What it seems is that she lacks motivation. To get her to be motivated you would have to appeal to her mathematical mind. Have her be the logic based part of the group, manage the time, make outlines. People that are usually math oriented are logic oriented people. I would also try to find something that intrinsically motivates her, something along the lines of a reward. It is very hard to make someone motivated from one exercise, so this will be an ongoing thing. You have to appeal to what makes her interested in and that she can do while also trying to find a reward system. In the future you can ween her off of rewards. You could also ask her to make a timeline or something that can be concrete. Also make her opinions valued, kids that grow up in broken homes are defensive and they feel they need to assert there dominance because they lack importance at home. Try and make her a leader in the group but have some kind of democracy intact. This will help her learn to work well with others while still feeling like she has some kind of control. It is hard to really say what is needed to be done without actually being there and assessing the situation there. I am going to be more of a in person kind of teacher taking things as they come and interacting in the real world. I don't do so well with hypothetical because it takes out one of my best ways to figure stuff out and that is being actually faced with the real problem.