Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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 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?
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?
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 is the best way to shunt these carriages so that each train can continue its journey?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
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?
Can you fit the tangram pieces into the outline of this junk?
How many different triangles can you make on a circular pegboard that has nine pegs?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Can you fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of Mai Ling?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
Can you cut up a square in the way shown and make the pieces into a triangle?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you make a 3x3 cube with these shapes made from small cubes?
Can you fit the tangram pieces into the outline of this telephone?
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 plaque design?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Make a cube out of straws and have a go at this practical challenge.
Exploring and predicting folding, cutting and punching holes and making spirals.
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?
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?
Can you fit the tangram pieces into the outlines of the workmen?
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 Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Here's a simple way to make a Tangram without any measuring or ruling lines.
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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 the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of this sports car?
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 outline of Little Ming playing the board game?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?