1. Pathways
  2. Geometry Journeys
  3. Folds and Holes
  4. Folding and Cutting

Folding and Cutting

 

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

 

FoldingCutting3.jpg

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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?
What about four pieces?
Five pieces ... six ... seven?

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

Comments

Submitted by Honey on Mon, 01/18/2016 - 18:59

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

Submitted by emp1001 on Tue, 01/19/2016 - 11:55

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

Submitted by joshua on Thu, 02/11/2016 - 12:04

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

Submitted by emp1001 on Thu, 02/11/2016 - 14:04

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

Submitted by Stuck on Tue, 04/05/2016 - 15:48

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?

Submitted by emp1001 on Tue, 04/05/2016 - 15:52

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?

Submitted by Year Four on Mon, 04/25/2016 - 11:11

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.

Submitted by em42 on Tue, 05/24/2016 - 10:31

I have got 23 pieces from 1 cut