Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
This challenge extends the Plants investigation so now four or more children are involved.
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
An investigation that gives you the opportunity to make and justify
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?
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?
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.
Can you continue this pattern of triangles and begin to predict how
many sticks are used for each new "layer"?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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.
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?
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?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Investigate the different ways you could split up these rooms so
that you have double the number.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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.
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
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?
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.
We need to wrap up this cube-shaped present, remembering that we
can have no overlaps. What shapes can you find to use?
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?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
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?
If the answer's 2010, what could the question be?
How many models can you find which obey these rules?
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
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?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
In how many ways can you stack these rods, following the rules?
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!
Investigate what happens when you add house numbers along a street
in different ways.
An activity making various patterns with 2 x 1 rectangular tiles.
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 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?
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?
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?
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?
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
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Suppose there is a train with 24 carriages which are going to be
put together to make up some new trains. Can you find all the ways
that this can be done?
Ben has five coins in his pocket. How much money might he have?