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.
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?
Sort the houses in my street into different groups. Can you do it in any other ways?
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.
How many models can you find which obey these rules?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
How many triangles can you make on the 3 by 3 pegboard?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
In how many ways can you stack these rods, following the 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.
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?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
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?
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?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
"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 players ...?
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?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Investigate and explain the patterns that you see from recording
just the units digits of numbers in the times tables.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
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?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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
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?
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.
The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
What is the largest cuboid you can wrap in an A3 sheet of paper?
This challenge extends the Plants investigation so now four or more children are involved.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?
In my local town there are three supermarkets which each has a
special deal on some products. If you bought all your shopping in
one shop, where would be the cheapest?
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!
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
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.