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

As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?

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?

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

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

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

Imagine a very strange bank account where you are only allowed to do two things...

Play this game to learn about adding and subtracting positive and negative numbers

Can you picture how to order the cards to reproduce Charlie's card trick for yourself?

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

How many moves does it take to swap over some red and blue frogs? Do you have a method?

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

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

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?

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

Design and test a paper helicopter. What is the best design?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Take a look at the video and try to find a sequence of moves that will take you back to zero.

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

Dotty Six is a simple dice game that you can adapt in many ways.

Look carefully at the video of a tangle and explain what's happening.

Charlie has created a mapping. Can you figure out what it does? What questions does it prompt you to ask?

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

A video clip of Jo Boaler talking about Complex Instruction.

Video showing how to use the Number Plumber

Alf and Tracy explain how the Kingsfield School maths department use common tasks to encourage all students to think mathematically about key areas in the curriculum.

The Enigma Project's James Grime has created a video code challenge. Watch it here!