A group of children from Manorfield Primary School, Stoney Stanton sent in lots of ideas:
S.B. and N.L. produced the following table of results:
||Number of pebbles on side
||Area of shape
||Perimeter of shape
PATTERNS AND FORMULAE
It was said in whole class discussion that the pattern for the size of the shapes was:
Squares: each side is the same length as the longest side of previous rectangle
Rectangle: one side is the same length as the side of the previous square, the other side is a "new length"
A.H and E.R also said:
The formula for the area = $2$ to the power of $(n-1)$.
The pattern for the new side of the rectangles is $+1$, $+2$, $+4$, $+8$, $+16$ ... (it doubles)
The pattern for the perimeter is $+2+2$, $+4+4$, $+8+8$, $+16+16$ ... (it doubles)
Now, Alice from St Thomas' Church of England Primary School, wrote;
On B (how many pebbles there are round the edges), the pattern starts on 4 adds 2 which makes 6 adds another 2 which is eight then adds 4 which makes 12 adds 4 again (16) adds 8 (24) adds 8 adds 16, and so on.
So it adds one thing twice then doubles the adding number and starts to do that again.
Amelia from NLCS sent in her ideas;
First double forward then double sideways and so on
Pebbles added: 2,3,6,10,20,36,72
Pebbles Outside: 4,6,8,12,16,24,32
Well done all of you - you obviously worked hard on this problem.