Folding, Cutting and Punching

A. This is a piece of A4 paper. There are two folds. How is it folded? If I cut down the red line how many pieces will I get?

With one cut it is easy to produce two separate pieces from a sheet of paper but can you produce three pieces by folding and making one straight cut?
What about four pieces?
Five pieces?
Can you explain any results?

B. Here is my folded piece of A4 paper again. If I made two holes with a hole-punch where they are marked, how many holes do you think there will be when the paper is unfolded?

Now fold your piece of paper and make a hole with a hole-punch.

Try predicting what the paper will look like when it is opened out.

You could sketch how you think the folds and the holes will appear.

Try making different folds and a different number of holes.

Can you explain any results?

C. You can explore spirals by systematically cutting paper in half and placing down the remainder of the paper to make a pattern.

Here is one idea:

Try other ways to cut your paper or place it on the other bits in a different pattern.