Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

How can you make an angle of 60 degrees by folding a sheet of paper twice?

Challenge Level

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

Challenge Level

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

Challenge Level

Surprise your friends with this magic square trick.

Challenge Level

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?

Challenge Level

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?

Challenge Level

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

Challenge Level

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

Challenge Level

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?

Challenge Level

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?

Challenge Level

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

Challenge Level

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?

Challenge Level

Can you make the birds from the egg tangram?

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

Challenge Level

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Challenge Level

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?

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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 ...

Challenge Level

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

Challenge Level

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

Challenge Level

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

Challenge Level

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.

Challenge Level

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

Challenge Level

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

Challenge Level

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