Purpose

The purpose of this multi-level task is to engage students in using deductive reasoning to justify an index rule.

Description of Mathematics

This 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 numerical exploration, and/or by generalising with rules that have been established earlier. The approach should be chosen in sympathy with their skills and depth of understanding.

Activity

Task: Use the index rules you know, to show how you can say that

x^{0} = 1

### The arithmetic approach (show more)

- The student is able to find a pattern that leads to justifying the rule, using concrete examples.

### The procedural algebraic approach (show more)

- The student is able to justify the rule, using concrete examples and then generalising.

### The conceptual algebraic approach (show more)

- The student is able to justify the rule by generalising with known facts.

Attachments

Zero_full.pdf425.8 KB

Zero_arithmetic.pdf185.5 KB

Zero_procedural-algebraic.pdf183.5 KB

Zero_conceptual-algebraic.pdf271.75 KB