Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
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?
What is the best way to shunt these carriages so that each train can continue its journey?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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?
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?
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?
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Move just three of the circles so that the triangle faces in the opposite direction.
A variant on the game Alquerque
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?
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
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,. . . .
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.
Exchange the positions of the two sets of counters in the least possible number of moves
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
An activity centred around observations of dots and how we visualise number arrangement patterns.
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
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?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
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 game for two players on a large squared space.
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!
A game for two players. You'll need some counters.
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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 outlines of the watering can and man in a boat?
Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
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?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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 outlines of the candle and sundial?
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.
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.
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.
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?