Bemidbar 32:1-32 record negotiations between Moshe and the tribes of Gad and Reuven for land on the east bank of the Jordan River (see our discussion http://lobashamayim.blogspot.co.il/2011/07/bemidbar-chapter-32-other-side.html). Bemidbar 32:33 then records that Moshe gave some of the land on the east bank not just to the tribes of Gad and Reuven but also to half the tribe of Menashe. This is surprising since the tribe of Menahse had never been mentioned before in chapter 32 and had not requested land on the east bank. Why did Menashe get land on the east bank if they were not involved in the negotiations between Moshe and the tribes of Reuven and Gad? Why did only half the tribe of Menahse get land? Why was the tribe of Menashe divided by the Jordan River?
Ramban (on 32:33) explains that when the tribes of Reuven and Gad were granted land on the east bank, it was recognized that the land was too much for two tribes. Volunteers were asked who would want to live there and then some of the tribe of Menashe requested the land.
Luzzatto (on 32:33) suggests that after the deal with the tribes of Gad and Reuven was made, some members of the tribe of Menashe on their own took the initiative to conquer more land on the east bank, 32:39.
My guess is that since the deal with the tribes of Reuven and Gad separated these tribes from the other tribes due to the Jordan River, there was a desire to re-connect the tribes of Gad and Reuven with the other tribes. This was done by splitting another tribe that half of the tribe would be on the east side of the Jordan and half of the tribe would be on the west side. With this idea, we can apply the principle of transitivity. The tribes of Reuven and Gad would be connected with the split tribe on their side (the eastern side) of the Jordan River, the split tribe would be connected with its other half on the other side (the western side) of the Jordan River, and this half of the tribe would be connected with the remaining tribes who all lived on the western side of the Jordan River.
This same idea can also explain, why Moshe designated three cities of refuge on the east side of the Jordan River, see our discussion on Bemidbar 35:13,14 "Three and three."