Here is an example of a lesson I did on linear equations where my objective was to show that they are equations of first degree. The reason I do it this way is because I tend to find that students only see first degree equations as being of the form: mx + b, meaning that they can ONLY look like, say:
2x + 3 = 5.
An equation of the first degree (aka linear equation) with a single variable is defined by the following statement:
mx + b = 0 where $m \neq 0$ and $m, b \in R$
or any other equation that is equal to the above statement.
$(x + 1)(x - 1) = x^2 + 2x + 1$ is an linear equation.
$x^2 - 1 = x^2 + 2x + 1$ $\leftrightarrow -1=2x+1$ $\leftrightarrow 2x + 2 = 0$
Thus: x + 1 = 0
Since I was chided in a previous post for not providing context, I will do so now: I shared this approach with a College Algebra class (first year college students) and it is NOT an honors class. What do you think about my approach? I welcome any comments (positive or negative).