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

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

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

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

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?

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

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Can you make the birds from the egg tangram?

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.

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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

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

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

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

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?

What do these two triangles have in common? How are they related?

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?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes 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?

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?

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?

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?

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

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?

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

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

How many models can you find which obey these rules?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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 ...

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?

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.

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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

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?

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

You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?

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

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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

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

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?