Pragmatics is foundational to language use and learning. Computational cognitive models have been successfully used to predict pragmatic phenomena in adults and children – on an aggregate level. It is unclear if they can be used to predict behavior on an individual level. We address this question in children (N = 60, 3- to 5-year-olds), taking advantage of recent work on pragmatic cue integration. In Part 1, we use data from four independent tasks to estimate child-specific sensitivity parameters to three information sources: semantic knowledge, expectations about speaker informativeness, and sensitivity to common ground. In Part 2, we use these parameters to generate participant-specific trial-by-trial predictions for a new task that jointly manipulated all three information sources. The model accurately predicted children’s behavior in the majority of trials. This work advances a substantive theory of individual differences in which the primary locus of developmental variation is sensitivity to individual information sources.