The purpose of this activity is to engage students in using a given rule, to deduce another rule. This is an example of the deductive reasoning required for forming successful geometric proofs.
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: To show that the sum of the internal angles of any triangle is 180°, a triangle can be torn into three parts so that the three internal angles can then be lined up. Use this practical idea, to find a relationship, or rule, between the number of sides of any polygon and the sum of its internal angles.
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 finds a pattern that leads to a rule, using practical exploration.
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The student builds the angle sums of polygons in a sequential way, using practical exploration to generalise the rule for sum of interior angles, with guidance.
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The student builds the angle sums of polygons in a sequential way, using practical exploration to generalise the rule for sum of interior angles, independently.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/inside-irregular-polygons at 8:53pm on the 26th February 2024