Collaborative problem solving (CPS) has been shown to both engage and benefit students' learning of mathematics. However, there is evidence that group work is not always easy to facilitate, in part because educators lack details about learners' engagement during group work: the processes of problem solving involved, and how these are engaged. In this exploratory study, we focused on these processes in the moments of related math activity, or math moments, engaged by two groups of interested, urban, middle-school aged students during four sessions of work in the Virtual Math Teams (VMT) environment. We examined three phases of their problem solving: Exploring, Constructing, and Checking. In addition, to further describe the students' cognitive and behavioral engagement, we considered both the process of students' use of executive functions (EF), during problem solving, termed executive functions in practice (EFP), as well as the stage of CPS (Participation, Cooperation, and Collaboration), during phases of problem solving. We learned that the relation between each phase of problem solving, categories of EFP, and stages of CPS vary; for example, the problem-solving phase of Exploring was found to have a more positive effect on EFP and CPS than either Constructing or Checking. Implications for educational practice, and next steps for related research are described.