Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
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 game for two players. You'll need some counters.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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?
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?
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?
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.
An activity centred around observations of dots and how we visualise number arrangement patterns.
A variant on the game Alquerque
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?
Exchange the positions of the two sets of counters in the least possible number of moves
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
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 make a 3x3 cube with these shapes made from small cubes?
Move just three of the circles so that the triangle faces in the opposite direction.
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
A game for two players on a large squared space.
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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?
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?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Here are shadows of some 3D shapes. What shapes could have made them?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Can you fit the tangram pieces into the outlines of the candle and sundial?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Which of these dice are right-handed and which are left-handed?
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.
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?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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 outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of these clocks?
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 outlines of these people?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
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.
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 find ways of joining cubes together so that 28 faces are visible?
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!
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 workmen?
Can you fit the tangram pieces into the outline of the telescope and microscope?