Have a go at this 3D extension to the Pebbles problem.
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
It starts quite simple but great opportunities for number discoveries and patterns!
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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.
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
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?
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?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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!
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A challenging activity focusing on finding all possible ways of stacking rods.
This challenge extends the Plants investigation so now four or more children are involved.
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.
How many models can you find which obey these rules?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Explore one of these five pictures.
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.
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?
In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.
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?
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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?
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.
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.
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 ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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
In how many ways can you stack these rods, following the rules?
A follow-up activity to Tiles in the Garden.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
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?
Can you find ways of joining cubes together so that 28 faces are
What do these two triangles have in common? How are they related?