Models related to the topic of chemical kinetics are critical for predicting and explaining chemical reactivity. Here we present a qualitative study of 15 general chemistry students' reasoning about a method of initial rates task. We asked students to discuss their understanding of the terms rate law and initial rate, and then analyze rate and concentration data in order to construct a rate law. We also asked participants to critique rate laws constructed by hypothetical students. We discuss five patterns in the students' approach to the method of initial rates task, ranging from the use of surface-features, such as stoichiometric coefficients in the construction of a rate law, to more sophisticated interpretations and mathematization of the trends in the data. Findings highlight specific difficulties with inter-related competences required to engage in the task, such as interpreting data and reasoning mathematically, and provide insight into assessment strategies for similar tasks.