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?

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

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

Surprise your friends with this magic square trick.

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

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

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

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

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

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

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 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?

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

Here is a chance to create some Celtic knots and explore the mathematics behind them.

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

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

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

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.

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

How many models can you find which obey these rules?

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?

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?

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

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

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

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

Here are some ideas to try in the classroom for using counters to investigate number patterns.

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

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

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

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

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

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

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

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?

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

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

I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?

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

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.

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

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.