The problem-solving process is investigated for five groups of students when solving context-rich problems in an introductory physics course included in an engineering programme. Through transcripts of their conversation, the paths in the problem-solving process have been traced and related to a general problem-solving model. All groups exhibit backward moves to earlier stages in the problem-solving process. These earlier stages are revisited by the groups for identifying sub-problems, setting parameter values or even restating the goal. We interpret this action as coming from the fact that the students have not yet developed a knowledge base and a problem-solving scheme. Connected to the backward moves in the process are opportunities for the group members to build such a knowledge base from contributions and experiences from all group members. Problem contents that induce such moves are identified and can thus be considered by science teachers when constructing problems for group work.