Can You Step Through an Index Card?

Can You Step Through an Index Card?

Discovery Place Kids Huntersville

In case you need to hear this first – math is awesome! Think of anything that is part of your life that brings you joy and meaning, and you will find math is a critical ingredient.

When working with three-dimensional shapes in solid geometry, there are many aspects and measurable characteristics given to structures such as volume or perimeter.

  • Surface area is the quantity of the total area that all the surfaces of an object occupy.
  • Volume is the amount of space that an object takes up. 

The average surface area of a 3 x 5-inch notecard is 15 square inches. However, if we cut the card a certain way, we can redistribute that surface area from within the volume of the card.

In this hands-on activity, surface area allows us to do the impossible and morph an index card into something more. Let’s try it!

Learning Time: 10-15 minutes

Prep Time: 5-10 minutes

Age Range: Elementary – Middle School

Materials List

  • An index card or piece of paper
  • Scissors


  1. First, ask yourself if you think you can fit through a piece of paper or even an index card! This is a fantastic opportunity to practice your problem-solving skills. Take a few minutes to try and figure it out.
  2. Follow along with our video and begin the activity by folding your index card in half lengthwise, also known as “hot dog style.”
  3. Next, turn the folded side facing towards you and cut two slits on each side of the card. Be careful not to cut all the way through or cut the piece completely off.
  4. A very important step: Carefully cut open the creased side of your card, being careful to not cut the two loops you just made.
  5. Now, make similar cuts evenly across the entire length of the card, remembering not to cut the pieces off.
  6. Next, flip your card over and cut the same slits but in between your earlier cuts.
  7. Now that you’ve cut all your pieces, gently open your card to reveal a chain of loops that creates a large circle.
  8. Can you step through the circle you created? Or, at least put it over your head?

Things to Try

  • How could you make your ring of paper longer? 
  • What’s the smallest piece of paper you can cut and still step through? 
  • What happens if you make the cuts closer together? 
  • Have younger kids who are still working on scissor skills? Try this activity with a bigger piece of paper!