This activity challenges you to make collections of shapes. Can you
give your collection a name?
Find out what a "fault-free" rectangle is and try to make some of
Can you put these shapes in order of size? Start with the smallest.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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....?
Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?
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 investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
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 cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
Can you fit the tangram pieces into the outline of the child walking home from school?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
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.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you fit the tangram pieces into the outline of Granma T?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
Can you fit the tangram pieces into the outline of this telephone?
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.
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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 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 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?
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?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
How many different rhythms can you make by putting two drums on the
Exchange the positions of the two sets of counters in the least possible number of moves
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 triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Complete the squares - but be warned some are trickier than they
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?