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

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?

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

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.

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

How many different symmetrical shapes can you make by shading triangles or squares?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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?

Can you visualise what shape this piece of paper will make when it is folded?

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

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.

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

Can you explain why it is impossible to construct this triangle?

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?

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle.

Make a flower design using the same shape made out of different sizes of paper.

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

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

In how many ways can you fit all three pieces together to make shapes with line symmetry?

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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?

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

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?

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

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

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

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

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

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 picture where this letter "F" will be on the grid if you flip it in these different ways?

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

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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?

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

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

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

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

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?

Can you use the interactive to complete the tangrams in the shape of butterflies?

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

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