Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .
The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?
Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
Can you discover whether this is a fair game?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Find all the ways to cut out a 'net' of six squares that can be folded into a cube.
Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?
A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?
A huge wheel is rolling past your window. What do you see?
Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
A bus route has a total duration of 40 minutes. Every 10 minutes, two buses set out, one from each end. How many buses will one bus meet on its way from one end to the other end?
Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.
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.
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
Can you mark 4 points on a flat surface so that there are only two different distances between them?
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
Can you fit the tangram pieces into the outline of Little Ming?
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?
These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?
What is the shape of wrapping paper that you would need to completely wrap this model?
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?
In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?
Every day at noon a boat leaves Le Havre for New York while another boat leaves New York for Le Havre. The ocean crossing takes seven days. How many boats will each boat cross during their journey?
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.
Can you find a way of representing these arrangements of balls?
When dice land edge-up, we usually roll again. But what if we didn't...?