The purpose of this multi-level task 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.

The background knowledge and skills that need to be established before and/or during this task are outlined in the diagram below:

This task may be carried out with practical exploration, and/or by generalising with the rule that has been established from the internal angles of a triangle. The approach should be chosen in sympathy with students' skills and depth of understanding.

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 arithmetic approach (show more)

- The student is able to find a pattern that leads to a rule, using practical exploration.

### The procedural algebraic approach (show more)

- The student is able to use a given rule, to find a new rule, using practical exploration and then generalising, with guidance.

### The conceptual algebraic approach (show more)

- The student is able to use a given rule to find a new rule, using practical exploration and then generalising, independently.