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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Exchange the positions of the two sets of counters in the least possible number of moves
A variant on the game Alquerque
Move just three of the circles so that the triangle faces in the opposite direction.
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?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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?
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 shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
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 cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these two grids?
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 does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as 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?
What is the best way to shunt these carriages so that each train can continue its journey?
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?
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.
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?
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?
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?
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?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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?
A game for two players. You'll need some counters.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
A game for two players on a large squared space.
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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.
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!
Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
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?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
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?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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.
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.
Here are shadows of some 3D shapes. What shapes could have made them?