State abstraction is an effective technique for planning in robotics environments with continuous states and actions, long task horizons, and sparse feedback. In object-oriented environments, predicates are a particularly useful form of state abstraction because of their compatibility with symbolic planners and their capacity for relational generalization. However, to plan with predicates, the agent must be able to interpret them in continuous environment states (i.e., ground the symbols). Manually programming predicate interpretations can be difficult, so we would instead like to learn them from data. We propose an embodied active learning paradigm where the agent learns predicate interpretations through online interaction with an expert. For example, after taking actions in a block stacking environment, the agent may ask the expert: "Is On(block1, block2) true?" From this experience, the agent learns to plan: it learns neural predicate interpretations, symbolic planning operators, and neural samplers that can be used for bilevel planning. During exploration, the agent plans to learn: it uses its current models to select actions towards generating informative expert queries. We learn predicate interpretations as ensembles of neural networks and use their entropy to measure the informativeness of potential queries. We evaluate this approach in three robotic environments and find that it consistently outperforms six baselines while exhibiting sample efficiency in two key metrics: number of environment interactions, and number of queries to the expert. Code: https://tinyurl.com/active-predicates