OT: Long division (by hand)

Older daughter is a bit bored in math class at school, so I thought that I would teach her long division.

Problem is that I all but forgot how we did it at school (easy/medium difficulty ones I do quickly in my head, and harder one I get the calculator out).

I have no problem with the "standard" cases, e.g.

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not sure how to generalise the special cases for her. For example 321/3 or 206/3 - try it on paper and see what I mean. I can see the answer in my head before I start, but am not sure how to explain to her what to do with, say, the "0" in the middle of the operation with 306/3 for example.

Help please...

Reply to
JoeJoe
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My father could do square roots with a similar layout to long division. I wish I could remember how it went.

MBQ

Reply to
Man at B&Q

e.g.http://www.coolmath4kids.com/long-division/long-division-lesson-3.html>> But not sure how to generalise the special cases for her. For example 321/3

I'd be careful here as I only learnt the other day that modern maths teaching uses methods that are far different form those taught previously, and to teach her 'your' method will possibly make it that much more difficult and perhaps confusing when the class as a whole are introduced to it.

Long multiplication I understand is taught by arrays and long division by a process called 'clumping' - I couldn't take this immediately on board from the radio programme.

It might be worthwhile seeing if you can find a youngster in a class or two above your daughter's and see what system is being used.

Rob.

Reply to
robgraham

Before anyone chips in, I googled it:

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Reply to
Man at B&Q

Do these help?

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division around the world:
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Reply to
Man at B&Q

e.g.http://www.coolmath4kids.com/long-division/long-division-lesson-3.html>>>> But not sure how to generalise the special cases for her. For example 321/3

I saw that on the BBC site a few days ago:

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reality is that it's just the same old way of long multiplication and division, but represented differently. So for multiplication, rather than the shift and add method, you do all the multiplys individually then put them in a big box then add all the boxes up...

And the division thing is all about how many X's can you subtract from Y... Which is just long division done the other way.

I think it's slower and takes up more paper, however if it gets the principle over and allows pupils to learn relatively simply arithmetic without resorting to a calculator then I'm all for it.

Oddly enough the way they do multiplication is very similar to the way I do it - I never could remember my times tables and they've never stuck - I can multiply small numbers but not big ones, so things like 9 times

7 becomes 3 times 3 times 7 times to me...

Gordon

Reply to
Gordon Henderson

They appear to use different methods these days, at least from the way I was taught 40 odd years ago... I suggest you find out which one(s) the the school will teach and use one of those.

The BBC News web site had an article recently and a decent video of a couple of the methods. I could follow 'em but can't remember them well enough to explain 'em. B-)

___

3|321

3 into 3 goes 1

1 --- 3|321 300 - --- 21

3 into 2 (of the 21) doesn't

10 --- 3|321 300 - --- 21

3 into 21 goes 7

107 --- 3|321 300 - --- 21 21 - --- 0

But that is simple example. B-)

Reply to
Dave Liquorice

Top of the class that boy!

The trouble with the multiplication method shown on that Beeb webiste is that it works well for 1 or 2 digit multiplication, but falls down on larger numbers (or decimals and decimal fractions).

The great advantage of the traditional method of long division and multiplication is that it is a universal algorithm - it will work for all rational numbers.

Reply to
dom

============================================================================= Follow these steps - I *think* I've got them all. It's much easier to show than describe:

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Three into two won't go.

  1. Three into 20 goes 6 times = 18 remainder 2.
  2. Place the answer 6 above the line.
  3. Write 18 under 20 and subtract to show the remainder 2.
  4. Bring down 6 and write after 2 to show 26.
  5. Three into 26 goes 8 times = 8 remainder 2.
  6. Place the answer 8 above the line.
  7. Write 18 under 20 and subtract to show remainder 2.
  8. Put a nought after the 2 and put a decimal point in the top line.
  9. Three into 20 goes 6 times = 18 remainder 2.
  10. The answer is a recurring decimal.

Cic.

Reply to
Cicero

I sometimes wonder if they get enough practice in hand calculation to really get the principles and if that, and the tendency to grab a calculator, restricts development of proficiency in mental arithmetic.

I recently bought a book priced at =A314.99, reduced to =A310.50. At the cash desk a young lady, late-teens and obviously bright and articulate, scanned the book. It came up at full price. She commented that her 'maths' weren't up to calculating the reduction. On a quick guesstimate I suggested she try 30%. The problem was even more basic. She reached for an electronic calculator, entered both figures, and did a subtraction to get the difference - the figure she apparently needed for her cash machine. Seems she couldn't just mentally subract 10 from 14, and 50 from 99 and combine the two results.

Toom

Reply to
Toom Tabard

Thanks you all for your helpfull advice.

I will speak to the neighbour daughter later today to make sure I follow current teaching methods.

Reply to
JoeJoe

Worse than that, is the evident pride people take at being 'useless at maths'

Reply to
The Natural Philosopher

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According to today's news current teaching methods involve designating

20% of children as SEN (Special Educational Needs) and offering the rest counselling to cope with all their very diverse emotional problems.

Earlier generations seemed to manage to learn quite well without a daily dose of psychology or a calculator!

Cic.

Cic.

Reply to
Cicero

Generally a clip round the ear or half an hours detention was enough to focus the mind..

Reply to
The Natural Philosopher

A few years ago I bought a couple of 99p mugs and gave the girl a fiver. she had to work out my change on a calculator.

Reply to
JTM

I worked with a guy who could do 3 digit multiplication or division in his head. He had memorised the logarithms for all 3 digit numbers, so he just had to convert to logs, add or subtract, and convert back.

Reply to
Matty F

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Surely you're not suggesting grievous bodily harm or unlawful imprisonment for mummy's delicate darlings?

Cic.

Reply to
Cicero

Hmm.. Until retirement my wife worked part time as a Special Educational Needs co-ordinator.

I don't think her school had any system for raising key stage test results by excluding SEN children. They were sometimes allowed extra time (as allowed by testing rules) or had a *reader* to make sure they understood the question.

Competing schools who have a reputation for helping less able children tend to acquire more by parental choice so percentage figures may be warped.

The current publicity has avoided mentioning that a significant number of SEN children are the *miracle babies* born after a very short gestation.

I perhaps should not say but, schools employing a specialist co-ordinator are likely to get more help than those where it is an additional burden to a nominated teacher.

regards

Reply to
Tim Lamb

It also more closely mimics the way most people do it in their heads. i.e. break it into some smaller easier sums, do those and add the results.

Most assembler level programmers will tell you that all the basic operators are just variations on addition!(multiplication is just repeated addition, subtraction is negation and addition, division, repeated subtraction etc)

Reply to
John Rumm

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This (and an earlier version) is the story which prompted my comments:

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if the article isn't *entirely* correct (It is the Mail!) there is enough truth to suggest that something is radically wrong with our current education system.

We've seen and heard enough in recent years to suggest that discipline and order have very nearly collapsed in many schools to the detriment of pupils who want to learn. It seems that inadequate teaching (for whatever reason) is being propped up by using extra non-teaching staff as ancillaries.

The earlier Mail story (this morning) had a mini case study of a school which employs about 200 such staff including a full-time policeman.

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praise to good schools and good teachers but many are clearly failing with disastrous result both for pupils and the future of industry.

Cic.

Reply to
Cicero

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