Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
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.
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
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
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 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
These pictures show squares split into halves. Can you find other ways?
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?
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?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
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.
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?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Can you find ways of joining cubes together so that 28 faces are
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
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?
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
How many triangles can you make on the 3 by 3 pegboard?
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?
What do these two triangles have in common? How are they related?
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?
Sort the houses in my street into different groups. Can you do it in any other ways?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
How many models can you find which obey these 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?
An activity making various patterns with 2 x 1 rectangular tiles.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
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?
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.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
In how many ways can you stack these rods, following the rules?
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, 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?
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
We need to wrap up this cube-shaped present, remembering that we
can have no overlaps. What shapes can you find to use?
Bernard Bagnall describes how to get more out of some favourite
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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