don steward
mathematics teaching 10 ~ 16

Tuesday, 3 April 2012

7 pins

the work on a 7 (isometric) pin arrangement followed an article by WA Ewbank (Nov 1984) and the task was developed by Dave Kirkby, then at Sheffield City Polytechnic (who produced many fine ideas in my view)

the work begins by finding the angle drawn between any two lines
"if one point holds hands with two others what situations are there?"
(obtaining a variety rather than an exhaustive search)

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

some of these angle options can be presented to students and there is often an interesting variety of reasons given

reasons are usually and appropriately based on the angle in an equilateral being 60 degrees

this is a good task for encouraging (i.e. pressing for) deductive arguments (rather than, "it just looks like it...")

then students can be asked to draw all the triangles they can find, joining dot to dot:

and then decide what each of the corner angles is in each triangle

and check that their sum is 180 degrees

there are five different quadrilaterals (all with special names)

the corner angles and the sum of these can be worked out for each quadrilateral

the 'arrowhead' can produce problems and some students need reminding that it is the inside angles that are required

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

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