# Folding and Cutting

Below is a picture of a piece of A4 paper. There are two folds.

Can you see how it is folded?  (Take a look here if you'd like to be shown.)

If I cut down the dotted line how many pieces will I get?

With one cut it is easy to produce two separate pieces from a sheet of paper.

However, can you produce three pieces by folding and making one straight cut?
Five pieces ... six ... seven?

Can you fold and then make one cut to produce identical pieces?

### Folding and cutting

If you cut along the dotted line you will get 3 pieces

### Re: Folding and cutting

Thanks for your comment, Honey. How do you know you will get three pieces? Can you explained how you arrived at this answer?

### how?

I do not understand can someone help plz i would be grateful thx for reading my comment

### Re: how?

Joshua, could you tell us what you have done so far please? That way, we might be able to help you more easily.

### Geometry is quite confusing.

Geometry is quite confusing. I like the idea of folding and cutting, but I don't understand what the instructions mean. Can you explain them to me?

### Re: Geometry is quite confusing

I'm sorry that you are having difficulties. Can you let us know what you have tried so far? Which part are you having trouble with?

### We are getting there

We found that one option to achieve three identical sized pieces was to...

...fold it in half, then - imagining quarters - cut the quarter nearest to the crease, whereby you fold out one third and the other two come from the right of the cut line. We also realised it was beneficial to think logically before creating fold lines to imagine the outcome in your head first, without wasting paper. A tactic for getting the most pieces of paper possible was to use an A5 piece of paper and fold in half as many times as possible, then cut a straight line down the middle - we folded it four times, and got 8 pieces in return (they weren't identical though).

Something interesting we are investigating further - sometimes this doesn't work! - is that no matter how many times you fold the piece of paper, when you cut it you receive less than the amount of folds.