In recent years, there has been increasing interest within the engineering education research community to prepare engineering students to address wicked problems (WPs) such as climate change, resource scarcity and violent conflict. Previous research suggests that engineering students are able to address WPs if they are given adequate support, but there is a lack of research on what kinds of support are needed. This paper aims to reduce this gap by reporting on students' performance in, and approaches to, addressing WPs when different scaffolding strategies were used in different parts of a rubric-based intervention. The intervention aimed to provide undergraduate engineering students with an understanding of the nature of WPs and with a structured way of addressing them. For each part of the intervention, we discuss affordances for learning provided by the different scaffolding strategies. The results suggest that strong cognitive scaffolding can support students' understanding of the nature of WPs and students' performance in written responses to WPs, but possibly also limits deep engagement with WPs and transfer of learning to other contexts.