A game for two players. You'll need some counters.
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. . . .
A variant on the game Alquerque
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 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 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 fit the tangram pieces into the outline of Little Ming?
Can you cover the camel with these pieces?
Move just three of the circles so that the triangle faces in the
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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!
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.
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.
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?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
A game for two players on a large squared space.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
What happens when you try and fit the triomino pieces into these
Exchange the positions of the two sets of counters in the least possible number of moves
What is the least number of moves you can take to rearrange the
bears so that no bear is next to a bear of the same colour?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
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. . . .
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?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
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 outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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?
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
Can you fit the tangram pieces into the outlines of these clocks?
How many balls of modelling clay and how many straws does it take
to make these skeleton shapes?
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 this shape. How would you describe it?
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?
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 these rabbits?
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
Lyndon Baker describes how the Mobius strip and Euler's law can
introduce pupils to the idea of topology.
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,. . . .