So I have been trying to find the perfect lesson to show my students where we can use integers (more specifically, negative integers) to gain greater insights into something. I am not quite there, but am getting closer. I have finally settled on a credit card ledger activity where they will "shop" for some items, charge them to a credit card, make minimum payments, get interest added and hopefully see how dangerous credit cards can be in the end. All the while the will hopefully see and internalize the rules for adding when we have the same sign or different sign and even multiplying with different signs. It will be good, just not perfect.
It will probably come out in the next month or two, I have an order of operations lesson I am editing now that will be released the first or second week of september.