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Math Help - Maybe this forum is too advanced for me.

  1. #1
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    Maybe this forum is too advanced for me.

    Hello,

    I'm a primary school teacher who was challenged by a year 5 child to explain how to solve the following without switching and negating.

    1234 - 4321 =

    I acknowledge that I would switch the numbers so as to solve 4321 - 1234 in a written column method and then make the answer negative, but was at a loss to explain why it couldn't be solved without doing this.

    Surely, mathematically, it can be written in columns with 1234 above the 4321 and then solved as 1234 - 4321 by exchanging/borrowing?... or can it not?

    Bye for now.
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    Re: Maybe this forum is too advanced for me.

    Quote Originally Posted by Connie View Post
    Hello,

    I'm a primary school teacher who was challenged by a year 5 child to explain how to solve the following without switching and negating.

    1234 - 4321 =

    I acknowledge that I would switch the numbers so as to solve 4321 - 1234 in a written column method and then make the answer negative, but was at a loss to explain why it couldn't be solved without doing this.

    Surely, mathematically, it can be written in columns with 1234 above the 4321 and then solved as 1234 - 4321 by exchanging/borrowing?... or can it not?

    Bye for now.
    In short, no you can't. It's because subtracting a larger number from a smaller one is an entirely different concept to subtracting a smaller number from a larger one

    In order to extend your knowledge so that you can subtract a larger number from a smaller one, you need think of addition and subtraction not as accumulating or liquidating of quantities, but rather the movement right (for +) and left (for -) on a number line.

    If you want to do something like 1234 - 4321, what you are really doing is starting at 1234 on a number line, then moving 4321 units to the left. Obviously you are going to go past 0. The answer is going to tell you where you end up, i.e. how many units away from 0, and in which direction (a + for to the right, and a - for to the left).
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  3. #3
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    Re: Maybe this forum is too advanced for me.

    Sincere thanks for that prompt reply. I'll explain to my pupil this morning. I've used number lines before, but presumed that whatever could be done on a number line could be solved in a written column method.

    Once again, thank you for the clarification.
    Last edited by Connie; June 12th 2012 at 01:46 AM.
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    Re: Maybe this forum is too advanced for me.

    i'm intrigued, let's try it shall we?

    1234
    -4321
    ------

    1 - 4 = -3, so we start with:

    1234
    -4321
    ------
    -3***

    2-3 = -1, and since we're "in the negatives", we just write down the 1:

    1234
    -4321
    ------
    -31**

    3-2 = 1. hmm. that's positive. but.....1 = -(-1), so to get something bigger (so we "stay in the negatives"), we need to "borrow" -10 from the previous 3 digit, making it 2, so that our previous subtraction becomes 2-2 = 0, and our current subtraction becomes 3-12 = -9 (which we keep, since it's "in the negative" like our first sign):

    1234
    -4321
    ------
    -309*

    4-1 = 3 = -(-3). so we need to do our "borrowing" trick again, and take -10 from the 2 digit, so our previous subtraction of 3-12, becomes 3-11 = -8, and our current subtraction becomes 4-11 = -7. then we're done:

    1234
    -4321
    ------
    -3087.

    so, let's see if this actually worked. if A-B = C, then B+C = A, so let's add 4321 and -3087, which will be the "normal" kind of subtraction:

    4321
    -3087
    ------
    1234

    hey! it works! (but it IS a bit confusing. note i worked "left-to-right". we could have worked "right-to-left", but i wanted to convey that we "start out in the negative", which isn't clear when you work "right-to-left").
    Thanks from Reckoner
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