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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
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?
You can move the 4 pieces of the jigsaw and fit them into both
outlines. Explain what has happened to the missing one unit of
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
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?
In how many ways can you fit all three pieces together to make
shapes with line symmetry?
How many different symmetrical shapes can you make by shading triangles or squares?
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .
In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .
Can you maximise the area available to a grazing goat?
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.
The triangle ABC is equilateral. The arc AB has centre C, the arc
BC has centre A and the arc CA has centre B. Explain how and why
this shape can roll along between two parallel tracks.
Make a cube out of straws and have a go at this practical
Can you fit the tangram pieces into the outlines of the chairs?
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
Seven small rectangular pictures have one inch wide frames. The
frames are removed and the pictures are fitted together like a
jigsaw to make a rectangle of length 12 inches. Find the dimensions
of. . . .
Can you fit the tangram pieces into the outline of the child walking home from school?
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?
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
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Try this interactive strategy game for 2
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
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outlines of these people?
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 Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?
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 the candle and sundial?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Can you fit the tangram pieces into the outline of Granma T?
What shape has Harry drawn on this clock face? Can you find its
area? What is the largest number of square tiles that could cover
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
Have a go at this 3D extension to the Pebbles problem.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Can you find ways of joining cubes together so that 28 faces are