In this feature, we bring together a range of paper-folding tasks, which offer opportunities for mathematical exploration. The article outlines how paper folding can help learners to deepen their understanding of geometry, to become more fluent with mathematical language, to persevere and become more curious about something they see.

Many of the tasks below are of a similar format whereby initially learners are challenged to visualise the shape they will get when they fold a piece of paper along the creases shown in a photo. They are then invited to make those shapes in different sizes, create a pattern and then arrange the patterns in different ways to make particular designs.

We hope you will be inspired to introduce your learners to the world of paper folding and look forward to receiving photos of their creations.

Many of the tasks below are of a similar format whereby initially learners are challenged to visualise the shape they will get when they fold a piece of paper along the creases shown in a photo. They are then invited to make those shapes in different sizes, create a pattern and then arrange the patterns in different ways to make particular designs.

We hope you will be inspired to introduce your learners to the world of paper folding and look forward to receiving photos of their creations.

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### Purposeful Paper Folding

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

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### Paper Partners

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

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### Paper Patchwork 1

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

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### Paper Patchwork 2

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

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### Folding Flowers 1

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

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### Folding Flowers 2

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

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### Regular Rings 1

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?

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### Modular origami polyhedra

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

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### Repeating Patterns

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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### Exploded Squares

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

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### Paper Curves

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

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### Bryony's Triangle

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

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### Paper folding - models of the Platonic solids

A description of how to make the five Platonic solids out of paper.