In class we looked at various models to understand what happens when we add and subtract integers. Some of us prefer to use a number line while others understand better using chips and zero pairs.
Remember: Memorizing a rule will only get you so far. You want to be able to understand why the rule works and came into existence. Understanding helps you develop the reasoning skills to solve novel problems.
This video demonstrates adding integers. When you are adding integers of the same sign the sum has the sign of the two addends. For example, (-3) + (-7) = (-10) When adding integers of different signs, take the absolute value of both numbers and subtract. The sign of the sum is the sign of the larger absolute value. Another way to think about it is to think about whether you had more negatives or positives in your problem. For example, 5 + (-17) = (-12). I have subtracted 5 from 17 (using absolute value). I notice that there are 17 negatives and only 5 positives so the sum must be negative.
Here's a nice video to help you understand why it is necessary to add the opposite integer when you see subtraction problems.