This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
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?
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 ways these aliens count in this
challenge. You could start by thinking about how each of them would
write our number 7.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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.
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?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
Investigate the different ways you could split up these rooms so
that you have double the number.
How many different sets of numbers with at least four members can
you find in the numbers in this box?
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?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position
yourself so that you are 'it' if there are two players? Three
In how many ways can you stack these rods, following the rules?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
Sort the houses in my street into different groups. Can you do it in any other ways?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
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 find all the different right-angled
triangles you can make by just moving one corner of the starting
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
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?
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.
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
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
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?
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?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
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?
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
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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 cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
An investigation that gives you the opportunity to make and justify
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 what happens when you add house numbers along a street
in different ways.
Can you create more models that follow these rules?
How many models can you find which obey these rules?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?