square dissections

chop up a square into two pieces, the 'left' piece and the 'right' piece
do the same thing, in the same way, for the next largest square
and so on...

work out the areas of the two pieces - right and left
for each size of square

work out the perimeters of the two pieces - right and left
for each size of square

try to find general rules
and justify them in relation to the diagrams

explore the sum of the two area expressions, the left area plus the right area...

some options:

 

 

thanks to Nick Foster for this idea