Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots 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?
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
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?
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?
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
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?
Explore the different snakes that can be made using 5 cubes.
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.
Find all the numbers that can be made by adding the dots on two dice.
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?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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.
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?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
My coat has three buttons. How many ways can you find to do up all
Have a go at this game which involves throwing two dice and adding
their totals. Where should you place your counters to be more
likely to win?
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?
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?
Ben has five coins in his pocket. How much money might he have?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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?
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
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Terry and Ali are playing a game with three balls. Is it fair that
Terry wins when the middle ball is red?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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
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
You have 5 darts and your target score is 44. How many different
ways could you score 44?
How many different shapes can you make by putting four right-
angled isosceles triangles together?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
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
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
How many different rhythms can you make by putting two drums on the
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?
Investigate the different sounds you can make by putting the owls
and donkeys on the wheel.