Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Use the clues to colour each square.
What is the best way to shunt these carriages so that each train
can continue its journey?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
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?
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?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Can you cover the camel with these pieces?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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
What happens when you try and fit the triomino pieces into these
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Can you find all the different ways of lining up these Cuisenaire
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
An activity making various patterns with 2 x 1 rectangular tiles.
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many different rhythms can you make by putting two drums on the
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?
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.