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

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?

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?

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

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

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

A simple visual exploration into halving and doubling.

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?

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

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

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

Can you find the values at the vertices when you know the values on the edges?

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

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

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. . . .

A introduction to how patterns can be deceiving, and what is and is not a proof.

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

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

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.

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?

Can you make a hypothesis to explain these ancient numbers?

This article explores the process of making and testing hypotheses.

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

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

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

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

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?

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.

"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?

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