We propose a joint model that performs instance-level feature selection and classification. For a given case, the joint model first skims the full feature vector, decides which features are relevant for that case, and makes a classification decision using only the selected features, resulting in compact, interpretable, and case-specific classification decisions. Because the selected features depend on the case at hand, we refer to this approach as context-aware feature selection and classification. The model can be trained on instances that are annotated by experts with both class labels and instance-level feature selections, so it can select instance-level features that humans would use. Experiments on several datasets demonstrate that the proposed model outperforms eight baselines on a combined classification and feature selection measure, and is able to better emulate the ground-truth instance-level feature selections. The supplementary materials are available at https://github.com/IIT-ML/IJCAI23-CFSC.