Smart homes provide support to cognitively impaired people (such as those suffering from Alzheimer's disease) so that they can remain at home in an autonomous and safe way. In order to be efficient and responsive, cognitive assistance requires models of this impaired population. This paper presents a way to model and simulate the progression of dementia of the Alzheimer's type by evaluating performance in the execution of an activity of daily living (ADL). This model satisfies three objectives: first, it models an activity of daily living; second, it simulates the progression of the dementia and the errors potentially made by people suffering from it, and, finally, it simulates the support needed by the impaired person. To develop this model, we chose the ACT-R cognitive architecture, which uses symbolic and subsymbolic representations. The simulated results of 100 people suffering from Alzheimer's disease closely resemble the results obtained by 106 people on an occupational assessment (the Kitchen Task Assessment).