Pierced polygons

Purpose

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

Achievement Objectives
GM5-5: Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
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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Level Five