We study genus one fibered Calabi-Yau threefolds from the point of view of gauged linear sigma models. In the case of 5-sections this predicts the existence of homologically projective dual pairs. In the case of 6-sections this predicts equivalences with a particular class of noncommutative threefolds determined by the presence of a topologically nontrivial flat B-field. In either case, this analysis can be extended to yield predictions for higher genus Gopakumar-Vafa invariants.