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.
A follow-up activity to Tiles in the Garden.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
If the answer's 2010, what could the question be?
"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
Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
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.
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
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?
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?
Place the 16 different combinations of cup/saucer in this 4 by 4
arrangement so that no row or column contains more than one cup or
saucer of the same colour.
Here are many ideas for you to investigate - all linked with the
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?
Investigate what happens when you add house numbers along a street
in different ways.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Investigate these hexagons drawn from different sized equilateral
Bernard Bagnall describes how to get more out of some favourite
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.
An investigation that gives you the opportunity to make and justify
Investigate the different shaped bracelets you could make from 18
different spherical beads. How do they compare if you use 24 beads?
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?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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 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?
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?
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
Why does the tower look a different size in each of these pictures?
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 tiles do we need to tile these patios?
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.
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
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?
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.
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?
Bernard Bagnall looks at what 'problem solving' might really mean
in the context of primary classrooms.
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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
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
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.
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
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
In this investigation we are going to count the number of 1s, 2s,
3s etc in numbers. Can you predict what will happen?