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

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?

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

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?

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

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.

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

Can you make the birds from the egg tangram?

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?

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

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 each work out the number on your card? What do you notice? How could you sort the cards?

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

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

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

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

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

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?

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

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

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?

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.

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?

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

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

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?

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

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?

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?

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?

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

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

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?

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?

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?

How many models can you find which obey these rules?

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

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?

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

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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

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

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