How many different journeys could you make if you were going to
visit four stations in this network? How about if there were five
stations? Can you predict the number of journeys for seven
This train line has two tracks which cross at different points. Can
you find all the routes that end at Cheston?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
An investigation that gives you the opportunity to make and justify
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
A little mouse called Delia lives in a hole in the bottom of a
tree.....How many days will it be before Delia has to take the same
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Can you find the chosen number from the grid using the clues?
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
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.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!