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.
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?
This activity investigates how you might make squares and pentominoes from Polydron.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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 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?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
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?
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
Can you find all the different ways of lining up these Cuisenaire
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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.
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?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found 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?
An environment which simulates working with Cuisenaire rods.
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
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?
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?
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 ...?
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?
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?
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?
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 digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Can you fill in the empty boxes in the grid with the right shape
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?
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?
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?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Sam sets up displays of cat food in his shop in triangular stacks.
If Felix buys some, then how can Sam arrange the remaining cans in
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?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can