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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
Squares: 1,2,4,8,16,32,64,128
Pebbles
Age 7 to 11
Challenge Level 
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 | Shape | Number of pebbles on side | Area of shape | Perimeter of shape |
| 1 | Square | 2x2 | 1cm$^2$ | 4cm |
| 2 | Rectangle | 2x3 | 2cm$^2$ | 6cm |
| 3 | Square | 3x3 | 4cm$^2$ | 8cm |
| 4 | Rectangle | 3x5 | 8cm$^2$ | 12cm |
| 5 | Square | 5x5 | 16cm$^2$ | 16cm |
| 6 | Rectangle | 5x9 | 32cm$^2$ | 24cm |
| 7 | Square | 9x9 | 64cm$^2$ | 32cm |
| 8 | Rectangle | 9x17 | 128cm$^2$ | 48cm |
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
Squares: 1,2,4,8,16,32,64,128
Well done all of you - you obviously worked hard on this problem.
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