A toy has a regular tetrahedron, a cube and a base with triangular
and square hollows. If you fit a shape into the correct hollow a
bell rings. How many times does the bell ring in a complete game?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
A game for two players on a large squared space.
Exchange the positions of the two sets of counters in the least possible number of moves
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?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
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!
What is the best way to shunt these carriages so that each train
can continue its journey?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
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. 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.
One face of a regular tetrahedron is painted blue and each of the
remaining faces are painted using one of the colours red, green or
yellow. How many different possibilities are there?
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.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
How can you paint the faces of these eight cubes so they can be put
together to make a 2 x 2 cube that is green all over AND a 2 x 2
cube that is yellow all over?
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 the lobster, yacht and cyclist?
Can you cut up a square in the way shown and make the pieces into a
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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 outlines of the chairs?
Can you fit the tangram pieces into the outline of these rabbits?
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?
Which of these dice are right-handed and which are left-handed?
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
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 outline of Mai Ling?
What is the greatest number of squares you can make by overlapping
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
Can you work out what is wrong with the cogs on a UK 2 pound coin?
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 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?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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 telephone?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
Can you fit the tangram pieces into the outlines of these people?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?