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?
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
These pictures show squares split into halves. Can you find other ways?
Can you create more models that follow 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.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Explore the triangles that can be made with seven sticks of the
Sort the houses in my street into different groups. Can you do it in any other ways?
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.
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
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?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Can you find ways of joining cubes together so that 28 faces are
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
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 this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
How many models can you find which obey these rules?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How can you arrange these 10 matches in four piles so that when you
move one match from three of the piles into the fourth, you end up
with the same arrangement?
Have a go at this 3D extension to the Pebbles problem.
What do these two triangles have in common? How are they related?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
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 is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
In how many ways can you stack these rods, following the rules?
A challenging activity focusing on finding all possible ways of stacking rods.
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 challenge extends the Plants investigation so now four or more children are involved.
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 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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Investigate the different ways you could split up these rooms so
that you have double the number.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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.
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.
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?