But if your project is public work, being informal might come back to bite you. So formal is better. I believe the AIA has a form you can use. We dreamt up this form below for a small public project that was, uncharacteristically for us, becoming adversarial.
Note that it needs to be clear that you just want a price, and only afterwards will a Change Order be issued (if the price is acceptable). In many instances, you might be chasing someone's dream that doesn't have a direct role in the project - the boss's boss - making the situation a bit political.
The formal approach always works, and it takes just a few minutes longer to implement.