It has been shown to be problematic for teachers to use Krutetskii´s definition of mathematical abilities to recognize mathematically highly able pupils (MHAPs). Aiming to concretize what teachers can notice in pupils’ problem-solving processes, we connect a 10-year-old boy’s problemsolving process to some of the abilities defined by Krutetskii. The results give clear descriptions of what teachers can observe in pupils’ mathematical activities to notice their mathematical potential. We concretize, for example, how a pupil’s abilities to grasp a problem’s formal structure and to generalize can be observed. To be able to notice MHAPs, teachers need research-based support on how and what to observe in their pupils. Our proposed guide needs to be tested and validated to explore if it will help teachers to notice MHAPs s and subsequently support their learning.