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 shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
What is the best way to shunt these carriages so that each train
can continue its journey?
Can you fit the tangram pieces into the outlines of the workmen?
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?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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?
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.
Here's a simple way to make a Tangram without any measuring or
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?
Can you make a 3x3 cube with these shapes made from small cubes?
Can you fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outline of this goat and giraffe?
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
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 fit the tangram pieces into the outlines of the candle and sundial?
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?
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 cut up a square in the way shown and make the pieces into a
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?
Try this interactive strategy game for 2
In each of the pictures the invitation is for you to: Count what
you see. Identify how you think the pattern would continue.
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.
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.
What is the greatest number of squares you can make by overlapping
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
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 shape. How would you describe it?
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?
Can you fit the tangram pieces into the outlines of these clocks?
An activity centred around observations of dots and how we visualise number arrangement patterns.
Can you fit the tangram pieces into the outlines of these people?
Can you find ways of joining cubes together so that 28 faces are
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Use the lines on this figure to show how the square can be divided
into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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?
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?
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
Have a look at what happens when you pull a reef knot and a granny
knot tight. Which do you think is best for securing things