Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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!
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Can you fit the tangram pieces into the outline of the rocket?
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 Little Ming?
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
Can you fit the tangram pieces into the outline of this plaque design?
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
Can you fit the tangram pieces into the outline of Mai Ling?
Can you fit the tangram pieces into the outline of this telephone?
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.
Can you fit the tangram pieces into the outlines of the chairs?
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 Little Fung at the table?
Can you fit the tangram pieces into the outline of this sports car?
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 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 these clocks?
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
Can you fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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 workmen?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
What is the greatest number of squares you can make by overlapping three squares?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Here is a chance to play a version of the classic Countdown Game.