There are 3 methods to divide a pregnancy: Development, Gestation, and Conception.
Development marks 12 weeks as the end of the first Tri, because all major organs have formed and baby officially becomes a fetus.
Gestation divides 40 weeks by 3, which means 13w3d is the end of 1st Tri.
Conception takes the 38 weeks after conception, divides by 3 then adds two weeks. This puts the end of 1st Tri at 14w5d.
I personally prefer the development method. Once major organ systems have formed and the baby becomes a fetus the risk of m/c is greatly lowered as well as the risk for major birth defects. Also, that means second tri is that much closer and that makes me happy.