Current successes of machine learning architectures are based on computationally expensive algorithms and prohibitively large amounts of data. We need to develop tasks and data to train networks to reach more complex and more compositional skills. In this paper, we illustrate Blackbird's language matrices (BLMs), a novel grammatical dataset developed to test a linguistic variant of Raven's progressive matrices, an intelligence test usually based on visual stimuli. The dataset consists of 44800 sentences, generatively constructed to support investigations of current models' linguistic mastery of grammatical agreement rules and their ability to generalise them. We present the logic of the dataset, the method to automatically construct data on a large scale and the architecture to learn them. Through error analysis and several experiments on variations of the dataset, we demonstrate that this language task and the data that instantiate it provide a new challenging testbed to understand generalisation and abstraction.