This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view. . . .

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. . . .

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

An activity centred around observations of dots and how we visualise number arrangement patterns.

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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?

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

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?

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?

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.

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

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?

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

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?

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

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

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

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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?

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?

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

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

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

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

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.

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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

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?

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

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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

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.

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

Can you fit the tangram pieces into the outlines of the candle and sundial?

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

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

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

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Which of the following cubes can be made from these nets?

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

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 the workmen?

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?