While the importance of collaborative problem-solving has been highlighted as an important skill by the OECD (Organisation for Economic Co-operation and Development), no specific model exists for mathematics facilitators to implement when engaging their students in group problem-solving. In this paper, we introduce the CoPs model for Collaborative Problem-solving in mathematics, a structured approach to facilitating group-work of this kind. We outline the theoretical foundations of the CoPs model as well as its implementation in practice. We then consider its usage in a case study with 89 highly-achieving post-primary school students from numerous mixed schools around Ireland and discuss student feedback on the experience of the CoPs model as an approach to collaborative problem-solving in mathematics. Students were positive about this approach to collaborative problem-solving, suggesting that this model may provide an approach that teachers could introduce into classroom settings when teaching problem-solving in mathematics.