We present a new Convolutional Neural Network (CNN) model for text classification that jointly exploits labels on documents and their component sentences. Specifically, we consider scenarios in which annotators explicitly mark sentences (or snippets) that support their overall document categorization, i.e., they provide rationales. Our model exploits such supervision via a hierarchical approach in which each document is represented by a linear combination of the vector representations of its component sentences. We propose a sentence-level convolutional model that estimates the probability that a given sentence is a rationale, and we then scale the contribution of each sentence to the aggregate document representation in proportion to these estimates. Experiments on five classification datasets that have document labels and associated rationales demonstrate that our approach consistently outperforms strong baselines. Moreover, our model naturally provides explanations for its predictions.