Ordering the selection of training data using active learning can lead to improvements in learning efficiently from smaller corpora. We present an exploration of active learning approaches applied to three grounded language problems of varying complexity in order to analyze what methods are suitable for improving data efficiency in learning. We present a method for analyzing the complexity of data in this joint problem space, and report on how characteristics of the underlying task, along with design decisions such as feature selection and classification model, drive the results. We observe that representativeness, along with diversity, is crucial in selecting data samples.