A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Why does the tower look a different size in each of these pictures?
Bernard Bagnall describes how to get more out of some favourite
In this challenge, you will work in a group to investigate circular
fences enclosing trees that are planted in square or triangular
This problem is intended to get children to look really hard at something they will see many times in the next few months.
Bernard Bagnall looks at what 'problem solving' might really mean
in the context of primary classrooms.
Follow the directions for circling numbers in the matrix. Add all
the circled numbers together. Note your answer. Try again with a
different starting number. What do you notice?
Explore Alex's number plumber. What questions would you like to
ask? Don't forget to keep visiting NRICH projects site for the
latest developments and questions.
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?
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?
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 make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
If the answer's 2010, what could the question be?
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?
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
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?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
We need to wrap up this cube-shaped present, remembering that we
can have no overlaps. What shapes can you find to use?
Investigate the numbers that come up on a die as you roll it in the
direction of north, south, east and west, without going over the
path it's already made.
Here are many ideas for you to investigate - all linked with the
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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.
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?
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?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
What is the largest cuboid you can wrap in an A3 sheet of paper?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
This activity asks you to collect information about the birds you
see in the garden. Are there patterns in the data or do the birds
seem to visit randomly?
In this article for teachers, Bernard gives an example of taking an
initial activity and getting questions going that lead to other
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?
In my local town there are three supermarkets which each has a
special deal on some products. If you bought all your shopping in
one shop, where would be the cheapest?
Can you find ways of joining cubes together so that 28 faces are
Sort the houses in my street into different groups. Can you do it in any other ways?
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?
Here is your chance to investigate the number 28 using shapes,
cubes ... in fact anything at all.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
Explore ways of colouring this set of triangles. Can you make
An activity making various patterns with 2 x 1 rectangular tiles.
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
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.