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.
How many different sets of numbers with at least four members can
you find in the numbers in this box?
Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Investigate and explain the patterns that you see from recording
just the units digits of numbers in the times tables.
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.
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.
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?
This article for teachers suggests ideas for activities built around 10 and 2010.
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
These pictures were made by starting with a square, finding the
half-way point on each side and joining those points up. You could
investigate your own starting shape.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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.
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?
Bernard Bagnall looks at what 'problem solving' might really mean
in the context of primary classrooms.
Investigate the different ways you could split up these rooms so
that you have double the number.
Place four pebbles on the sand in the form of a square. Keep adding
as few pebbles as necessary to double the area. How many extra
pebbles are added each time?
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?
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.
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?
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?
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?
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
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?
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?
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 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?
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.
Can you continue this pattern of triangles and begin to predict how
many sticks are used for each new "layer"?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
I cut this square into two different shapes. What can you say about
the relationship between them?
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?
An investigation that gives you the opportunity to make and justify
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
If the answer's 2010, what could the question be?
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.
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?
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
"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
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.