Fold and Cut Challenge

sponsored by

Mathnasium Logo Hi-Res Black on

What shapes are possible to cut from a folded sheet of paper? What shapes are impossible to cut from a folded sheet of paper? 


Did you know that mathematicians have proven that every shape made of straight edges can be folded and cut out with a single straight cut? It takes quite a lot of folding to cut out complicated shapes, but it’s mathematically possible. 

Activity Instructions

Observers (Pre-K through 2nd Grade)

Can you fold a piece of paper in half and then cut out the following shapes?  All you need for this challenge is a few pieces of paper and some scissors.  Starting with a paper that is folded in half, try making a:

  • Rectangle

  • Square

  • Circle

  • Heart

  • Triangle

  • Star

  • Plus sign

  • The letter H

  • The letter X

  • The letter M

  • A person

Activity Instructions

Explorers (3rd Grade through 5th Grade)

Can you take a piece of paper and fold it so that with a single, straight cut you can cut a square out from the middle of the paper?  Mathematicians have proven that this is possible!


Give it a try on your own, then watch this video to learn more about the “Fold and Cut” theorem.  Once you’ve conquered the square, try some of these even harder shapes, which you can still create with just ONE straight cut (if you fold your paper just right).

Turn It In

Observers:  Take a picture of your creations and post them to Padlet.

Explorers: Take a picture of your creations, or make a short video of yourself making that single cut and unfolding your creation, and post to Padlet.

If you haven't printed the bingo board page, please print it now. Cross off this activity square, since you've completed it.


You'll bring your bingo board print-out to the PS29 garden on  Sunday, May 23 between 2-4pm to collect your prize. If you're not in Brooklyn, email us and we will send you your prize.