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

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

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

Can you make the birds from the egg tangram?

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

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

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?

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

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

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

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?

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?

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

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?

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.

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

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

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

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?

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

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

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

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?

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

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

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

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?

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

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

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?

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?

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

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 work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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 ...

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?

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.

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

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

How many models can you find which obey these rules?

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

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?

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?

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

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

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

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?