regular octagon loops

in England this task was devised by a group called SEAC (a national assessment agency), many moons ago (1992) to assess students on an investigative task
green plastic octagon templates were distributed to all England schools
they might be lurking, dustily, in cupboards

be aware that octagons drawn on squared paper are not regular and lead to erroneous data

you can buy regular octagon paper plates for a group to work with
but accurate recording is still difficult...

the 'growing in a line' case can be explored using a semi-regular tessellation of regular octagons and squares