My five year old wanted lots of little paper boxes for a pretend store and I wanted a way in which he could make some by himself. So I devised this method:
Take a standard sheet of printer paper. Make a hamburger fold. (A hamburger fold is a fold that divides the long-side of the sheet in two, making the resulting piece short and fat. The opposite of a hamburger fold is a hotdog fold, which divides the short side of a sheet in two and leaves you with a paper that looks long and thin like a hotdog.)
Now make a second fold the same direction. This fold is going to be a hotdog fold. Take a moment to admire the wonder and amazement that doing a fold the same direction twice creates different results.
Now you should have a piece of paper folded so that it is four layers thick, long and thin. Fold this band of paper into thirds the other direction.
Then unfold the whole thing. You should have a piece of paper with crease-lines dividing it into twelve squares.
The next stage I described to my son as cutting the legs to make a caterpillar. For each of the sides that has four squares and three crease lines, cut the three crease lines up to the end of one square.
In the second picture I’ve highlighted the pieces of the paper that will be the walls and lid of the box. Take three squares from the same side of the “caterpillar” and layer them on top of each other. Glue or staple them together to make one wall of the box. Then do the same thing to the three squares on the other side of the caterpillar.
The three squares become the lid with two long sides flaps that can be tucked in to hold the lid down.