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 see why 2 by 2 could be 5? Can you predict what 2 by 10
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
A game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
A game for two players on a large squared space.
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Can you mentally fit the 7 SOMA pieces together to make a cube? Can
you do it in more than one way?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
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!
Can you fit the tangram pieces into the outline of Little Ming?
Exchange the positions of the two sets of counters in the least possible number of moves
How many different triangles can you make on a circular pegboard that has nine pegs?
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 game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Can you make a 3x3 cube with these shapes made from small cubes?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
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?
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
Blue Flibbins are so jealous of their red partners that they will
not leave them on their own with any other bue Flibbin. What is the
quickest way of getting the five pairs of Flibbins safely to. . . .
Can you mark 4 points on a flat surface so that there are only two
different distances between them?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
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?
Can you fit the tangram pieces into the outlines of these clocks?
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
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 quadrilaterals can be made by joining the dots
on the 8-point circle?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
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?
Can you fit the tangram pieces into the outline of Granma T?
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?
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 outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Show that among the interior angles of a convex polygon there
cannot be more than three acute angles.
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?