What happens when you try and fit the triomino pieces into these
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?
Can you cover the camel with these pieces?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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 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?
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?
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.
What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.
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?
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.
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
Exchange the positions of the two sets of counters in the least possible number of moves
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
How many different triangles can you make on a circular pegboard that has nine pegs?
Move just three of the circles so that the triangle faces in the
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 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!
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
A variant on the game Alquerque
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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 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?
A game for two players. You'll need some counters.
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?
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?
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.
A game for two players on a large squared space.
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?
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 this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of the chairs?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outline of these convex shapes?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?