Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
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 again?
Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outline of the rocket?
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .
Can you fit the tangram pieces into the outline of these convex shapes?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
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 junk?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Fung at the table?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
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. . . .
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 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. . . .
Can you fit the tangram pieces into the outlines of the candle and sundial?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Can you fit the tangram pieces into the outline of the telescope and microscope?
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 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 fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
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?
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?
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?
In how many ways can you fit all three pieces together to make shapes with line symmetry?
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 outlines of the workmen?
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. . . .
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 fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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.
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.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?