If you fold a piece of paper and use a hole punch, can you predict the pattern you produce?
For this task, you'll need a hole punch and pieces of A6 paper ($\frac{1}{4}$ of an A4 sheet).
Take one piece of paper. Fold it in the way pictured below and then punch a hole as shown.
Can you guess where the holes will be before you unfold it? Were you right?
Now have a go at this one.
Can you guess where the holes will be before you unfold it? Were you right?
And what about this one?
Can you guess where the holes will be before you unfold it? Were you right?
What do you notice?
Can you fold up the paper and use the hole punch just once to make these patterns of holes?
How many holes can you make by folding the paper once? Twice? Three times?