Challenge Level

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

Challenge Level

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

Challenge Level

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Challenge Level

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

Challenge Level

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Challenge Level

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Challenge Level

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

Challenge Level

Make a cube out of straws and have a go at this practical challenge.

Challenge Level

Reasoning about the number of matches needed to build squares that share their sides.

Challenge Level

Exploring and predicting folding, cutting and punching holes and making spirals.

Challenge Level

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

Challenge Level

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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?

Challenge Level

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

Challenge Level

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Challenge Level

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Challenge Level

Can you each work out what shape you have part of on your card? What will the rest of it look like?

Challenge Level

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Challenge Level

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Challenge Level

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

Challenge Level

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Challenge Level

Follow these instructions to make a three-piece and/or seven-piece tangram.

Challenge Level

Can you cut up a square in the way shown and make the pieces into a triangle?

Challenge Level

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

Challenge Level

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

Challenge Level

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

Challenge Level

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Challenge Level

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

Challenge Level

Did you know mazes tell stories? Find out more about mazes and make one of your own.

Challenge Level

Can you make the birds from the egg tangram?

Challenge Level

Can you make five differently sized squares from the interactive tangram pieces?

Challenge Level

An activity making various patterns with 2 x 1 rectangular tiles.

Challenge Level

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

Challenge Level

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Challenge Level

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Challenge Level

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

Challenge Level

How can you make a curve from straight strips of paper?

Challenge Level

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

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?

Challenge Level

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

Challenge Level

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Challenge Level

Follow these instructions to make a five-pointed snowflake from a square of paper.

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

Challenge Level

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

Challenge Level

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

Challenge Level

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

Challenge Level

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?