This work is focused on upper-secondary school students' ability to use the periodic table of elements to solve problem tasks. Eye-tracking and retrospective think-aloud methods were used to evaluate the reasoning behind the students' (N = 8) performance, i.e., to map the strategies they used and problems they faced when solving the tasks. The data from the eye-tracker were submitted to a quantitative analysis-time fixation duration evaluation on predefined areas of interest. The think-aloud method supporting the eye-tracking record together with the students' transitions also enabled a qualitative analysis of the students' procedure. Most of the students failed the tasks. The main reason was their lack of fundamental knowledge together with low reading and problem-solving skills, in addition to a lack of motivation to solve more demanding tasks. Their knowledge and ability to use the periodic table was proved insufficient to the corresponding curricular objective. The students mostly used expansive strategies, however, due to some problems (e.g., low prior knowledge, misunderstanding, or inattentive reading), they used limiting strategies (e.g., deducing from the task structure or guessing answers), and failed the tasks. These results offer a solid foundation for subsequent steps toward improving classroom practice, which stresses the need to focus on problem-solving and strategy development more during (chemistry) lessons. Also, the results call for extra support for the periodic table's teaching conception.