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.
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
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?
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?
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?
Can you create more models that follow these rules?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
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.
How many models can you find which obey these rules?
A challenging activity focusing on finding all possible ways of stacking rods.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
This challenge extends the Plants investigation so now four or more children are involved.
We went to the cinema and decided to buy some bags of popcorn so we
asked about the prices. Investigate how much popcorn each bag holds
so find out which we might have bought.
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?
How many triangles can you make on the 3 by 3 pegboard?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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?
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.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
We need to wrap up this cube-shaped present, remembering that we
can have no overlaps. What shapes can you find to use?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Can you find ways of joining cubes together so that 28 faces are
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
What is the largest number of circles we can fit into the frame
without them overlapping? How do you know? What will happen if you
try the other shapes?
In how many ways can you stack these rods, following the rules?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
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?
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?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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
Investigate the number of paths you can take from one vertex to
another in these 3D shapes. Is it possible to take an odd number
and an even number of paths to the same vertex?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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 continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?