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 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 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.
A game for two players on a large squared space.
Move just three of the circles so that the triangle faces in the
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.
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?
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.
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?
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!
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?
A game for two players. You'll need some counters.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
What happens when you try and fit the triomino pieces into these
A variant on the game Alquerque
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you cover the camel with these pieces?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Exchange the positions of the two sets of counters in the least possible number of moves
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 outline of Wai Ping, Wah Ming and Chi Wing?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
Can you fit the tangram pieces into the outline of this telephone?
Which of the following cubes can be made from these nets?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
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 fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of Little Fung at the table?
How many balls of modelling clay and how many straws does it take
to make these skeleton shapes?
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 outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
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
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
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,. . . .
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of