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?

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

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

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?

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.

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

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

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.

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.

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 explain why it is impossible to construct this triangle?

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

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.

Exchange the positions of the two sets of counters in the least possible number of moves

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.

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

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

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

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. . . .

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?

Seeing Squares 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?

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

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

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

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?

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

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?

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

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. . . .

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?

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

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.

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?

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

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!

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

If you move the tiles around, can you make squares with different coloured edges?