Visual Learners do not necessarily respond to positive and negative numbers. So in my "Land of Quadrants" stories, I have characters represent numbers. Who is more perfect to represent negative numbers than Darth Vadar. I tell the students that the negative in front of a number means that the number has gone to the dark side. It would be in the left quadrant and bottom quadrants on an algebra graph.
When kids are trying to solve equations adding and subtracting positive and negative numbers, I tell them to imagine the equations as a battle. The negative sign is "really" a light sabor. For example, in the problem
-3 + 8 you can see that the positive fighter is the plus eight. Darth Vadar in this problem is the negative 3. He has the light sabor. I ask the kids, "Who won the fight?" The light side wins because he is bigger (or has more power). So the answer is a positive number. After MANY examples just like this one, they get it. The answer is 5.
So, what happens when you have two bad guys, or two numbers with negative signs. For example, in the problem -6 -9 or -6 + (-9) these two equations are exactly the same, just written a different way. But, when there are two negatives, that is a lot of negative power, so the answer stays on the DARK SIDE of the numberline (or left quadrant). The answer to this problem is -15. If a student is given enough examples of the above negative equations written the same way, they will begin to understand this concept easier. You can also reinforce that a lot of times in algebra, negative numbers (bad guys) are put in parenthesis. The parenthesis in the Land of Quadrants are actually body armour like Darth Vadar wears.
So, what if the dark side (the negative number) is bigger? In the problems -9 + 5 or
5 + (-9) or 5-9 these might be confusing to a visual learner. But...look who is holding the light sabor. The negative sign in the first problem is obvious that it belongs to the nine. The negative number in the second problem is obvious because the -9 is in armour. But, the third problem sometimes throws kids off. It is EXACTLY the same problem as the others, but written in another way. The negative sign is actually in front of the 9, so it belongs to him. This time THE DARK SIDE WINS because he has more power or is a bigger number. So the answer will ALWAYS be a NEGATIVE number. The negative number that is the solution is -4. Just subtract the two numbers and add a sword I tell the kids.
Welcome to my Land of Quadrants.