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

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

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

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

Can you make a 3x3 cube with these shapes made from small cubes?

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

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?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

What happens when you try and fit the triomino pieces into these two grids?

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

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

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

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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

Move just three of the circles so that the triangle faces in the opposite direction.

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?

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?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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

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,. . . .

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?

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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

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?

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?

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

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

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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

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

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Can you find ways of joining cubes together so that 28 faces are visible?

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

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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?

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

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?