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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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?
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?
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 cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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
Try this interactive strategy game for 2
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
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 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?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
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?
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.
Can you cut up a square in the way shown and make the pieces into a
Can you fit the tangram pieces into the outlines of the chairs?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Can you make a 3x3 cube with these shapes made from small cubes?
Can you fit the tangram pieces into the outlines of these clocks?
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 this telephone?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Exchange the positions of the two sets of counters in the least possible number of moves
Can you fit the tangram pieces into the outline of Little Fung at the table?
Which of these dice are right-handed and which are left-handed?
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 these people?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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 candle and sundial?
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 Little Ming?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
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?
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 Granma T?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
An activity centred around observations of dots and how we visualise number arrangement patterns.
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?