There are so many things you can do with paper while exploring mathematics. Folding and cutting paper leads to some pretty amazing mathematics!
Folding paper together with someone is a great way to build relationships and generate curiosity; folding together also fosters mathematical vocabulary and helps to deepen mathematical understanding.
For example, give someone a non-square piece of paper and ask them to create a square out of it while thinking out-loud. Then ask them how they know that the paper is "square".
There are many different types of origami, but we will feature some modular origami here. Modular origami consists of putting a number of identical pieces together to form a complete model.
The stellated icosohedron shown here is an example of modular origami. This model is made up of sonobe units. Here is a link to the How to Make a Stellated Icosohedron. Other models for this unit include a cube and an octahedron.
Making:
Pinwheel to Octagon (Sherri Burroughs)
Hexa-tetraflexagon (Museum of Math)
Hexaflexagons (Vi Hart)
The Forgotten Flexagon (Numberphile video featuring Matt Parker)
Red Tag Art (Cute and Easy Crafts for Parents and Teachers)
Fortune Teller (wikihow)
Cutting a Mobius Strip (ThinkTwice animation)
Unexpected Shapes Part 1 (Numberphile video featuring Tadashi Tokieda )
Unexpected Shapes Part 2 (Numberphile video featuring Tadashi Tokieda )
Romantic Mathematical Shape: mobius-loop hearts (Stand-up Maths video featuring Matt Parker)
Mobius Play List (Vi Hart)
Discovering:
Proving the Theorem of Pythagoras (University of Toronto, Vi Hart)
Investigating area and more! (Mark Driscoll, MEI, YouCubed)
Fold and Cut Theorem (Numberphile video featuring Katie Steckles
How to trisect an angle using origami (Numberphile video featuring Zsuzsanna Dancso)
If you have a favourite paper folding /cutting activity not featured here, please share it with us. Thanks!