Can you lay out the pictures of the drinks in the way described by the clue cards?

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.

These clocks have only one hand, but can you work out what time they are showing from the information?

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

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?

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?

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Drawing a triangle is not always as easy as you might think!

Work in groups to try to create the best approximations to these physical quantities.

Can you find a quadratic equation which passes close to these points?

Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices

We had some clear descriptions of the relationships between functions and their graphs.

Rajeev sent us a great description of his exploration of different quadratic mappings.

This very difficult toughnut received a lot of attention over the last few months. If you wish to see how the pattern was made, read on.

Many NRICH tasks have been designed with group work in mind. Read about Jo Boaler's research on the benefits of collaborative work and watch a clip of a teacher working in this way.

Group work depends on effective team work. This article describes attributes of effective team work and links to "Team Building" problems that can be used to develop learners' team working skills.

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...