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?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

What is the greatest number of squares you can make by overlapping three squares?

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Can you make the birds from the egg tangram?

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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?

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

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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

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

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

Here is a version of the game 'Happy Families' for you to make and play.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

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

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.

Use the tangram pieces to make our pictures, or to design some of your own!

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

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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 ...

Delight your friends with this cunning trick! Can you explain how it works?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

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

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

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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?

How many models can you find which obey these rules?

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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

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

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

A game in which players take it in turns to choose a number. Can you block your opponent?

How can you make an angle of 60 degrees by folding a sheet of paper twice?

Which of the following cubes can be made from these nets?

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

A game to make and play based on the number line.

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?