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.
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?
The first thing that Tom did is an important, helpful strategy
whenever you are problem solving, he used a tool. In this case it
was matchsticks. Being able to 'build' the problem and see how it
'looks' and then being able to move pieces of the problem around is
one of the most useful and vital ideas in solving problems.
Organising your findings into an easy to read table is also
important. This way patterns get revealed making it easier to
predict what happens next.
Here's Tom's ideas for the Sticky
I used matchsticks to work out the answers for the one, two,
three and four rows of triangles. I put my answers in a table and
saw there was a pattern and I worked out what I thought the answer
would be for five rows. I checked it with the matchsticks and it
This can be explained using equations. Letters can be used to
represent the different pieces of information. This saves writing
out the full words each time. Tom used:
m = number of matches
t = number of triangles and
r = number of rows
By looking at the table above, Tom was able to work out
t = r 2
(which is the same as saying that the number of triangles is the
same as the number you get when you square number of rows -
meaning, you multiply by the number of the rows by the same
I didn't know how to write this as an equation so I went to
"Ask Nrich" and they told me it was:
m = t + r*(r+3)/2
Using "Ask Nrich" is using your initiative Tom.
Do you understand the equation our mathematical helpers gave you,