Researchers pointed at modelling activities as affecting positively students’ learning including motivation to learn, but little research has studied students’ motivation to learn mathematics during their engagement in modelling activities with technology. Three groups of 4-5 students carried out the Roc modelling activity utilizing the internet and GeoGebra. The data was collected using video recording and students’ solution texts. Inductive and deductive content analysis were used to analyze the data. The research results indicated that the groups experienced motivational patterns that included both sympathy and mastery styles, where these styles were accompanied with confirming styles in general, but sometimes with rebellious styles too. In addition, carrying out the modelling activity using the internet and GeoGebra, the group members were engaged primarily with processes-based motivational styles, but doing so, they kept in mind their goal to build a mathematical model of the Roc bird.