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

Can you fit the tangram pieces into the outlines of the camel and giraffe?

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?

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.

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

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 the candle?

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

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 Little Ming?

Why do you think that the red player chose that particular dot in this game of Seeing Squares?

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

Can you fit the tangram pieces into the outline of Mah Ling?

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

How many different triangles can you make on a circular pegboard that has nine pegs?

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

Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Can you fit the tangram pieces into the outlines of the convex shapes?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

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.

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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

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.

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

Can you work out what is wrong with the cogs on a UK 2 pound coin?

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 work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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

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

Can you fit the tangram pieces into the silhouette of the junk?

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

Can you fit the tangram pieces into the outline of the playing piece?

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

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