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A group of children from Manorfield Primary School, Stoney Stanton sent in lots of ideas:
T.K and A.H said:The pattern: As you double it each time, the shape changes from a square to a rectangle repetitively as each time you add a square to make a rectangle (square $+$ square = rectangle) and add a rectangle to make a square (rectangle $+$ rectangle = square).
A.H and E.R said:We have noticed that each shape changes from a square to a rectangle because if you add a square to a square you get a rectangle e.g.:
S.B. and N.L. produced the following table of results:
|Number||Shape||Number of pebbles on side||Area of shape||Perimeter of shape|
A.H and E.R also said:
Well done all of you - you obviously worked hard on this problem.