Although this investigation cannot, perhaps, be extended as far as some, it is very useful for getting children to develop rules for how it works.
Start by giving everyone a sheet of A4 paper to cut into 4. This is made into a little book by putting the sheets together and folding. The pages are numbered starting on the outside at 1.
Sheets can then be omitted to make 3, 2 and even 1 page books, and two or more made into longer books (they will all need to be re-numbered). Making a table of results is a very useful exercise. Possible headings could be: number of sheets; number on last page; sum of numbers on one page. At this point a pattern should appear. Try to get some predictions going. (If some children cannot see what is happening get them to make a list of the two numbers on a sheet).
Some questions to ask if anyone is stuck:
The extra book given at the end is different because the numbering starts inside the cover.
An extension can be made by finding out about patterns of numbering the pages of books (possibly a child's picture book) which has pages which fold in.
