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

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.

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

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

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.

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?

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

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?

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?

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?

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?

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

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

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

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

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

How many models can you find which obey these rules?

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?

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

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

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?

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

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?

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

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

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

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

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?

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

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 ...

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

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

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 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.

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

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?

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

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

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?

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

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

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.

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

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