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.
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!
Exchange the positions of the two sets of counters in the least possible number of moves
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
A game for two players on a large squared space.
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.
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 outline of the telescope and microscope?
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 outline of Little Ming?
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 chairs?
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?
Can you fit the tangram pieces into the outline of the child walking home from school?
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
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
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
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.
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Granma T?
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.
Exploring and predicting folding, cutting and punching holes and
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
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?
Can you make a 3x3 cube with these shapes made from small cubes?
Try this interactive strategy game for 2
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
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 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?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
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?
What is the greatest number of squares you can make by overlapping
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
Can you find ways of joining cubes together so that 28 faces are
Can you fit the tangram pieces into the outline of this sports car?
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 Little Fung at the table?
Can you fit the tangram pieces into the outline of this goat and giraffe?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
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.