Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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 cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these two grids?
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 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.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
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 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 shape. How would you describe it?
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!
Make a cube out of straws and have a go at this practical challenge.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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?
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 outline of Little Fung at the table?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
How many different triangles can you make on a circular pegboard that has nine pegs?
Exchange the positions of the two sets of counters in the least possible number of moves
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of this telephone?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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 Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of these convex shapes?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
A game for two players. You'll need some counters.
Can you fit the tangram pieces into the outline of these rabbits?
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 fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
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?
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 sports car?
Can you fit the tangram pieces into the outline of this goat and giraffe?