In college physics, students often learn a slew of kinematic equations:
I'm a big fan of only teaching this one:
There are four reasons I like just using this, both personally and for teaching. It's all-purpose; conundrum-focused; tool-and-representation-infused; and intuition-refining.
First: The equation works all the time. There are no caveats to remember. As I've gotten older, this is the first of my two "go-to" ideas in kinematics. I will say that I almost never use the 2nd or 4th equation from above to solve any real or textbook problem.
Second: You get to engage students with the conundrums of figuring out what the average velocity is for a variety of situations: unchanging velocity, steadily changing velocity, piece-wise changing, non-linear changing, etc.
Third: You can explore various techniques like weighted averages or riemann-sums using data from tables, graphs, and other representations. It naturally builds in ideas of approximation.
Fourth: With these tools, you get to explore the boundaries of intuition (e.g., looking at this graph, what would you guess the average velocity to be? Or the famous example of determining the average speed when traveling 45 mph one way and 60 mph the other way on a round trip)
This is me guessing what the average velocity should be for a few situations:
At the end of the day, for instruction, you are likely to still have to fold in ideas about instantaneous velocity, changing velocity, and acceleration. It's something I want to talk about, but I'm going to leave it for another post.