How does a child's vocabulary production change over time? Past research has often focused on characterizing population statistics of vocabulary growth. In this work, we develop models that attempt to predict when a specific word will be learned by a particular child. The models are based on two qualitatively different sources of information: a representation describing the child (age, sex, and quantifiers of vocabulary skill) and a representation describing the specific words a child knows. Using longitudinal data from children aged 15-36 months collected at the University of Colorado, we constructed logistic regression models to predict each month whether a word would be learned in the coming month. Models based on either the child representation or the word representation outperform a baseline model that utilizes population acquisition norms. Although the child- and word-representation models perform comparably, an ensemble that averages the predictions of the two separate models obtains significantly higher accuracy, indicating that the two sources of information are complementary. Through the exploration of such models, we gain an understanding of the factors that influence language learning, and this understanding should inform cognitive theories of development. On a practical level, these models may support the development of interventions to boost language acquisition.