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On rest and recovery days it is important to avoid doing the worst thing you can do for your body... nothing. Examples of rest and recovery activities are walking, static stretch exercises (after a warm up and loosening up period), dynamic stretching, swimming, water running, and riding a bike.
Active recovery is not done with the purpose of burning calories or improving gains; the role of rest days is to actually allow your muscles to recover and studies have showed that muscle protein synthesis increases rapidly after resistance training and is nearly double at 24 hours post-workout.