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?
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?
Anne completes a circuit around a circular track in 40 seconds.
Brenda runs in the opposite direction and meets Anne every 15
seconds. How long does it take Brenda to run around the track?
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.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Can you mentally fit the 7 SOMA pieces together to make a cube? Can
you do it in more than one way?
Can you fit the tangram pieces into the outline of Little Ming?
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 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Bilbo goes on an adventure, before arriving back home. Using the
information given about his journey, can you work out where Bilbo
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?
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?
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.
Can you fit the tangram pieces into the outline of the telescope and microscope?
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?
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Can you fit the tangram pieces into the outline of this telephone?
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?
Can you find a way of representing these arrangements of balls?
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?
Can you fit the tangram pieces into the outline of these rabbits?
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?
Exchange the positions of the two sets of counters in the least possible number of moves
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
A rectangular field has two posts with a ring on top of each post.
There are two quarrelsome goats and plenty of ropes which you can
tie to their collars. How can you secure them so they can't. . . .
Try this interactive strategy game for 2
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
A huge wheel is rolling past your window. What do you see?
Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
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.
At the time of writing the hour and minute hands of my clock are at
right angles. How long will it be before they are at right angles
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
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. . . .
How many different triangles can you make on a circular pegboard that has nine pegs?
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. . . .
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
An activity centred around observations of dots and how we visualise number arrangement patterns.
Can you fit the tangram pieces into the outlines of these people?
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
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?
A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
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!
Can you fit the tangram pieces into the outline of this goat and giraffe?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
Here's a simple way to make a Tangram without any measuring or