How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
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?
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
Have a go at this 3D extension to the Pebbles problem.
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. . . .
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
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.
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
In how many ways can you fit all three pieces together to make
shapes with line symmetry?
Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
A triangle ABC resting on a horizontal line is "rolled" along the
line. Describe the paths of each of the vertices and the
relationships between them and the original triangle.
Can you visualise what shape this piece of paper will make when it is folded?
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
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?
It is possible to dissect any square into smaller squares. What is
the minimum number of squares a 13 by 13 square can be dissected
When dice land edge-up, we usually roll again. But what if we
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.
Try this interactive strategy game for 2
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Can you fit the tangram pieces into the outlines of these clocks?
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
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 the child walking home from school?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
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 chairs?
How many different triangles can you make on a circular pegboard that has nine pegs?
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 outline of Granma T?
Make a flower design using the same shape made out of different sizes of paper.
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 work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
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?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Can you mark 4 points on a flat surface so that there are only two
different distances between them?
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?
Can you fit the tangram pieces into the outlines of these people?
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?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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?