The story in three lines. Lan and Inkling fold Kami in half and in half again, and step into a school hallway in California in January 2002. Sam's grandpa says no paper can be folded in half more than seven times, and Sam's square is stuck at six. Lan nearly stamps it flat before Mark stops her. Reading a drawing that counts the layers, the cast fold a long, thin strip of till paper eight times and Inkling works out the two hundred and fifty-six layers, while far down the hallway a teenage girl folds a much longer strip.

One question to ask. "Why could the long strip be folded more times than the square?" The answer the story wants: every fold doubles the layers, so each new fold has to bend round a thicker stack, and that takes more paper. Then ask how many layers eight folds make.

One thing to do at the table. Fold an ordinary sheet in half as many times as you can, counting the layers out loud each time: 1, 2, 4, 8, 16, 32. Then try a long strip cut from the edge of a newspaper, folding it the same way every time. Write the numbers in a column and look at how fast they grow.

The grown-up layer. In January 2002 Britney Gallivan, a high-school student in California, folded a strip of toilet paper about 1,200 metres long in half twelve times in the same direction. A month earlier she had worked out how long a strip must be for each number of folds. The layers double with every fold, so the paper needed grows even faster. Doubling is the idea behind halving, powers of two, and why a small change can grow very large.

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