This paper targets on solving the high collision problem in the massive machine-to-machine communications. The main idea is to restrict the numbers of allowable contentions to the low-energy devices (LEDs) by using the proposed make-or-break (MOB) backoff scheme such that the unnecessary energy consumption can be reduced. And, consequently, the high-energy devices (HEDs) can have higher probability to attain time slots for data transmissions. However, the restriction mechanism may detain the data forwarding process. To solve this dilemma, the adaptive frame structure is developed to compensate the loss of throughput. The analytical as well as simulation results demonstrate that with a huge amount of machine type devices (MTDs), the proposed scheme can outperform the conventional counterpart in the aspects of the head-of-line delay, energy efficiency and accommodation of the MTDs.