Integer Operations – why???

In my support classes, I’m trying to focus on standards this year – helping students understand what a standard means, how to study to address a standard and what it looks like to meet standard.  In my 7th grade support class, we’re working on integer operations.

In the past, I have used this Integer Foldable (from Everybody is a Genius) with some success. I still like it and I’ve had students add it to their notebooks, but I’m also trying to address a more conceptual understanding of what it means to add, subtract, multiply and divide with integers. We’ve been using integer chips and number lines and I’m starting to see a solid understanding in most of my students…. except for some division.

Why, oh, why is a negative divided by a negative positive??

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One Response to Integer Operations – why???

  1. David Wees says:

    Here is one analogy that may be helpful.

    If a group of people owes $50 (eg. they have a total of -50 dollars) and each of them owes $10 (eg. each person has -10 dollars) how many people are in the group?

    Here is another analogy. We can see this is true by extending patterns on multiplication, and then remembering that division is the inverse operation of multiplication.

    3 x 3 = 9
    3 x 2 = 6
    3 x 1 = 3
    3 x 0 = 0

    Since the right hand side is decreasing by 3 each time the number being multiplied by one decreased, we can extrapolate to see that 3 x -1 = -3, so that it fits the pattern.

    Similarly:

    3 x -3 = -9
    2 x -3 = -6
    1 x -3 = -3
    0 x -3 = 0

    Using the same logic…

    -1 x -3 = 3.

    I hope this helps.

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