Precise measurements of Arctic sea ice mass balance are necessary to understand the rapidly changing sea ice cover and its representation in climate models. During the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition, we made repeat point measurements of snow and ice thickness on primarily level first- and second-year ice (FYI, SYI) using ablation stakes and ice thickness gauges. This technique enabled us to distinguish surface and bottom (basal) melt and characterize the importance of oceanic versus atmospheric forcing. We also evaluated the time series of ice growth and melt in the context of other MOSAiC observations and historical mass balance observations from the Surface Heat Budget of the Arctic (SHEBA) campaign and the North Pole Environmental Observatory (NPEO). Despite similar freezing degree days, average ice growth at MOSAiC was greater on FYI (1.67 m) and SYI (1.23 m) than at SHEBA (1.45 m, 0.53 m), due in part to initially thinner ice and snow conditions on MOSAiC. Our estimates of effective snow thermal conductivity, which agree with SHEBA results and other MOSAiC observations, are unlikely to explain the difference. On MOSAiC, FYI grew more and faster than SYI, demonstrating a feedback loop that acts to increase ice production after multi-year ice loss. Surface melt on MOSAiC (mean of 0.50 m) was greater than at NPEO (0.18 m), with considerable spatial variability that correlated with surface albedo variability. Basal melt was relatively small (mean of 0.12 m), and higher than NPEO observations (0.07 m). Finally, we present observations showing that false bottoms reduced basal melt rates in some FYI cases, in agreement with other observations at MOSAiC. These detailed mass balance observations will allow further investigation into connections between the carefully observed surface energy budget, ocean heat fluxes, sea ice, and ecosystem at MOSAiC and during other campaigns.