These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

What can you see? What do you notice? What questions can you ask?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Here's a simple way to make a Tangram without any measuring or ruling lines.

Can you cut up a square in the way shown and make the pieces into a triangle?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

A game for 2 people. Take turns joining two dots, until your opponent is unable to move.

Can you make a 3x3 cube with these shapes made from small cubes?

I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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.

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?

Square It game for an adult and child. Can you come up with a way of always winning this game?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

Can you fit the tangram pieces into the outline of this sports car?

Can you fit the tangram pieces into the outline of this goat and giraffe?

Can you fit the tangram pieces into the outline of these convex shapes?

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

Can you fit the tangram pieces into the outline of the rocket?

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

Can you fit the tangram pieces into the outline of these rabbits?

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

Can you fit the tangram pieces into the outline of this plaque design?

Can you fit the tangram pieces into the outline of this junk?

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .

Can you fit the tangram pieces into the outlines of the workmen?

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

Can you fit the tangram pieces into the outlines of the candle and sundial?

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

Which of these dice are right-handed and which are left-handed?

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.