So much of what we teach in algebra consists of how to rearrange one expression into another that is equivalent. But, I think I’ve often lost site of that forest for the trees that clutter all of the techniques and rules. So, I wanted to establish early on in this course the idea of two expressions being equivalent due to the properties of real numbers that we had just worked with. I try to keep the examples relatively simple and the number crunching appropriate.
The Lesson: CCAlgI.Unit #1.Lesson #5.Equivalent Expressions
Click here to watch the video.
perhaps note that evaluating expressions at specific values can determine if expressions are not equivalent (counterexample) but equivalence is suggested by checking not proven?
Meg,
I point this out in videos when I present the evidence for equivalency. I agree that equivalency cannot be proved with examples but that we can certainly know that two expressions are not equivalent if we find a value of the replacement variable where they are not equal.