A variant on the game Alquerque
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. You'll need some counters.
Move just three of the circles so that the triangle faces in the
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?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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.
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?
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?
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,. . . .
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.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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
How many different triangles can you make on a circular pegboard that has nine pegs?
Exchange the positions of the two sets of counters in the least possible number of moves
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?
Can you cover the camel with these pieces?
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.
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 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?
An activity centred around observations of dots and how we visualise number arrangement patterns.
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
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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 plaque design?
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?
Can you fit the tangram pieces into the outline of these rabbits?
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 telescope and microscope?
Can you fit the tangram pieces into the outline of the child walking home from school?
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?
This article for teachers describes a project which explores
thepower of storytelling to convey concepts and ideas to children.
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Fung at the table?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
This second article in the series refers to research about levels
of development of spatial thinking and the possible influence of
How many balls of modelling clay and how many straws does it take
to make these skeleton shapes?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
Can you fit the tangram pieces into the outlines of the chairs?