How to help child understand long division

[angeltattoo]

My daughter is in Yr 6 and in her mock sats it is clear she is struggling with long division.

I want to help her but so want to do so in a way that is consistent with how she is being taught at school.

Are there any resources any teachers can recommend that would help? Work books or online videos?

Thanks in advance. She hates me 'teaching' her anything, wouldn't believe a word I said in lockdown, loves to hear it all from her teachers though.

So I want to help without the friction! So a guide or video that is consistent with how she is being taught at school would be much appreciated.

We are on half term and her homework is to do the work she got wrong in her sats papers so I can't ask at a school and it needs doing before she goes back.

When my Dd was much younger I used piles of coins or a circle of paper (cake or pizza) to explain division. I know my sister never understood the binary system.

Not sure that would work as you say she’s older and there is possible friction.

I believe you can buy revision books, so that may help.

My Dd eventually got an A in her GCSE maths. That’s not really a brag as it’s all down to the fact that around this time she started getting a lift to school with the Maths Teacher! So I’m guessing they talked about maths a lot in those car rides. So many thanks to Mrs. Brown!

I guess I’m wondering if your Dd would better at getting help from someone that’s not you. That’s just the way it is with some teenagers and their mums. I’m not thinking of a maths tutor, just someone in the family or a friend she would work with better.

But definitely look for those revision books first. I think you’ll be spoiled for choice.

following because I'm a grown up who also doesn't understand long division.

Do the school have their calculation policy on their website? If so then it should give you examples of how it is taught for her age group at the school.

Corbett maths has a video that explains it really clearly. https://corbettmaths.com/2020/05/22/long-division-video/
I would watch that, then write her loads of calculations- both whole and with remainders- to solve.
Big thing to work on is writing out the multiples correctly in my experience (y6 teacher)

Or speak to her teacher about the method they use in school and ask for examples so that you can understand the method yourself before you help her.

Do the same calculation using both short and long division side by side for a few questions. Use relatively simple numbers to divide by, eg 15 and have a list of multiples to help down the side of the page.

Keep practising the long division method, say one every day. It will become easier and embedded after a while.

There is a good YouTube video called Long Division Rap - Never Give Up. It helps to embed the steps and children always love it.

Has she done it by repeated subtraction, and does she understand that

so 11 -> 123321
subtract 110000 (11x10000)
leaves 13321
subtract 11000 (11x1000)
leaves 2321
subtract 2200 (11x200)
leaves 121
subtract 110 (11x10)
leaves 11
subtract 11 (11x1)
leaves 0

How many 11s subtracted? 11211
So 11 into 123321 is 11211

Then show along side how the long division would be written.

Also this is a good article:

https://thirdspacelearning.com/blog/teach-long-division-method-ks2-steps/?utm_source=Facebook&utm_medium=Social&utm_content=Teaching_Long_Division_Blog&utm_campaign=Blog_Posts&fbclid=IwAR0lPwucweCJQgrqoszB-tmGNSCWLkfd0LfOEbCZht0XS9sds5S1Tzg3QJE_aem_AeFM9lq_RKvAVRy2jJ0XwizAMZEjjqIJyChEPprcC7-wLeivStDh3e8WbWpFB2UxSV4

Year 6 TA here. There should be lots of revision on this in class but the first step is to make sure she understands short division method ( unofficial name bus stop). Is she confident with what happens with remainders. If she is confident with this then you can run the long division method side by side to show her that all the long bit does is help you to work out what the remainders are at each step. Working out remainders mentally when working with larger numbers is more difficult and mistakes can be made, much easier to use column subtraction. Good luck.

I know this doesn't help in the here and now bit if she genuinely can't do it herself I really would leave the homework and explain to the teacher that it wasn't completed as she was unable to access it and you are not currently in a position to help her, so she needs them to demonstrate again. They need to know that she's still struggling.

Hopefully if you flag it up with them and ask them to show you how they teach it you can then work on this at home to support her, but it could be causing problems further down the line if you help now and she sends it all back correct, as they may not realise how much she's struggling with it.

To me, it seems completely bizarre to be setting corrections as homework. If she has lots of corrections, she clearly didn't understand it and needs support to correct it. That is their job to support her with, not your job! (and I say that as a teacher)

Thanks so much everyone.

I completely agree it would be better coming from anyone but me

I will ask her teachers and ask them to help, their policy is not on the website.

And thanks for the links, we will look at them this weekend.

Much appreciated!

This has explained it perfectly, thank you so much - this didn't come up in my google search and has helped immensely.

So she can do small numbers easily and couldn't work out how or why she needed to do it another way. Your explanation of why makes perfect sense (from a professional, and not mum!) so she can understand why she needs to other way too. Thank you!

