  In this paper, we are interested in obtaining a unified approach for
$C^{1,\alpha}$ estimates for weak solutions of quasilinear parabolic equations,
the prototype example being \[
  u_t - \text{div} (|\nabla u|^{p-2} \nabla u) = 0. \] without having to
consider the singular and degenerate cases separately. This is achieved via a
new scaling and a delicate adaptation of the covering argument developed by
E.~DiBenedetto and A.~Friedman.
