Absolute Value and Real Life.

  Absolute value graphs as a lovely V shape and often is taught as being the distance away from zero.  The sign tells the direction while the number indicates distance but how is this used in real life?  I never thought about it until I did yesterday's topic and bingo, this hit me!

One example of this used in real life comes from the speedometer.  Say you are a delivery person who travels back and forth between two towns that are 15 miles apart.  Mathematically you may end the day with a total of zero due to a complete round trip is + 15  +(- 15) but the number of miles if you added the values together might be 6 trips at 30 miles each trip would be 180 miles.  So the speedometer looks at absolute value regardless of direction.

Another example is when you are traveling a much slower or faster speed than traffic is going.  For instance you are going 55 mph with everyone else and all the sudden this guy whips out of nowhere going 80 mph.  The difference is 30 mph which is an absolute value because you are traveling 30 mph slower or -30 but we don't express the negative, we only use a positive value.

What about currency exchange.  Often time currency exchange places charge a commission on top of the exchange and it doesn't matter whether you gain or lose value on the money, the commission is always going to be an absolute value.

Take this idea a step further.  In the financial community the money involved in transfers is always treated as a positive value even if the number is negative.  So if an institution loses money, the amount is still expressed as a positive value.  We never say it has a -$600,000 balance, rather we might say, its total loss was $600,000 last year.  The word loss indicated its negative but we do not say -$600,000.


In addition, the voltage in your toaster is an absolute value which means your toaster works properly.

So many ways its used in real life without us knowing about it.  I love knowing this so I can point out its use to make it more real to my students.  This connection might make it easier for them to transfer the knowledge.  I'm off to write some problems for class.  Let me know what you think on this topic!

inequalities and graphing apps.

In algebra 2, we are learning to graph linear and absolute value inequalities using a graphing app.  I like the free graph calc for graphing as it has so many choices and resembles a regular graphing calculator.  It does not seem to support graphing inequalities which is fine with me because the students can graph the base linear or absolute value equation, then do the analysis to determine if they need a dotted or solid line and which part is shaded in.  Too often my students just copy down the result from the graphing calculators or a regular calculator without checking to see if its reasonable. 
Yesterday, all the high school teachers gave students a directions test during study hall. The test had them writing down things like the letter D in the middle of the page, writing down their favorite musical group in a corner, etc.  We did this because the majority of our students do not read directions.  As expected, most students failed the test but the kids got such a charge out of the test.  What they don't know is that they will get another one next month.
Finally, the tech dept and I are still working to figure out how I can have students either send the material to me using e-mail or get it to me via a drop box type of situation.  I am not allowed to use google docs, regular e-mail accounts, drop box or any other type of app like that.  So it is a challenge.  I am doing some research and have a couple possibilities that I need to explore hopefully over the weekend.  I hope by January to greatly reduce the paper flow.