Special relativity is both exciting and challenging in that it requires developing new intuitions about relativistic situations. How can we help students make sense of special relativity when their intuitions are classical? This paper will discuss student sensemaking about special relativity in a sophomore-level course designed to explicitly teach and support physics sensemaking. The course particularly emphasizes two sensemaking strategies: visualization with spacetime diagrams and the development of rules of thumb. Rules of thumb, like "proper time is the shortest time," serve as footholds when solving problems in special relativity. Specifically, we present an analysis of students' use of rules of thumb in their written solutions to homework problems. We found that students draw upon time rules, length rules, and relativity rules to solve the Twin Paradox. We also discuss how rules of thumb fit with other theoretical constructs.