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?

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

What is the greatest number of squares you can make by overlapping three squares?

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

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

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?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

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

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

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

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 the candle and sundial?

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

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

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?

Can you fit the tangram pieces into the outlines of these clocks?

Can you fit the tangram pieces into the outline of the child walking home from school?

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

Make a cube out of straws and have a go at this practical challenge.

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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

Reasoning about the number of matches needed to build squares that share their sides.

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

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

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

A package contains a set of resources designed to develop pupils' mathematical thinking. This package places a particular emphasis on “visualising” and is designed to meet the needs. . . .

Can you fit the tangram pieces into the outline of Granma T?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

An activity centred around observations of dots and how we visualise number arrangement patterns.

Can you find a way of representing these arrangements of balls?

What is the shape of wrapping paper that you would need to completely wrap this model?

Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?