Well I am a school social worker and don't work with this age now, but did for many years. I have a million of these but I will just share a few. Some good ones that I have done is the lego building one (which I thought of first due to the name of the group, LOL). You build something with lego's and put it in the other room and allow one member of the team to go and see it and then go back and help the team to replicate it. After they try for a bit you let another member come in and see it and go back. It's really great. Although you may have to make it pretty complicated based on the group. If there are lot of kids you could do 2 groups....but I find when you do that then there is more competition and less team building.
Also a simple one is the paper tower. The group gets a stack of plain 8 1/2 x 11 paper and is asked to work together and build the tallest tower they can only using the paper they have. (the tallest way I have seen done is to fold the paper into triangles the long way and pile them up on top of eachother at an angle. You can get at least 3-4 that way). But who knows GT kids may find different ways. It's interesting to watch and see what they come up with. then you talk after about how it worked, what roles people took, how people handled frustration (well I do all that because that is the point...but I guess that's not your point so you wouldn't have to do all that).
One more, there is a game called over under through. you need 2 long ropes and some sort of stands to tie them to (trees, volleyball stands, etc.). Tie two ropes horizontally between the two stands so there is enough room for each member of the group to get his body between the two ropes...but will need some help to do this. The height of the rope can vary based on your group. Then you challenge the group to get all it's members from one side to the other successfully...but they have to follow the rules. Which are: no one may touch the ropes at any time or the whole team starts over; one person must go over the top of the highest rope; one person must go under the lowest rope; the rest of the team must go between the two ropes; and you may not go around the ropes. This is a really fun activity if you have the stuff for it.
Hope some of those are helpful.
