Why does the tower look a different size in each of these pictures?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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
Here is your chance to investigate the number 28 using shapes,
cubes ... in fact anything at all.
Can you find ways of joining cubes together so that 28 faces are
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.
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
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.
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.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
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?
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?
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.
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?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
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.
We need to wrap up this cube-shaped present, remembering that we
can have no overlaps. What shapes can you find to use?
In how many ways can you stack these rods, following the rules?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Here are many ideas for you to investigate - all linked with the
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?
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.
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
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?
Sort the houses in my street into different groups. Can you do it in any other ways?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
What is the largest cuboid you can wrap in an A3 sheet of paper?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
In this article for teachers, Bernard gives an example of taking an
initial activity and getting questions going that lead to other
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?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
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?
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
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?
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?
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!
An activity making various patterns with 2 x 1 rectangular tiles.
Explore ways of colouring this set of triangles. Can you make
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?