Spatiotemporal predictive learning, which predicts future frames through historical prior knowledge with the aid of deep learning, is widely used in many fields. Previous work essentially improves the model performance by widening or deepening the network, but it also brings surging memory overhead, which seriously hinders the development and application of this technology. In order to improve the performance without increasing memory consumption, we focus on scale, which is another dimension to improve model performance but with low memory requirement. The effectiveness has been widely demonstrated in many CNN-based tasks such as image classification and semantic segmentation, but it has not been fully explored in recent RNN models. In this paper, learning from the benefit of multi-scale, we propose a general framework named Multi-Scale RNN (MS-RNN) to boost recent RNN models for spatiotemporal predictive learning. We verify the MS-RNN framework by thorough theoretical analyses and exhaustive experiments, where the theory focuses on memory reduction and performance improvement while the experiments employ eight RNN models (ConvLSTM, TrajGRU, PredRNN, PredRNN++, MIM, MotionRNN, PredRNN-V2, and PrecipLSTM) and four datasets (Moving MNIST, TaxiBJ, KTH, and Germany). The results show the efficiency that RNN models incorporating our framework have much lower memory cost but better performance than before. Our code is released at \url{https://github.com/mazhf/MS-RNN}.