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Division - Aaaah!

Discussion in 'Primary' started by CarrieV, Jun 25, 2011.

  1. CarrieV

    CarrieV Lead commenter

    I would teach as 10 lots of 4 as a "40" jump on the number line ( as most can manage to multiply a single digit by 10!) and then carry on to 60 from there.
  2. Ask for the calculation policy and it should tell you there how you should teach for each level. I would use standard written method if they understand both methods you have described.
  3. Try estimating and use known number facts. They should know that 4X10 is 40 which isn't enough. So then they can try 4 X 20 which will be too much. The answer has to be in-between the two somewhere. This could cut down on the amount of chunking or they could could keep using this method until they have an answer.
  4. minnieminx

    minnieminx New commenter

    I would teach them to jump all the way to 40 in one go 'because we can't be bothered drawing ten little jumps when we know where we will get to. Might as well take a giant leap all the way there.' Then keep going in 4s until 40.
  5. I think these methods of division are a good example of modern
    attempts to make things easier and clearer making things far more
    complicated and, as you've noted, tedious than they need to be. Sure
    it's useful to use chunking etc a few times to demo what division
    actually represents in the real world. Then it'd make life immeasurably
    simpler to switch ASAP to using a practical algorhythm:
    4 in to 6 goes 1 (write that down), remainder 2. carry that to the next column to make 20. 4 into 20 goes five. Write that. See, now you have written 1 5 Ta da! 15.

    Simples. And you don't need to know anything more complicated
    than your easy times tables - though you can use it in the same way for
    divisors in double or triple figures or more if adept. The old ways are
    the best.
    However, you should not listen to me, as I am deeply
    unfashionable, grumpy and telling you something different from what the
    numeracy strategy says, which, as you know, is heresy.

    But I am of a generation that can do arithmetic without getting a calculator out.

  6. minnieminx

    minnieminx New commenter

    But it isn't that simple. I taught maths in secondary schools before the NNS and believe me children were NOT better at dividing having been taught the old ways.

    4 into 6 doesn't go miss cos 6 is bigger than 4.
    4 into 6 doesn't go cos 6 isn't in the 4 times table.
    4 into 6 goes once so I write a one. 4 into 0 goes 0 so I write a 0 and the answer is then 10.
    And so on and so on.

    Much easier to count up in 4s until you get to 60.
  7. I cannot bring myself to LOL.- it is sad.
    Yeh, well, I suppose those pupils would have to go back a few steps before they get onto the really really hard stuff, such as working out hwo many times 4 goes into 6.
    Are you saying that the counting up in 4s and similar methods so beloved of the NNS is dumbing down for all to suit the needs of the truly inumerate? If so, I agree. However, you may have to be burned at the stake.
  8. minnieminx

    minnieminx New commenter

    Noooo I'm saying that children have always found division hard. Talk to the vast majority of adults about what maths was hard/impossible at school and almost all will say long division.

    The newer methods are not more complicated, nor easier, just different. They do get rid of the problems of the past, but also create some new ones. Some people find them easier and some harder.

    The dumbing down of mathematics to make numeracy is mainly only an issue in secondary schools. Primary maths is basic everyday numeracy and ever has been. I do occasionally miss not teaching trigonometry and all that jazz, but hey primary maths is cool for now!
  9. If they are "just different," then why are they prescribed (the prescription implies to me that someone thinks they are "better").
  10. minnieminx

    minnieminx New commenter

    They aren't. You are free to teach in any way you wish, subject to school calculation policy.

    And the 'not necessarily better, just different' is my own opinion based on no evidence at all!
  11. I have bad experiences of trying to teach things not in the NNS.
    eg Most dreary teacher in the world (who is senior to me): "Don't do that lesson. It doesn't say in the NNS to use an abacus for this!"
    Me "It doesn't say that you can't."
    Result, **** and fan.
  12. minnieminx

    minnieminx New commenter

  13. Ay, I can laugh now, but it still has a hollow ring. She was a right b**** and so was her mate.
  14. In my school, we would teach our year 5s that calculation using the written method we call 'bus stop' division (you know the one!) It requires some times table knowledge (doesn't everything) but on the whole, seems to work well.
  15. Anonymous

    Anonymous New commenter

    The bus stop method is great.... if they understand it. I do tutoring and I see many mistakes using this method. I do secondary as well and it still bugs me when a "bright" 15 year old does not understand if 5X = 30, how do we find X.
    Division is complicated. With my tutoring, I still do pictures, diagrams and reinforce it to real life examples (at all levels) as well as linking it to chunking / numberlines to really make sure they understand what is happening.
    e.g. You make 60 cupcakes. You put 4 in a box. How many boxes do you need? Some children need the security of pictures, some count in 4's and some go for the 10 boxes - 40 cakes, 11 = 44, etc.
    It is a step by step, build it up slowly process. I do not agree with doing the bus stop method if they do not have a firm grasp of division. But this is an argument that rages in maths - do you teach a method or do you teach them to understand how division works? The same applies to the grid method or subtraction - do they understand why they "borrow" or do they know that is just what they do to answer the question?
    We are probably too good at teaching methods without addressing basic understanding and this shows itself later at high school.
  16. CarrieV

    CarrieV Lead commenter

    I'm of the "teach them to understand" persuasion- and pedantic with it. So personally I couldn't say "4 into 6 goes once" as it's not 6, it' 60! ( But that might well just be me) [​IMG]

  17. I find using the chunking method better if the children add up their 'chunks' to get to the target number. Too many children I have taught could chunk, especially x10 etc, but then would get tangled up in the subtraction element. So we turned it on its head and added the chunks and used other known facts so for your example:
    10 x 4 = 40
    Another 10x4 ? No, too many so
    Half it and try
    5 x 4 = 20
    10x and 5x would reach the target of 60 et voila!

    We had lots of light bulb moments during that lesson!

  18. I'm all for students
    understanding, as first preference. However, if someone really doesn't
    by the age of 15, it's not likely that they ever will. The
    beauty of the method I described is that it will give you the right
    answer, whether you understand the mathematics or not, and that's got to
    be useful in adult life. Why deprive learners of this tool?

    Is this really possible? If they are genuinely "bright" they sure have been badly taught!

  19. I teach Year 5 lower maths and have spent many an hour agonising over the fact that my class 'don't get' place value, inverse number relationships, blah blah, and have come to the conclusion, rightly or wrongly, that whether they understand what's really going on or not, it is still massively useful to be able to work stuff out using a pen and paper.
    I totally understand the frustration of secondary maths teachers who then run into kids who 'don't get it', but I think you've got more chance than we have. At 9 and 10, many kids just aren't able to grasp all the abstract concepts that the curriculum says they need to understand.

  20. Waiguoren

    Waiguoren New commenter

    GSM, you might be interested in Timez Attack - they've just released the division game. It's freely downloadable (for the base version) and I'm using it all the time with my Year 1s, who love it. I use the lowest level, of course - dividing and multiplying by 2.
    It might help your Year 4/5 with concepts, and it might help with motivation! I remember a Year 4 teacher who told me that he had a child who just couldn't understand or be interested in multiplying, and when I told him about this it made a huge difference.

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