how to demonstrate ÷ by negative #?
How would I demonstrate to 3rd graders that dividing a positive number by a negative number results a negative number? For example, 6 ÷ 3 = 2 can be shown by 6 items separated into 3 groups would have 2 items in each of the 3 groups. How can this be visualized? I'm really struggling here. Thanks guys!
Update:So how can VISUALLY I show that 8 ÷ (-2) = -4??? Thanks yall! :D
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I've always thought of negatives as orientation, especially when adding and subtracting on a number line (negative to the left positive to the right). With multiplication and division that's a little more difficult, but still possible with this set-up. So division could still be splitting into groups, but instead of keeping the groups for yourself you're giving them to someone else. So for example
8/(-2)
would mean you need to give someone 8 items in 2 groups, so you'd give 4 items away (-4) twice. Similarly,
(-8)/(-2)
would mean they have 8 items that they want to get rid of. So you get 4 items twice. The numerator's sign would dictate where the items begin, and the denominator's sign would dictate where they end up in relation to where they start (negative is away, positive stays).
So 8/(-2) = (-8)/2
since in the first you give 2 groups, while in the second they keep two groups, but start with the items.
This may not be the best way, but it's analogous to the old way so it's not that much of a stretch.