How do they teach division in year 5/6

(23 Posts)
LeMousquetaireAnonyme Sat 15-Jun-13 07:26:18

Thanks for that past, DD1 is in Y3 and just changed school. She was utterly baffled by doing divisions with a number line. They did number line 1st term of Y2 for simple additions and subtractions as a revision from Y1 and that was it. She is able to do some big divisions with another method (not mine). I think they put her down a group because of that, so she went on doing "reading time" instead which leaves her hmm.

I think the children should be able to use what they feel comfortable with and especially what makes sense to them.
Not everybody think the same way, DD1 is very logical (extremely) and knows all her time tables (it was the curriculum where she was so not exceptional), she would be completely lost if she had to do it the way you said. She would need an explanation and a very logical reason to why this is better than what she is doing. I know I am worried she is a vulcan too

Not sure if it helps but I can get a vague understanding to be able to talk to her teacher. I don't want to push DD1 where she doesn't belong and I am all for learning different ways of doing things, but a bored DD1 is not good for anyone and I am scared that she is going to learn to coast like me and her DF.

PastSellByDate Fri 14-Jun-13 15:07:40

LeMousquetairaeAnonyme:

I think you raise a good point - but for someone on the other side of learning to divide at those initial stages of tackling 'big division problems' that can genuinely be too many tasks at once.

I think you have to envision (as is the case in our school) children that are secure with multiplication x2, x5 and x10 - and maybe can know a few of the other tables - but really struggle with x6 -x9 and x12.

In those situations - they're more likely to work with multiples of 2 digit numbers like 34 in x1 (34), x2 (68), x10 - 340 and x5 (170) - because they can work those out fairly straightforwardly.

There then seems to be a stage where children are encouraged to work out mutliples of bigger numbers alongside the division problem - so what 1 - 5 x 34 might be (to then refer back to) as they do the problem.

Your suggestion - really is ye olde fashioned long division (so putting the number above - for the number of multiples.

It's not too far down the road - but chunking is that initial reflection on division being multiple subtractions just as multiplication is multiple divisions.

Hope that makes sense.

What I will say LeMous. is that what is concerning is schools insisting on children using one particular method and literally scolding them for using another method that works or makes sense for them.

I think in principle it's meant to be that children are shown a number of methods and can ultimately settle on what works for them - but in practice there can be a real insistence on not using long/ short division method.

A teacher fresh from a teacher training day (and therefore clearly the world's expert now) informed me and DH that long division shouldn't be taught to children until very late in Y5 at the earliest.

Helpfully - DH asked is that everywhere do you think? or just here?

HTH

LeMousquetaireAnonyme Fri 14-Jun-13 12:46:20

gosh that is unnecessarily complicated.
What happened with chunking the logical way?

How many times 3 in 15? =>5 but because we have 34 to fit in 159, 5 times too big so try 4, 4 times 34 out of 1598 leaves 238 and thats 7 times 34 (how many 3 in 23 => 7, does it fit 34 yes) then 0 left so answer is 47.

HumphreyCobbler Fri 14-Jun-13 12:22:38

juststartingtothink - chunking does not replace the 'old way', it is just the lead up to it.

I can confirm that just teaching an efficient written method to begin with can leave some people totally bemused. I was that person. I did the steps with no idea WHY I was doing them. Once you understand the reasons behind it the written method is great to learn.

Chunking works really well as a mental method too, and a check that the written method has not gone wrong. I was explaining chunking to my DH the other day (A at A level etc etc) and he said that is his mental method for long division.

justsstartingtothink Fri 14-Jun-13 12:12:24

Great links, PSBD! Thank you.

PastSellByDate Fri 14-Jun-13 11:21:47

half not have.

PastSellByDate Fri 14-Jun-13 11:21:30

Lordy:

Apologies just saw my error on this:

What would half of 1000 x 34 be (or 500 x 34) - that would be 17000 (Still too big but getting warmer).

Should read:

What would have of 100 x 34 be (or 50 x 34) - that would be 1700....

Apologies - sticky number pad (guess who's DD2 spilled apple juice recently!).

PastSellByDate Fri 14-Jun-13 11:15:46

Should have explained method 2 was long division/ now short division method.

PastSellByDate Fri 14-Jun-13 11:13:49

Hi MNBlackpoolLandfield:

Many schools use inverse multiplication to initially introduce division. A helpful way of thinking about it is to be sharing something evenly among a certain number of people.

e.g. A teacher has purchased a bag of 60 candies for her class of 30 pupils. How many candies should she give each child?

The next step is to talk over remainders - so when there isn't enough to go around. Again a useful concept is to describe it as sharing something out evenly.

e.g A parent has sent along a box of 30 biscuits with a group of 14 boy scouts. You want to be fair, so how many biscuits should you give each boy scout? And how many will be left over?

