Pierced polygons

Purpose

The purpose of this multi-level task is to engage students in an investigation applying geometric properties of polygons.

Description of Mathematics

The background knowledge presumed for this task is outlined in the diagram below:

The task can be presented with graded expectations to provide appropriate challenge for individual learning needs.

Activity

 

Task: Investigate the sum of the internal angles of a regular polygon that has another regular polygon removed from its centre.


 

The arithmetic approach (show more)

  • The student is able to apply geometric properties of polygons to find solutions to the problem.

The procedural algebraic approach (show more)

  • The student is able to apply geometric properties of polygons to find a pattern that can be used to solve the problem.

The conceptual algebraic approach (show more)

  • The student is able to apply geometric properties of polygons to find a pattern that can be used to solve the problem.

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