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 Post subject: Expanded and long divisionPosted: Wed Dec 05, 2012 7:27 am

Joined: Mon Mar 08, 2010 1:03 pm
Posts: 1413
Can anyone tell me what is the difference between these two? I've had an idea in my head about what long division is, but DS's school calls this version 'expanded division'. When I try and google it, I find about 12 different ways to do 'expanded division'. Can anyone help?

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 Post subject: Re: Expanded and long divisionPosted: Wed Dec 05, 2012 8:27 am

Joined: Fri Jul 16, 2010 9:22 am
Posts: 3664
Bananas...I think its easy to confuse with maths ( and that's just us ) so maybe you should ask ds teacher how they teach long division these days? Our school very kindly put on a teaching session for parents...which I forgot to attend ....probably too busy on here.......

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 Post subject: Re: Expanded and long divisionPosted: Wed Dec 05, 2012 10:03 am

Joined: Tue Jul 21, 2009 9:56 pm
Posts: 8228
Yes you need to ask school how they teach it - and it could of course vary from teacher to teacher!

The principle generally is first of all to look at division as being repeated taking away and do it with small numbers.

Then do it with bigger numbers - e.g. start with 3 digits divided by 2 digits. Do the taking away as chunks - easy multiples of the number you are dividing by.

So say you are dividing 358 by 18, the child might try taking away 10 lots of 18 first - 180, and then start taking away 2 lots of 18 at a time, and then down to one lot of 18 at a time, until you get to a number less than 18 which is the remainder.

Then the child counts up how many lots of 18 they have taken away.

This can be arranged neatly and vertically.

There are then some quite cool ways of showing how the "drop down" method of long division (the one you were taught at school probably) relates to doing chunking "perfectly first time round".

I've got that worked out on a piece of paper somewhere, but I'm not quite sure how to show it on here.

You can get by without the final method to a pretty high level, but personally I find it faster and more accurate so I aim to have taught it and practised it enough with DD1 before she sits the 11plus so that I can see whether she finds it faster and more accurate than the "chunking".

There are of course some other quick routes through depending on the numbers you are given where you might not need to chunk or long divide at all because there is some other "trick" with the numbers.

I don't think our school will be teaching formal "long division" in time for the 11plus. I think in the new maths curriculum it is going to be brought in as a requirement at primary level maths, but at the moment it is not.

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 Post subject: Re: Expanded and long divisionPosted: Wed Dec 05, 2012 7:45 pm

Joined: Mon May 16, 2011 1:05 pm
Posts: 4020
My DD hates chunking with a passion. This is a child that loves maths. She had one of her legendary (but infrequent) rants over chunking homework. This was following by another legendary rant the following year when they had to do more chunking homework as some of the class couldn't remember how to do it. After the first rant, I did something I try not to do and taught her how to do long division. I can teach maths, I've taught up to GCSE maths to adults in the past. I don't like teaching DD stuff in advance as I like to know how the teacher teaches it first, so theres no chance of confusion. If, on the rare occasion she struggles then, I teach.

So guess what, when she did get taught long division, according to DD I had taught her the 'wrong' way.

Lesson here, if you are unsure how about the methods used, ask the teacher.

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 Post subject: Re: Expanded and long divisionPosted: Wed Dec 05, 2012 8:25 pm

Joined: Fri Oct 12, 2007 12:42 pm
Posts: 3813
Location: Chelmsford and pleased
There are a huge variety of methods for both multiplication and division. Varieties on the algorithm that most parents learnt at school and many other methods that incorporate those use in other countries.

One method is very similar to traditional long division, but with the subtract ions written down the side. This is sometimes used as a bridge from chunking to the more traditional method.

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 Post subject: Re: Expanded and long divisionPosted: Wed Dec 05, 2012 10:46 pm

Joined: Mon Mar 08, 2010 1:03 pm
Posts: 1413
Well, thank you for all the replies! I have to say, I'm no clearer than when I started . Why are so many different methods taught to so many different kids? DS has already had 3 different teachers teach him 3 different grid methods and now he's had the expanded method done in two different ways too. My feeling at the moment, is that, if I ask the teacher, he will tell me the way he teaches it and in 6 months' time, DS will be a different version by someone else.

All of it leads to confusion and lack of confidence in DS which really makes me . When I go through any one of the methods he completely gets it but then, when he returns to the classroom and is taught a variation on a theme, he is utterly befuddled.

I've taught him the 'bring down' method; he loves it and is very quick at it. I suppose I'd better (rather grumpily) find out about this 'chunking' method.

