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?
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.
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 work out what kind of rotation produced this pattern of
pegs in our pegboard?
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
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.
How many different symmetrical shapes can you make by shading triangles or squares?
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.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Try this interactive strategy game for 2
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
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. . . .
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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?
How many different ways can I lay 10 paving slabs, each 2 foot by 1
foot, to make a path 2 foot wide and 10 foot long from my back door
into my garden, without cutting any of the paving slabs?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
Here's a simple way to make a Tangram without any measuring or
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
Exchange the positions of the two sets of counters in the least possible number of moves
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of this junk?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Can you fit the tangram pieces into the outline of these rabbits?
Which hexagons tessellate?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you cut up a square in the way shown and make the pieces into a
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Can you fit the tangram pieces into the outline of these convex shapes?
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
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 telephone?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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 the candle and sundial?
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.
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!
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?
Which of these dice are right-handed and which are left-handed?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
Can you arrange the shapes in a chain so that each one shares a
face (or faces) that are the same shape as the one that follows it?
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.