It takes practice to find the words that fit any given situation. Math is no exception. Below are are student-generated data tables for two functions. What patterns do you see in the numbers?
As $x$ gets close to the denominator value, $y$ gets bigger!
As $x$ gets close to the numerator value, $y$ gets smaller!
were two common student observations. "That's a great idea, but you're not expressing it quite right! The numbers -5, -29, -59, and -299 are actually getting smaller as they get more negative. Similarly, the numbers -1.000, -0.111, -0.053, and -0.010 are getting bigger as they get less negative. Can you rephrase your observations so that they take negative numbers into account?"
How about you? How would you advise students? To see how I steered students, click here.
I started this blog to share my transformation from math nerd to math nerd who loves to share math with young people. I teach high school in Hanoi, Vietnam. Your comments are always welcome.