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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
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?
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?
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?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
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.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
What does the overlap of these two shapes look like? Try picturing
it in your head and then use the interactivity to test your
Move just three of the circles so that the triangle faces in the
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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
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?
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
A game for two players. You'll need some counters.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
What are the next three numbers in this sequence? Can you explain
why are they called pyramid numbers?
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?
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?
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 the lobster, yacht and cyclist?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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.
This second article in the series refers to research about levels
of development of spatial thinking and the possible influence of
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outlines of the chairs?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
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!
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
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?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?