Box and Draper suggested two methods for augmenting resolution III fractional replications of a 2nexperiment. One method identifies a particular factor of interest and augments the design to obtain estimates of the corresponding main effect and all two-factor interactions involving that factor so that they are not aliased with other two-factor interactions. The second method provides an augmented design that allows one to estimate all main effects unaliased with two-factor interactions. In particular, the second method provides foldover designs. Both methods consist of adding another fraction to the original design. The purpose of this note is to show how these augmentation methods can be obtained as fractional replications of a larger design involving an additional blocking factor. This provides both a simple justification of the blocking methods and a basis for discussing hidden block effects.