The story in three lines. Lan and Inkling fold Kami into a little paper roof and step into a London printing room in 1871, where Nell's father prints the proofs of wood-engraved book pictures and the ink flies into his hair. He has left his paper cap at home, and the only paper Nell may use is a long sheet of newspaper. Lan nearly cuts it square before Mark stops her. Reading the printed picture of a carpenter in a folded hat, the cast fold the newspaper hat from the long sheet, and it stays on all afternoon at the press, which Inkling checks before she names it.

One question to ask. "Why was the long sheet the right shape after all?" The answer the story wants: the hat's pointed roof uses two corners, and the brim needs paper left over underneath, so the sheet has to be longer than it is wide. Then ask what went wrong when the second corner went past the middle line.

One thing to do at the table. Take a sheet of newspaper, or any paper longer than it is wide. Fold the top edge down to the bottom edge. Make a soft middle crease, fold both top corners down to it, then fold one bottom strip up in front and one up behind. Try it on. Then try the same folds with a square, and talk about why the square makes a smaller, stubbier hat.

The grown-up layer. Printers, carpenters, masons and painters once folded paper hats from newspaper to keep ink, dust and paint off their hair. John Tenniel drew the Carpenter in Through the Looking-Glass (1871) wearing the box-shaped version, which begins as this simple newspaper hat. Most paper folding starts from a square, but not all of it: the shape of the sheet is part of the design.

Let your child tell the story back in their own words first.