Build a multi-level structure
Using boxes laid on their sides, build a structure with different levels.
We started with balsa wood boxes, like the kind you get when you purchase clementines. They stood up well, but they were hard to knock down. However, they might be a good choice for older children or mixed in with shoe boxes.
For structures built entirely with shoeboxes, you might need to put some shoe boxes behind the main structure to hold it upright until the game starts. You also might avoid playing the game on a windy day.