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

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?

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

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?

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

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.

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?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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

Can you make the birds from the egg tangram?

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

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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

These practical challenges are all about making a 'tray' and covering it with paper.

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

How many models can you find which obey these rules?

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

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

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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?

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?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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?

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?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

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

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

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

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

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

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?

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?

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

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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?

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?

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

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

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

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

Can you deduce the pattern that has been used to lay out these bottle tops?

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

This activity investigates how you might make squares and pentominoes from Polydron.

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

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

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