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?
Explore one of these five pictures.
How many different sets of numbers with at least four members can
you find in the numbers in this box?
"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 ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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 these hexagons drawn from different sized equilateral
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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.
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 numbers?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Bernard Bagnall describes how to get more out of some favourite
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?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
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?
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?
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
How many tiles do we need to tile these patios?
Why does the tower look a different size in each of these pictures?
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
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
A follow-up activity to Tiles in the Garden.
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.
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?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
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.
Bernard Bagnall looks at what 'problem solving' might really mean
in the context of primary classrooms.
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
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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?
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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?
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.
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.
In how many ways can you stack these rods, following the rules?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?