After I have received some of them, I have found out that the sponsor wants more than what we have been programming for. How do I handle a situation like this?

Part of what you need to do is triage the project: what can be finished, what can be finished only by scaling back and what cannot be finished in the time allowed (and needs to be dropped in "this release"). One book that gives examples of dealing with this sort of situation is called Catastrophe Disentanglement.

The culture of previous projects in the company is to wing it and hope that everything falls into place in the end.

I've worked for people like this. I have not found any simple strategy that is effective at planning that can survive them (indeed, I've had bosses who believe that planning is "evil" and will intentionally undermine any effort to react with anything other than last minute crises), and it takes more skill than I have to work around active intereference. The book Death Marchenter link description here describes some of the rationale behind "wing and a prayer" project management, but more importantly deals with how you should cope with it (because sometimes the only rational response is to quit).

Death March is a quick read (like an evening), and your local library may have a copy. Catastrophe Disentanglement is a harder and longer read, it will require some effort to think about the techniques it explains and to sit down and trim your deliverables.

After I have received some of them, I have found out that the sponsor wants more than what we have been programming for. How do I handle a situation like this?

Part of what you need to do is triage the project: what can be finished, what can be finished only by scaling back and what cannot be finished in the time allowed (and needs to be dropped in "this release"). One book that gives examples of dealing with this sort of situation is called Catastrophe Disentanglement.

The culture of previous projects in the company is to wing it and hope that everything falls into place in the end.

I've worked for people like this. I have not found any simple strategy that is effective at planning that can survive them (indeed, I've had bosses who believe that planning is "evil" and will intentionally undermine any effort to react with anything other than last minute crises), and it takes more skill than I have to work around active intereference. The book Death March describes some of the rationale behind "wing and a prayer" project management, but more importantly deals with how you should cope with it (because sometimes the only rational response is to quit).

Death March is a quick read (like an evening), and your local library may have a copy. Catastrophe Disentanglement is a harder and longer read, it will require some effort to think about the techniques it explains and to sit down and trim your deliverables.