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

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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?

Exploring and predicting folding, cutting and punching holes and making spirals.

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

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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

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

What shape is made when you fold using this crease pattern? Can you make a ring design?

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

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

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

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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

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

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

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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 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?

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?

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

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 find a way of counting the spheres in these arrangements?

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

This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.

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

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

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

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.

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

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.

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

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 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 outlines of the rabbits?

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

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 Mah Ling and Chi Wing?

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

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

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?

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

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

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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

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