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Recent years have seen a rapid reduction in the summer Arctic sea ice extent. To both understand this trend and project the future evolution of the summer Arctic sea ice, a better understanding of the physical processes that drive the seasonal loss of sea ice is required. The marginal ice zone, here defined as regions with between 15 % and 80 % sea ice cover, is the region separating pack ice from the open ocean. Accurate modelling of this region is important to understand the dominant mechanisms involved in seasonal sea ice loss. Evolution of the marginal ice zone is determined by complex interactions between the atmosphere, sea ice, ocean, and ocean surface waves. Therefore, this region presents a significant modelling challenge. Sea ice floes span a range of sizes but sea ice models within climate models assume they adopt a constant size. Floe size influences the lateral melt rate of sea ice and momentum transfer between atmosphere, sea ice, and ocean, all important processes within the marginal ice zone. In this study, the floe size distribution is represented as a power law defined by an upper floe size cut-off, lower floe size cut-off, and power-law exponent. This distribution is also defined by a new tracer that varies in response to lateral melting, wave-induced break-up, freezing conditions, and advection. This distribution is implemented within a sea ice model coupled to a prognostic ocean mixed-layer model. We present results to show that the use of a power-law floe size distribution has a spatially and temporally dependent impact on the sea ice, in particular increasing the role of the marginal ice zone in seasonal sea ice loss. This feature is important in correcting existing biases within sea ice models. In addition, we show a much stronger model sensitivity to floe size distribution parameters than other parameters used to calculate lateral melt, justifying the focus on floe size distribution in model development. We also find that the attenuation rate of waves propagating under the sea ice cover modulates the impact of wave break-up on the floe size distribution. It is finally concluded that the model approach presented here is a flexible tool for assessing the importance of a floe size distribution in the evolution of sea ice and is a useful stepping stone for future development of floe size modelling.