Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
Investigate how logic gates work in circuits.
Can you set the logic gates so that the number of bulbs which are
on is the same as the number of switches which are on?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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
You have 27 small cubes, 3 each of nine colours. Use the small
cubes to make a 3 by 3 by 3 cube so that each face of the bigger
cube contains one of every colour.
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
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?
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
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?
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
You can move the 4 pieces of the jigsaw and fit them into both
outlines. Explain what has happened to the missing one unit of
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
Try this interactive strategy game for 2
Do you know how to find the area of a triangle? You can count the
squares. What happens if we turn the triangle on end? Press the
button and see. Try counting the number of units in the triangle
now. . . .
An interactive activity for one to experiment with a tricky tessellation
How many times in twelve hours do the hands of a clock form a right
angle? Use the interactivity to check your answers.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
What are the coordinates of the coloured dots that mark out the
tangram? Try changing the position of the origin. What happens to
the coordinates now?
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
A game for two or more players that uses a knowledge of measuring
tools. Spin the spinner and identify which jobs can be done with
the measuring tool shown.
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
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?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
Can you find all the different ways of lining up these Cuisenaire
Can you beat the computer in the challenging strategy game?
A train building game for 2 players.
Use the interactivity or play this dice game yourself. How could
you make it fair?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Choose the size of your pegboard and the shapes you can make. Can
you work out the strategies needed to block your opponent?
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
How many different triangles can you make on a circular pegboard
that has nine pegs?
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 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Match the cards of the same value.
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
What shaped overlaps can you make with two circles which are the
same size? What shapes are 'left over'? What shapes can you make
when the circles are different sizes?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Use the interactivity to make this Islamic star and cross design.
Can you produce a tessellation of regular octagons with two
different types of triangle?
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?