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?
Thank you to Adrian from South Greenhoe Middle
School, Lucy and Sarah from Archbishop Sancroft High School and
pupils from Heacham Middle School who all sent correct solutions.
Here is a summary of their responses:
The next three numbers in the sequence will be
$1^2 + 2^2 + 3^2 + 4^2 = 30$
$1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 55$
$1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 = 91$
The numbers are called pyramid numbers because if you take some
balls of the same size and you build them into pyramids, you will
need to make square-based pyramids with one ball at the top, four
in the next layer down, nine in the next layer down and so on.
Perhaps you can draw pictures for these