How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
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
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
What is the best way to shunt these carriages so that each train
can continue its journey?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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?
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 smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
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?
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 find ways of joining cubes together so that 28 faces are
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
How can you arrange these 10 matches in four piles so that when you
move one match from three of the piles into the fourth, you end up
with the same arrangement?
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?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you make a 3x3 cube with these shapes made from small cubes?
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.
Make a cube out of straws and have a go at this practical
Exploring and predicting folding, cutting and punching holes and
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 cut up a square in the way shown and make the pieces into a
Can you fit the tangram pieces into the outline of Mai Ling?
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 the child walking home from school?
Can you fit the tangram pieces into the outlines of these clocks?
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 fit the tangram pieces into the outlines of the candle and sundial?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
What are the next three numbers in this sequence? Can you explain
why are they called pyramid numbers?
Can you fit the tangram pieces into the outline of these rabbits?