Find out what a "fault-free" rectangle is and try to make some of
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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?
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. . . .
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?
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
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
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
Exchange the positions of the two sets of counters in the least possible number of moves
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.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
How many times in twelve hours do the hands of a clock form a right
angle? Use the interactivity to check your answers.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Can you fit the tangram pieces into the outline of Granma T?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outlines of the candle and sundial?
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!
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 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Can you find all the different triangles on these peg boards, and
find their angles?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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?
Can you fit the tangram pieces into the outlines of the chairs?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
What is the greatest number of squares you can make by overlapping
Can you find all the different ways of lining up these Cuisenaire
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Square It game for an adult and child. Can you come up with a way of always winning this game?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
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?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Fung at the table?
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?
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?