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Computer-based simulations and real materials influence students’ understanding of functional relationships in different ways. Based on written responses of an intervention study to foster functional thinking in Mathematics with materials or simulations, we conducted a qualitative content analysis and analyzed students’ justifications of assigning graph and situation. We found that using real materials made students focus on states and single points on a graph. The use of simulations enhanced students to think about change and encouraged them to use the graph for argumentation. Different abilities, necessary to work with graphs of functions were promoted. As a consequence, the use of simulations and real materials should be combined to reach the most beneficial fostering of understanding functional relationships.