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 is the best way to shunt these carriages so that each train
can continue its journey?
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?
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
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?
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 two players on a large squared space.
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!
An activity centred around observations of dots and how we visualise number arrangement patterns.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
Which of these dice are right-handed and which are left-handed?
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.
Can you make a 3x3 cube with these shapes made from small cubes?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
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?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
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.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Exchange the positions of the two sets of counters in the least possible number of moves
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
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
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
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?
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Make a flower design using the same shape made out of different sizes of paper.
Can you fit the tangram pieces into the outlines of these people?
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?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
Which of the following cubes can be made from these nets?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Exploring and predicting folding, cutting and punching holes and
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
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 chairs?
Can you find ways of joining cubes together so that 28 faces are
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of the telescope and microscope?