During the past few years, the social interactions of students have been limited. The act of social distancing has not only exacerbated developmental gaps in social and emotional learning (SEL) (Vaillancourt et al. 2021) but also interrupted mathematics instruction (Lewis et al. 2021). Teachers are searching for strategies that promote mathematical problem solving, while also fostering a sense of community that maximizes SEL development. One strategy that Kathryn Lavin Brave and Jillian Miller have found to be particularly effective involves the use of Fermi Questions. Fermi Questions, also referred to as "back-of-the-envelope calculations" (Kenyon 2008/2009), were named after Nobel Prize-winning physicist Enrico Fermi, who was lauded for both his theoretical and practical achievements and was also known for his ability to make reasonable estimates with limited data. The following article describes how the authors used Fermi Questions to illuminate the connections between the Standards for Mathematical Practice (SMP; NGA Center and CCSSO 2010) and the SEL competencies. In the subsequent sections, they recount their experiences with Fermi Investigations, specifically with a collaborative group of third- and fifth-grade students. They also provide snapshots of student performance during the course of the investigation to describe how the implementation of Fermi Questions promotes arithmetical expertise and a sense of community in the mathematics classroom.