Do we have to teach the EngageNY or Common Core curriculum modules in order?

The implementation of Common Core curriculum is a local decision in New York State, and you are certainly able to teach the modules in any order that fits best with your classroom.

When it comes to the possibility of eliminating a module, two questions need to be considered: 1) are you maintaining the balance of informational and literary texts, and 2) are all the standards still being covered? 

A minor consideration is whether modules you might be eliminating mention an activity, text, or protocol that will be needed in a later module or vice versa (a later module references an activity, text, or protocol that was eliminated from a previous module). This is something that can easily be adjusted for but teachers should be aware of this possibility.