Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
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.
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
Try this interactive strategy game for 2
In how many ways can you fit all three pieces together to make
shapes with line symmetry?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the 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.
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 symmetrical shapes can you make by shading triangles or squares?
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
How can you paint the faces of these eight cubes so they can be put
together to make a 2 x 2 cube that is green all over AND a 2 x 2
cube that is yellow all over?
Can you fit the tangram pieces into the outline of this goat and giraffe?
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 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?
Can you fit the tangram pieces into the outline of this sports car?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
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?
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
Here's a simple way to make a Tangram without any measuring or
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of these convex shapes?
Can you cut up a square in the way shown and make the pieces into a
In each of the pictures the invitation is for you to: Count what
you see. Identify how you think the pattern would continue.
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
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?
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 this plaque design?
Can you fit the tangram pieces into the outline of this junk?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
A game has a special dice with a colour spot on each face. These
three pictures show different views of the same dice. What colour
is opposite blue?
Can you fit the tangram pieces into the outline of the rocket?
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 the telescope and microscope?
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?
Which of these dice are right-handed and which are left-handed?
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 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.
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?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Make a cube out of straws and have a go at this practical
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.
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?
Reasoning about the number of matches needed to build squares that
share their sides.
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
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.