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

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

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

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?

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

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.

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

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

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

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

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

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?

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?

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

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?

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

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

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

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

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

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

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

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

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.

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

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

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...

Video showing how to use the Number Plumber

Steve has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

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?

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

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.

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

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

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

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

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

Which of these triangular jigsaws are impossible to finish?

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

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?

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

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

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?

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

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?