Purpose

The purpose of this multi-level task is to engage students in using algebraic equations, graphs and/or tables to solve a problem.

Description of Mathematics

This 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: Are there any values for x such that: x^{2} = x ?

Extension: What about x^{n} = x (where n is any whole number)?

### The arithmetic approach (show more)

- The student is able to find a solution to the equation in the intersection of the two relationships, y=x and y=x
^{2}.

### The procedural algebraic approach (show more)

- The student is able to solve a quadratic to find all the solutions possible.

### The conceptual algebraic approach (show more)

- The student is able to generalise to find all the solutions for y=x
^{n}.

Attachments

OverlappingPowers_arithmetic.pdf352.88 KB

OverlappingPowers_full.pdf512.64 KB