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Cluster mergers leave distinct signatures in the ICM in the form of shocksand diffuse cluster radio sources that provide evidence for the acceleration ofrelativistic particles. However, the physics of particle acceleration in theICM is still not fully understood. Here we present new 1-4 GHz Jansky VeryLarge Array (VLA) and archival Chandra observations of the HST Frontier FieldsCluster Abell 2744. In our new VLA images, we detect the previously known$\sim2.1$ Mpc radio halo and $\sim1.5$ Mpc radio relic. We carry out a radiospectral analysis from which we determine the relic's injection spectral indexto be $\alpha_{\rm{inj}} = -1.12 \pm 0.19$. This corresponds to a shock Machnumber of $\mathcal{M}$ = 2.05$^{+0.31}_{-0.19}$ under the assumption ofdiffusive shock acceleration. We also find evidence for spectral steepening inthe post-shock region. We do not find evidence for a significant correlationbetween the radio halo's spectral index and ICM temperature. In addition, weobserve three new polarized diffuse sources and determine two of these to benewly discovered giant radio relics. These two relics are located in thesoutheastern and northwestern outskirts of the cluster. The correspondingintegrated spectral indices measure $-1.81 \pm 0.26$ and $-0.63 \pm 0.21$ forthe SE and NW relics, respectively. From an X-ray surface brightness profile wealso detect a possible density jump of $R=1.39^{+0.34}_{-0.22}$ co-located withthe newly discovered SE relic. This density jump would correspond to a shockfront Mach number of $\mathcal{M}=1.26^{+0.25}_{-0.15}$.

VLA Radio Observations of the HST Frontier Fields Cluster Abell 2744: The Discovery of New Radio Relics