Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
Exchange the positions of the two sets of counters in the least possible number of moves
A variant on the game Alquerque
Move just three of the circles so that the triangle faces in the opposite direction.
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.
A game for two players. You'll need some counters.
A game for two players on a large squared space.
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
What is the greatest number of squares you can make by overlapping three squares?
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 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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.
Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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!
What happens when you try and fit the triomino pieces into these two grids?
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
Can you cover the camel with these pieces?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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 the candle and sundial?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Here are shadows of some 3D shapes. What shapes could have made them?
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 Little Fung at the table?
Can you fit the tangram pieces into the outlines of these clocks?
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 this shape. How would you describe it?
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?
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 child walking home from school?
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.
How many balls of modelling clay and how many straws does it take to make these skeleton shapes?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Can you fit the tangram pieces into the outlines of these people?
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
Can you fit the tangram pieces into the outline of Little Ming?
Can you fit the tangram pieces into the outline of Granma T?
Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Can you find ways of joining cubes together so that 28 faces are visible?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.