You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
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
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
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
An investigation that gives you the opportunity to make and justify
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Place the 16 different combinations of cup/saucer in this 4 by 4
arrangement so that no row or column contains more than one cup or
saucer of the same colour.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
What is the greatest number of counters you can place on the grid
below without four of them lying at the corners of a square?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
How many models can you find which obey these rules?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
An activity making various patterns with 2 x 1 rectangular tiles.
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
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.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
In how many ways can you stack these rods, following the rules?
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.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
Can you rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
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
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
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
What could the half time scores have been in these Olympic hockey
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
This activity investigates how you might make squares and pentominoes from Polydron.