Sea ice is composed of discrete units called floes. The size of these floes can determine the nature and magnitude of interactions between the sea ice, ocean, and atmosphere including lateral melt rate, momentum and heat exchange, and surface moisture flux. Large-scale geophysical sea ice models employ a continuum approach and traditionally either assume floes adopt a constant size or do not include an explicit treatment of floe size. Observations show that floes can adopt a range of sizes spanning orders of magnitude, from metres to tens of kilometres. In this study we apply novel observations to analyse two alternative approaches to modelling a floe size distribution (FSD) within the state-of-the-art CICE sea ice model. The first model considered, the WIPoFSD (Waves-in-Ice module and Power law Floe Size Distribution) model, assumes floe size follows a power law with a constant exponent. The second is a prognostic floe size-thickness distribution where the shape of the distribution is an emergent feature of the model and is not assumed a priori. We demonstrate that a parameterisation of in-plane brittle fracture processes should be included in the prognostic model. While neither FSD model results in a significant improvement in the ability of CICE to simulate pan-Arctic metrics in a stand-alone sea ice configuration, larger impacts can be seen over regional scales in sea ice concentration and thickness. We find that the prognostic model particularly enhances sea ice melt in the early melt season, whereas for the WIPoFSD model this melt increase occurs primarily during the late melt season. We then show that these differences between the two FSD models can be explained by considering the effective floe size, a metric used to characterise a given FSD. Finally, we discuss the advantages and disadvantages to these different approaches to modelling the FSD. We note that the WIPoFSD model is less computationally expensive than the prognostic model and produces a better fit to novel FSD observations derived from 2-m resolution MEDEA imagery but is unable to represent potentially important features of annual FSD evolution seen with the prognostic model.