The Dijkstra's algorithm is an algorithm that determines the shortest paths needed to go from a starting node to any node in a graph. In this article, the process and results of an activity that included route formation among the provinces in the Aegean region using Dijkstra's algorithm are shared. The activity was designed based on a mathematical modeling process (real life problem, mathematical problem, mathematical solution, interpreting the solution). The activity was implemented with 15 middle school students attending a Science and Art Center. The students actively participated in the activity and throughout the lesson they tried to solve the problem. The students successfully implemented the algorithm and completed the problem solving process. Future applications of this activity can be planned by taking into account some student difficulties (e.g., simple erros, not drawing the route although the value of nodes are calculated correctly) observed in this application.