Cluster mergers leave distinct signatures in the intracluster medium (ICM) in the form of shocks and diffuse cluster radio sources that provide evidence for the acceleration of relativistic particles. However, the physics of particle acceleration in the ICM is still not fully understood. Here we present new 1-4 GHz Jansky Very Large Array (VLA) and archival Chandra observations of the HST Frontier Fields Cluster Abell 2744. In our new VLA images, we detect the previously known ∼2.1 Mpc radio halo and ∼1.5 Mpc radio relic. We carry out a radio spectral analysis from which we determine the relic's injection spectral index to be . This corresponds to a shock Mach number of under the assumption of diffusive shock acceleration. We also find evidence for spectral steepening in the post-shock region. We do not find evidence for a significant correlation between the radio halo's spectral index and ICM temperature. In addition, we observe three new polarized diffuse sources and determine two of these to be newly discovered giant radio relics. These two relics are located in the southeastern and northwestern outskirts of the cluster. The corresponding integrated spectral indices measure -1.81 0.26 and -0.63 0.21 for the SE and NW relics, respectively. From an X-ray surface brightness profile we also detect a possible density jump of co-located with the newly discovered SE relic. This density jump would correspond to a shock front Mach number of .