The purpose of this activity is to engage students in an investigation applying geometric properties of polygons.
This activity assumes the students have experience in the following areas:
The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.
The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.
Task: Investigate the sum of the internal angles of a regular polygon that has another regular polygon removed from its centre.
The following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.
Introduce the problem. Allow students time to read it and discuss in pairs or small groups.
Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.
Allow students time to work through their strategy and find a solution to the problem.
Allow students time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.
The student applies geometric properties of polygons to investigate the angles in specific examples.
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The student applies geometric properties of polygons to find a pattern that can be used to solve the problem.
Click on the image to enlarge it. Click again to close.
The student applies geometric properties of polygons to find a pattern that can be used to solve the problem.
Printed from https://nzmaths.co.nz/resource/pierced-polygons at 2:35am on the 20th April 2024