Lesson Plan: Iterated Functions Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use an iterative formula to approximate the roots of an equation.
Students will be able to
- understand how to form an iterative formula for a function,
- sketch a staircase or cobweb diagram to represent an iterative process graphically,
- understand how to identify when an iterative formula diverges with a given starting value and that we can find different iterative formulas or starting values that may converge differently,
- use iterative formulas to find approximations for roots of equations when given the iterative formula and a starting value.
Students should already be familiar with
- evaluating functions,
- identifying whether a function has a root in a given interval,
- differentiation of standard functions.
Students will not cover
- the Newton–Raphson method.