Can you do long division?

[Noperope]

Attempting to help dd with her 11plus homework and feeling more and more stupid by the minute. Could you work out 324 divided by 4 with only pen and paper? No cheating and you must show your work, not just write the answer!

What do you think the difference is between basic maths and maths where you can use a calculator?

A car does 70 mpg. A gallon is 4.5 litres. I do 200 miles. Petrol costs £1.37 a litre

How many gallons of fuel did I use?
How many litres?
How much did it cost me?
What was the cost per mile?
How many litres per mile does my car do?

At what point would you say a calculator is needed?

(All these calculation can be worked out with written multiplication and division)

Yes. But I won’t lie, my maths was definitely ‘refreshed’ by helping my children prep for the 11+. Just hope I remember it all now it’s back in there!

You wouldn't need to use that example you've given in your day to day life, but if someone works say in retail they would need to know the the examples I have given, but I've noticed that they don't know basic stuff like percentages or how much change to give when given £10.26 when it comes to £6.26.

@cakeorwine

Chunking works really well - it makes sense and you can see how you get the groups to get to the answer

How do you get the groups if you don't know the multiples of 17?

Yes.
I was very good at maths at school, but I couldn't help DS when he struggled because the way I was taught is completely different from how they teach it now, so it all just added to the confusion.

You can work up

But again - you do need at some point to know multiples, but you can do it in smaller ones - smaller steps.

As long as you can do say 10 x 17, 20 x 17 etc

@cakeorwine

*But again - you do need at some point to know multiples, but you can do it in smaller ones - smaller steps.

As long as you can do say 10 x 17, 20 x 17 etc*

I am confused.

Your objection to long division was you had to work out multiples and instead you advocate chunking. Then you say with chunking you need to know multiples at some point.

What is the difference?

Can you explain how you would do 8041 divided by 17 by chunking.

With computers.

Actually it is probably far older than that. It's like ÷ is actually a fraction with dots where numbers should be.

I do agree that everyone needs to learn basic maths, and calculating 10%, 25% and so on is something y6s should be able to do in their head. I disagree that they should spend a week (and it does take that many lessons!) learning how to divide by 97 without using a calculator.

You might want to check your working

Watching Countdown over breakfast and doing the numbers helps me keep up arithmetic skills. Don't expect to see me on the show though, I'd lose most letters rounds.

In answer to the original question, yes, though rarely used.

Quite easily.

8041 / 17
Depends on your approach - so let's look at the 17 x table
17 x 2 = 34
17 x 3 = 51
17 x 4 = 68
17 x 5 = 85
17 x 6 = 102
17 x 7 = 119

So we can then use our maths knowledge to know that

17 x 400 = 6800 (we don't use 17 x 500 as that's 8500 and that's too high)

17 x 400 = 6800

We could keep track of what we are doing (8041 - 6800 = 1241)

That's very near 17 x 70 = 1190

1241 - 1190 = 51

That's handy: 17 x 3 = 51

So you have:

17 x 400
17 x 70
17 x 3

So 400 + 70 + 3 = 437

I know it's like long division - as you need to write out the 17 x table and there is some taking away as well to keep track - but I like this as it clearly demonstrates the groups involved - and division and multiplication is all about groups.

I feel that long division is a method but if someone had to explain why each step works, I think they would struggle.

People aren’t doing long division often irl, but learning numeric long division is a good foundation for being able to factor a polynomial by long division later. Each skill provides the stepping stone to the next. If a student doesn’t learn simple long division, they will struggle with polynomials later.

I have a soft spot for long division, because it was the first bit of maths I remember having an issue with.

Couldn't work out how you knew what number to subtract in the first place. Once I realised it was a guess everything became clear.

(I know, it's an estimate. But guess explained it.)

I think tables up to 12 times may be because there were 12 pennies in a shilling.

I am sure a student who didn't do or understand long division at primary school would be able to quickly learn how to factor a polynomial by long division at A-Level - I know I certainly did - because if you are doing A-level maths, then you have hopefully got a good understanding of algebra and maths by then - and have done well at it.

Dear Lord, at my god awful primary school in late 70s even we learned long division in Y5/6, and learnt busstop in year 2.

I did maths to first year university level, it was my "minor" subject for my PGCE, I actually taught it for a few years at secondary level.

By the time I had my own kids in the 90's the "maths in education" bods had got hold of the curriculum and I was as lost as the kids were with much of it at primary school. I couldn't explain it the way "Miss" did, and my easy shortcuts were rejected. I was more help once they got to GCSE.

It was a source of great annoyance to me that kids (like I was) who were more numerate than literate could not now progress and experience success in maths because of the level of literacy required to understand what was being asked.

I was always way ahead in maths and it took until secondary school for my literacy to catch up.

I was just scrolling through to comment on this. I was helping a friend's son with A level maths when I realised he needed to relearn long division to deal with polynomials - he'd learnt it once in primary and never used it again since. So I checked with my daughter a year behind him and hastily reviewed long division with her too.

coi I like long division. But I really really enjoy polynomial long division ...

I was just trying to explain the rational for still teaching the skill in a world of calculators.
Everything builds and each exposure to a concept helps.

yes, if a student doesn’t master it on the first pass, they have other opportunities, especially with the way math is taught now.

That was why we got a tutor. I'm a solicitor and was getting some of the verbal reasoning wrong, never mind the maths, and I didn't even know where to start with the non-verbal reasoning. I did a verbal reasoning test for a job and got 100% and got the job after trying to do the 11+ ones. The test for the job was so easy in comparison. I didn't grow up in a grammar school area and had never seen anything like the sorts of questions in the 11+. As for maths, I wasn't able to help DDs after about Y5. It seemed much more advanced - they were doing algebra which my school didn't teach until Y9.

324 divided by 7 isn't long division.

All you have to do is divide 32 by 7, then carry 4, then divide 44 by 7, then carry 2. After that, you place a decimal point on your top and bottom rows and continue carrying remainders to the zeros beyond until you get fed up.

7)324.0000000

7)324 = 46.285 etc.

Agree with so many others.

Yes, I can (and do sometimes) do long division on paper, with a pen, but that question is a straightforward 'in your head' division, only dividing by a single digit number.

324 divided by 7

 46.28

7)324
28
44
42
2.0
1.4
6.0
etc etc

I really think teaching something in year 6 which takes up large amounts of curriculum time, and many children struggle with, on the basis it will help them understand something if they are one of the small percentage of pupils who go on to do A level maths, is madness.