Studies of scientific practice demonstrate that the development of scientific models is an enactive and emergent process (e.g., Pickering 1995; Chandrasekharan and Nersessian 2017). Scientists make meaning through processes such as perspective taking, finding patterns, and following intuitions. In this paper, we focus on how a group of fourth grade learners and their teacher engaged in interpretation in ways that align with core ideas and practices in kinematics and computing. Cycles of measuring and modeling--including computer programming--helped to support classroom interactions that highlighted the interpretive nature of modeling and participation in model construction as a knowledge-building process. We draw on literature from the history and philosophy of science in order to analyze the students' interpretive actions as forms of epistemic and representational agency, constituting a construct we term "disciplined interpretation." We demonstrate how students' disciplined interpretative moves help to position them as owners of their own design decisions and their rights to interpret the phenomena they were modeling, data collected from those phenomena, and the scientific and computational models themselves. We present four extended episodes that characterize the nature of activity in the classroom and the development of students' disciplined interpretations in terms of learning to recognize scientific patterns amid complex perceptual fields, and to represent them in ways that support sensemaking.