Geometry Journeys

What can you discover by simply folding and cutting paper?

The Geometry Journeys pathway on wild.maths.org introduces students to the wonderful world of paper folding. We hope it will deepen students' understanding of geometry and encourage them to be curious about what they see.

The collection of related NRICH tasks below are ideal for teachers who want to promote creativity in the classroom. They are designed for classroom use, with accompanying Teachers' Notes and Resources.

Purposeful Paper Folding

Age 5 to 11

In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.

Paper Partners

Age 5 to 7 Challenge Level:

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

Paper Patchwork 1

Age 5 to 7 Challenge Level:

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

Paper Patchwork 2

Age 5 to 7 Challenge Level:

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

Folding Flowers 1

Age 7 to 11 Challenge Level:

Can you visualise what shape this piece of paper will make when it is folded?

Folding Flowers 2

Age 7 to 11 Challenge Level:

Make a flower design using the same shape made out of different sizes of paper.

Regular Rings 1

Age 7 to 11 Challenge Level:

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Fitted

Age 7 to 11 Challenge Level:

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Plaited Origami Polyhedra

Age 7 to 16 Challenge Level:

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

Regular Rings 2

Age 7 to 11 Challenge Level:

What shape is made when you fold using this crease pattern? Can you make a ring design?