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

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!

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

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

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

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?

Can you make the birds from the egg tangram?

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?

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

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

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

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. . . .

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?

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

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

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?

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?

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.

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?

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?

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?

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.

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

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?

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

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

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?

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

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

How many models can you find which obey these rules?

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?

You could use just coloured pencils and paper to create this design, but it will be more eye-catching if you can get hold of hammer, nails and string.

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

Learn to write procedures and build them into Logo programs. Learn to use variables.

What happens when a procedure calls itself?

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.

Learn about Pen Up and Pen Down in Logo

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.

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

Write a Logo program, putting in variables, and see the effect when you change the variables.

More Logo for beginners. Now learn more about the REPEAT command.

Turn through bigger angles and draw stars with Logo.