Overlapping powers

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: x2 = x ?

Extension: What about xn = 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=x2.

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=xn.

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