Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

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.

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

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

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

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

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

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

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

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

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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?

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

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.

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

I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?

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 ...

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

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

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

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

Make one big triangle so the numbers that touch on the small triangles add to 10.

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .

Find your way through the grid starting at 2 and following these operations. What number do you end on?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

What can you see? What do you notice? What questions can you ask?

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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.

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

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.

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

A game for 2 people. Take turns joining two dots, until your opponent is unable to move.

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

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?

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

Can you find a way of counting the spheres in these arrangements?

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

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?