board and use an up-down sawing motion all around the outline. Assembling Without Glue: If you are working with a cardboard box, you can assemble the usual box-way, for instance, tucking in the flaps: When making flat structures (like cardboard cookies and that fraction puzzle ), Elmer's White Glue works OK. It's especially safe for children. When making 3D structures however, I don't use Elmer's White Glue. It's strong enough for wood, yes, but it dries slowly and requires either a clamp or someone to actually hold the pieces together in place overnight. If I am joining two pieces that don't require special, fiddly positioning, I use a hot glue gun. It's fast and strong. Otherwise, I use my UHU craft glue - it's fast, but not instant like hot glue. I can slide things around to position them for a few seconds before it dries. If you remember, attaching thin cardboard together at their edges requires an overlap tab. Thick corrugated cardboard, having an actual edge of its own, doesn't require a tab. Glue can be applied directly to the edge to adhere it to a surface. Here is a series of pictures to show you how a curved surface was glued to a flat circular base - this was Rapunzel's Tower from here : How Do I Design Cardboard Structures? Ah, the million-dollar question. I don't know. You'd have to look around you and get inspired, I guess. Look at architecture. Look at toys. Let the ideas percolate