Exchange the positions of the two sets of counters in the least possible number of moves
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
Can you fit the tangram pieces into the outline of Mai Ling?
What is the greatest number of squares you can make by overlapping
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Here are the six faces of a cube - in no particular order. Here are
three views of the cube. Can you deduce where the faces are in
relation to each other and record them on the net of this cube?
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 candle and sundial?
Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
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.
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?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
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?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of the workmen?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
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?
Can you find ways of joining cubes together so that 28 faces are
Exploring and predicting folding, cutting and punching holes and
How many different triangles can you make on a circular pegboard that has nine pegs?
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.
Make a cube out of straws and have a go at this practical
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
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Try this interactive strategy game for 2
Can you fit the tangram pieces into the outline of this telephone?
Can you cut up a square in the way shown and make the pieces into a
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?
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 quadrilaterals can be made by joining the dots
on the 8-point circle?
Can you make a 3x3 cube with these shapes made from small cubes?
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 Little Ming?
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 outline of Little Ming and Little Fung dancing?
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?
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
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!
Can you fit the tangram pieces into the outline of these rabbits?