Polygons rich task

A complete lesson on the theme of star polygons. An excellent way to enrich the topic of polygons, with opportunities for pupils to explore patterns, use notation systems, and make predictions & generalisations. No knowledge of interior or exterior angles needed. The investigation is quite structured and I have included answers, so you can see exactly what outcomes you can hope for, and pre-empt any misconceptions.

Pupils investigate what happens when you connect every pth dot on a circle with n equally spaced dots on their circumference. For p>1 this generates star polygons, defined by the notation {n,p}. For example, {5,2} would mean connect every 2nd dot on a circle with 5 equally spaced dots, leading to a pentagram (see cover image).

Pupils are initially given worksheets with pre-drawn circles to explore the cases {n,2} and {n,3}, for n between 3 and 10.
After a chance to feedback on this, pupils are then prompted to make a prediction and test it.
After this, there is a set of deeper questions, for pupils to try to answer.
If pupils successfully answer those questions, they could make some nice display work!

To finish the lesson, I’ve included a few examples of star polygons in popular culture and a link to an excellent short video about star polygons, that references all the ideas pupils have considered in the investigation.

I’ve included key questions and other suggestions in the notes boxes.

Please review if you buy as any feedback is appreciated!