Have a go at this 3D extension to the Pebbles problem.
Sort the houses in my street into different groups. Can you do it in any other ways?
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?
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.
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?
We need to wrap up this cube-shaped present, remembering that we
can have no overlaps. What shapes can you find to use?
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?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
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?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
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 tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This challenge extends the Plants investigation so now four or more children are involved.
How many models can you find which obey these rules?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
Can you create more models that follow these rules?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
What do these two triangles have in common? How are they related?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
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.
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.
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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.
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?
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?
We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Investigate the number of faces you can see when you arrange three cubes in different ways.
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do 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 you could split up these rooms so
that you have double the number.
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?
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?
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?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.