Then comes more complicated division problems (so division with numbers beyond the multiplication tables 1 - 12). And that's where chunking is introduced. In part this reflects the fact that although your DC may be great at his or her times tables, they probably don't know what 37 x 16 is off the top of their head. Chunking is a way of breaking that information down into more manageable units. (extended long division).

METHOD 1:

1598 divided by 34.

- apologies if this doesn't display well (top of bus stop here)
34 /1598

Gosh no idea.

Well what would 10 x 34 be - 340 (very small - would have to do that a lot)

What would 100 x 34 be - 3400 (Well that's way to big).

What would half of 1000 x 34 be (or 500 x 34) - that would be 17000 (Still too big but getting warmer).

So we know we want it >10 x 34 but < 50 x 34.

Now you can do this as a series of subtractions (that's the chunking)

--
34 / 1598
- 680 (34 x 20)
______

918
- 680 (34 x 20)

_____________

238

Now you're below 10 x 34 (below 340) - so you need to look carefully at what you're working with.

Estimating here would be a good idea - just to try ideas out.

So 34 is pretty close to 30. and 238 is pretty close to 200.

So how many times could 30 go into 200?

well if you divide both sides by 10 you get 3 into 20 - can't use 7 because that's 21 - so it has to be 6. So you now know it's likely to be 6, maybe 7 because the numbers were rounded.

so you could work out what 34 x 6 is equal to:

Can be done either by adding 34 six times (in a column) or just straightforward multiplication:

34
x 6
_______
24
180
____
204

back to the problem:

--
34 / 1598
- 680 (34 x 20)
______

918
- 680 (34 x 20)

__________

238
- 204 (34 x 6)
______________
34
- 34 (34 x 1)
_______________________

0

Now comes the clunky bit of chunking:

To work out the answer you have to add up all the multiples of 34 you used. In this case 20 +20 +6 +1 = 47

So that's the answer you write on top of the bus stop.

---------------------
Now this could have been done any number of ways. Your DC may have been happier working with 10s - and just continually subtracting 340 (10 x 34) from 1598.

This is a half-way house method on the road to ye olde long division (now known as short division).

A method which I think you'll know.

Where can you find visual explanations of how to do this:

This is a student from University of Bath Math Deptartment explaining it (yes it is the mathsfactor screen) - but it goes through slowly & step by step.

www.youtube.com/watch?v=eF4h76R99_Q

Now you may want to support learning ye olde long division/ now short division as well:

Some free videos can be found on how to do division using this method on Khan Academy here:

https://www.khanacademy.org/math/arithmetic/multiplication-division

You can start at the beginning of division for the review (Division 1 & 2) or you can go down to Long division (Division 3 & 4) for working with bigger numbers - just depends on your DC's confidence.

Where can you get practice:

As ever Woodlands Junior school has lots of practice:
resources.woodlands-junior.kent.sch.uk/maths/division.htm - but these are generally easier and working inverse multiplication skills.

BBC KS2 Bitesize has this game www.bbc.co.uk/bitesize/ks2/maths/number/multiplication_division/play/ - which is really testing those long multiplication/ division skills. It may be too challenging at first.

Old fashioned worksheet practice:

Long division with no remainders: www.math-drills.com/division.shtml#longnr

Long division with remainders: www.math-drills.com/division.shtml#longwr

My personal view is that chunking as a method - does ensure that all those skills are in working order. It's long winded - but it really makes you think through the whole process. Because once you go onto shortcut methods (long division, without really writing out much) - it's much more difficult to track where and when mistakes are being made - and it's harder for the person doing the work to figure out what is going wrong as well - which is why I think a lot of people just give up on maths.
----------------

One final word: at this stage you may notice various weaknesses in calculation skills (addition, subtraction, carrying numbers as well as multiplication/ division skills). It can be really frustrating and you may feel yourself about to say 'But you should know this, you did this already....' - But it's a new context and a lot of skills to operate all at once. It may mean biting your tongue - but try and be patient.

However, keep an eagle eye on their working out. Really be a stickler for writing out all those steps and lining up columns and showing all work. They'll moan like mad - but it's worth being thorough now and really ensuring all those basic skills are there - because as we all know it doesn't get easier from here on out.

HTH

alibeen Fri 14-Jun-13 10:14:59

I just read a blog that explains what 'chunking' is, found it useful as I hadn't a clue what my child was talking about and was at a loss as to how to help them with long division. blog.komodomath.com/

justsstartingtothink Fri 14-Jun-13 09:46:07

T&T and Babies: thanks for the explanations. I'm not convinced, as I think the "old way" worked well for many generations (as did the "old way" of teaching reading...). Nonetheless, it's very helpful to know the rationale for "chunking" so, again, thank you!

