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?
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?
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.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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
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 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?
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
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?
How many different rhythms can you make by putting two drums on the
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?
Can you find all the different ways of lining up these Cuisenaire
My coat has three buttons. How many ways can you find to do up all
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
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?
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
Explore the different snakes that can be made using 5 cubes.
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
Investigate the different ways you could split up these rooms so
that you have double the number.
If you had 36 cubes, what different cuboids could you make?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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.
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Lorenzie was packing his bag for a school trip. He packed four
shirts and three pairs of pants. "I will be able to have a
different outfit each day", he said. How many days will Lorenzie be
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
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?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
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?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?