We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

A simple visual exploration into halving and doubling.

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

This problem explores the shapes and symmetries in some national flags.

Work out how to light up the single light. What's the rule?

In this problem, we're going to find sets of letter shapes that go together.

This interactivity allows you to sort logic blocks by dragging their images.

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

This interactivity allows you to sort letters of the alphabet into two groups according to different properties.

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

Can you decode the mysterious markings on this ancient bone tool?

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

"Tell me the next two numbers in each of these seven minor spells", chanted the Mathemagician, "And the great spell will crumble away!" Can you help Anna and David break the spell?

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

Two video clips of classes organised into groups to work on Counting Cogs.

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?

95% of people in Britain should live within 10 miles of the route of the Olympic Torch tour. Is this true?