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 Post subject: Re: Expanded and long divisionPosted: Wed Dec 05, 2012 11:39 pm

Joined: Fri Oct 12, 2007 12:42 pm
Posts: 3813
Location: Chelmsford and pleased
Back in the days, it was realised that there was more than one way to skin a cat! There always has been and always will be. Not all children are the same and they find a method that suits them.

I have taught a variety of methods for long multiplication. The grid is simple for all, very quick and easy to use and once taught always remembered; the algorithm that most of us learnt in school is short and precise, as long as children remember where to put the zeros! Napier's bones appeals to the bright because they love the magic! All the rest are variations on a theme.

Division is similar, a variety of methods. My favourite for speed is putting the numbers as a fraction and then cancelling. Once down to a smaller number, short division can be used quickly and simply.

The main problem is that what clicks for one child won't necessarily click for another. One of the highlights of my teaching career was showing a 15 yr old the grid and enabling him to multiply. He was bottom set and disaffected, but that was his Eureka moment, happily rather than the E he would have got, he gained a C.

Bright children, so most forum members' children can cope with any strategy, but those with dyslexia need some cues. I am really pleased that education has embraced the plurality of maths. It has never been a rigid subject at heart.

I love maths and it is often massacred by people thinking that only their way is right.

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 Post subject: Re: Expanded and long divisionPosted: Thu Dec 06, 2012 7:12 am

Joined: Mon Mar 08, 2010 1:03 pm
Posts: 1413
I understand what you are saying, Moved. Different methods work for different kids. My son also had a Napiers Bones homework, which worked ok until we got a '10' and 2 numbers and then it took a while to realise one added a 1 onto another number to make just 2 numbers you could add (if I'm remembering correctly; it was a while ago). I've no problem with the number of methods available to teach different DC, I've a problem with the inconsistency in just one set within one year group (now two year groupings) of methods taught, before the previous method had been properly bedded in. I think it just leads to confusion. As I said, when my son was taught the grid method, he was taught 3 different sorts of grid, by 3 different teachers, in one year, til he lost track where he was supposed to put which answer. I also don't think it's just my DS. This is a constant gripe at the school gate.

Personally speaking, I like your fraction method as well!

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 Post subject: Re: Expanded and long divisionPosted: Thu Dec 06, 2012 10:26 am

Joined: Tue Jul 21, 2009 9:56 pm
Posts: 8228
I understand exactly what you are saying Fatbananas. If he gets long division by the drop down method, and you think he fully understands it, and he is fast and accurate at it, and he would use a quicker method if the question didn't need formal long division e.g. 5000 divided by 25, then "Hallelujah".

I would tell your son to try and enjoy all the different methods the teachers are teaching them (10 varieties of chunking and drop-down etc) and to always try and see why they are actually producing the same result - compare and contrast their pros and cons, which situation to use them in etc etc. Then tell him to stick in the 11plus to the method he finds fastest and most accurate and practise this every weekend so it doesn't get swamped out.

He needs some tools to use in the stress of a fast exam which are at his fingertips rather than having to do arithmetic from longwinded first principles. Clearly you don't want him doing a formal long division when it could be done by a faster method because the numbers have been chosen to be easy, but otherwise he can use formal long division (e.g. for 4 digit numbers divided by a two digit prime number ... simplifying fractions won't work well there!).

Yes, the idea of check with the teacher first will not work in some schools. We would have three possible answers from our school depending on the teacher (a) why do you want to know? (b) please don't teach your child anything at home (c) being told a method but then it being done differently by a different teacher (and some weeks maths is taught by 4 different teachers to my DD1)

Good luck!

Which year group is he?

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 Post subject: Re: Expanded and long divisionPosted: Thu Dec 06, 2012 1:03 pm

Joined: Mon Mar 08, 2010 1:03 pm
Posts: 1413
Quote:
I would tell your son to try and enjoy all the different methods the teachers are teaching them (10 varieties of chunking and drop-down etc) and to always try and see why they are actually producing the same result - compare and contrast their pros and cons, which situation to use them in etc etc.

Yes, Mystery, I think this is key. I think there isn't sufficient analysis of this done in the classroom.

Quote:
Then tell him to stick in the 11plus to the method he finds fastest and most accurate and practise this every weekend so it doesn't get swamped out.

You're right; every weekend we've been doing just 1 example of the (my) drop down method and it's why he (a) remembers it and (b) is fast. I'd ideally like to have an example of all that he learns and the different formats that it comes in!

He's in year 4; I'm trying to plug gaps and more so that we're really bedding it in in year 5. Not going too badly so far ... but feel I should now be doing more writing with him (hence my other thread )

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