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?
If I use 12 green tiles to represent my lawn, how many different
ways could I arrange them? How many border tiles would I need each
This problem is intended to get children to look really hard at something they will see many times in the next few months.
Investigate these hexagons drawn from different sized equilateral
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
Investigate what happens when you add house numbers along a street
in different ways.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Explore ways of colouring this set of triangles. Can you make
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?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
Here is your chance to investigate the number 28 using shapes,
cubes ... in fact anything at all.
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
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.
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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?
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?
Bernard Bagnall describes how to get more out of some favourite
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
If the answer's 2010, what could the question be?
Here are many ideas for you to investigate - all linked with the
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?
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
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!
An activity making various patterns with 2 x 1 rectangular tiles.
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?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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?
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.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
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?
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 a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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.
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.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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.
Why does the tower look a different size in each of these pictures?
Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?
How many tiles do we need to tile these patios?