In this paper, we document the results of the implementation of a series of activities related to an optimisation problem. The objective is describing how the construction of mathematical meanings is promoted when the students face the problem through different representations. The activities, addressed towards 15 year old students, surge from a free interpretation of the construct "Hypothetical Learning Trajectory" (HLT) by Simon (1995), considering different representations and utilising digital technologies. With this, we propose a route to tackle variation problems based on HLT similar to the proposed.