A variant on the game Alquerque
Move just three of the circles so that the triangle faces in the
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 two players. You'll need some counters.
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
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.
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?
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?
Exchange the positions of the two sets of counters in the least possible number of moves
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?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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,. . . .
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.
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.
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.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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 game for two players on a large squared space.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
An activity centred around observations of dots and how we visualise number arrangement patterns.
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.
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.
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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?
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 watering can and man in a boat?
Which of these dice are right-handed and which are left-handed?
Here are shadows of some 3D shapes. What shapes could have made
This second article in the series refers to research about levels
of development of spatial thinking and the possible influence of
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
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 chairs?
Can you fit the tangram pieces into the outline of the child walking home from school?
Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Square It game for an adult and child. Can you come up with a way of always winning this game?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
I found these clocks in the Arts Centre at the University of
Warwick intriguing - do they really need four clocks and what times
would be ambiguous with only two or three of them?
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?