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?

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?

A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?

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?

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

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

Whirl a conker around in a horizontal circle on a piece of string. What is the smallest angular speed with which it can whirl?

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

The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!

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

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

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?

Which of these triangular jigsaws are impossible to finish?

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

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

Watch the video to see how Charlie works out the sum. Can you adapt his method?

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

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.

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

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?

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

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.

A video clip of Jo Boaler talking about Complex Instruction.

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

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?

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?

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

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

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

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

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

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

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

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

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

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

How can you quickly sort a suit of cards in order from Ace to King?

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

In this problem, we define complex numbers and invite you to explore what happens when you add and multiply them.

Video for teachers of a talk given by Dan Meyer in Cambridge in March 2013.

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

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?

Take a look at the video showing rhombuses and their diagonals...

Take a look at the video showing areas of different shapes on dotty grids...

If you can sketch y=f(x), there are several related functions you can also sketch...

Try out some calculations. Are you surprised by the results?

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

Newspapers said that eating a bacon sandwich every day raises the risk of bowel cancer by 20%. Should you be concerned?

"Statins cut the risks of heart attacks and strokes by 40%"

Should the Professor take statins? Can you help him decide?

When you're on trial for murder, it can be crucial that the court understands probability...

In 1% of cases, an HIV test gives a positive result for someone who is HIV negative. How likely is it that someone who tests positive has HIV?

If $y=x^2-6x+c$, and we vary $c$, what happens to the roots when $c>9$?

What do you think is going to happen in this video clip? Are you surprised?

What do you see as you watch this video? Can you create a similar video for the number 12?

Watch this animation. What do you see? Can you explain why this happens?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

Does this 'trick' for calculating multiples of 11 always work? Why or why not?