mathematical formulae years before learning their proofs from first principles.

Exactly! Same here. My boy's Y5 teacher did do a bit of eye-rolling at all this and said she had to teach it this way. She also said that it was easy, our way, to come unstuck with sums involving lots of noughts. She cited something like 1000200004000 or something. Since the sums coming home were along the lines of the one I mentioned before, it seemed a little unfair to "diss" my method because of its relative failure with a sum such as that. I let it go. I suppose you pick your battles.

Apologies for veering Villagedad - I know you're interested in education in a broad sense so am assuming you won't mind too much!

First-timer · Post by **First-timer** » Tue Nov 10, 2009 2:58 pm

Milla, I think the teacher was grasping at straws/spinning a yarn. A number like that is not more difficult to deal with using traditional methods. In fact, the exchange method of subtraction (modern method) is particularly problematic when the larger number has an internal zero (even more so when there are several). I grew up with the old "borrow one pay one back" method and yes, I knew it wasn't really "one" that I was borrowing and yes, I understood how it worked. I actually think the exchange method is no more transparent but hey, that's progress!

I think you are quite right that you need to choose your battles. You wouldn't get anywhere in a situation where teachers are obliged to deliver the curriculum in a specific way. Many teachers themselves find the prescribed methods frustrating but they have to toe the line.

Back to the OP - I too would start with practical sharing using buttons/pasta/sweets/pennies. Stick within the multiplication tables your child already knows to reinforce the relationship between division and multiplication.When it comes to larger numbers you'll have to decide if you want to follow the school's method (in which case ask them for an explanation) or the one with which you are more familiar.

As an aside - this dumbing down under the guise of promoting understanding is no new thing. A former colleague of mine who had just turned thirty proudly announced that he did not know nor had he ever known any multiplication tables but that he understood how to work out multiplication sums. I asked how and he said (as though revealing a mysterious secret) that it could be done through repeated addition! I then asked how on earth he coped with high school maths and he said he wasn't that good at it so didn't take it as an option.

He added that as long as he has his mobile 'phone he doesn't need to be able to do calculations anyway. He has a point and I'm a dinosaur.

wonderwoman · Post by **wonderwoman** » Tue Nov 10, 2009 3:43 pm

Hi Villagedad
Practical methods are best, sharing out equally etc as said by other posters. Division is repeated subtraction so can be done on a number line counting back, usually in Y3. This leads nicely on to chunking, so hated by others. It is all about starting with small steps and then combining them so that calculations are quicker and more efficient. Chunking is a quick, efficient method. It wouldn't usually be used for 658/7, except as an example, it would be used for 658/17. It is my preferred method of long division, much quicker than the method I was taught in school (traditional long division).
Without doubt children have far more understanding of how the number system works and can apply that knowledge to other problems.
I don't know any teachers who dislike the 'new' methods, unless their mathematical knowledge is lacking.
It's like taking off 0 when dividing by 10 - it's not correct and it's not helpful to teach children that.

Incidentally all my older children are very able mathematicians - they used the methods taught in primary and had no trouble at all with Y7 maths taught at grammar.

First-timer · Post by **First-timer** » Sun Nov 15, 2009 2:28 pm

wonderwoman wrote: I don't know any teachers who dislike the 'new' methods, unless their mathematical knowledge is lacking.

So, teachers who dislike the new methods are deficient? Isn't that just "The Emperor's New Clothes"? Gosh, I know lots of deficient teachers, then

.

kentsussexborder · Post by **kentsussexborder** » Sun Nov 15, 2009 3:55 pm

When working through maths problems with my DS I always used the methods I learnt at school (i.e. remainder 1, carry one over etc) - I'm confident with these and my DS picked them up very quickly. But it did lead to issues with the school when he had to show his working because it wasn't done by their preferred method.

I have a Yr 3 DD and as she still struggles with her number bonds to 10 we are having major difficulties with division. The sweets suggestion sounds good and I think we will have to practise it many, many times... I'm hoping it will work as well with a bar of Galaxy chocolate broken into pieces!