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.

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?

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

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

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

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

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?

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

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

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 find a way of counting the spheres in these arrangements?

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 ...

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

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

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

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

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

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.

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?

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

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

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

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

Here are shadows of some 3D shapes. What shapes could have made them?

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

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.

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?

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

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

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

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?

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

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?

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?

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

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

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

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?