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. . . .
A game for two players. You'll need some counters.
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.
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?
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?
A game for two players on a large squared space.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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.
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?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
A variant on the game Alquerque
Move just three of the circles so that the triangle faces in the
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
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.
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Exchange the positions of the two sets of counters in the least possible number of moves
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
How many different triangles can you make on a circular pegboard that has nine pegs?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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
An activity centred around observations of dots and how we visualise number arrangement patterns.
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
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?
Here are shadows of some 3D shapes. What shapes could have made
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
How many balls of modelling clay and how many straws does it take
to make these skeleton shapes?
Which of these dice are right-handed and which are left-handed?
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.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Can you fit the tangram pieces into the outlines of the candle and sundial?
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?
What can you see? What do you notice? What questions can you ask?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
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.
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.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th