Today from Bedtime Math: When Books Flip Upside Down

When you read a book and flip through the pages, do you ever wonder how that book was made? The printers don't print little pages and then stick them together. They actually print 8 or more pages at once on a really huge sheet of paper. Then they fold the paper in half, then in half again, and in half again, until they have 8, 16 or even more layers. They slice off the edges so the papers can peel apart, and you have a book! A sheet that makes 4 rectangles of paper has 8 pages, since there are words on both sides; that's called a "quarto." An "octavo" makes 16 pages, and the sheets keep doubling to as high as 128 pages. Of course, some pages end up flipping over, so the words on those had to be printed upside-down to start. It takes a lot of geometry thinking to line up each page the right way, or you're going to have to read half that book upside-down.

Wee ones: How many sides does a rectangle have?

Little kids: If you fold a piece of paper in half and then in half again, then unfold it, how many rectangle sections does it now have? (If you want, try it with a piece of paper to see!) Bonus: What if you fold it in half one more time before unfolding - now how many sections does it have?

Big kids: If you stack 4 long pieces of paper, staple in the middle, and fold the whole thing over to make a 16-page book (with the very front as page 1), which 2 page numbers face each other in the middle? Bonus: If you fold the top half of a piece of paper down over the bottom, then fold the left side over to the right, you'll have 8 pages. If the front page is 1, where did the words on page 3 start off on the sheet? (See if you can fold it in your head! or else try with a real piece of paper.)

Answers:

Wee ones: 4 sides.

Little kids: 4 sections. Bonus: 8 sections.

Big kids: Pages 8 and 9, the two middle numbers counting from 1 to 16. Bonus: The top left corner facing front.