A game for two players. You'll need some counters.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
An activity centred around observations of dots and how we visualise number arrangement patterns.
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?
What does the overlap of these two shapes look like? Try picturing
it in your head and then use the interactivity to test your
Move just three of the circles so that the triangle faces in the
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?
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!
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?
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 make a 3x3 cube with these shapes made from small cubes?
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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 dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
Here are shadows of some 3D shapes. What shapes could have made
Which of these dice are right-handed and which are left-handed?
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 split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Can you fit the tangram pieces into the outlines of the candle and sundial?
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?
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.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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 the child walking home from school?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
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 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 find ways of joining cubes together so that 28 faces are
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 outlines of the workmen?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
This second article in the series refers to research about levels
of development of spatial thinking and the possible influence of
Can you fit the tangram pieces into the outline of the telescope and microscope?
Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?