Here are some ideas for teaching positives and negatives. This year we are using MEP Math, which is available online for free. Some of these ideas are from MEP and some we thought of while working through the concept:
1. Cutaway views of cities or buildings teach the idea of above and below ground.
2. Talk about "so much cash on hand" and "so much debt" and then find the balance.
3. How far above sea level is a mountain? How far below sea level is a portion of the ocean floor?
4. The physics of sound: high pitches are positive while low pitches are negative (Little La thought of this one).
5. BC/BCE and AD/CE on the timeline.
6. Summer and winter temperatures.
(Discovering the "why" of integers captures the student's imagination, and then he is ready to learn the "how". I always needed lots of this sort of discovery before a mathematical process would stick in my head.)