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Please Help! Modern Methods of Long Multiplication and Division!

Discussion in 'Mathematics' started by Anonymous, Mar 22, 2011.

  1. Anonymous

    Anonymous New commenter

    Now this will be an interesting thread. I predict certain people will favour traditional multiplication and division whilst others will try and do methods that help the children actually understand what they are doing.

    Personally - chunking for division and grid method for multiplication. However schools build up to this over the primary years.
    Once confident with this, then short division , long division and short multiplication - but some children will just not get that and are happy to do a method they are comfortable with. As long as it gets them the right answer, then that's fine with me.

    Others might disagree.
  2. All pupils should be drilled from aged 6/7 to 11 on long multiplication and long division and those without learning difficulties are expected to know it without being prompted.
    When they arrive at secondary school they are expected to be fluent, if not then introduce the 'grid' and the bus stop to get the job done. (if they are not able to do it, please dont give them a level 5 tag and pack them off with your figures in tact)
    I have many y11s who are going to get Cs who can do neither effectively, therefore they stumble through the grid and bus stop just to get the job done.
    Strange how the vast majority of Eastern European kids can do long division/multiplication regardless of whether they are great at maths or not. Many look like [​IMG] when the UK born kids sit in year 10/11 lessons without a clue.
  3. I think that it is really odd that you ask if we always use grid as I never do!


    Long Multiplication ... Standard Algorithm and Napier's Bones ... the recent thread on this that showed the Japanese method had me interested ... http://www.youtube.com/watch?v=e-P5RGdjICo

    Long division ... Chunking then standard algorithm without the working out

    In both cases I check to see what has been done in Primary and allow students to use their preferred method

    With able students I would teach full algorithm for long division as I see it as essential for AS and onwards
  4. I am intrigued ... how do you do long division and expect the kids to do it

    Bus Stop IS the standard algorithm
  5. Maths_Mike

    Maths_Mike New commenter

    Here we go again.

    What evidence is there that the children understand the grid method any more than any other method - i suspect none.

    The method you refer to as traditional for say 123 x47 requires the children to work out 123 x7 and then 123 x 40 and add them together. It aslo provides a nice way of alligning digits to make this fairly easy.

    How is this any harder to understand than doing (100+20+3) x (40 + 7)

    Please expalin I just dont get it!

    The problem woul;d be if the algorithm was taught with now explanantion etc but the same could be said of any method I suspect.

    As for chunking it is an appropraite name for a a method that makes you wanna puke.

  6. Nazard

    Nazard New commenter

    I also suspect none. But an absence of evidence is not the same as evidence of absence (or something!).
    It isn't. But the grid method is a great way to link multiplication and area (IMO) and can then also be used to introduce expanding algebraic brackets. For example, expanding (x+y+2)(2x+5y) is much nicer using boxes because FOIL/nose&smile/parrots/claws/etc don't do the job.
    Yep - I agree. It is annoying to see the grid method turned into an algorithm, without any of the explanation/understanding being involved.
  7. I find myself in full agreement with Nazard on the topic of FOIL/claws ect. I actually only recently came across FOIL and always try to appreciate the good points of any method but with that particular one I could see no merit.

    I agree with Nazard too that teaching grid method for multiplication without any of the understanding of place value that it requires is a nonsense.

    In general, I do my best to teach understanding in each topic, otherwise maths just becomes a mess of rules that pupils have little appreciation of and have no idea where anything comes from or how it fits together.

    I would agree with Betamale about how essential tables are, without that then there is very little hope for them as regards enjoying very many of the other topics in maths.
  8. The thing is though:
    A child can do 23 x 24 using grid method / long multiplication and gets and answer.
    Ask them - ok, what is 23 x 25 or 24 x 24 - without using a method and only having the previous answer, will they do it?
    They can do 186 / 6 using bus stop / chunking / whatever. OK - what is 186 / 3, 186 / 12?

    You can pick and learn any method - but how many truly understand and can apply it?
  9. I agree robyn147 about using one answer to find another, it is a concept pupils find difficult but one which with some hand holding I think a fair few can grasp. It's something which I think has improved as the majority come from primary with at least some methods for doubling/halving.
  10. bbibbler

    bbibbler New commenter

    For my high flyer, I do not care what method they use, but they must know many different methods and make imformed choices. Most have mental statagies that involve multiplying by the nearest "easy" number and then adding/subtracting the difference.

    Student who come to us in year 7 without long multiplication get drilled in the latice/Gelosia method. I do play with the Japenese cross method but that is only really usful when all the digits are small.

  11. Hi, perhaps I should have said short division (as the bus stop method) Vs the long division.
    I find, from anecdotal evidence and experience, that once kids have got to y7 without the skill of long division and multiplication its often 'easier' to follow the grid method or short division to 'get a job done'. Thats anecdotal though and certainly not universal with some kids still able to take the methods on and use them.
    I just cannot help thinking its a skill kids should have long before 'maths' is played with and the longer they go without the skill the harder it becomes to get them to dial into it.
    My year 7 'level 5' pupils 3-4 out of 30 can divide and multiply double digit numbers........
  12. Yes this is a fair point and,as a primary maths 'specialist', my main concern is that children understand the concept of the operations first. Some children are taught a 'method' (and yes there is variety) without understanding the 'concept' and there is a difference between understanding the concept of the calculation and understanding the method used to calculate. For long multiplication and long division this is what I would say:
    • they should understand the concepts of multiplication and divsion, so, if they are working out '124 x 67' they understand they are working out 124, 67 times or 67, 124 times. Similarly for division if they are working out 346 divided by 23, they know they are trying to find out how many groups of 23 there are in 346.
    • they should have a good understanding of place value and their tables so they can make a rough estimate, so for the above examples they might estimate 100 x 70, or 350 divided by 25
    Ideally I would want children to be able to explain how they are calculating however they must be able to explain what they are actually calculating. They will only ever be able to apply a method (even if they don't understand the inner workings but have learnt the method) if they understand the concept of the calculation.

