Accurate per-flow monitoring is critical for precise network diagnosis, performance analysis, and network operation and management in general. However, the limited amount of memory available on modern programmable devices and the large number of active flows force practitioners to monitor only the most relevant flows with approximate data structures, limiting their view of network traffic. We argue that, due to the skewed nature of network traffic, such data structures are, in practice, heavily underutilized, i.e. sparse, thus wasting a significant amount of memory. This paper proposes a Sparse Approximate Data Structure (SPADA) representation that leverages sparsity to reduce the memory footprint of per-flow monitoring systems in the data plane while preserving their original accuracy. SPADA representation can be integrated into a generic per-flow monitoring system and is suitable for several measurement use cases. We prototype SPADA in P4 for a commercial FPGA target and test our approach with a custom simulator that we make publicly available, on four real network traces over three different monitoring tasks. Our results show that SPADA achieves 2× to 11× memory footprint reduction with respect to the state-of-the-art while maintaining the same accuracy, or even improving it.