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As the demand for wireless data grows to unprecedented levels, cellular service providers have been investigating different ways to meet this growing demand. The deployment of small cells with reduced transmission powers and reduced coverage areas is being considered as one potential solution. Using the same spectrum employed by existing macro cells, small cells allow increased spatial reuse of bandwidth, thus providing the potential for improved user rates. One challenge for small cells, though, is that due to their weaker signals (lower transmission powers, antennas with smaller antenna gains), the coverage area tends to be significantly reduced and the incremental benefit of deploying each small cell is limited. In this paper, resource partitioning is proposed along with suitably modified cell selection criteria to improve the performance of heterogeneous networks comprising small and macro cells that operate in the same swath of spectrum. Our simulation results demonstrate that with four small cells deployed per sector, 5%-ile and 50%-ile user throughputs both improve by ~150% relative to the same case without resource partitioning.