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.
Can you find all the different ways of lining up these Cuisenaire
Investigate the different ways you could split up these rooms so
that you have double the number.
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.
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?
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?
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?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
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 ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
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?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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
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
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?
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
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?
How many different rhythms can you make by putting two drums on the
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
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.
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
Terry and Ali are playing a game with three balls. Is it fair that
Terry wins when the middle ball is red?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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?
Investigate the different sounds you can make by putting the owls
and donkeys on the wheel.
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 eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
How many different shapes can you make by putting four right-
angled isosceles triangles together?
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
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
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.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
My coat has three buttons. How many ways can you find to do up all
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Can you fill in the empty boxes in the grid with the right shape