We present three problems modeled after animal learning experiments designed to test online state construction or representation learning algorithms. Our test problems require the learner to construct compact summaries of their past interaction with the world in order to predict the future, updating online and incrementally on each time step without an explicit training-testing split. The majority of recent work in Deep Reinforcement Learning focuses on either fully observable tasks, or games where stacking a handful of recent frames is sufficient for good performance. Current benchmarks used for evaluating memory and recurrent learning make use of 3D visual environments (e.g., DeepMind Lab) which require billions of training samples, complex agent architectures, and cloud-scale compute. These domains are thus not well suited for rapid prototyping, hyper-parameter study, or extensive replication study. In this paper, we contribute a set of test problems and benchmark results to fill this gap. Our test problems are designed to be the simplest instantiation and test of learning capabilities which animals readily exhibit, including (1) trace conditioning (remembering a cue in order to predict another far in the future), (2) positive/negative patterning (a combination of cues predict another), (3) and combinations of both with additional non-relevant distracting signals. We provide baselines for the first problem including heuristics from the early days of neural network learning and simple ideas inspired by computational models of animal learning. Our results highlight the difficulty of our test problems for online recurrent learning systems and how the agent's performance often exhibits substantial sensitivity to the choice of key problem and agent parameters.