How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How many different symmetrical shapes can you make by shading triangles or squares?
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.
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.
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
Try this interactive strategy game for 2
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
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 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. . . .
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?
In how many ways can you fit all three pieces together to make
shapes with line symmetry?
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?
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
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 visualise what shape this piece of paper will make when it is folded?
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?
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.
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?
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.
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?
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 cheap and simple toy with lots of mathematics. Can you interpret
the images that are produced? Can you predict the pattern that will
be produced using different wheels?
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 fit the tangram pieces into the outline of Granma T?
Can you cut up a square in the way shown and make the pieces into a
Make a cube out of straws and have a go at this practical
Make a flower design using the same shape made out of different sizes of paper.
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?
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP
: PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED.
What is the area of the triangle PQR?
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 Wai Ping, Wah Ming and Chi Wing?
What shape is made when you fold using this crease pattern? Can you make a ring design?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Can you fit the tangram pieces into the outline of these convex shapes?
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 outline of this junk?
Can you fit the tangram pieces into the outlines of the chairs?
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Here's a simple way to make a Tangram without any measuring or