Try this interactive strategy game for 2
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Where can you put the mirror across the square so that you can
still "see" the whole square? How many different positions are
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?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
Exploring and predicting folding, cutting and punching holes and
Use the lines on this figure to show how the square can be divided
into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?
An activity centred around observations of dots and how we visualise number arrangement patterns.
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
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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Here's a simple way to make a Tangram without any measuring or
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?
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?
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.
How many different triangles can you make on a circular pegboard
that has nine pegs?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Think of a number, square it and subtract your starting number. Is
the number you’re left with odd or even? How do the images
help to explain this?
Can you make a 3x3 cube with these shapes made from small cubes?
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?
Can you find ways of joining cubes together so that 28 faces are
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
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 each of the pictures the invitation is for you to: Count what
you see. Identify how you think the pattern would continue.
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
I've made some cubes and some cubes with holes in. This challenge
invites you to explore the difference in the number of small cubes
I've used. Can you see any patterns?
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
Have a look at what happens when you pull a reef knot and a granny
knot tight. Which do you think is best for securing things
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 Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
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?
Make a cube out of straws and have a go at this practical
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?
Which of the following cubes can be made from these nets?
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.
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!
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. . . .