Approaches to STEM integration and the representative role of each STEM discipline are two main issues in the research on integrated STEM education. To tackle the two issues, a conceptual framework was proposed for designing a model-development sequence of STEM tasks based on mathematical reasoning (Mr) for Mr-STEM connection, interaction, and coordination between ways of understanding and ways of thinking. Lastly, one exemplary design process is provided and design principles are further suggested. The conceptual framework for designing a sequence of Mr-STEM tasks is theory-based and practice-oriented. The application of the framework has the potential to make the design and analysis of STEM tasks more relevant to the exploration and application of mathematics in integrated STEM education.