Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
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 triangles can you make on the 3 by 3 pegboard?
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.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
What do these two triangles have in common? How are they related?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
This practical problem challenges you to create shapes and patterns
with two different types of triangle. You could even try
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
An activity making various patterns with 2 x 1 rectangular tiles.
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?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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.
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.
Can you find ways of joining cubes together so that 28 faces are
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Can you create more models that follow these rules?
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
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?
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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!
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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.
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?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
It starts quite simple but great opportunities for number discoveries and patterns!
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?
In how many ways can you stack these rods, following the rules?
How many models can you find which obey these rules?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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.
A challenging activity focusing on finding all possible ways of stacking rods.
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?