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 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?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Exchange the positions of the two sets of counters in the least possible number of moves
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?
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.
Move four sticks so there are exactly four triangles.
A game for two players on a large squared space.
A group activity using visualisation of squares and triangles.
What is the greatest number of squares you can make by overlapping
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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?
What shape has Harry drawn on this clock face? Can you find its
area? What is the largest number of square tiles that could cover
What shape is the overlap when you slide one of these shapes half
way across another? Can you picture it in your head? Use the
interactivity to check your visualisation.
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.
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 fit the tangram pieces into the outlines of the watering can and man in a boat?
Which of these dice are right-handed and which are left-handed?
Here are shadows of some 3D shapes. What shapes could have made
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
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 outlines of the candle and sundial?
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 workmen?
Can you arrange the shapes in a chain so that each one shares a
face (or faces) that are the same shape as the one that follows it?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
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 outlines of the chairs?
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 clocks?
How many balls of modelling clay and how many straws does it take
to make these skeleton shapes?
Which of the following cubes can be made from these nets?
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 and Little Fung dancing?
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?
Reasoning about the number of matches needed to build squares that
share their sides.
Make a cube out of straws and have a go at this practical
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
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.
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of Little Ming?
Can you fit the tangram pieces into the outline of Granma T?
This second article in the series refers to research about levels
of development of spatial thinking and the possible influence of
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some
of the small cubes in the ways described, how many will have holes
drilled through them?
Can you work out what is wrong with the cogs on a UK 2 pound coin?