How can a person walk through a sheet of paper?
In this challenge activity discover how one piece of paper can go a long way. It's time to think outside the box!
What You Need
- 8 1/2 x 11 piece of paper
- Scissors
- Pen (not absolutely necessary)
Safety First!
Use care when handling sharp scissors.
What To Do
Challenge: Using one piece of paper and a pair of scissors, can you make a hole in the paper that is large enough to walk through? Try to figure it out before reading the solution.
Solution: There may be other ways to complete this challenge, here is one solution:
- Fold paper in half (width-wise is easiest).
- Cut a slit in the paper, starting from the folded edge until you almost reach the other end.
- Alternate along your paper, cutting from the folded edge and then cutting from the unfolded edge.
- Make sure the end cut also starts from the folded edge.
- Cut along the fold, in between where the two arrows in the above image are.
- Open it up. It should be one big circle!
Discovery
By making all of these cuts, essentially you’re making one rectangular piece of paper into a long narrow strip that is still connected at its two ends. Even though the area of your piece of paper has not changed, you’ve now increased the perimeter of the shape that you’re trying to step through. This gives a person plenty of room to pass through.
Understanding the relationship between perimeter and area is important for many tasks. For instance, if you were putting trim in a room, a rectangular room might need a lot less trim than an irregularly shaped room of the same area.
- Try to make as large of a perimeter as you can. How many people can you fit?
- Can you find another solution to the problem?
For more information on this topic check out these Let's Talk Science resources:
- How can I get a quarter through a dime sized hole? (Hands-on Activities) - Can you think like an engineer? Try to solve a tricky size and shape problem in this activity.
What’s happening?
By making all of these cuts, essentially you’re making one rectangular piece of paper into a long narrow strip that is still connected at its two ends. Even though the area of your piece of paper has not changed, you’ve now increased the perimeter of the shape that you’re trying to step through. This gives a person plenty of room to pass through.
Why does it matter?
Understanding the relationship between perimeter and area is important for many tasks. For instance, if you were putting trim in a room, a rectangular room might need a lot less trim than an irregularly shaped room of the same area.
Investigate further
- Try to make as large of a perimeter as you can. How many people can you fit?
- Can you find another solution to the problem?
For more information on this topic check out these Let's Talk Science resources:
- How can I get a quarter through a dime sized hole? (Hands-on Activities) - Can you think like an engineer? Try to solve a tricky size and shape problem in this activity.