Can a quarter fit through a dime-sized hole?

In two dimensions, the hole is smaller than the quarter. In three dimensions, though, the hole can be stretched and manipulated to make a slit big enough for the quarter to drop through.

Topology is the mathematical study of shapes and spaces. Topology involves looking at the shapes that result through stretching, transforming, deforming, folding and twisting.

Students will also stretch their math brains with this topological exercise.

### Objectives

• Develop mathematical reasoning.

• Make connections and solve problems.

• Explain the importance of observation when doing math.

### Materials

• Per student:
sheet of paper
scissors
pencil
dime
quarter

### Key Questions

• Can the quarter fit through the small hole?

### What To Do

1. Put the dime on the centre of the sheet of paper.
2. Trace around the dime with the pencil.
3. With the scissors, carefully cut out the dime-sized circle.
4. Notice that the quarter cannot fit through the dime-sized hole. Challenge students to get the quarter through the hole without ripping the paper. Give them some time to try it.
5. To let the quarter drop through the hole:
• Bend the paper in half. Drop the quarter inside the fold, so that it sits in the hole.
• Hold the paper with one hand on each side of the quarter. Move your hands up and together. The hole will flex and the quarter will drop through.

Teacher Tip: Check out this video of the trick either before you demonstrate the trick or after the student have had a chance to try it out. (They use British coins, but the idea is the same.)

### Extensions

• How small a hole can you fit the quarter through?
• Can you fit a loonie through a dime-sized hole?