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.
article
Purposeful paper folding
In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.
problem
Favourite
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?
problem
Favourite
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?
problem
Favourite
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?
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Folding flowers 1
Age
7 to 11
Challenge level
Can you visualise what shape this piece of paper will make when it is folded?
problem
Folding flowers 2
Age
7 to 11
Challenge level
Make a flower design using the same shape made out of different sizes of paper.
problem
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?
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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.
problem
Favourite
Repeating patterns
Age
5 to 7
Challenge level
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
problem
Favourite
Exploded squares
Age
5 to 7
Challenge level
This practical activity challenges you to create symmetrical designs by cutting a square into strips.
problem
Straight to curves
Age
5 to 11
Challenge level
How can you make a curve from straight strips of paper?
problem
Paper curves
Age
7 to 11
Challenge level
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
problem
Favourite
Bryony's triangle
Age
7 to 11
Challenge level
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.