Problem-based learning (PBL) has the potential to enhance both cognitive and affective engagement but has been criticised for being unsuitable for learners with low levels of knowledge and skills, such as South African learners from poor backgrounds. In such cases, guided problem-based learning (GPBL), which includes direct instruction and teacher prompting, may be more effective. However, little is known about the extent to which GPBL can replicate the cognitive and affective benefits of PBL for such learners in the context of middle-school mathematics problem-solving. It is also not clear what the optimal granularity of teacher prompting should be within GPBL. To address these issues, this instrumental case study was conducted with 26 higher-achieving Grade 8 and 9 learners from schools serving poor communities. These learners participated in a GPBL week-long extracurricular holiday mathematics programme in which they were guided to use trigonometry to determine the maximum height reached by a water rocket. Data were collected through video recordings, field notes, written work, and audio-recorded group discussions, and were coded using the multidimensional problem-solving (MPS) framework to identify cognitive and affective behaviors. The learners' affective responses suggested general positivity towards effortful problem-solving. Their cognitive responses suggested successful engagement in some, but not all, aspects of problem-solving. Although fine-grained prompting did not promote exploratory discussion, it was found to be necessary to guide productive mathematical activity. Medium-grained prompting, which did lead to exploratory discussion, did not appear to be directly productive, although it did appear to enhance learners' receptivity to subsequent fine-grained prompting.