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 for two players on a large squared space.
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.
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Exchange the positions of the two sets of counters in the least possible number of moves
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 game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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?
Can you fit the tangram pieces into the outline of the child walking home from school?
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.
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 playing the board game?
Can you fit the tangram pieces into the outline of this telephone?
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 brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
Can you fit the tangram pieces into the outlines of these clocks?
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?
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?
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 fit the tangram pieces into the outline of Granma T?
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 cut up a square in the way shown and make the pieces into a
Can you make a 3x3 cube with these shapes made from small cubes?
Try this interactive strategy game for 2
Can you find ways of joining cubes together so that 28 faces are
What is the greatest number of squares you can make by overlapping
Can you fit the tangram pieces into the outline of Little Ming?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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.
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 Mai Ling?
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?
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 these convex shapes?
Here's a simple way to make a Tangram without any measuring or
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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 junk?
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?
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.