  13. Can't comment on the name but the method is probably my favourite one!
  14. Hi
    I too would love all kids to understand the concept of what they do. I cant help thinking though that numeracy is not maths and the majority of secondary school maths up to C grade only relies on recalling multiplication/addition/subtraction/division facts.
    Look at schools who have less than 40% maths A*-C.
    It would be great for kids to understand and discover the ideas behind the algorithm. Many issues I have in maths with Y10/Y11 is their inability to do basic calculations and recall number fact.
    Area of a rectangle....7cm x 8cm.....many many write the wrong answer as the cannot recall the FACT that 8 x 7 is 56. They can access the topic but the numeracy (which at this level needs to be little more than fact) lets them down
    Few of mine did this one recently
    3x + 28 = 10x -7
    28 = 7x -7
    35 = 7x
    x = 6
    C grade
    C grade
    C grade
    U grade, level 3-4 skill, therefore loss of marks.
    I really dont think we need to spend time worrying about why but just focus on rote learning numeracy facts. Once this is nailed and an automated response, THEN discover the notion of sharing object for example or looking at facts and so on.
    Kids reach for their times tables in their planner in the way we used to do it for the periodic table in science. If they were drilled in multiplication and division up to 12, can access the postive and negative integer line then they can open up to maths.
    For the high flying kids you discover, but for now kids (IMO and IME) need rote learning and numeracy should be an entirely different subject to maths.
  15. Hello Betamale,
    We do agree, in some respect, I think. My point was that they must understand what multiplication is all about (and know their tables) before rote learning a multiplication method. I am not against rote learning. But the example you gave:
    35=7x needs them to:
    • 'read' this as 35 is equal to 7 times something.(therefore understand multiplication)
    • know that 7 times 5 is 35 (which is rote)
    • conclude that x must be 5
    How can they do that problem if they don't understand the concept of multiplication? My point was that they often learn a method (either rote learning or by trying to explain it) without actually understanding the concept of the calculation they are trying to work out. I don't care what method they use (well I do a bit - obviously you want efficiency etc) as long as they know what they are actually working out.
    I do agree that there is a difference between numeracy and maths. I do, however, diasgree that numeracy (at any level) is little more than knowing facts. It involves knowing facts but being numerate requires understanding of the basic concepts of calculation.
  16. Anonymous

    Anonymous New commenter

    Don't you teach tables in secondary school? Ban them from the planner. Regular practise.
    I was tutoring some Y6's today - we were looking for real life questions based around percentage and fractions. Had pretty much done the SATs ones so we looked at some Foundation GCSE ones. They were shocked by the paper - they honestly thought KS2 SATs looked harder.
    I showed them an algebra one: 5x = 35 and said "That means 5 times a number is 35".
    "Oh - 5" - well actually it was a bit harder: 3X + 4 = 13.
    Tables need constant practise and application - in both secondary and primary.

  17. I work for Family Learning and spend my time teaching adults to use the methods that are taught in school today. Greater emphasis is placed on primary school children using a variety of methods so that they are exploring number. Parents get very confused when children bring homework home that relies on a knowledge of different methods. An exemplar using the desired method would help stop many a tantrum. Grid method and chunking both have their place and for some children are the only way to understand what they are doing. By Year 6 many children are using the traditional short methods but with a real understanding of how it works, place value and having a feel for what the answer is. Many of the parents I teach have a 'light bulb' moment and suddenly maths ceases to be scary.

  18. gogojonny

    gogojonny New commenter

    Year 6 is too late. You're asking kids to learn one when, and then learn a whole new different way? No wonder they are confused. It's like teaching a kid how to kick a ball, then showing them a whole new different way 4 years later. It just does not work.
    I've read that Maths for Mums and Dads book and it seriously made me want to cry. There was nothing wrong with the old method.
    Family Learning? They seriously employ people to teach funny maths methods to parents?
  19. Hi
    I think the time spent explaining multiplication is little more than repeated addition cannot take more than a couple of lessons. I appreciate numeracy is more thank knowing facts BUT knowing the facts will not limit so many kids at a certain D/C/B garde GCSE level these days and that is the issue. If mine could multiply and divide by fact they would be one grade (as a wild guess) up on what they are. If they knew what it was all about then they would be further up the chain but there comes a time when rote/fact learning is very beneficial to kids who are going no further with their maths
    I teach them, but by the time you get somebody who has not been drilled and take them in Y11 they are weak. I have been told I am wrong for making my year 7/8 stand and rote learn them. "Its not good teaching"
    Parents often repell them and its not fashionable.
    I would expect my 8 year olf newphew to be ok on the middle of the current foundation paper. He is able but not outstanding.
  20. frustum

    frustum Star commenter

    I gave top set year 8 an arithmetic test this week - less than half got the long multiplication right. It looks like most understand the method they are using (which varies) - but tables are an issue. They were reminiscing about the weekly tables test from primary, and I think that some of them could really use the regular practice.
    I have often seen TES threads about "how to occupy my tutor group for 10/15 minutes each day". So do any schools make use of tutor time for arithmetic practice? Would a sheet of tables/guzintrs/4 rules once a week make a significant difference?

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