The Neglected Number Line
I just finished my first tutoring session with a student I met through WyzAnt, and it went wonderfully! Denise and I seemed to really hit it off, and we got a lot done in our time together.
One of the things we talked about tonight was the number line. It was great for explaining why .777 is bigger than .7, or why -.777 is smaller than -.7. It's a really wonderful visual aid for students like Denise that learn visually. Ironically, I remember being in algebra myself several years ago and thinking, "This is so dumb - when and why would I ever need to use this?!" However, the farther I go into mathematics, the more I start to recognize and appreciate its numerous uses.
Take, for example, calculus: you use the number line to test values within certain intervals to find out whether the intervals are positive or negative. From this, you can determine whether or not an interval is increasing or decreasing, concave up or concave down, relative extrema, and even points of inflection. The number line makes it so much easier to visualize the intervals you are testing, and also to pick values to test. It helps to write in the + and - symbols over the number line too, so it's easy to see where the sign changes (or where you have a relative extrema/P.O.I). In fact, if you think about it, just that tiny little number line can help you accomplish something as great as graphing a complex function by hand while starting with nothing more than the equation of the function itself.
For these reasons, I'd like to dedicate this post to the often neglected and unappreciated number line. You have helped me a lot more than I ever thought you would as both a tutor and a mathematician. Keep up the good work!