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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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.
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
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?
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?
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 many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
An investigation that gives you the opportunity to make and justify
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
What happens when you round these three-digit numbers to the nearest 100?
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
This challenge is about finding the difference between numbers which have the same tens digit.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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?
Can you find all the different ways of lining up these Cuisenaire
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Find out what a "fault-free" rectangle is and try to make some of
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
An activity making various patterns with 2 x 1 rectangular tiles.
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
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....?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Can you make a train the same length as Laura's but using three
differently coloured rods? Is there only one way of doing it?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
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?