This study scrutinizes the influence of project-based learning (PBL) and inquiry-based learning (IBL) on fourth graders' teamwork skills and critical thinking in math classes. A historical review reveals that while they have positive effects in multiple fields, their sole use in elementary math teaching is yet to be explored. 55 fourth-grade students from Manas No. 1 Primary School in Xinjiang were randomly chosen using a quasi-experimental design. They were divided into experimental and control groups. The experimental group was taught with a combination of PBL and IBL while the control group received traditional teaching. Quantitative assessment of teamwork skills and critical thinking shows that the combined method is more effective. The results emphasize the importance of developing shift-based and inquiry-centered learning programs. Nevertheless, the study has limitations such as a small sample and a short time frame. Further examination in different cultural, educational, subject, and class-level contexts is required for process reliability before generalizing the findings.