If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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.
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 group activity using visualisation of squares and triangles.
A game for two players on a large squared space.
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?
What is the greatest number of squares you can make by overlapping
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?
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.
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!
Eight children each had a cube made from modelling clay. They cut
them into four pieces which were all exactly the same shape and
size. Whose pieces are the same? Can you decide who made each set?
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.
Move four sticks so there are exactly four triangles.
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?
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
How many pieces of string have been used in these patterns? Can you
describe how you know?
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
How many loops of string have been used to make these patterns?
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 is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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?
Which of these dice are right-handed and which are left-handed?
Here are shadows of some 3D shapes. What shapes could have made
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outline of the child walking home from school?
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?
Can you find ways of joining cubes together so that 28 faces are
Exploring and predicting folding, cutting and punching holes and
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
How many balls of modelling clay and how many straws does it take
to make these skeleton shapes?
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.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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.
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 outlines of the chairs?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Reasoning about the number of matches needed to build squares that
share their sides.
An activity centred around observations of dots and how we visualise number arrangement patterns.
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
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?
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th