BabiesAreLikeBuses Thu 13-Jun-13 22:37:35

What i have noticed by teaching it is that the kids understand it better, apply it to real life problems easily and have amazing mental maths skills compared to lots of adults! I was taught the old ways myself, most of us teachers were. The kids know no differently, they're happy with the method, transfers easily to decimals etc. BUT it is one where many parents come and see me as to them it seems long winded or just doesn't make sense.

TeenAndTween Thu 13-Jun-13 22:19:20

juststarting

The reason they teach more interim steps these days, eg number lines in general, then for division chunking, is that they are concerned that children not only learn a method that works but they have an understanding of why the method works.

This better feel for numbers makes people generally more numerate and hopefully means that they have a better feel for "reasonableness" of an answer. If you are just following a method without understanding it, you have less chance of realising that your answer is ridiculous if you have made a mistake.

The chunking method leads nicely into long division, but it is more forgiving. eg in the initial question, with chunking you can first subtract 680, then another 340 and so on. With long division you do need to get completely correct how many 34s there are in 159 (for which as I said above, I would have to list on the RHS of my paper).

My DD1 was able to 'get by' quite nicely without 'proper' long division until she was ready for it mid year 7. Now y9 she still doesn't use the most compressed method for long multiplication, but tbh she doesn't need to. Whereas I did jump her straight from number lines to column addition & subtraction without some of the interim methods as I wasn't convinced they would help her.

justsstartingtothink Thu 13-Jun-13 22:08:38

Ah.... it's called "chunking"?!?!? I saw my son do a division problem this way a few weeks ago and thought it was a bit odd. I just let him get on with it and thought I'd explore the method later. What's wrong with the long-standing way of doing division? ie
_
34| 1598 (trying to set up a traditional division frame!). start thinking "34 doesn't "go into" 1 or 15 so how many times does it go into 159? 4 times -- so put 4 over the 9, then multiply by 34 to get 136, subtract from 159 to get 23, bring down the 8 to get 238 and ask "how many times does 34 go into 238? 7 times, so put 7 over the 8 and multiply by 34 to get 238, subtract from 238 to get 0 -- so answer is 47. (If final subtraction doesn't yeild 0 then the answer would be 47, remainder X (or continue out to a few decimals if they've learned decimals.) It's hard to show this method in writing on a website but not hard to explain in person. It's the way I learned -- and assume most people learned?!?!? -- when I was around 9 or 10 years old. I went to a "bog standard" state school (in the US), definitely mixed abilities, and most if not all of my classmates could understand this method (assuming they already knew times tables....).

MNBlackpoolandFylde Thu 13-Jun-13 21:19:19

I did ask her, she has a processing disorder and her answer made no sense at all.

TeenAndTween Thu 13-Jun-13 20:33:55

Actually OP, what you should be doing is asking your DD how she normally does division, using a simpler example, eg 616 divided by 7. She should then be able to explain to you how whe does it, and then you show her how to adapt that method to the harder problem.
(Of course if she then can't do that one either you have a problem).

MNBlackpoolandFylde Thu 13-Jun-13 20:32:59

Thanks, very different to how we did it!

TeenAndTween Thu 13-Jun-13 20:31:27

tbh I think expecting them to be able to do 30x34=1020 is a bit advanced. Not actually doing that calculation, but doing that calculation as a pre-cursor to the division.

I would only get that far just before moving to 'proper' long division, when you have to be able to take off the biggest chunk each time.

(if I were doing this by proper long division, I would write down the first part of the 34x table on the right hand side of my paper to help me work out the biggest chunk)

Pozzled Thu 13-Jun-13 20:19:35

I would also use chunking for a question like that. I would expect them to be able to use larger 'chunks' though- e.g. if 10 x 34=340, then 30 x 34=1020.

TeenAndTween Thu 13-Jun-13 20:17:28

agree with Babies.

the step just before that is to do repeated subtraction on a number line, taking off the same chunks of 340.

StuffezLaYoni Thu 13-Jun-13 20:15:13

My method of choice is exactly as babies has said. I would check with her teacher to see which method they are currently working on, so as to best support her. smile

BabiesAreLikeBuses Thu 13-Jun-13 20:13:42

Depends on the school, do they say on the web? Lots use chunking which is repeated subtraction, eg take a chunk of 34s away:
1598
-340. (10 lots of 34)

1258
-340 (10 lots of 34)

918 Keep going until you get below 34 (or to zero) they may take bigger chunks away eg 20 lots of 34 is 680.

At the end they work out how many lots of 34 they have taken away in total and this is the answer.

Hth

MNBlackpoolandFylde Thu 13-Jun-13 20:08:52

Trying to help dd with 1598 divide by 34. What methods do they use in school now because I do not want to teach her my way and confuse her.

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