In this paper, we investigate the performance of multiple-input multiple-output (MIMO) fading channels assisted by a reconfigurable intelligent surface (RIS), through the employment of partition-based RIS schemes. The proposed schemes are implemented without requiring any channel state information knowledge at the transmitter side; this characteristic makes them attractive for practical applications. In particular, the RIS elements are partitioned into sub-surfaces, which are periodically modified in an efficient way to assist the communication. Under this framework, we propose two low-complexity partition-based schemes, where each sub-surface is adjusted by following an amplitude-based or a phase-based approach. Specifically, the activate-reflect (AR) scheme activates each sub-surface consecutively, by changing the reflection amplitude of the corresponding elements. On the other hand, the flip-reflect (FR) scheme adjusts periodically the phase shift of the elements at each sub-surface. Through the sequential reconfiguration of each sub-surface, an equivalent parallel channel in the time domain is produced. We analyze the performance of each scheme in terms of outage probability and provide expressions for the achieved diversity-multiplexing tradeoff. Our results show that the asymptotic performance of the considered network under the partition-based schemes can be significantly enhanced in terms of diversity gain compared to the conventional case, where a single partition is considered. Moreover, the FR scheme always achieves the maximum multiplexing gain, while for the AR scheme this maximum gain can be achieved only under certain conditions with respect to the number of elements in each sub-surface.