Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
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,. . . .
Can you find ways of joining cubes together so that 28 faces are visible?
Move just three of the circles so that the triangle faces in the opposite direction.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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 variant on the game Alquerque
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
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 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?
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Exchange the positions of the two sets of counters in the least possible number of moves
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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?
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 predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
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?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
What happens when you try and fit the triomino pieces into these two grids?
This article for teachers describes a project which explores thepower of storytelling to convey concepts and ideas to children.
Can you cover the camel with these pieces?
A game for two players. You'll need some counters.
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!
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.
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you make a 3x3 cube with these shapes made from small cubes?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
A game for two players on a large squared space.
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
An activity centred around observations of dots and how we visualise number arrangement patterns.
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?
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.