IEEE802.16e is expected to support mobility for broadband wireless access with the capability of delivering high data rates over long ranges. We consider IEEE 802.216e scheme for scheduling and mapping higher layer data into the basic resource allocation units (slots) of OFDMA frames. Then, we introduce two simple allocation schemes that consider fair allocation among users with adaptive modulation. Both scheduling and mapping approaches are based on the quality of service (QoS) requirements of each service flow in terms of data rate and bit error rate (BER). The performance of both algorithms is studied by simulation. The results show that the proposed algorithms yield fairness among real-time and non real-time service flows as well as guaranteeing their constraint in term of QoS and outage probability.