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.
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
"Tell me the next two numbers in each of these seven minor spells",
chanted the Mathemagician, "And the great spell will crumble away!"
Can you help Anna and David break the spell?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
A tower of squares is built inside a right angled isosceles
triangle. The largest square stands on the hypotenuse. What
fraction of the area of the triangle is covered by the series of
How many different sets of numbers with at least four members can
you find in the numbers in this box?
Can you find a way to identify times tables after they have been shifted up?
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
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?
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.
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
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?
Investigate the successive areas of light blue in these diagrams.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Investigate these hexagons drawn from different sized equilateral
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
Square numbers can be represented on the seven-clock (representing these numbers modulo 7). This works like the days of the week.
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Investigate what happens when you add house numbers along a street
in different ways.
Liitle Millennium Man was born on Saturday 1st January 2000 and he will retire on the first Saturday 1st January that occurs after his 60th birthday. How old will he be when he retires?
An environment which simulates working with Cuisenaire rods.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Three people chose this as a favourite problem. It is the sort of
problem that needs thinking time - but once the connection is made
it gives access to many similar ideas.
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
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?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
July 1st 2001 was on a Sunday. July 1st 2002 was on a Monday. When
did July 1st fall on a Monday again?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Three circles have a maximum of six intersections with each other.
What is the maximum number of intersections that a hundred circles
Make new patterns from simple turning instructions. You can have a
go using pencil and paper or with a floor robot.
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
How do you know if your set of dominoes is complete?
Have a go at this 3D extension to the Pebbles problem.
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
There are lots of ideas to explore in these sequences of ordered
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Choose any 4 whole numbers and take the difference between
consecutive numbers, ending with the difference between the first
and the last numbers. What happens when you repeat this process
over and. . . .
What is the total area of the first two triangles as a fraction of
the original A4 rectangle? What is the total area of the first
three triangles as a fraction of the original A4 rectangle? If. . . .
Make some intricate patterns in LOGO
Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . .