Vibes,
SIN-EWR is normally over the N Pacific, across Canada to the Toronto area, then on to EWR. Occasionally they take the polar route, I believe.
EWR-SIN is one of two routes: polar, which is due north from EWR to the North Pole, then Russia and China (incl. Hong Kong FIR) and on to SIN, and North Atlantic, northern Fennoscandia, Russia and on to SIN. The polar route is not used during the winter months as air temperatures in the polar region are too low and fuel freezing is a danger.
You can follow the flight path of SIA 21 and 22 in N American airspace (at least part of it) on Aeroseek.com (in combination with Google Earth). If SIA 21(EWR-SIN) heads due north from the New York area, you know it's on the polar route but the coverage normally stops somewhere over northern Quebec. If it's heading toward Boston and New Brunswick, it's doing the N Atlantic. SIA 22 (SIN-EWR) can be followed all the way from off the British Columbia and Alaska coast to EWR.
Rockhound