You also need to explain that other methods of calculation start with the smallest number. With division you start with the highest number

so using £321

You share the hundreds between 3 people then the 20 they can’t share that so move to be with the ones. 22 divided by 3 is 7 - £107 each

Start with low numbers so she can visualize it

I have seen even children quite gifted in maths struggle with long division. Some can't do it, Some do it but in a very error-prone way because they are filled with disgust, Some can do it, but heartily despise it. I can't really blame them.

As far as I've seen, a lot of the problems arise because there are two things to be taught and most approaches don't distinguish them:

a) the concept - what are we trying to do, and why? i.e. what does division really mean? Long division can't make sense until we understand that division is just repeated subtraction ( or at least that's the most useful viewpoint for this task).

b) the long division process, or algorithm. The "why" for this is simply that although repeated subtraction would always work, it would take too long. So we need a more efficient way. Instead of subtracting one copy of the divisor at a time, we try to substract off batches of 10 or 100 or 1000 at once. Basically, we subtract off as many copies as we can at each stage, until we can't subtract off any more. The whole arcane procedure of "bus stops", bringing down the next digit etc. is just a book-keeping device for batchwise repeated subtraction (and IMHO a procedure that has been obsolete since the arrival of hand-held calculators in the 1970s).

There is also the tedium of the long division process, which can dent the enthusiasm of even children who are otherwise keen on maths.
My suggestions:
Keep practice sessions short: 3 or 4 long division questions. not 10.
Stop flogging a dead horse. the number of marks on any paper for long division is likely to be small. Focus on things in maths that the child can do, to improve engagement and confidence. Come back to it every few weeks until it clicks.
Keep it in perspective. Long division is a very small part of maths, and in the real world (even as mathematician), we never need to do it , because we have calculators (and for IGCSE maths, all papers allow calculators, so there are options to avoid "manual" division). Some fairly successful mathematicians never learned long division at all (https://www.conradwolfram.com/writings/should-long-division-be-the-pinnacle-of-primary-maths-educat.html)

Before you try to teach the school's method, I'd check it is actually a method that makes sense.

My DD was taught a weird method at school and a more standard method at home. When they went to revise at school DD used the home method and her teacher realised that it was easier, so then taught that to the class. She's probably not the only teacher using a weird method.

Go to the ‘home learning’ section of the White Rose website and there are videos for every objective in the primary curriculum. Long division comes under the second unit in y6.

y6 teacher here. Honestly, I wouldn’t worry too much. I think it’s such a pointless method to teach in primary. Why do we expect children to divide by a number where they don’t know the times table?! In real life I would never divide by 37 on paper, I’d use a bloody calculator. Working out the 37 times table is time consuming. Dividing by numbers up to 12, as well as 100, 1000 etc and even 25, 15, fine. Other random 2 digit numbers - I don’t get it.

In terms of SATS, the final question is almost always a 2 digit long division. So if she doesn’t learn the method she can still score 38/40 if she’s secure in everything else. If she is literally fine on everything else on the y6 curriculum, crack on and nail this. Otherwise, it’s the first thing I’d stop worrying about. Get everything else secure first.

If they understand multiplication then they will understand long division. The first should be taught before the second and then it’s just doing it over and over again.

I would add that if you don’t want to fumble around with a calculator then long division is a good skill but then I’m an oldie

Teach her to do long division in a short division way if that makes sense. If she's dividing by 27, count up in 27s (to about 5 X 27) and write these at the side of the question somewhere, you can add more later if you need to). Use the first two digits of the number she's dividing, divide them by 27 then carry any remainders, do that with the next two digits (one will be the remainder) and so on until the end of the division.
Or use Does McDonalds Sell Cheeseburgers (link below). This won't really teach her what is happening as well as the first method but will help her remember the stages in proper long division if she is ready for that. The first method works for most children.

m.youtube.com/watch?v=1Wrp0Qc_gDM

One of the easiest ways is to divide by factors ( unfortunately doesn't work for prime numbers). If the question asks you to divide by 24, first divide by 6 and then divide the answer by 4, much easier as the majority of children know their 4 and 6 times tables. You could alternatively divide by 12 and then divide answer by 2. You choose the factors you feel most confident with.

ha, @piisnot3 I still remember the absolute lightbulb moment when 8yo me realised

"ohhhhhh, it's a GUESS!"

Stop flogging a dead horse. the number of marks on any paper for long division is likely to be small.

Unfortunately not. It’s always two questions in the arithmetic paper, worth 2 marks each. That’s 4 out of 40, so 10% of the marks. There will also be one or two in the reasoning papers.

As a Y6 teacher, some of my children can do this now at this time of the year - with lots of practice between now and May, the vast majority will be secure by then. There’s plenty of time - but we can’t write it off completely, that’s not an option.

I am really surprised at this thread because I didn't think kids learnt this at school anymore. My children are 12 and 19 and neither of them have ever been taught long division. Apparently the teacher told my eldest that there was no point as everyone uses calculators now. We're in Scotland.

There are different methods my son couldn’t do the one the teachers at school taught him so we researched other methods. He got an A in A level maths this year so my advice find a method that works for your DD.