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?
What happens when you try and fit the triomino pieces into these two grids?
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?
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?
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?
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?
A game for two players on a large squared space.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
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?
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?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
Move just three of the circles so that the triangle faces in the opposite direction.
What is the best way to shunt these carriages so that each train can continue its journey?
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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 variant on the game Alquerque
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.
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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!
A game for two players. You'll need some counters.
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?
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 many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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 it up?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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?
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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 outline of Granma T?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
How many balls of modelling clay and how many straws does it take to make these skeleton shapes?
Can you fit the tangram pieces into the outlines of these clocks?
This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.
Can you fit the tangram pieces into the outlines of these people?
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?
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 outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of the chairs?