Progression

There have been times we were working on an Advanced Project, and we needed to use earlier ideas and we thought, wouldn't it have been great, if when those earlier ideas were taught, the teacher gave specific focus to examples that would be used later on, such as when working on the advanced project.

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As an example of this progression, the first stage is learning to add and subtraction fractions, specifically 1/6, 1/3 and 1/2.  This math shows up at the second stage where you are learning to multiply matrices.  Later, at the third stage, you are working with Representations and it is necessary to work with two important matrices--you saw them in Linear Algebra when you multiplied them together to get an Identity Matrix.

 

The above paragraph describes a journey through several topics (Fractions, Matrices, Representation Theory).  We might also consider it a progression to go between two topics if it takes a lot of work to get from A to B.  For example, it might take two pages of calculations to begin by deriving two Kinematic Equations (relating position to time and velocity to time), using those to derive a kinematic equation that is independent of time, and then using algebraic manipulation to go from that equation to the equation for Potential Energy (using Kinetic Energy for the final bridge).