In this study, we analyse the students’ performances while working on a teaching material that is designed to study some families of functions, through the mathematical modelling of physical phenomena and the use of iPads. This study is done following the theoretical and methodological framework of the Local Theoretical Models. Our research aim is to develop a Local Theoretical Model and to collect, analyse and explain the students' performances when they work in a teaching model that takes into account the use of technology and the incorporation of an analysis of the qualitative properties of the phenomena and the families of functions in the teaching material itself. A study of a group and a case study were conducted. The study of the group was carried out in a class of 16 Year 11 students and they were asked to study three phenomena: the bounce of a ball, the lengthening of a spring and the cooling of a liquid. The structure of the lessons were: first, to analyse the qualitative properties of the phenomena and the families of functions; second, to represent the phenomenon in classroom and take the data using the apps Video Physics and Graphical Analysis; third, to find the formula of a function which describes the phenomenon trying to fit a graph to the data using the app Desmos; fourth, answer several questions to study the characteristics of the function and its adequacy in relation to the phenomenon in more detail. Afterwards, 4 students were selected to participate in a case study that consisted of an interview with teaching, in which selected students had to study a fourth phenomenon: the heating of an object. After analysing the data, we found that apps: 1) allowed the students to focus on the central actions of the tasks, making calculations or representing graphs for them; 2) made them to reflect on the reference taking and the definition of variables; 3) let them give different meanings to the parameters in the formula in relation to the types of transformations of the graph. Regarding the qualitative analysis of the phenomena, it was found that it is a key element in the management and control of the modelling process, influencing students’ decision-making, allowing them to validate the function chosen as a model and verifying if their previous decisions or ideas were correct. Finally, a students’ tendency to base their answers in their prior conceptions about height and lengthening was observed and also difficulties related to the description of the phenomena and the exponential function.In this study, we analyse the students’ performances while working on a teaching material that is designed to study some families of functions, through the mathematical modelling of physical phenomena and the use of iPads. This study is done following the theoretical and methodological framework of the Local Theoretical Models. Our research aim is to develop a Local Theoretical Model and to collect, analyse and explain the students' performances when they work in a teaching model that takes into account the use of technology and the incorporation of an analysis of the qualitative properties of the phenomena and the families of functions in the teaching material itself. A study of a group and a case study were conducted. The study of the group was carried out in a class of 16 Year 11 students and they were asked to study three phenomena: the bounce of a ball, the lengthening of a spring and the cooling of a liquid. The structure of the lessons were: first, to analyse the qualitative properties of the phenomena and the families of functions; second, to represent the phenomenon in classroom and take the data using the apps Video Physics and Graphical Analysis; third, to find the formula of a function which describes the phenomenon trying to fit a graph to the data using the app Desmos; fourth, answer several questions to study the characteristics of the function and its adequacy in relation to the phenomenon in more detail. Afterwards, 4 students were selected to participate in a case study that consisted of an interview with teaching, in which selected students had to study a fourth phenomenon: the heating of an object. After analysing the data, we found that apps: 1) allowed the students to focus on the central actions of the tasks, making calculations or representing graphs for them; 2) made them to reflect on the reference taking and the definition of variables; 3) let them give different meanings to the parameters in the formula in relation to the types of transformations of the graph. Regarding the qualitative analysis of the phenomena, it was found that it is a key element in the management and control of the modelling process, influencing students’ decision-making, allowing them to validate the function chosen as a model and verifying if their previous decisions or ideas were correct. Finally, a students’ tendency to base their answers in their prior conceptions about height and lengthening was observed and also difficulties related to the description of the phenomena and the exponential function.