In this article we report the influence of contextual factors on mathematics and science teachers' reasoning in risk-based decision-making. We examine previous research that presents judgments of risk as being subjectively influenced by contextual factors and other research that explores the role of context in mathematical problem-solving. Our own approach has been to develop carefully designed software tools that support the user to empathize with a hypothetical person, Deborah, who suffers from a medical condition. The tools were used by a group of teachers who were asked to help Deborah decide whether to have an operation that could cure the condition but which carries particular risks. In order to make this decision, the teachers were required to model the risks of the operation and also the lifestyle decisions that Deborah might make. We trace the teachers' efforts to coordinate judgments of likelihood and impact. The data emphasize the sensitivity of reasoning to matters of context; we set out in detail the various ways in which the process was affected by context. (Contains 3 figures and 2 footnotes.)