Students were divided into teams of 5. Each team received a box that was labeled Top Secret. In each box, we put a variety of supplies - marshmallows & spaghetti, tape and popsicle sticks, clay and straws, etc. Basically a variety of something that is tall and something that can connect.
Once each team received their box, their challenge was to build a tower. We had multiple categories for which the students could aim for, including Tallest Tower, Most Exotic & Sturdiest.
The teams began and after working with their materials, some realized they could borrow from other teams. Before long, teams started combining, and in the end we had three very distinct towers built.
I really liked this activity because it gave the kids a tangible challenge in which they had limited supplies, but room for whatever creativity their brains wandered upon - and they had to work together. There were clear parameters (the supplies and their original groups) but also a lot of room for exploration and creative thinking.