7 pins

this work on a 7 pin arrangement (isometric) follows an article by W.A. Ewbank (in Nov 1984)

and the task was developed by Dave Kirkby (then at Sheffield City Polytechnic)

a ppt is here

it can be beneficial to start work on the sum of the interior angles of polygons with a restricted set of angles, in this case multiples of 60 degrees (and some of 30 degrees)
[companion resources involve multiples of 45 degrees, on a square grid]

the work begins by finding the angles between any two lines drawn connecting dots
"if one point holds hands with two others what situations are there?"

there are 6 different angles, joining dots:
30, 60, 90,
120, 240 and 300
(7 if you include 180)

reasons for various angles can usually be given in relation to 60 degrees being the angle in an equlateral triangle

students list all the interior angles and then sum them

[this links with the sheets for 'isometric angles']