Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
A game for two players on a large squared space.
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.
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?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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 Little Ming?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
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!
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?
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?
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.
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.
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?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you fit the tangram pieces into the outline of this plaque design?
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?
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
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 these convex shapes?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of the rocket?
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.
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 make a 3x3 cube with these shapes made from small cubes?
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?
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?
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of the telescope and microscope?
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?
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?
Can you fit the tangram pieces into the outline of Little Fung at the table?
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 fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
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 outlines of the workmen?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Which of these dice are right-handed and which are left-handed?